{ "schemaVersion": 1, "version": "simple", "label": "Simplified English", "status": "Complete English reading; review draft.", "blocks": { "front-title-001": "HARMONY\nExplained through its natural principles", "front-title-002": "IN FOUR BOOKS.", "front-title-003": "BOOK I. How harmonic ratios and proportions relate to one another.", "front-title-004": "BOOK II. What chords are, how they behave, and everything that can help make music perfect.", "front-title-005": "BOOK III. Basic principles of composing music.", "front-title-006": "BOOK IV. Basic principles of musical accompaniment.", "front-title-007": "By Monsieur RAMEAU, organist at Clermont Cathedral in Auvergne.", "front-title-008": "Decorative image on the title page.", "front-title-009": "PRINTED BY\nJean-Baptiste-Christophe Ballard, the King’s sole music printer. Paris, rue Saint Jean-de-Beauvais, at the Mont-Parnasse.", "front-title-010": "M. DCC. XXII. means 1722.\nPrinted under a printing privilege granted by the King.", "front-preface-001": "PREFACE.", "front-preface-002": "Music has progressed. As our ears have become more sensitive to its wonderful effects, our minds seem less eager to investigate its true principles. Reason has therefore lost some of its standing, while practical experience has gained authority.", "front-preface-003": "The surviving ancient writings show that reason enabled their authors to discover most of music's properties. Experience still confirms most of their rules. Even so, people now favor practical experience alone and neglect the benefits that reasoning could offer.", "front-preface-004": "Experience can show us what music does, but experience alone cannot explain its underlying principle as precisely as reason demands. Conclusions based on experience are often wrong. At best, they may leave doubts that only reasoning can clear up. Consider a question: how can we prove that our music is more perfect than ancient music, when ours no longer seems able to produce the effects that ancient writers claimed for theirs? We might reply that familiar things stop surprising us. What first amazes us gradually becomes ordinary entertainment as we get used to it. But that explanation would establish equality at most, not superiority. Instead, we could state a clear principle and draw reliable conclusions from it. If these show that our music has reached the highest possible perfection, far beyond the ancients, we would know what to believe. See Book II, Chapter XXI. We would also understand the earlier point about familiarity more clearly. Knowing the boundaries of the art would make us more willing to pursue it. People with exceptional musical taste and ability would no longer worry that they lack the knowledge needed to succeed. Reason would clear away the doubts that experience can continually create, giving us solid grounds to expect success in music.", "front-preface-006": "Modern musicians—meaning musicians since Zarlino*—should have followed the ancients in explaining why their methods work. They could then have removed many prejudices directed against them, as well as prejudices they themselves still hold and struggle to abandon. Practical experience serves them almost too well. It can mislead them into neglecting a thorough study of the musical beauties it reveals every day. Their knowledge then remains personal: they cannot explain it to others. They do not notice this problem. They are more surprised that others fail to understand them than that they fail to explain themselves clearly. This is a harsh criticism, I admit. Yet I may still deserve it myself, despite my efforts to escape it.", "front-preface-007": "Whatever the case, I hope this criticism affects other musicians as it has affected me. My main reason for publishing these new investigations is to revive the admirable desire to match and surpass one another’s work that once existed. I want to present music with its natural simplicity, so that the mind can understand its properties as easily as the ear hears them.", "front-preface-008": "* Zarlino was a celebrated writer on music, writing about 150 years before this book. Later works on the same subject offer only weak copies of his work.", "front-preface-010": "No one person can fully explore such a deep subject. However careful he is, he will almost certainly overlook something. Still, every new discovery added to earlier work opens a path for someone else to go farther.", "front-preface-011": "Music is a science, so it must have definite rules. Those rules must come from a clear basic principle. Mathematics is almost essential to discovering that principle. I had practiced music for many years and gained considerable experience, but I must admit that mathematics alone made my ideas clear. It revealed and removed confusion that I had not even noticed. At first, I could not distinguish a basic principle from a rule. Then the principle became both simple and obvious to me. Its consequences gave me rules, all referring back to that same foundation. I began to understand what the rules meant, how to apply them correctly, how they related, and how to arrange them: always let the simpler lead gradually to the less simple. Even the right terminology became clear. These were things I had not previously understood. Their clarity made me agree with something someone had once said while I was praising modern music's perfection: the musicians of our century ought to understand music as well as they compose it beautifully. Feeling the effects of an art or science is not enough. We must understand them well enough to explain them. That is my main aim in this work, arranged in four books.", "front-preface-012": "THE FIRST BOOK summarizes how sounds, consonances, dissonances and chords relate. It finds harmony's basic principle in a single sound and explains its most important properties. The first division of this sound produces its octave, which seems almost identical to it. The sound then uses that octave to form every chord. All chords consist only of the fundamental sound and its third, fifth and seventh. The octave is what makes their many different forms possible. This book also explains other properties. They are less directly useful in practice, but they help lead us toward it. The demonstrations are fairly simple throughout.", "front-preface-013": "THE SECOND BOOK gives equal attention to theory and practice. It represents the basic principle through a musical part called the fundamental bass. It explains that bass's properties and those of the intervals, chords and modes that depend entirely on it. It also considers what can make music perfect in performance. Where useful, it draws on the first book's reasoning, practical experience and leading musical writers. But it still criticizes those writers when they are mistaken. The new ideas should convince different readers in different ways: reason for scholars, experience for people who trust only their ears, and an explanation of possible errors for people who defer too readily to their teachers' rules. The book prepares readers to accept the rules willingly. The next books explain them in a systematic order and in more detail.", "front-preface-014": "THE THIRD BOOK presents a special method for learning composition very quickly. It has already been tried. Yet people usually need their own experience before they believe claims like this, so I will not insist on it. I ask anyone unfamiliar with the method to look at its results before rejecting it. Someone who wants to learn usually cares more about succeeding than about the particular teaching method.", "front-preface-016": "So far, no published rules teach composition at the level of perfection it has now reached. Skilled composers themselves honestly admit that experience alone gave them almost all their knowledge. When they teach, they often have to finish with the musicians' proverb Cætera docebit usus: practice will teach the rest. Some kinds of excellence do depend on talent and taste, and experience can help those more than theoretical knowledge can. Even then, thorough understanding must guide us so that experience does not mislead us. At the very least, it lets us connect new ideas produced through experience to their true foundation. It also helps us use talent and taste, which might otherwise be wasted. I have therefore looked for a quicker, easier way to reach the excellence that previously required practical experience alone. The first step is a clear, precise, reasoned understanding of all harmony. I explain just three intervals. These generate two main chords and every movement of the fundamental bass; that bass also determines the movement of the other parts. Everything else depends on understanding this foundation. A first reading of the book can provide it, as readers can readily discover.", "front-preface-017": "THE FOURTH BOOK teaches accompaniment on harpsichord and organ. It explains hand position, fingering and everything that can help you learn the practical skill as quickly as possible.", "front-preface-019": "The same basic rules also apply to other instruments whose accompaniment technique is similar to that of the harpsichord.", "front-preface-020": "The last two books are closely connected. Both will therefore help someone interested only in practical composition or only in practical accompaniment. For a fuller understanding, consult the second book too—assuming I have left nothing out. I have tried to overlook nothing, as my long explanations and repetitions make clear. Still, I am certain others can improve on what I have done. My verbosity comes both from wanting to make everything understandable and from the limitations of my ability. The first book is, in a sense, unnecessary for practical work. Use it as you see fit. It stands first only because it supplies the proof behind the treatise's account of harmony.", "front-preface-021": "My professional duties prevented me from supervising the printing. I therefore had to reread the work carefully afterward. I found several necessary changes and corrections; these are collected in the supplement at the end. At the beginning are two tables: a table of contents and an explanation of terms readers need to understand. They introduce the whole work, which I dedicate to the public.", "front-preface-022": "Citations of Zarlino's Harmonic Institutions refer to the edition printed in Venice in 1573.", "front-contents-title": "CONTENTS\nof This Treatise, Divided into Four Books.", "front-contents-009": "BOOK ONE. — Relationship of Harmonic Ratios and Proportions.\nChap. I. — Music and Sound. — 1\nChap. II. — Different Ways of Knowing the Relationships between Sounds. — 2\nChap. III. — Origin and Relationships of Consonances. — 3\nARTICLES.\nI. — Principle of Harmony, or the Fundamental Sound. — 5\nII. — Unison. — 6\nIII. — Octave. — ibid.\nIV. — Fifth and Fourth. — 10\nV. — Thirds and Sixths. — 12\nVI. — Summary of This Chapter, Containing the Properties of the Preceding Demonstration in a Single String. — 15\nChap. IV. — Properties of Harmonic and Arithmetic Proportions. — 17\nChap. V. — Origin and Relationships of Dissonances. — 22\nChap. VI. — Compound Intervals, Especially the Ninth and Eleventh. — 28\nChap. VII. — Harmonic Division, or the Origin of Chords. — 29", "front-contents-010": "Chap. VIII. — Chord Inversion. — 34\nARTICLES.\nI. — Major Perfect Chord and Its Derivatives. — 34\nII. — Minor Perfect Chord and Its Derivatives. — 36\nIII. — Seventh Chord Formed by Adding a Minor Third to the Major Perfect Chord, and Its Derivatives. — 37\nIV. — Seventh Chord Formed by Adding a Minor Third to the Minor Perfect Chord, and Its Derivatives. — 39\nV. — Seventh Chord Formed by Adding a Major Third to the Major Perfect Chord, and Its Derivatives. — 40\nVI. — Seventh Chord Formed by Adding a Minor Third below the Minor Perfect Chord, and Its Derivatives. — 41\nVII. — Diminished-Seventh Chord Formed by Adding a Minor Third to the Harmonically Divided Diminished Fifth, and Its Derivatives. — ibid.\nChap. IX. — Observations on All the Preceding Chords. — 45\nChap. X. — Different Ratios That May Be Assigned to the Same Chord. — 46\nChap. XI. — Relating Ratios Derived from Divisions to Vibrations and Multiplications of Lengths. — 47\nBOOK TWO. — Nature and Properties of Chords, and Everything That Can Make Music Perfect.\nChap. I. — Fundamental Sound of Harmony and Its Progression. — 49\nChap. II. — Chords Assigned to Fundamental Sounds and Their Progression. — 52\nChap. III. — Nature and Properties of the Octave. — 54\nChap. IV. — Nature and Properties of the Fifth and Fourth. — ibid.", "front-contents-011": "Chap. V. — Perfect Cadence, Where the Nature and Properties of All Intervals Meet. — 54\nChap. VI. — Interrupted Cadence. — 61\nChap. VII. — Irregular Cadence. — 64\nChap. VIII. — Imitating Cadences through Inversion. — 67\nChap. IX. — Evading Cadences by Imitating Them. — 68\nChap. X. — Chords by Supposition, Also Used to Evade Cadences by Imitating Them. — 73\nChap. XI. — Fourth and Eleventh. — 77\nChap. XII. — Chords by Borrowing, Used to Evade Perfect Cadences by Imitating Them. — 79\nChap. XIII. — Rule for Dissonance Progression Derived from Fundamental-Chord Progression. — 81\nChap. XIV. — Observations on the Progression of Thirds and Sixths. — 87\nChap. XV. — When to Omit the Seventh from a Ninth Chord. — 93\nChap. XVI. — Dissonant Consonances: the Fourth and the False Idea Attached to It by Extraneous Rules. — 95\nARTICLES.\nI. — Principle of Dissonance: Which Sound of an Interval Is Dissonant, and Which Sound the Preparation and Resolution Rule Concerns. — 97\nII. — Original Chord of All Dissonant Chords: Number of Dissonances and Sounds It Contains, and Its Limits. — 100\nIII. — Treating the Fourth as Dissonant When the Bass Syncopates Destroys Music’s Finest and Most General Rule. — 104\nIV. — Authors’ Faults in Establishing Harmonic Rules: Their Different Principles and the Errors They Spread. — 105\nChap. XVII. — License. — 109\nARTICLES.\nI. — Origin of License. — ibid.\nII. — Licenses Derived from the Interrupted Cadence. — 112", "front-contents-012": "III. — How One Dissonance Can Resolve through Another. — 113\nIV. — How the Seventh Can Also Resolve to the Octave. — 118\nV. — How the Sixth Can Accompany the Seventh. — 122\nVI. — Cases Where a Dissonance Appears to Be Prepared by Another Dissonance. — 123\nChap. XVIII. — Establishing the Rules, with Instruction in Composing a Fundamental Bass. — 125\nARTICLES.\nI. — Establishing the Rules. — ibid.\nII. — Composing a Fundamental Bass beneath Any Kind of Music. — 134\nChap. XIX. — Continuation of the Previous Chapter, Showing That Melody Comes from Harmony. — 138\nChap. XX. — Properties of Chords. — 141\nChap. XXI. — Modes. — 143\nChap. XXII. — Source of the Freedom to Move from One Mode or Key to Another. — 149\nChap. XXIII. — Meter. — 150\nChap. XXIV. — Properties of Modes and Keys. — 157\nChap. XXV. — Usefulness of This New Me-Method of Marking Different Meters. — 158\nChap. XXVI. — Number of Measures in Each Air and Its Particular Tempo. — 159\nChap. XXVII. — Suitable Verse Forms for Each Air and Rules for Setting Words to Music. — 161\nChap. XXVIII. — Design, Imitation, Fugue, and Their Properties. — 162\nChap. XXIX. — Intervals Distinguished as Major or Minor, Just or Perfect, Augmented or Diminished. — 163", "front-contents-013": "BOOK THREE. — Principles of Composition.\nChap. I. — Introduction to Practical Music. — 169\nChap. II. — Fundamental Bass. — 185\nChap. III. — Perfect Chord, the Starting Point for Four-Part Composition. — 186\nChap. IV. — Chord Succession. — ibid.\nChap. V. — Some Rules to Observe. — 191\nChap. VI. — Seventh Chord. Articles I and II. — 192\nChap. VII. — Observations on Dissonance. — 197\nChap. VIII. — Key and Mode. — 198\nChap. IX. — Harmonic Modulation with a Diatonic Bass Progression. — 200\nChap. X. — Continuo Bass. — 206\nChap. XI. — Bass Progression, Which Also Determines Chord Progression; Relating a Derived Chord to Its Foundation. — ibid.\nChap. XII. — Further Rules Drawn from the Preceding Example. — 215\nChap. XIII. — Perfect Cadence. — 216\nChap. XIV. — Leading Note and the Resolution of All Dissonances. — 217\nChap. XV. — Eleventh, Called the Fourth. — 219\nChap. XVI. — Irregular Cadence. — 221\nChap. XVII. — Related Bass Progressions That Leave the Upper Parts’ Harmony Unchanged. — 225\nChap. XVIII. — Preparing Dissonances. — 229\nChap. XIX. — Cases Where Dissonances Cannot Be Prepared. — 233\nChap. XX. — Exact Enumeration of Bass Progressions According to the Dissonances Used. — 235\nChap. XXI. — Second Chord. — 241\nChap. XXII. — Keys and Modes in General. — 244\nARTICLES.\nI. — Major Keys. — ibid.\nII. — Minor Keys. — 245\nChap. XXIII. — Passing from One Key to Another, Also Called Modulation. — 248\nChap. XXIV. — Continuation of the Previous Chapter’s Rules. — 251", "front-contents-014": "Chap. XXV. — Identifying the Chords Required by Bass Notes in Any Progression. — 254\nARTICLES.\nI. — Cadences and Everything Relating to a Melodic Conclusion. — ibid.\nII. — Imperfect Cadences. — 257\nIII. — Identifying the Key of Imperfect-Cadence Progressions. — 258\nIV. — Determining Whether a Diatonic Melody Will Rest on Tonic or Dominant. — 264\nChap. XXVI. — Using the Seventh on All Notes of a Key in Diatonic Progression. — 266\nChap. XXVII. — One Dissonance in Successive Chords on Different Notes, and Its Resolution on Seemingly Foreign Notes. — 267\nChap. XXVIII. — All Licenses, Beginning with the Interrupted Cadence. — 270\nChap. XXIX. — Augmented-Fifth Chord. — 273\nChap. XXX. — Ninth Chord. — 275\nChap. XXXI. — Eleventh Chord, Called the Fourth. — 278\nChap. XXXII. — Augmented-Seventh Chord. — 281\nChap. XXXIII. — Augmented-Second Chord and Its Derivatives. — 282\nChap. XXXIV. — Chromatic Movement. — 286\nARTICLES.\nI. — Descending Chromatic Movement. — ibid.\nII. — Ascending Chromatic Movement. — 288\nChap. XXXV. — Practicing Everything Explained So Far. — 291\nARTICLES.\nI. — Bass Progression. — ibid.\nII. — Using Consonant and Dissonant Chords. — 292\nIII. — Major Dissonances Caused by the Leading Note, and Their Bass Notes. — 294", "front-contents-015": "IV. — Minor Dissonances. — 294\nV. — Consonances Preferred for Doubling. — 295\nVI. — Meter and Beat. — ibid.\nVII. — Syncopation. — 296\nChap. XXXVI. — Two-Part Composition. — 299\nChap. XXXVII. — False Relations. — 302\nChap. XXXVIII. — Making a Melody above a Bass. — 303\nChap. XXXIX. — Figured Melody, or Supposition. — 308\nARTICLES.\nI. — Figured Melody through Consonant Intervals. — ibid.\nII. — Figured Melody through Diatonic Intervals. — 311\nChap. XL. — Making a Fundamental Bass beneath an Upper Part. — 313\nChap. XLI. — Composing a Continuo Bass beneath an Upper Part. — 323\nChap. XLII. — Useful Observations on the Previous Chapter. — 327\nChap. XLIII. — Rules for Composition in Two, Three, and Four Parts. — 329\nChap. XLIV. — Design, Imitation, and Fugue. — 331\nAfter these chapters come several examples, including a quintet and different canons.\nBOOK FOUR. — Principles of Accompaniment.\nChap. I. — Distinguishing Intervals through Keyboard Layout. — 363\nChap. II. — Differences between Major and Minor Intervals, and between Perfect, Augmented, and Diminished Intervals. — 366\nChap. III. — Hand Position and Finger Arrangement. — 371\nChap. IV. — Finding Chords on the Keyboard. — 372\nChap. V. — Useful Observations on All Chords. — 377\nChap. VI. — Keys and Modes. — 381", "front-contents-016": "Chap. VII. — Order of Chord Succession within Each Key’s Octave. — 388\nChap. VIII. — General Rules. — 392\nChap. IX. — Different Chords Following the Seventh Chord on a Stationary Note. Articles I and II. — 397\nChap. X. — Second Chord. — 401\nChap. XI. — Sixth Chords. — 402\nChap. XII. — Augmented-Second Chord and Its Derivatives. — 404\nChap. XIII. — Chords by Supposition. — 406\nARTICLES.\nI. — Ninth. — ibid.\nII. — Augmented-Fifth Chord. — 407\nIII. — Augmented-Seventh Chord. — ibid.\nIV. — Eleventh Chord, Called the Fourth. — ibid.\nChap. XIV. — Relationships among All the Preceding Chords. — 408\nChap. XV. — Preparing and Resolving All Dissonances to Identify the Current Key and the Chords Belonging to Each of Its Notes. — 411\nARTICLES.\nI. — Major Dissonance. — ibid.\nII. — Minor Dissonance. — 414\nChap. XVI. — Chromatic Movement. — 416\nChap. XVII. — Recapitulation of Different Chord Successions. — 418\nChap. XVIII. — Rules Needed for Good Accompaniment. — 426\nChap. XIX. — Figuring a Continuo Bass and Identifying the Chord Denoted by Each Figure. — 428\nChap. XX. — Distinguishing the Bass Notes That Must Bear a Chord. — 429", "front-contents-end": "END OF CONTENTS.", "front-terms-001": "GLOSSARY,\nExplaining Essential Terms.", "front-terms-002": "A", "front-terms-003": "ACCOMPANIMENT. See Book Four. page 363", "front-terms-004": "CHORD. All chords come from one. Inversion reduces them all to a division into thirds. Chapter VII, Book I. 102. 114. 126. 127 and 128", "front-terms-005": "Every chord’s principle lies in one sound. 5. 127 and 133", "front-terms-006": "There are only the perfect chord and the seventh chord. 45. 61. 378 and 379", "front-terms-007": "Fundamental harmony rules make consonant and even dissonant chords easy to use and supply every imaginable melody. They always show which sounds complete a chord. 72 and 73", "front-terms-008": "The seventh chord is always contained in chords by supposition. 74 and 75", "front-terms-009": "Every dissonant chord consists only of combined consonances. 95", "front-terms-010": "To reason correctly, consider chord notes both against the bass and against each other. page 96", "front-terms-012": "Every bass note moving by consonant intervals may receive a consonant chord [printed “Conso-sonant”]. 395", "front-terms-013": "See Perfect, Rule, Consonance, and Octave.", "front-terms-014": "HIGH-PITCHED. This is the proper name for high sounds, just as low-pitched names low sounds.", "front-terms-015": "High sounds are contained in the low sound. 3 and 5", "front-terms-016": "B", "front-terms-017": "FUNDAMENTAL BASS, or FUNDAMENTAL SOUND. It can exist only if it always lies beneath the other parts. page 134", "front-terms-018": "See Imply and Suppose.", "front-terms-019": "The only intervals assigned to fundamental-bass progression are the third, fifth, and seventh. 49 through 51", "front-terms-020": "Its most perfect progression descends by thirds, fifths, and sevenths. 132", "front-terms-021": "The most perfect of these is the fifth, which seems to return to its source, and so forth. page 129", "front-terms-023": "This progression forms the perfect cadence. 57", "front-terms-024": "Dissonance can be prepared and resolved only in one of these progressions. 81. 87 and 110", "front-terms-025": "When the fundamental bass ascends by these same intervals, the dissonance cannot be prepared. 84 through 87", "front-terms-026": "Descending a fifth and ascending a fourth are equivalent in these progressions. 185", "front-terms-027": "Zarlino compares the bass to the earth and says it must move slowly and by separate steps. 49", "front-terms-028": "The intervals used for fundamental-bass progression must also accompany it. 52", "front-terms-029": "The fundamental bass produces a very good effect in choruses. 138", "front-terms-030": "See Cadence, Principle, and Progression.", "front-terms-031": "C", "front-terms-032": "CADENCE. A perfect cadence is formed by a fundamental bass descending a fifth or ascending a fourth. page 50", "front-terms-033": "The perfect cadence proves where dissonance belongs. 53", "front-terms-034": "Definition of the perfect cadence. 54", "front-terms-035": "It determines every interval’s progression except the octave and fifth, and so forth. page 55", "front-terms-037": "Example of the perfect cadence. 57", "front-terms-038": "Zarlino says music needs a bass to avoid confusion, and a perfect cadence needs a descending fifth in the bass. Yet most of his examples omit it. 58", "front-terms-039": "A cadence is called interrupted when the dominant ascends diatonically in the bass or other parts. 61 through 63", "front-terms-040": "This cadence is admitted only by license. 110", "front-terms-041": "Benefits obtainable from it. 271 and 272", "front-terms-042": "An irregular cadence has a bass rising a fifth, and so on. Its dissonance moves irregularly, but may always be left out. See the Supplement.", "front-terms-043": "A cadence is called imperfect when the perfect cadence’s bass is absent but can be implied. 257", "front-terms-044": "Knowing all these cadences is essential to understanding harmony. See the Supplement.", "front-terms-045": "Inverting these cadences creates harmonic variety and produces melody. 67", "front-terms-046": "Ways to maintain a long sequence of melody and chords without any conclusion. page 68", "front-terms-048": "Distinguishing a cadence from its imitation. 68 and 69", "front-terms-049": "Evading cadences by imitating them. 70", "front-terms-050": "The example is written correctly in the Supplement.", "front-terms-051": "Progression of chords by supposition originates in the first three cadences. 75 and 77", "front-terms-052": "Modulation derives from the perfect cadence. 144. 145 and 148", "front-terms-053": "The perfect cadence suffices to explain every musical rule. 129", "front-terms-054": "CANON. Definition of canon. 359 through 362", "front-terms-055": "CENTER. The principle of harmony may be regarded as the harmonic center. 127", "front-terms-056": "CLASH. Sounds clash in a way related to the collision of solid bodies. See the Supplement.", "front-terms-057": "This clash occurs between a dissonance and its nearest consonance. Ibid.", "front-terms-058": "COMMA. Determining how many commas make up a whole tone. 27", "front-terms-059": "A ratio much smaller than the comma is needed to form the intervals. Ibid.", "front-terms-060": "CHROMATIC. Semitone motion creates the chromatic genus. Harmonically it mainly involves the sixth and seventh notes in minor. page 293", "front-terms-062": "Making the tonic a tonic dominant reveals the chromatic. 70", "front-terms-063": "A part moving by semitones has a chromatic progression.", "front-terms-064": "COMPOSE. COMPOSITION. Invent pleasing melodies, combine sounds well, give each sound suitable movement, and understand how intervals and chords relate. Composition puts into practice everything needed for perfect music.", "front-terms-065": "Composition should first be taught in 4 parts. 239 and 240", "front-terms-066": "Qualities required for good composition. 143 and 162", "front-terms-067": "Accompaniment is, in a sense, necessary for reaching an understanding of composition sooner. 140", "front-terms-068": "CONJUNCT. Conjunct progression or steps include diatonic and chromatic motion.", "front-terms-069": "See Diatonic and Chromatic.", "front-terms-070": "CONSONANCE. An interval whose sounds are very pleasing together. Consonances are thirds, fourths, fifths, and sixths. Consonant progression means melodic movement by one of them.", "front-terms-072": "Origin of consonances, their order there, order of perfection, and mutual relationships. pages 3. 4. 5. 15 and 16", "front-terms-073": "There are only three primary consonances. 13 and 14", "front-terms-074": "There are dissonant consonances. 96 and 102", "front-terms-075": "COUNTERPOINT means composition. Musicians use it for music built on a specific subject, usually a church chant.", "front-terms-076": "Counterpoint is divided into simple, figured, and other types. See Monsieur de Brossard’s Dictionary.", "front-terms-077": "Plainchant predates knowledge of good modulation and repeatedly breaks the natural order. Harmonizing it requires rules shaped by its defects, because those rules serve the chant.", "front-terms-078": "Many musicians still favor those rules without examining their basis. Those who hear true harmony find them unnecessary. Good modulation offers simpler, more accurate rules, certain to work if the given subject follows good modulation, as it must. See Plainchant below and Book II, Chapters XVIII, XIX, and XXI.", "front-terms-080": "STRING. A string stretched to produce a sound teaches us the relationships between sounds. page 2", "front-terms-081": "Divide this string according to the natural sequence of numbers to obtain every necessary harmonic benefit. 3. 4. 15. 16 and 21", "front-terms-082": "Sound relates to sound as string relates to string. 3", "front-terms-083": "People commonly say “beautiful strings” to express beauties found in harmony and melody.", "front-terms-084": "BODY. Unity, the principle of numbers, represents the sounding body from which relationships between sounds are proved. 18", "front-terms-085": "D", "front-terms-086": "DIATONIC. Diatonic progression moves the melody through successive degrees of the natural voice, following the scale or perfect diatonic system. page 23", "front-terms-088": "See System and Progression.", "front-terms-089": "DISJUNCT. Disjunct progression includes consonant and dissonant motion.", "front-terms-090": "See Consonance and Dissonance.", "front-terms-091": "DISSONANCE. Intervals that clash to the ear. Dissonant progression means moving a melody by one of them.", "front-terms-092": "Origin and relationships of dissonances. 22. 24 and 27", "front-terms-093": "The seventh chord is the origin of all dissonant chords. 31 and 38 through 45. 96. 98 and 101", "front-terms-094": "All dissonances are major or minor, like the thirds from which they originate and whose properties they consequently follow. 45. 55. 81 and 130", "front-terms-095": "The leading note is the origin of all major dissonances. 56 and 137", "front-terms-096": "A major dissonance is such only when joined by the minor dissonance. 137", "front-terms-097": "The seventh is the origin of all minor dissonances. 98", "front-terms-098": "Dissonance must be used with great discretion. 142", "front-terms-099": "Reflection on resolving dissonances. 137", "front-terms-100": "See Cadence, Division, Ratio, Progression, Prepare, Resolve, Fundamental Bass, Second, Seventh, and Tritone.", "front-terms-102": "DOMINANT. Definition of dominant. page 56", "front-terms-103": "Distinctions among dominants. 68. 69 and 200", "front-terms-104": "E", "front-terms-105": "BORROWING. A new practical term distinguishing a kind of chord usable only in minor keys. pages 43. 79. 80 and 81", "front-terms-106": "Proof of this borrowing. 282 through 285. See Second.", "front-terms-107": "EXPERIENCE. See Music.", "front-terms-108": "F", "front-terms-109": "FUNDAMENTAL. See Fundamental Bass.", "front-terms-110": "FUGUE. A musical ornament whose only principle is good taste. page 358", "front-terms-111": "Fugue may have been invented for four-part pieces. 331", "front-terms-112": "For more on this subject, read Book III, Chapter XLIII.", "front-terms-113": "G", "front-terms-114": "LOW-PITCHED. See High-Pitched.", "front-terms-115": "H", "front-terms-116": "HARMONY. Several sounds combined to affect the ear agreeably.", "front-terms-117": "Harmony is perceived only at the first instant of each beat. page 134", "front-terms-118": "Melody comes from harmony. 23. 138 and 139", "front-terms-119": "Perfect harmony consists in four parts. 140 and 141", "front-terms-120": "Harmonic progression comes from arithmetic progression. 17 and 20", "front-terms-121": "See Cadence, String, Proportion, Melody, Meter, Music, Number, and Principle.", "front-terms-122": "I", "front-terms-123": "IMITATION. Definition of imitation. 193 and 332", "front-terms-124": "IMPERFECT. Thirds and sixths are variable consonances called imperfect. The term should also describe inversions of the perfect cadence. See Cadence.", "front-terms-125": "Some inversions of the perfect chord are called imperfect chords. 35", "front-terms-126": "INTERVAL. Definition and names of intervals. 2", "front-terms-127": "Distinguishing inverted intervals from uninverted ones through arithmetic operations. 17", "front-terms-128": "Formation of intervals. 27. See Ratio and Tritone.", "front-terms-129": "IRREGULAR. See Cadence.", "front-terms-130": "L", "front-terms-131": "LICENSE. Origin of musical licenses. page 110", "front-terms-132": "LENGTH. See Ratio.", "front-terms-133": "M", "front-terms-134": "MELODY. One part’s tune. Music is melodious when each part’s melody is as beautiful as its harmony.", "front-terms-135": "As far as can be judged, ancient music was founded on melody alone. pages 142. 143 and 146", "front-terms-136": "Zarlino explains this perfectly well. 142", "front-terms-137": "See Cadence and Harmony.", "front-terms-138": "METER. Descartes says animals could dance in meter. 150", "front-terms-139": "Meter may be derived from the principle of harmony. Ibid.", "front-terms-140": "Useful practices for training the ear in meter. 151", "front-terms-141": "The numbers 2, 3, and 4 alone suffice to indicate every meter. Ibid.", "front-terms-142": "The same signs are used for equal-beat and unequal-beat movement, making them hard to distinguish. 156", "front-terms-143": "A note before the clef may indicate each beat’s value by its own duration, thus distinguishing slow from fast tempo. 152", "front-terms-144": "A note before the clef shows the key and makes solmization easier, regardless of how many sharps or flats follow the clef. page 158", "front-terms-146": "MODE. A mode gives the diatonic order of notes within an octave and the order of chords made from those notes.", "front-terms-147": "Modes are derived from the perfect diatonic system. 143 and 144", "front-terms-148": "There are only two modes. 143", "front-terms-149": "Errors of the ancients and Zarlino in establishing modes, and the probable cause of Zarlino’s error. 145 through 148", "front-terms-150": "Understanding modulation greatly helps determine whether music is well composed. 135. See Cadence, Key, Tritone, Third.", "front-terms-151": "MUSIC. What music is and what it consists of. 1", "front-terms-152": "We may hear music’s effects directly, but understanding its properties requires reason. 125", "front-terms-153": "We hear many chords, but reason shows that all come together in one. Reason should therefore guide judgment. 126", "front-terms-154": "Musical experience alone cannot convince us. page 106", "front-terms-156": "But reason can supply what is missing. 114", "front-terms-157": "Music is subordinate to arithmetic. 18 and 19", "front-terms-158": "While arithmetic progression must increase, harmonic progression must decrease. 11", "front-terms-159": "To apply the natural numerical sequence to harmony, imagine that numbers indicate divisions of unity, and so forth. 11 and 19", "front-terms-160": "What a good musician must observe in creating works. 143", "front-terms-161": "See Mode.", "front-terms-162": "N", "front-terms-163": "NUMBER. All harmony’s power has been attributed to numbers. page 3", "front-terms-164": "Only three consonant numbers form the perfect chord. 34 and 35", "front-terms-165": "Observations on the power of three. 35", "front-terms-166": "A number multiplied geometrically always represents, so to speak, the same sound, and so forth. 7", "front-terms-167": "The number 5 can represent unity. 13", "front-terms-168": "The number 3, where the fourth arises, cannot head a chord without inverting its natural order. 21 and 22", "front-terms-169": "If numbers are understood as divisions of unity, everything becomes simple, familiar, precise, just, and correct. page 21", "front-terms-171": "See String, Body, and Music.", "front-terms-172": "TONIC NOTE. LEADING NOTE. See Sound and Leading.", "front-terms-173": "NINTH. Difference between ninth and second. 28 and 78", "front-terms-174": "The ninth interval and its chord derive from the fifth. 32", "front-terms-175": "This chord proves that the seventh can resolve to the octave. 118 and 119", "front-terms-176": "When a ninth chord sounds above a tonic, avoid adding the seventh. 94", "front-terms-177": "See Eleventh, Seventh, Suppose, and Tritone.", "front-terms-178": "O", "front-terms-179": "OCTAVE. Definition and properties of the octave. pages 6 through 17, and also 54", "front-terms-180": "All chord variety arising from inversion comes from the octave’s power. 15 and 16", "front-terms-181": "The octave should be called aequisonance rather than consonance. 7. 15 and 16", "front-terms-182": "See Principle and Simulated.", "front-terms-183": "ELEVENTH. Difference between eleventh and fourth. 28 and 77", "front-terms-184": "The eleventh and ninth are primary intervals of their kinds; the fourth and second are inversions. The same applies to their chords. 29 and 78", "front-terms-185": "The full eleventh chord is very harsh. Removing its middle notes produces the form called heteroclite. page 76", "front-terms-187": "See Suppose.", "front-terms-188": "P", "front-terms-189": "PERFECT. The perfect chord consists of the fifth and the two thirds.", "front-terms-190": "Chords arising from inversion of the perfect chord. pages 34. 35 and 36", "front-terms-191": "Any chord besides the perfect chord must consist of the perfect chord plus one of its parts. 31. See Cadence.", "front-terms-192": "PLAINCHANT. Plainchant suits harmony only in keys conforming to the perfect system. Its melody could be made easier and more flowing. 147", "front-terms-193": "PREPARE. Put a consonance on the same pitch before a minor dissonance. The rule has exceptions. 84 through 87", "front-terms-194": "Dissonance need not always be prepared on weak beats, and major dissonance can never be prepared. 86", "front-terms-195": "Dissonance absolutely must be prepared by a consonance. 123 and 125", "front-terms-196": "PRINCIPLE. Harmony’s principle resides in a single sound. 5 and 127", "front-terms-197": "The fundamental sound uses its octave as another endpoint for all intervals produced by dividing it. This shows that the fundamental is their beginning and end. page 8", "front-terms-198": "Everything agreeing with the principle agrees equally with its octave. Ibid.", "front-terms-199": "The principle is implied in its octave. 8 and 9", "front-terms-200": "Always seek the principle in fundamental chords. 117", "front-terms-201": "The principle resides not merely in fundamental chords, but more precisely in their lowest sound. 133", "front-terms-202": "The foundation exists only within its octave. If a chord extends beyond it, its foundation must be treated by supposition. 32 and 33", "front-terms-203": "See Suppose.", "front-terms-204": "Zarlino knew this principle but lost sight of it in his operations and rules. 18 through 21", "front-terms-205": "Dissonance derives its principle from the perfect chord, and so forth; that chord derives its principle from its lowest sound, and so forth. 109", "front-terms-206": "See Viol and Center.", "front-terms-207": "PROGRESSION. While fundamental-bass progression must be consonant, upper-part progression must be diatonic. page 52", "front-terms-209": "One part may be given the progression belonging to another. Ibid.", "front-terms-210": "Dissonance must move diatonically, and the sounds preceding and following it must be consonant. Ibid.", "front-terms-211": "See Fundamental Bass, Cadence, String, Harmony, Music, Proportion, Ratio, Consonance, Dissonance, Chromatic, Diatonic, Conjunct, and Disjunct.", "front-terms-212": "PROPORTION. A relationship between two or more sounds compared together.", "front-terms-213": "Harmonic or arithmetic proportion gives consonances an especially pleasing order. 4", "front-terms-214": "The ratio 2 to 4, giving the octave, affects the ear much like 2 to 2, giving the unison. 7", "front-terms-215": "Harmonic proportion or progression derives from arithmetic proportion; their relationship. 17 and 20", "front-terms-216": "Faults apparently caused by favoring harmonic over arithmetic proportion. 18. 19 and 20", "front-terms-217": "Sound ideas about harmony supplied by arithmetic proportion. 21 and 22", "front-terms-218": "The difference between harmonic and arithmetic proportions partly caused the ancients’ errors in arranging modes. page 147", "front-terms-220": "Q", "front-terms-221": "FOURTH. Origin of the fourth. pages 10 and 11", "front-terms-222": "Although the fourth can produce a seventh through its squares, it cannot divide that seventh harmonically. 31", "front-terms-223": "The fourth in second and small-sixth chords is consonant. 99 and 102", "front-terms-224": "See Number, Eleventh, and Tritone.", "front-terms-225": "FIFTH. Origin of the fifth and its precedence over the fourth. 10 and 11", "front-terms-226": "The fifth is the first consonance, excluding the octave. 5", "front-terms-227": "The fifth and thirds compose all chords. 29. 30. 31 and 32", "front-terms-228": "The fifth is the primary object of all chords. 12. 32 and 54", "front-terms-229": "The fifth cannot serve as the limit of intervals. 13", "front-terms-230": "No chord is complete without the fifth, hence without the two thirds composing it. 30", "front-terms-231": "Squaring the fifth produces an interval beyond an octave. Its chord is tolerable only because the fifth divides that interval harmonically. 32", "front-terms-232": "The first bass note of a descending fifth or ascending fourth may, and indeed should, bear a seventh chord. page 69", "front-terms-234": "If you feel harmony, a melodic ending almost forces you to supply a bass falling a fifth, and so on. 50", "front-terms-235": "Sometimes the right hand can hardly avoid consecutive fifths in harpsichord accompaniment. They help link chords smoothly. Learning that connection is easier if this small fault is allowed than if composition rules are enforced strictly.", "front-terms-236": "It may not even be a fault in accompaniment. The harmonic foundation is intact, and Italians freely use it in these cases.", "front-terms-237": "See Fundamental Bass, Simulated, Tritone, and Cadence.", "front-terms-238": "R", "front-terms-239": "RATIO. Different ratios assignable to one chord. pages 26 and 46", "front-terms-240": "Vibration ratios match division ratios; length ratios are their inversions. pages 47 and 48", "front-terms-241": "Catalogue of natural and inverted ratios for all intervals. page 26", "front-terms-242": "See String.", "front-terms-243": "INVERT. INVERSION. Rearrange the natural order in which sounds form perfect harmony.", "front-terms-244": "Inversion comes from the octave’s power. 7. 15 and 16", "front-terms-245": "Most theorists have considered interval inversion merely as the difference between one interval and another. 16", "front-terms-246": "Zarlino understood interval inversion but forgot chord inversion. 20 and 111", "front-terms-247": "Distinguishing inverted and uninverted intervals through arithmetic operations. 17", "front-terms-248": "Inversion is the key to all harmonic variety. 10 and 114", "front-terms-249": "Knowledge of inverted chords developed only over time. 132", "front-terms-250": "Inversion becomes clearer as we penetrate harmony’s secrets. 11", "front-terms-251": "Some musicians wrongly allow inversion of supposition chords because they do not understand either principle.", "front-terms-252": "See Suppose.", "front-terms-253": "OCTAVE EQUIVALENT. Definition of an octave equivalent. page 6", "front-terms-255": "RULE. Rules derive from principles, not principles from rules. 113 and 126", "front-terms-256": "Rules originating in fundamental harmony hold only within the chords assigned to that harmony. 90 and 91", "front-terms-257": "Seek a derived chord’s properties in its fundamental chord. 103", "front-terms-258": "The rule requiring every dissonance to be prepared by a consonance has no exception. 104", "front-terms-259": "Proof of errors in modern rules. 105 through 109, and 132", "front-terms-260": "Faults of commentators on the first rules. 125 and 143", "front-terms-261": "The fundamental bass determines every rule concerning consonances. 128 and 129", "front-terms-262": "Different principles behind the rule allowing a syncopated bass beneath a dissonance. 107 and 108", "front-terms-263": "See Cadence and Counterpoint.", "front-terms-264": "S", "front-terms-265": "RESOLVE. In music, this means every dissonance must be followed diatonically by a consonance.", "front-terms-266": "Major dissonances must resolve upward by semitone; minor ones downward diatonically. pages 55 and 130", "front-terms-267": "SECOND. Minor dissonance is always recognized in a second or seventh. page 100", "front-terms-269": "The second is an inverted seventh, as shown in the squares on page 38.", "front-terms-270": "Origin of the augmented second and how it borrows its foundation from the fundamental sound. 41 through 44", "front-terms-271": "This borrowing generates as many chords as a tonic dominant’s seventh chord. 80. 283. 284. 404 and 405", "front-terms-272": "See Seventh.", "front-terms-273": "SEMITONE. This word derives from Greek and means half-tone.", "front-terms-274": "The semitone ornaments all harmony and melody and always carries the major dissonance’s movement. Zarlino explains it well but abandons it where its effect is strongest. 55 through 57", "front-terms-275": "The minor semitone distinguishes major from minor thirds, hence all intervals classed as major, minor, augmented, or diminished. 27", "front-terms-276": "Distinguishing major and minor whole tones and semitones, and so forth, is useless in practice. 364", "front-terms-277": "See Leading and Tritone.", "front-terms-278": "LEADING. Definition of the leading note. 56 and 217", "front-terms-279": "The leading note identifies the current key. 258", "front-terms-280": "See Dissonance.", "front-terms-281": "SEVENTH. All dissonances come from the seventh. Without it, the major dissonance is consonant. Page 38’s squares show the seventh added to the perfect chord, generating all dissonances.", "front-terms-283": "See also the Supplement.", "front-terms-284": "In natural, fundamental harmony, the seventh can resolve only to the third. page 121", "front-terms-285": "The seventh chord combining minor and major dissonances is the most fruitful of all. 45", "front-terms-286": "The seventh, second, and ninth should not be distinguished as major or minor. 166 and 168", "front-terms-287": "All borrowed chords begin from the diminished seventh. Put it below the chord, where it forms the lower sound of the inverted interval, an augmented second. 43 and 44", "front-terms-288": "The seventh’s different forms, such as diminished fifth or ninth, and its resolutions to different intervals result only from different bass progressions. 67", "front-terms-289": "Monsieur de Brossard erred in accompanying the augmented seventh. 167", "front-terms-290": "He also erred about its relationship to the diminished second. 166", "front-terms-291": "See Chord and Dissonance.", "front-terms-292": "See also Second and Tritone.", "front-terms-293": "SIMULATED. Definition of two simulated octaves or fifths, their use, and ways to avoid them. pages 120 and 121", "front-terms-294": "SIXTH. Origin of sixths. 12 through 14", "front-terms-295": "Sixth and sixth–fourth chords require the fundamental sound to be understood as implied in its octave. 9", "front-terms-296": "See Third.", "front-terms-297": "SOLMIZE. See Meter and Transpose.", "front-terms-298": "SOUND. Sound is music’s principal object. 1", "front-terms-299": "Its distinctions in practical music. 2", "front-terms-300": "Knowing the relationships between sounds. 2 through 4", "front-terms-301": "Sustained sounds in some way escape our attention. 122", "front-terms-302": "See Fundamental Bass, String, Chord, Principle, Imply, and Suppose.", "front-terms-303": "IMPLY. “Imply” and “suppose” are often treated as synonyms, but they mean different things. An implied sound could be added to a chord where it is missing. An implied fundamental belongs below the other sounds. In supposition, one sound stands for another that is missing or comes before or after. The fundamental must then be placed immediately above the extra, or supernumerary, sound in a chord by supposition. See Suppose. This careful use of the terms for the fundamental sound preserves their literal meanings.", "front-terms-305": "SUPPOSE. SUPPOSITION. Previously this named passing notes used for melodic effect that do not fit the surrounding chord. It should more precisely name added sounds that change a chord’s perfection by stretching it beyond an octave.", "front-terms-306": "There are only two chords by supposition, from which two others derive. page 406", "front-terms-307": "The ninth chord’s extra sound cannot fit into page 38’s squares. It sits immediately below the fundamental, which it therefore represents by supposition.", "front-terms-309": "This supernumerary sound cannot be inverted. page 74", "front-terms-310": "See Cadence.", "front-terms-311": "SYNCOPATION. With dissonance, the term points to a clash against the nearest consonance. See the Supplement.", "front-terms-312": "The term has another practical meaning, explained on page 296.", "front-terms-313": "Syncopation concerns only the dissonant sound. 98. 99 and 108", "front-terms-314": "SYSTEM. Perfect diatonic system. 23", "front-terms-315": "Chromatic system. 28", "front-terms-316": "The ancients found the model of modulation in the perfect diatonic system but abandoned it in their multiplicity of modes. 145 and 146", "front-terms-317": "T", "front-terms-318": "BEAT. See Meter.", "front-terms-319": "TERM. Some musicians err because they do not understand the force of terms. page 124", "front-terms-320": "THIRD. Origin of thirds. 12. 13 and 14", "front-terms-321": "The fifth and thirds compose all chords. 29 through 32", "front-terms-322": "Thirds may be regarded as the sole object of all chords. 33 through 44", "front-terms-323": "The third is distinguished as major or minor. page 130 and the demonstration on page 4", "front-terms-325": "The third is the only consonance that can resolve dissonance in natural, fundamental harmony. 53 and 121", "front-terms-326": "Dissonant chords formed by adding a minor third above the perfect chord are more tolerable than those formed by adding a major third. 33. 34 and 40", "front-terms-327": "The major third must ascend; the minor third must descend. 55. 88 and 89", "front-terms-328": "Every interval classed as major, minor, augmented, or diminished must follow the properties of these thirds. 55 and 130", "front-terms-329": "The third of the fundamental sound or tonic determines the mode’s kind. There are therefore only two modes, major and minor. 143", "front-terms-330": "Only thirds and sixths should be distinguished as major and minor. 165", "front-terms-331": "Descartes erred about the origin of the minor third and sixths. 14", "front-terms-332": "Thirds partake of consonance and dissonance. 87", "front-terms-333": "The major third may descend. 90", "front-terms-334": "Minor thirds and minor sixths may ascend in harmony inverted from the fundamental. 91 through 93 and the Supplement.", "front-terms-336": "TONE / KEY. “Ton” has two meanings. First it is a whole tone, the distance between two sounds. Theory distinguishes major and minor whole tones. 22 and 23", "front-terms-337": "This distinction is useless in practice. 364 and 367", "front-terms-338": "Different ratios for minor and major whole tones cause corresponding differences in all interval ratios except the octave and augmented seventh. 25 and 26", "front-terms-339": "Second, “ton” means key and often stands for mode. The note organizing modulation within its octave is therefore called the tonic.", "front-terms-340": "Mode can change only from major to minor or vice versa, but the tonic may be taken on any of the chromatic system’s twenty-four notes. 149", "front-terms-341": "Consonances determine chords, the fundamental bass and therefore upper-part motion, and ways of changing key or mode. Ibid.", "front-terms-342": "Distinguishing key from mode. pages 149 and 198", "front-terms-344": "Determining whether a note bearing a perfect chord is tonic, and the consequences for choosing chords. 264 and 265", "front-terms-345": "See Meter.", "front-terms-346": "TRANSPOSE. The two modes begin on C and A. Using another starting note transposes the mode or key.", "front-terms-347": "Most Italians leave out the main key-signature sharp in transposed major modes. Almost all French musicians leave out the main flat in transposed minor modes. See the Supplement.", "front-terms-348": "Order of sharps and flats in transposed modes. Ibid.", "front-terms-349": "Avoiding the need to count post-clef sharps and flats when solmizing, and the difficulties that counting causes beginners. Ibid.", "front-terms-350": "Monsieur Frere erred in his new notation for transposed minor modes. Ibid.", "front-terms-351": "TRITONE. An augmented fourth spans three whole tones. Sometimes it is really a perfect fourth changed by modulation, rather than a tritone in the usual sense. Modulation similarly alters fifths, seconds, sevenths, and ninths. Knowing modulation prevents mistakes. See page 236.", "front-terms-353": "Masson called a fourth altered by modulation a tritone, although that fourth was not dissonant. 65 and 66", "front-terms-354": "V", "front-terms-355": "VIBRATION. See Ratio.", "front-terms-356": "VIOL. Evidence from musical instruments concerning the principle and its octave. page 6", "front-terms-358": "Z", "front-terms-359": "ZARLINO or ZARLIN. Celebrated music author whom Monsieur de Brossard calls the Prince of Modern Musicians.", "front-terms-360": "Errors in Zarlino’s rules partly arose because he considered only two sounds at once. page 89", "front-terms-361": "This author judges perfectly the astonishing effects the ancients attributed to their music. 142", "front-terms-362": "See Invert, Cadence, Principle, Mode, and Semitone.", "front-terms-363": "End of the Glossary.", "I-title-001": "HARMONY\nExplained through its natural principles", "I-title-002": "WITH RULES for composing music and playing accompaniment;", "I-title-003": "IN FOUR BOOKS.", "I-title-004": "BOOK ONE.\nHow harmonic ratios and proportions relate to one another.", "I01-1": "CHAPTER ONE.\nMusic and Sound.", "I01-2": "Music is the science of sounds. Sound is therefore its main subject.", "I01-3": "People usually divide music into harmony and melody. Yet melody is only one part of harmony. Knowing harmony is enough to understand all the properties of music fully. The following discussion will prove this.", "I01-4": "We shall leave physics to define sound. Harmony considers sounds only as low or high in pitch. It does not consider their loudness or length. All knowledge of harmony must be based on how high sounds relate to low sounds:", "I01-5": "Low sounds have the lowest pitches, like the sounds of male voices. High sounds have the highest pitches, like the sounds of female voices.", "I01-6": "An interval is the distance between a low sound and a high sound. Different distances between sounds make different intervals. The degrees of these intervals get their names from numbers. The first degree can only be called one. Two sounds on that same degree therefore make a unison. The second degree is a second; the 3rd is a third; the 4th, a fourth; the 5th, a fifth; the 6th, a sixth; the 7th, a seventh; and the 8th, an octave. The same pattern continues. Here we assume that the first degree is always the lowest. The other degrees are reached by raising the voice, one natural degree at a time.", "I02-1": "CHAPTER TWO.\nDifferent Ways to Discover the Relations Between Sounds.", "I02-2": "To find how sounds relate to one another, investigators took a string and stretched it until it could make a sound. They used movable bridges to divide it into several parts. They compared each resulting length with the others. They found that the string’s first five divisions contained every sound or interval that could agree with another.", "I02-3": "Some investigators compared the numbers that describe the string’s divisions. Others looked separately at the lengths produced by those divisions and compared the numbers that describe those lengths. Others noticed that sound cannot reach the ear without air. They therefore compared the numbers that describe the vibrations of the different lengths. There are still other ways to find these relations: different string thicknesses, different tensions made with weights, wind instruments, and so on. We need not examine all of them here. The finding was that all consonances* are contained in the first six numbers. Thicknesses and weights are exceptions. For them, we must use the squares of those basic numbers. This is why the whole power of harmony came to be attributed to numbers. The remaining task was to apply the numbers correctly to whichever operation was chosen as the basis of a system.", "I02-5": "Notice that the numbers for string divisions and vibrations follow their natural order. Everything in these methods follows the rules of arithmetic. Numbers for string lengths run in the reverse order. This destroys some rules of arithmetic—or, more exactly, requires us to reverse them. We shall see how in its proper place. For harmony, choosing one operation rather than another should make no difference. We shall nevertheless use only operations in which the numbers follow their natural order. These make everything much easier to understand.", "I02-6": "* See the Table of Terms.", "I.03-001": "CHAPTER THREE.", "I.03-002": "The Origin of Consonances and Their Relations.", "I.03-003": "* Sounds relate to one another as strings do. Every string contains all shorter strings within its length, but it does not contain longer ones. In the same way, all high sounds are contained in a low sound. The reverse does not hold: a high sound does not contain all low sounds. We must therefore find the higher term by dividing the lower one. The division must be arithmetical—that is, into equal parts—and so on. Let A B be", "I.03-004": "A — D — C — E — B", "I.03-005": "the lowest term. To find a higher term that forms the first consonance with it, I divide A B into two. Two is the first of all numbers. Point C shows this division. The interval between A C and A B is then the first consonance: the octave, also called the diapason. To get the consonances that come immediately after this first one, I divide A B into three equal parts. This gives two higher terms, A D and A E, rather than just one. They produce two consonances of the same kind: a twelfth and a fifth. I can also divide A B into 4, 5, or 6 parts. I cannot divide it further, because the ears’ capacity does not go beyond that, and so on.", "I.03-006": "* Descartes, Compendium of Music, p. 60.", "I.03-008": "To make the proposition clearer, take seven strings. Numbers will show their divisions. Assume that all seven strings are tuned to the same pitch, or unison. We need not make them equal in any other way. Put the numbers beside the strings in their natural order, as the next demonstration shows. Each number tells us how many equal parts to divide its string into. One point needs attention. The number 7 cannot give a pleasing interval, as those familiar with music know. We therefore replace it with 8. It is the first number after 7 that is twice one of the first six numbers. Compared with 1, it gives a triple octave. This does not increase the number of proposed numbers: 6 and 8 give the same interval as 3 and 4. A number always represents the number of which it is twice the value.", "I.03-009": "DEMONSTRATION.", "I.03-010": "Sounds and divisions (top to bottom):\nC 8\nG 6\nE 5\nC 4\nG 3\nC 2\nC 1\nIntervals between neighboring rows:\n6–8 Fourth; 5–6 Minor third; 4–5 Major third;\n3–4 Fourth; 2–3 Fifth; 1–2 Octave.\nOther relations:\n5–8 Minor sixth; 3–5 Major sixth;\n1–3 Twelfth; 1–4 Double octave; 1–8 Triple octave.", "I.03-011": "Remember first that all these numbers show divisions of one whole. They also show divisions of the complete string represented by 1.", "I.03-012": "The order of the numbers determines both when consonances arise and how perfect they are. The octave between 1 and 2 comes first. It is more perfect than the fifth between 2 and 3. Next comes the fourth between 3 and 4, and so on. Always follow the natural order of the numbers, and admit the sixths only at the end.", "I.03-013": "The note names show that string 1, its octave 2, its double octave 4, and its triple octave 8 produce what is, so to speak, the same sound. Arrange the notes in the order given by the numbers and string divisions, and you get the most perfect harmony imaginable. Anyone can test this. We shall now discuss the special properties of each sound or consonance in separate articles, so that each can be understood more clearly.", "I.03-014": "ARTICLE ONE.", "I.03-015": "The Principle of Harmony, or the Fundamental Sound.", "I.03-016": "First assume that the whole string, represented by 1, makes a certain sound. To study the sound’s properties, compare them with the properties of that single string. We may even compare them with the properties of one, or unity, which is the starting point of all numbers.", "I.03-017": "1. All the strings equal to the first have divisions marked on them. Each string’s number tells us how many parts it has. These divisions clearly show that every part comes from the first string: every part is contained within that first, single string. The sounds made by the divided strings are therefore generated from the first sound. That first sound is their principle and foundation.", "I.03-018": "2. Dividing the fundamental sound generates other sounds. Their different distances from it make different intervals. The fundamental sound is therefore the principle of those intervals.", "I.03-019": "3. Finally, joining these different intervals makes different consonances. Their harmony cannot be perfect unless the first sound stands below them as their base and foundation. The demonstration shows this. The first sound is therefore also the principle of the consonances and of the harmony they create.", "I.03-020": "The next articles will show which sounds are most closely related to this principle and how it uses them.", "I.03-021": "ARTICLE TWO.", "I.03-022": "The Unison.", "I.03-023": "A unison is, strictly speaking, one sound. Several voices or instruments can produce it together. The seven strings in the earlier demonstration show this before they are divided. For this reason, people say that a unison is not a consonance. A consonance needs sounds of different pitches—one lower and one higher—and unison lacks that difference. Instead, unison relates to consonances as one, or unity, relates to numbers.", "I.03-024": "ARTICLE THREE.", "I.03-025": "The Octave.", "I.03-026": "A whole and its half have a relation that we understand immediately. The relation is just as natural when we compare the half with the whole. This gives us reason to favor the octave, whose ratio is 1 to 2. Unity is the principle from which numbers come, and 2 is the first number. The words “principle” and “first” are closely related and fit this case very well. In musical practice, the octave is simply called a “replica.” The replica is treated as the same thing as its source, as the note names in the earlier diagram show. It is considered less a chord in itself than an addition to chords. That is why some compare it to zero. Male and female voices naturally sing an octave apart while thinking they are singing the same sound, or unison. On flutes, the octave depends only on how strongly one blows. Take a viol with strings long enough that their vibrations can be seen. Sound one string with some force. Strings an octave below or above it will vibrate by themselves. With a fifth, only the higher string vibrates; the lower one does not. This proves that the octave’s principle is shared by both of its sounds. The principle of the fifth—and therefore of every other interval—lies only in the lower, fundamental sound. * Descartes got this point wrong because his evidence about the octave, taken from a lute, was false.", "I.03-028": "The octave also sets the limits of all intervals. A sound generated by dividing the principle can first be compared with that principle, then with its octave. These two comparisons give harmony only the difference caused by changing the order of two terms: for example, 2, 3 becomes 3, 2. Geometry calls this an inverted ratio or comparison. In harmony, it simply means moving a sound from a lower pitch to a higher one. When 2 comes first, it marks the low sound. When it comes last, it must mark the high sound. We must show that change by using the number of its octave: write 3, 4 instead of 3, 2. A number multiplied geometrically therefore represents, so to speak, the same sound, or a replica of the sound at its root. The earlier diagram proves this if we start multiplying from 2. Dividing unity generates 2 first. Unity lets 2 generate all the remaining sounds in its place, yet loses none of its own power. Whatever agrees with 2 agrees equally with 1. An octave, a double octave, a triple octave, and any further octaves are fundamentally the same interval. We distinguish them only as doubles or replicas. The same applies to the fifth and twelfth, and so on. Why multiply the ratio 1, 2? Only to find numbers between its terms that can agree with each term. For example, 3 lies between 2 and 4. The numbers 5, 6, 7 lie between 4 and 8. We can continue this process without limit. The ratios 2, 4 and 4, 8 remain the same as 1 to 2.", "I.03-029": "We have compared numbers with 1 and with 2, always placing them above 1 and above 2. The intervals produced correspond to one another. We can therefore expect almost equal relations if we compare those same numbers above 1 but below 2. There is a further point. Inverting the comparison means only moving a sound to its octave, or changing a number to its double. The sounds’ relation can therefore change only through a difference in proportion. That difference makes almost no difference to the ear: 2 to 4 has nearly the same effect as 2 to 2. Our reasoning and experience together give enough proof. This is why the octave has been given the same force as its principal, fundamental sound. Zarlino says:* “The octave is the mother, source, and origin of all intervals. Dividing its two terms generates all harmonious chords.” This is true in one sense. But all other sounds still come from dividing the single fundamental sound. So do all intervals and chords. To accept Zarlino’s view, we must add an explanation. The fundamental sound uses its octave as a second term. Every interval generated by division must correspond with that term. This makes it clearer that the fundamental sound is both their beginning and their end. The octave has only the properties that the fundamental sound gives it. More precisely, it is still the same sound moved to its octave or replica—or multiplied, if that is how we choose to describe it. This allows intervals to be determined in every direction for each sound it has generated. The generated sounds keep the properties they received when first compared with the fundamental. A sound that made a perfect consonance with the fundamental also makes one with its octave. An imperfect consonance or dissonance on one side remains the same on the other. A sound that had to rise or fall on one side rises and falls on the other. Whatever agrees on one side agrees on the other. Nothing changes, except one thing. Chords made from the principal consonances have a particular perfection when the fundamental sound is in its natural place: at the bottom. That perfection changes when the fundamental moves up to its octave. The same consonances now stand in a different order, creating variety. Try the earlier diagram. Its full arrangement of consonances gives very great satisfaction. Remove sounds 1 and 2, then remove sounds 1, 2, 3, 4. The satisfaction becomes less, though the result still does not offend the ear. This is even easier to notice as a piece of music proceeds.", "I.03-030": "* Descartes, p. 59.", "I.03-032": "These observations lead to a conclusion: any sound is always implied in its octave. * Descartes partly agrees. He says that whenever we hear a sound, its upper octave also seems to reach our ears in some way. He might have included the lower octave too. But, as we said, his proof from a lute was mistaken. He might also have included it if he had accepted Aristotle’s view. Desermes* reports that Aristotle says this in Problems 24 and 43: pluck the nete string, the higher sound of the octave, and the hypate string, the lower sound, will also be heard. The fading end of the high sound becomes the beginning of the low sound, like an echo or image of the high sound. Almost every musician says that a certain sound, note, or interval “is implied,” sometimes adding “in the bass.” People often use this expression before understanding its full force. Harmonic ratios give us only the perfect chord. To admit the sixth and sixth–fourth chords derived from it, we must assume that the perfect chord’s fundamental sound is implied in its octave. Otherwise, we destroy every principle. Experience adds further support. A chord made from a third and fifth is always perfect and complete even without the octave. Since the octave was generated first, this suggests that it is implied. Now put that octave above the third and fifth. It forms a sixth and fourth with them. The resulting chord is still good, although the fundamental sound itself is absent. The fundamental must therefore have been moved into its octave, or be implied there. This explains why the second chord is less perfect than the first even though they use the same sounds. So these expressions all mean the same thing: the principle is inverted, identified with its octave, moved into its octave, or implied in its octave. The octave’s high sound is not a new principle. It represents the principle that directly generated it and forms one whole with it. All sounds, intervals, and chords must begin and end in that whole. Still, every property of the octave, of sounds generally, of intervals, and of chords depends entirely on the one fundamental principle: the whole string, or unity.", "I.03-033": "* Zarlino, Terza parte, chapter 3, fol. 174.", "I.03-034": "* Descartes, p. 61.", "I.03-036": "* Desermes, p. 41.", "I.03-037": "ARTICLE FOUR.", "I.03-038": "The Fifth and the Fourth.", "I.03-039": "Dividing the whole string gives the sounds that form the fifth and fourth. They therefore come from the fundamental sound. But consider the intervals themselves. In this case, the fundamental directly generates only the octave and fifth. The fourth comes afterward as a consequence of the octave: it is the difference between the octave and the fifth. That is why the original chords do not mention the fourth. Their whole force is attributed to the fifth alone. They do not even mention the octave, though it came before the fifth and the fifth cannot exist without it. The octave is apparently left unmentioned because it is implied. Otherwise, we could never admit the fourth, since the fourth cannot exist without the octave.", "I.03-040": "We must now pay close attention to the inverted comparison described in the last article. It is the key to every kind of variety in harmony. Understanding it is enough to solve the greatest difficulties. We need only learn which intervals arise when we compare a middle number with each end of an octave. Take 3, the arithmetic mean between 2 and 4. Compared with 2, it gives a fifth. Compared with 4, it gives a fourth. The difference is that the interval measured from the octave’s low, fundamental sound must be more perfect than the interval measured from its high sound. There is also a difference of proportion, but it need not concern us. It comes only from the difference between an octave and a unison. It is as if we compared 3 with 2 and then with 2 again: no difference would result. The octave’s two sounds are so closely related that they scarcely differ from unison and seem to be one. This makes us judge that 2, 4 has almost the same effect on the ear as 2, 2. We should therefore also regard two intervals as almost equal when their only difference is the use of 2 or 4 as one term. Give preference to the interval where the fundamental is in its natural place, because that interval comes directly from it. This is why arithmetic proportion is used here. It simply means finding the middle of two given numbers: 3 between 2 and 4, for example. Those who worked by multiplication instead invented what they called harmonic proportion. It is just the reverse of arithmetic proportion, as the next chapter will show. Apply each proportion to its proper object, and each gives a fifth measured from the octave’s lower sound and a fourth measured from its higher sound. Apply one proportion to the other’s object instead, and it gives a fourth on the low side and a fifth on the high side. The deeper we examine harmony, the more often this reversal appears. Consider these examples. Numbers naturally progress upward in size; in harmony, the progression must go downward. Where arithmetic proportion serves one method, harmonic proportion gives the same result in the other. To follow arithmetic proportion, treat the numbers as divisions of one whole. To follow harmonic proportion, reverse the order of the numbers. To follow the numbers’ natural order while they represent divisions of one whole, divide a given string. To follow the reverse order, multiply the given string. Dividing produces higher sounds, as it should. Multiplying produces lower sounds, against the natural order, though harmonic proportion puts this right. Finally, the octave has the close relation we have described. Denying that relation would deny the evidence of reason and experience. Dividing the octave first gives the fifth, the first interval of its kind. It is a fifth only in relation to the octave’s low, fundamental sound. Next comes the fourth, which Descartes* calls the fifth’s “shadow.” We get it by reversing the two sounds that first made the fifth: move the octave’s low sound into its high sound. This last kind of inversion is the main subject of this work.", "I.03-042": "* Descartes, p. 69.", "I.03-043": "ARTICLE FIVE.", "I.03-044": "Thirds and Sixths.", "I.03-045": "All the sounds that form thirds and sixths are found in the divisions of the whole string. They therefore come from the fundamental sound. But among the intervals, only the octave, fifth, and major third come directly from that sound here. The minor third and the sixths follow from the fifth and octave. The minor third is the difference between the major third and the fifth. The sixths are the differences between each of the two thirds and the octave. We should consider this carefully, especially the case of the minor third.", "I.03-046": "All intervals come from the octave, and all begin and end there. The minor third must therefore belong within the octave too. It cannot belong only indirectly, between the major third and the fifth, as in this example. It must relate directly to the fundamental sound or its octave. Otherwise, a minor third could never move from its position. It would always stay in the middle of a chord and could never occupy the outside positions. Experience proves otherwise. So do the properties assigned to arithmetic and harmonic proportions. In our system, arithmetic proportion divides a fifth into a major third below and a minor third above. Harmonic proportion reverses this: minor third below, major third above. This reversal in the order of thirds is another kind of inversion. It clearly shows that inversion is the main basis of all variety in harmony.", "I.03-047": "For further proof, listen to the pleasing effect of all the consonances in the earlier diagram, in their given order. Consider each one’s properties. The octave is so closely joined to the principle that produces it that the two become inseparable. That is why the octave need not be mentioned afterward: it is implied. The fundamental then takes the fifth to form every chord. Joining with the third immediately determines how those chords are built. A fifth contains a major third and a minor third. Both cannot relate to the fundamental at the same time. But if one third appears to come directly from the fundamental, we must give the other the same right. Major and minor differ, but both intervals are still thirds. Also, a fifth cannot set the limits of intervals. Only the octave can do that. Everything between the fundamental principle and its fifth remains under the octave’s authority, because the octave is inseparable from the principle. We have already proved this. We can judge one interval by another only with the octave’s help. To judge the minor third, we must therefore leave the fifth and major third aside. The octave of the minor third’s own low, fundamental sound is then implied. It has the same rights that belong to the octave in the origin of all intervals. Consider three cases. The fifth between 2 and 3 comes directly from the fundamental of the octave 2, 4. Inverting it gives the fourth between 3 and 4. Moving the fundamental from 2 to its octave 4 is the same operation. The major third between 4 and 5 comes directly from the fundamental of the octave 4, 8. Inverting it gives the minor sixth between 5 and 8. The minor third between 5 and 6 comes directly from the fundamental of the octave 5, 10. Inverting it gives the major sixth between 6 and 10, or between 3 and 5. Thus the fifth and both thirds have the same kind of direct origin. The fourth and both sixths have the same kind of indirect origin. An objection remains possible: the minor third seems to have a different principle from the major third, fifth, or octave, because 5 is not a multiple of 2, with 2 taken here as unity. But the ratio 5 to 6 is used only to avoid fractions. It follows the natural order of numbers and the corresponding order of string divisions. We could express the same ratio as 1 to 1 1/5. Its principle would then be unity. The next article shows this.", "I.03-049": "1. & 1. 1/5", "I.03-050": "All this gives us three primary consonances: the fifth, the major third, and the minor third. They make the chord called natural or perfect. Three secondary consonances come from them: the fourth and the two sixths. These make two more chords, but both are inversions of the first chord. We leave the octave out of this count because it must be implied in every one of these chords. “Equisonance” is a better name for the octave than “consonance.” Most of the best authors have used that name for it.", "I.03-052": "* In his Harmonic Demonstrations, Zarlino notes that sixths are inverted thirds. But in his Institutions, he says that a sixth is made from a fourth and a third. That description makes us lose sight of his first statement.", "I.03-053": "* Descartes also got the origins of the minor third and the sixths wrong. He says that the minor third comes from the major third as the fourth comes from the fifth, and so on. Later he says that the major sixth comes from the major third. Later still, he says that the minor sixth comes from the minor third as the major sixth comes from the major third, borrowing its properties and nature. But the fourth comes from the fifth only through the octave’s power. In the same way, the minor sixth comes from the major third, and the major sixth from the minor third. The minor third itself does not share this same origin. Descartes’s conclusions are therefore all false except for what he says about the properties of sixths. He confused those properties with their origin. Thirds and sixths share properties only through being major or minor: each third and each sixth must belong to one of those kinds. Sharing properties because of that kind is quite different from coming or being derived from another interval. Still, these mistakes can be forgiven. Descartes only touched on the subject. His work otherwise makes it clear that, had he devoted himself to it, he would have taken it further than someone else.", "I.03-054": "We have given the two thirds equal force in relation to the fundamental sound. This does not mean that their positions can be treated as equally suitable. The natural division of the fifth gives each its most suitable place, especially for a deeper study of harmony. We shall repeatedly see that the higher position suits the major third less well than the minor third.", "I.03-055": "* Zarlino, Ragion. 2°, definition x, fols. 83 and 84. Terza parte, chapters 20 and 21, fols. 192 and 193.", "I.03-056": "* Descartes, p. 71.", "I.03-057": "ARTICLE SIX.", "I.03-058": "A Summary of This Chapter: Showing the Earlier Demonstration’s Properties on One String.", "I.03-059": "Only part of each string in the earlier demonstration is needed to prove everything we have said. We shall mark that part on one string, together with the number that shows its division into equal parts. For each part, measure from the number to the right-hand end of the string.", "I.03-060": "Points on the string, from left to right:\n1 2 3 4 5 6 8 10\nAbove the string:\n2–3 Fifth; 3–4 Fourth; 2–4 Octave.\n5–8 Minor sixth; 6–10 Major sixth; 5–10 Octave.\nBelow the string:\n1–2 Octave; 1–4 Double octave; 1–8 Triple octave.\n4–5 Major third; 5–6 Minor third; 4–6 Fifth; 4–8 Octave.", "I.03-061": "Focus only on these three octaves: 2, 4; 4, 8; and 5, 10. In each octave, compare its intermediate numbers with each endpoint. Comparing an intermediate number with the lower, fundamental endpoint always gives the primary interval. Comparing the same number with the higher endpoint gives that interval’s inversion. For example, in the octave 2, 4, the fifth 2, 3 produces the fourth 3, 4. In the octave 4, 8, the major third 4, 5 produces the minor sixth 5, 8. In the octave 5, 10, the minor third 5, 6 produces the major sixth 6, 10. In each case, we have simply moved a fundamental sound to its octave: 2 to 4, 4 to 8, and 5 to 10.", "I.03-062": "For an even clearer view, use the lengths made by the same divisions, but measure to the left from each number to the string’s end. Compare each length with the whole string, its principle, and with octave 2, which gives the other endpoint. Then 3 makes a fifth with 1 and a fourth with 2. The number 5 makes a major third with 1 and a minor sixth with 2. The number 6 makes a minor third with 1 and a major sixth with 2. Unity is now clearly the direct principle of the fifth and both thirds. Moving unity to its octave 2 changes these into the fourth and both sixths. We should not be surprised, then, when 2, 4, 5, or another number stands for unity. This is done only to avoid fractions.", "I.03-064": "DEMONSTRATION.", "I.03-065": "The Relations of Consonances in Lengths Measured to the Left.", "I.03-066": "Points on the string, from left to right:\n2 3 4 5 6 1\nAbove the string:\n3–1 Fifth; 5–1 Major third; 6–1 Minor third.\nBelow the string:\n2–3 Fourth; 2–5 Minor sixth; 2–6 Major sixth.", "I.03-067": "Chapter XI will explain how to find the ratios for consonances compared in this way.", "I.03-068": "Most theorists have treated the inversion between consonances as no more than the difference between one interval and another. But two kinds of difference must be kept separate. One is the difference between a consonance and an octave. The other is the difference between two consonances. The octave represents the fundamental principle. As Descartes says,* anything that agrees with one of its endpoints must agree with the other. But when we compare two consonances, only the octave’s principal sound matters. Its higher sound plays no part. This explains a difference in how we use our string. We can always measure primary consonances and their inversions toward the right, the more natural direction. Their difference comes only from the octave’s two endpoints. To find the difference between two successive consonances, we must instead measure toward the left. Chapter V will show this. Those consonances came only from the principal sound. To find their difference, we must return to that sound, their origin.", "I.03-069": "* Descartes, p. 64.", "I.03-070": "Consider two ways of finding interval ratios. One concerns intervals produced by moving the octave’s two sounds. The other concerns the distance between two intervals, without bringing in the octave. To invert an interval, simply double the smaller number in its ratio, or halve the larger number. These operations amount to the same thing. For example, start with the minor third 5, 6. Double 5 or halve 6, and the result is a major sixth. But to find the interval that is the difference between two other intervals, we need a rule of subtraction. The octave gives further proof of its great perfection. We can form it from a unison by dividing or multiplying one of the unison’s terms. A unison has the ratio 2 to 2. Halve or double either term, and we get an octave. It remains an octave whether it extends downward or upward.", "I.04-001": "CHAPTER FOUR.", "I.04-002": "Observations on Harmonic and Arithmetic Proportions.", "I.04-003": "Descartes proposes dividing a string into equal parts to prove where consonances come from. We have not presented this account here. It can be proved only by reversing the numbers’ natural order. The numbers then describe multiples of the lengths produced by the division. This completely disrupts harmony’s order. An octave should naturally be divided with the fifth in the lower position. This method puts the fourth there instead. Those who followed this reversed order therefore invented a new proportion, called harmonic proportion, to return chords to their natural form. Anyone who understands it must admit that it reproduces arithmetic proportion in every detail. If we reverse the order of the numbers, we must also reverse the proportion. Only then can the reversed method reproduce all the perfections of the natural order. When the objects of the two proportions differ only by inversion, their agreement is so clear that we need not discuss it further. This explains why most specialists in arithmetic and geometry who have not studied music merely mention harmonic proportion. They do not define its properties, apparently because they know of none that belong to it. The Reverend Father Pardie says:* “What has been said so far about this progression or proportion is not very useful. I do not wish to undertake to say extraordinary things here.” * Desermes writes at length on the subject. He specifically says that the air movements which produce consonances, dividing the octave into a fifth below and a fourth above, follow arithmetic proportion, not harmonic proportion. The numbers 2, 3, 4 show this. Later, he says that what people call harmonic proportion should therefore be called arithmetic proportion or progression. This may explain why the Greeks did not concern themselves with harmonic proportion. We need not decide whether they did. Instead, we should ask whether Zarlino had good reason to give it such attention. He is our main concern because later authors took him as their model. We are always sent to him for questions of practice. Some musicians still treat him as an oracle, and Monsieur de Brossard calls him the prince of modern musicians.", "I.04-005": "* Zarlino first says that music is subordinate to arithmetic. He says that unity, the starting point of numbers, represents the sounding body used to prove the relations between sounds. He also says that unison is the principle of consonances. But his demonstrations and rules forget all three points. The further he investigates, the further he moves away from his own declared principle. He proposes dividing a whole string, so the principle—the sounding body—cannot be entirely hidden. Yet he then makes us lose sight of it. He separately compares each length produced by the division, treating the whole string as merely another length. Instead of remaining the principle, the whole now depends on the parts that previously depended on it. He behaves as though our chief task were to make instruments. He asks us to measure lengths already determined by the very numbers that divided the string into equal parts. Yet the relations between those numbers already give us the fullest understanding of harmony we could want. For proof, we need only give the numbers a new meaning. Music is subordinate to arithmetic. But harmonic progression decreases while arithmetic progression increases. So let numbers mean different things in the two cases: in arithmetic, they multiply unity; in harmony, they divide unity into as many equal parts as the number contains units. Anyone studying only the properties of numbers then finds music simple and natural. Proof is just as easy by this method as by the other. Zarlino will not risk this assumption. Instead, he burdens us with a second operation. This reverses both the natural number order and the beautiful harmonic order found in the first string division. Anyone can test this. The test also shows that he falls, in a way, into the fault he meant to avoid. Each length must be measured with a common unit. Its number tells us how many units to apply. Applying that unit repeatedly makes the string longer. The number therefore describes multiplication of the given string, not its division. That string is the sounding body represented by unity. Admittedly, the largest number can represent the whole string, with smaller numbers representing its parts. But that largest number cannot be the principle in every case. Its size changes when we divide the string into more or fewer parts. Add more divisions, and the principle moves further away until we lose sight of it. Take 6, 5, 4, 3, 2, 1. Treat 6 as the principle and listen to all the sounds produced by the lengths those numbers specify. The result immediately disproves the idea. Remove 6 and treat 5 as the principle: the same problem remains. Remove 5 and use 4, and so on: again the same. This order has as many imperfections as the opposite order has perfections, according to the properties we assign to each. To repair his second operation, Zarlino needs a third. He tries to recover what he lost by multiplying these numbers in a particular way. Chapter XI explains how. The resulting new progression was called harmonic proportion, by him or by others. It yields only what arithmetic proportion had already given in the first divisions. But what was simple in arithmetic proportion is obscure in harmonic proportion. We leave behind the original root numbers and the lengths they specified. We must start new operations, as if all previous results were useless. Yet the new operations merely lead back to the lost path. We have wandered so far that the principle is now hard to recognize. * The Reverend Father Mersenne brings these truths home. He argues that the harmonic number is simply the number of movements of air stirred by the vibrating string. This number makes arithmetic division sweeter, more pleasing, easier, and more familiar than harmonic division.", "I.04-006": "* The Reverend Father Pardie, Book VIII, p. 100. ]", "I.04-007": "[ * Desermes, Book I on Music, Theorem 28, p. 237.", "I.04-008": "* Zarlino, Prima parte, chapter 20, fol. 37; chapter 40, fol. 61. Terza parte, chapter 11, fol. 183. ]", "I.04-011": "* Zarlino’s complicated harmonic operations would matter less if he kept returning to his original principle. Instead, he abandons it at once. He mentions it in the octave only in passing. He calls the octave the origin of all intervals, but forgets that it also produces their inversions, which he discusses in his Harmonic Demonstrations. When he accepts inversion of intervals, he forgets inversion of chords, although that simply follows from it. He treats the perfect chord as the principle because it is the only chord supplied by harmonic ratios. Yet he says nothing more about that chord’s own principle, or at least his applications do not relate to it. He discusses the bass, where the principle should always be found. His comparison of the bass with the earth shows that he knows this. Yet his rules and examples treat the bass otherwise. He discusses the perfect cadence and how its bass moves, but makes no valid connection with his modes. Still, a piece of music can end only with a perfect cadence in some mode. Finally, his discussion of dissonance has no foundation. His demonstrations, rules, and examples all obscure the principle. Book Two will examine this more closely.", "I.04-012": "* The Reverend Father Mersenne, Harm., book 1, De numero, pondere et mensura, article I, proposition VI.", "I.04-013": "* Zarlino, Dem. Harm., p. 2, definition x, fols. 83 and 84.", "I.04-015": "These are the great results Zarlino has obtained from harmonic proportion. But if we give numbers the meaning we described, everything becomes simple, familiar, precise, sound, and correct. The natural sequence of numbers is as simple and familiar as anything can be. Ordinary arithmetic alone provides the proof here. All the properties of harmony fit precisely within the number six. And the soundest and most correct approach finds the basic principle everywhere in unity, as we shall now explain.", "I.04-016": "1. If a chord does not show unity, look for it among its geometric multiples—or, more exactly, among those of 2, which represents unity. Even if this multiple is not the first number in the chord, it will be one of its numbers. Halve it to put it in its proper place. This also reveals the true chord involved. Chords reduced this way are always the fundamental forms of chords whose multiples of unity do not come first. For example, take 5, 6, 8 or 6, 8, 10. Halve 8, and also halve 10 where it occurs. Both give 4, 5, 6. These numbers form the perfect chord produced by dividing the fifth. Halving 10 does not change the chord's substance.", "I.04-017": "2. Sometimes 5 or its geometric multiples can represent unity. This applies only when unity and its own multiples are absent. Treat the multiples of 5 just as we treated the multiples of unity. Thus, to find the original form of 12, 15, 20, reduce 20 to 10, and so on.", "I.04-018": "3. When the fifth and major third lie at the bottom, unity is represented by one of its multiples, and this number always comes first. When the minor third lies at the bottom together with the fifth, unity is represented by a multiple of 5, again in first place. As we said,* we do this only to avoid fractions. But when the fifth is not at the bottom, the numbers representing unity no longer come first. This is why 3 and its multiples, which generate the fourth, cannot represent unity. Nor can they head a chord without reversing its natural order. The number 3 is a harmonic mean, and it must keep that role everywhere. If a multiple represents unity, a multiple also represents 3. If a multiple of 5 represents unity, then 3 is multiplied by 5 or by a multiple of 5. So neither 3 nor its multiples can be at the bottom without partly destroying the foundation. Indeed, unless that foundation could be understood as still implied, it would be completely destroyed. This gives us our only proof that inverted chords are perfect: their perfection comes from the truly perfect chord that produces them. The rules we establish for this will finish convincing us.", "I.04-019": "* Chapter III, Article V, p. 13.", "I.04-020": "See the demonstrations in chapter 6.", "I.04-022": "There is only a very small exception to all this. It occurs in two chords with a diminished fifth at the bottom, as shown in Chapter VII, Articles VI and VII. In these cases, the square or cube of 5 represents unity.", "I.04-023": "Once these closely related operations have given us a complete understanding of harmony's properties, we can explain the same ideas through other operations suited to whatever subject we want to apply them to. Here, however, our subject is harmony alone, so we will keep our original system. Still, the last chapter shows how closely the numbers for dividing and multiplying the string are related. The difference between them is simply an inversion.", "I.05-001": "CHAPTER FIVE.", "I.05-002": "The Origin and Relationships of Dissonances.", "I.05-003": "We can derive dissonances* from the same string divisions that produced consonances. Compare the lengths left on the left-hand side of each number. This also shows the difference between two neighboring consonances. The lengths to the left of 3 and 4 give a whole tone: the difference between a fifth and a fourth. Those to the left of 4 and 5 give a major semitone: the difference between a fourth and a major third. Those to the left of 5 and 6 give a minor semitone: the difference between a major and a minor third. Whole tones and semitones make the successive steps of the natural voice. Melody comes from these steps. This begins to show us that melody follows from harmony.", "I.05-004": "Whole tone; major semitone; minor semitone. Divided string, marks from left to right: 2. 3. 4. 5. 6. 1.", "I.05-005": "* See the Alphabetical Table.", "I.05-006": "Whole tone; major semitone; minor semitone. Marks: 2. 3. 4. 5. 6. 1.", "I.05-008": "To find the ratios of these dissonances, use this rule for subtraction. Write the ratios of two neighboring consonances one above the other to find their difference:", "I.05-009": "Fifth ratio: 2. 3. Fourth ratio: 3. 4. Product: 8. 9. [Cross-multiplication.]", "I.05-010": "The X tells us to multiply the first number of each ratio by the second number of the other. So 2 times 4 gives 8, and 3 times 3 gives 9. The resulting 8 to 9 is the ratio of the whole tone. Do the same with the fourth and major third, and so on. The difference between the fifth and major sixth is also a whole tone, but its ratio is 9 to 10. We therefore need two kinds of whole tone. We call the first major and this second one minor.", "I.05-011": "These observations led to the following system.", "I.05-012": "PERFECT DIATONIC SYSTEM.", "I.05-013": "There is:\nFrom C to D... a minor whole tone, as 9 to 10.\nFrom D to E... a major whole tone, as 8 to 9.\nFrom E to F... a major semitone, as 15 to 16.\nFrom F to G... a major whole tone, as 8 to 9.\nFrom G to A... a minor whole tone, as 9 to 10.\nFrom A to B... a major whole tone, as 8 to 9.\nFrom B to C... a major semitone, as 15 to 16.", "I.05-014": "We could derive some harmonic dissonances from the system above. But their true source should instead be sought in squaring a primary consonance's ratio, or in adding two primary consonances. The following demonstration proves this.", "I.05-015": "DEMONSTRATION OF THE ORIGIN of Dissonances.", "I.05-016": "Addition of the minor-third ratio 5. 6. to the fifth ratio 2. 3. Product giving the seventh ratio: 10. 18.\nSquare of the fourth ratio: 3. 4. / 3. 4. Product giving the same seventh ratio: 9. 16.\nAddition of the major-third ratio 4. 5. to the fifth ratio 2. 3. Product giving the augmented-seventh ratio: 8. 15.\nSquare of the minor-third ratio: 5. 6. / 5. 6. Product giving the diminished-fifth ratio: 25. 36.\nSquare of the major-third ratio: 4. 5. / 4. 5. Product giving the augmented-fifth ratio: 16. 25.\nSquare of the fifth: 2. 3. / 2. 3. Product giving the ninth ratio: 4. 9.\nAddition of the minor-sixth ratio 5. 8. to the major-sixth ratio 3. 5. Product giving the eleventh ratio: 15. 40.\nCubes of the minor-third ratio give the diminished seventh between 125 and 218.", "I.05-017": "The other dissonances come from inverting these. For example, invert a seventh to get a second, a diminished fifth to get a tritone, and a diminished seventh to get an augmented second. But dissonances obtained by inverting augmented ones have no place in harmony. These include the diminished second and diminished fourth. Augmented dissonances are allowed only through supposition: they can occur only with a ninth or eleventh. These intervals exceed an octave and therefore cannot be inverted. Book II, Chapters X and XI explains this more fully.", "I.05-018": "We said that harmonic dissonances could be formed only from primary consonances. Yet we have also formed them from the fourth and the sixths. The eleventh produced by the sixths, however, lacks a property the others have: inversion does not give it a new interval. It can also be treated as a doubled fourth. We could have left out the seventh produced by squaring the fourth, because it is the same seventh produced by adding a minor third to a fifth. We included it to show that this same seventh has two different ratios. Every interval except the octave and augmented seventh can have this difference. It comes from the major and minor whole tones distributed through the diatonic system. They differ by a comma, with a ratio of 80 to 81. The ear does not notice this difference, especially in intervals suitable for harmony and melody. Still, we should explain it in terms of the different notes from which an interval can be made. For example, the fourth C–F and the fourth D–G have different ratios. One contains two major whole tones; the other contains one major and one minor whole tone. That alone explains the difference.", "I.05-020": "Fourth from C to F.\nC to D. Minor whole tone 9. 10.\nD to E. Major whole tone 8. 9.\nProduct 72. 90.\nE to F. Major semitone 15. 16.\nProduct 1080. 1440.\nLowest terms of the product 3. 4.\n\nFourth from D to G.\nD to E... Major whole tone 8. 9.\nE to F... Major semitone 15. 16.\nProduct 120. 144.\nF to G... Major whole tone 8. 9.\nProduct 960. 1296.\nLowest terms of the product 20. 27.", "I.05-021": "We will list the two ratios of every interval so that they need not be calculated.", "I.05-022": "NATURAL AND ALTERED RATIOS of All Intervals.", "I.05-023": "Names of the intervals generated first. | Natural ratios according to the divisions. | Ratios altered by a comma. | Names of intervals inverted from the first. | Natural ratios of inverted intervals. | Ratios of inverted intervals altered by a comma.\nDiminished comma. | 2025. 2048. | | | | \nComma. | 80. 81. | | | | \nMinor or enharmonic diesis. | 125. 128. | | | | \nMajor diesis. | 243. 250. | | | | \nLesser semitone. | 625. 648. | | | | \nMinor semitone in theory, or augmented unison in practice. | 24. 25. | Medium semitone, exceeding the minor semitone by a comma. 128. 135. | Diminished octave. | 25. 48. | 135. 256. diminished by a comma.\nMajor semitone in theory, or minor second in practice. | 15. 16. | Maximum semitone, exceeding the major semitone by a comma. 25. 27. | Augmented or major seventh. | 8. 15. | \nMajor whole tone in theory, or second in practice. | 8. 9. | Minor whole tone, one comma smaller than the major whole tone. 9. 10. | Seventh. | 9. 16. | 5. 9. exceeding by a comma.\nAugmented whole tone, or diminished third. | 225. 256. | 125. 144. exceeding. | Augmented sixth. | 128. 225. | 72. 125. diminished.\nAugmented second. | 64. 75. | 108. 125. diminished. | Diminished seventh. | 75. 128. | 125. 216. exceeding.\nMinor third. | 5. 6. | 27. 32. diminished. | Major sixth. | 3. 5. | 16. 27. exceeding.\nMajor third. | 4. 5. | 81. 100. diminished. | Minor sixth. | 5. 8. | 50. 81. exceeding.\nFifth. | 2. 3. | 27. 40. diminished. | Fourth. | 3. 4. | 20. 27. exceeding.\nAugmented fifth. | 16. 25. | 81. 125. diminished. | Diminished fourth. | 25. 32. | 125. 162. exceeding.\nDiminished fifth. | 25. 36. | 45. 64. exceeding. | Tritone or augmented fourth. | 18. 25. | 32. 64. diminished.\nThese first five intervals have only one ratio and cannot be inverted; the others are composed by adding them.", "I.05-024": "These ratios let us work out the ratio of any interval ourselves. Multiply the ratios of smaller intervals to form larger ones. Subtract larger intervals to form smaller ones. For example:", "I.05-025": "Multiply the ratios of the two commas to form the minor diesis.", "I.05-026": "To form the major diesis, multiply the minor diesis ratio by 15552 to 15625. This last ratio represents only a very small part of a comma.", "I.05-027": "Lesser semitone: from the ratios of the minor diesis and comma.\nMinor semitone: from the ratios of the major diesis and comma.\nMedium semitone: from the ratios of the minor semitone and comma.\nMajor semitone: from the ratios of the minor semitone and minor diesis.\nMaximum semitone: from the ratios of the major semitone and comma.\nMinor whole tone: from the ratios of the major and minor semitones.\nMajor whole tone: from the ratios of the minor whole tone and comma.", "I.05-028": "This method shows how many commas make up a whole tone. We can continue multiplying until we reach the octave.", "I.05-029": "Working the other way, the difference between the major and minor whole tones gives the comma.", "I.05-030": "The minor semitone is the difference between intervals distinguished as major and minor, or as perfect, augmented, and diminished.", "I.05-031": "EXAMPLE.", "I.05-032": "Major third 4. 5. / Minor third 5. 6. → Minor semitone 24. 25.\nFifth 2. 3. / Diminished fifth 25. 36. → Minor semitone 72. 75.\nFifth 2. 3. / Augmented fifth 16. 25. → Minor semitone 48. 50.\nSeventh 9. 16. / Diminished seventh 75. 128. → Minor semitone 1152. 1200.\nSeventh 5. 9. / Augmented seventh 8. 15. → Minor semitone 72. 75.", "I.05-033": "Depending on which ratios we use, the difference between these intervals can also be a medium semitone or a major diesis.", "I.05-034": "Most of these semitones are essential when tuning organs and similar instruments. This has led to the following chromatic system.", "I.05-036": "Chromatic system ]", "I.05-037": "There is:\nC to C♯ | a minor semitone. | 24 to 25.\nC♯ to D | a major semitone. | 15 to 16.\nD to E♭ | a maximum semitone. | 25 to 27.\nE♭ to E | a minor semitone. | 24 to 25.\nE to F | a major semitone. | 15 to 16.\nF to F♯ | a minor semitone. | 24 to 25.\nF♯ to G | a maximum semitone. | 25 to 27.\nG to G♯ | a minor semitone. | 24 to 25.\nG♯ to A | a major semitone. | 15 to 16.\nA to B♭ | a maximum semitone. | 25 to 27.\nB♭ to B | a minor semitone. | 24 to 25.\nB to C | a major semitone. | 15 to 16.\nAs.", "I.05-038": "In the system, we can easily find the two ratios of each interval when it starts on different notes. This shows that we are free to use either ratio, depending on which notes we want to use to make the interval.", "I.05-039": "Our explanation of how each interval is formed shows exactly how this system relates to the earlier diatonic system.", "I.06-001": "CHAPTER SIX.", "I.06-002": "Compound Intervals, Especially the Ninth and Eleventh.", "I.06-003": "In Chapter III, Article III, p. 7, we noted that practice always treats compound intervals as their simple forms. There are two exceptions: the ninth and eleventh. Harmony accepts these only under their own names. Their progressions and chord structures are entirely different from those of the second and fourth, even though a ninth and eleventh can be called compound forms of those intervals. A ninth or eleventh can represent a second or fourth, and vice versa. This is because an octave adds no variety to harmony. We may move a sound up or down by one or more octaves, as long as it stays above the lower sound of the particular interval under discussion. Even so, different chords need different names. Above all, a chord that is primary in its kind should take the name of the interval containing all its sounds. The fifth is the primary object of every chord. Yet we call a chord a seventh chord when a seventh contains its other intervals. For the same reason, we call a ninth chord a ninth. We reserve the names second and fourth for inverted chords. The eleventh chord is primary in its kind, just like the seventh and ninth chords. Its compass also contains all the intervals of its chord. It must therefore take the name of the interval it naturally forms, to distinguish it from an inverted chord. The next chapter, Articles III and IV, will prove this. Chords formed from seconds and fourths consistently show the ratios of those intervals. But chords in which ninths and elevenths must sound show the ratios of these larger intervals instead. This will become clearer when we understand the origin of chords. For now, the reader needed preparation for names that might have seemed surprising. Book II, Chapters X and XI, will explain them more fully.", "I.07-001": "CHAPTER SEVEN.", "I.07-002": "Harmonic Division, or the Origin of Chords.", "I.07-003": "In our system, harmonic division is simply arithmetic division. Its only harmonic means are the fifth and the two thirds. A fourth or another interval appears only through the octave. Any difference we hear comes from rearranging the sounds of the fifth and thirds. Harmony invites us to mix these sounds freely. Their variety makes the perfection of the whole more strongly felt. But we must not lose sight of the principle that remains throughout. The fifth and thirds both divide the principal chords and build them, by squaring or adding their ratios. Apply multiplication and subtraction to these intervals, and we can derive every harmonious chord. For example, multiplying the two third ratios gives a fifth; subtracting them gives the two harmonic means that divide this fifth.", "I.07-005": "Major third 4. 5.\nMinor third 5. 6.\nProduct of multiplication 20. 30.\nResult of subtraction 24. / 25.\nPerfect chords 20. 25. 30. or 20. 24. 30.", "I.07-006": "Divide the fifth 20–30 at 25. This gives the major perfect chord, because its lower third is major. Divide the same fifth at 24. This gives the minor perfect chord, because its lower third is minor. The numbers 24 and 25 also give the ratio of the minor semitone, the difference between a major and a minor third.", "I.07-007": "Square the major-third ratio to get an augmented fifth. Square the minor-third ratio to get a diminished fifth. The subtraction operation in each case divides the resulting interval harmonically.", "I.07-008": "Major third 4. 5. / 4. 5.\nProduct of multiplication 16. 25.\nResult of subtraction 20.\n\nMinor third 5. 6. / 5. 6.\nProduct of multiplication 25. 36.\nResult of subtraction 30.", "I.07-009": "Now note that a complete chord must contain a fifth, and therefore the two thirds that make it. Every chord must come from the perfect chord formed by those two thirds. If no fifth sounds, the chord's foundation must be inverted, supplied through supposition, or borrowed. Otherwise the chord is incomplete—or simply no good. This is why we did not call the harmonically divided diminished and augmented fifths chords: the chords they produce are incomplete. Zarlino therefore established his diminished-fifth chord without a foundation, as we shall see elsewhere.", "I.07-011": "Any harmonious chord beyond the perfect chords above must be made from a perfect chord plus one of its parts: a third. For example, adding a third to a fifth gives a seventh. The subtraction operation gives the complete seventh chord.", "I.07-012": "Minor third 5. 6.\nFifth 2. 3.\nProduct of multiplication 10. 18.\nResult of subtraction 12. 15.\nSeventh chord 10. 12. 15. 18.\n\nMajor third 4. 5.\nFifth 2. 3.\nProduct of multiplication 8. 15.\nResult of subtraction 10. 12.\nSeventh chord 8. 10. 12. 15.", "I.07-013": "Multiply each perfect chord's ratios by the minor-third ratio to obtain two more seventh chords.", "I.07-014": "Major perfect chord 4. 5. 6.\nMinor third 5. 6.\nProduct of multiplying the two vertical ratios 20. 30.\nProduct of multiplying the lower ratio by the last two numbers of the upper ratio 25. 36.\nSeventh chord 20. 25. 30. 36.\n\nMinor perfect chord 10. 12. 15.\nMinor third 5. 6.\nProduct of multiplying the two vertical ratios 50. 72.\nProduct of multiplying the lower ratio by the last two numbers of the upper ratio 60. 90.\nSeventh chord 25. 30. 36. 45.", "I.07-015": "Squaring the fourth produces a seventh, but the fourth cannot divide that seventh harmonically.", "I.07-016": "The fifth is present throughout the seventh chords. In the first two, fifths appear between 8–12, 10–15, and 12–18. In the third, the fifth lies below, between 20–30. In the fourth, it lies above, between 30–45. All these chords fit within an octave above their lowest sound, which is their basic principle. They could not do otherwise. An octave is merely a repetition of a sound, so intervals larger than an octave must also repeat intervals found within it. We have already noted this. Yet the fifth has a special privilege. Squaring it gives a chord accepted in harmony even though it extends beyond an octave. We call this the ninth chord because the interval formed by squaring the fifth spans a ninth. Considered alone, that interval could simply be regarded as a repeated second.", "I.07-018": "Fifth 2. 3. / 2. 3.\nProduct of multiplication 4. 9.\nResult of subtraction 6.\n4. 6. 9.", "I.07-019": "This chord is divided into a fifth on each side. Its harmony is easy to understand. Divide each fifth further by a major or minor third, as naturally required, and the chord is formed. We could also obtain an eleventh by adding a minor third above the ninth. In that case, leave the lower fifth undivided. Perfect harmony naturally allows only four different sounds in a chord. For the sake of the fifth, its sole object, it can accept one extra sound, but no more.", "I.07-020": "To understand the range and makeup of chords, remember two things. First, the octave was generated mainly to set their boundary. Chords contain only intervals within that octave. Second, the fundamental sound chose the fifth as the basis for every chord, and combined with either third to determine each chord's construction. Keep these main objects of harmony in view. Then consider their other natural properties and the inversion already discussed. Reason can thereby support every new discovery made through experience. Suppose experience shows that some chords go beyond an octave. Reason tells us that their foundation can exist only within the octave. To preserve it, we must understand a new sound placed underneath it through supposition,a a fifth or third below. This sound counts as an extra,b even though its interval with the fundamental sound is one of the intervals that sound chose for building chords. Experience also shows that a diminished fifth often replaces the fifth. Reason attributes this to the strength of the thirds: their union can produce only chords that are more or less pleasing. Why is the diminished fifth accepted rather than the augmented fifth? Because the natural order originally gave the major third the lower position and chiefly gave the minor third the upper position. The minor third can always remain above, even when the fundamental sound also takes it below. Its upper position seems intended to show that we should prefer it when adding a dissonance to a perfect chord. Finally, experience shows that chords are not always divided into thirds. Reason shows that this happens only because the intervals forming those chords have been inverted.c", "I.07-022": "To make this easier to grasp, we can now treat thirds as the sole basis of every chord. A perfect chord joins two thirds. Every dissonant chord joins three or four thirds. Different arrangements of those thirds make the dissonant chords different. So, when we reduce harmony to its first elements, we must give thirds all its power. Here is a way to demonstrate this. Add a fourth proportional number to each perfect chord: this produces two seventh chords. Add a fifth proportional number to one of those seventh chords: this produces a ninth chord containing all four previous chords. This method does not, admittedly, produce the last two seventh chords in the preceding demonstration, the ones containing a diminished fifth. There the proportion between the first and third terms no longer matches that between the second and fourth. But the earlier operations showed a certain reversal in the thirds' arrangement. Could this suggest another way to find what the present method misses? We did not use arithmetic division alone to form a perfect chord. Once we divided a fifth with its major third below, the octave showed that we could also divide it with its minor third below. What one method loses, another finds. For example, the first operations did not give the diminished-seventh chord. These later ones will. Add a fourth proportional number to the ratios of the harmonically divided diminished fifth, and we find precisely 125, 150, 180, 216. See Chapter VIII, Article VII.", "I.07-023": "a See “Supposer” (“To supply by supposition”) in the Alphabetical Table.", "I.07-024": "b See the squares in the next chapter, Article III. Extra sounds cannot occur there.", "I.07-025": "c See the triangles and squares in the next chapter, Articles I and III.", "I.07-027": "Dissonant chords made by adding a minor third to either perfect chord are much easier to tolerate than those made by adding a major third. The major third's resonance partly smothers the sweetness of the fifth, which should dominate every chord. This makes diminished chords less harsh than augmented chords. Three major thirds added together cannot therefore make a harmonious chord. Even the augmented fifth, made of only two major thirds, is tolerable only within a mixture of five different sounds. Such a chord extends beyond an octave. We will learn more about this later.", "I.08-001": "CHAPTER EIGHT.", "I.08-002": "Chord Inversion.", "I.08-003": "Descartes says there are only three concordant numbers. We have likewise seen that there were only three main consonances: the fifth and the two thirds. The fourth and the two sixths come from them. We now need to see how these consonances are distinguished within chords.", "I.08-004": "ARTICLE ONE.", "I.08-005": "The Major Perfect Chord and Its Derivatives.", "I.08-006": "Start from the three prime numbers 2, 3, and 5, and take the composite numbers 4 and 6. This divides the fifth into two thirds, as required. The major perfect chord is therefore 4, 5, 6. Raise 4 an octave, giving 5, 6, 8. This is called a sixth chord because its outside sounds make a sixth. Next raise 5 an octave, giving 6, 8, 10. This is called a sixth–fourth chord: its upper sounds make a sixth and a fourth above the lowest sound. Every chord interval must be measured from that lowest sound. Raising 6 an octave as well would give 8, 10, 12, which has the same proportions as 4, 5, 6. We can go no further by repeatedly raising the lowest sound an octave. A perfect chord has only three different sounds, so this process gives only three different chords. The perfect chord is the first and fundamental one.", "I.08-008": "The two chords derived from the perfect chord are consonant. Even so, we call them imperfect. This distinguishes them from their source chord and also reflects their different properties.", "I.08-009": "Notice the great power of 3. The fifth, the source of every chord, is formed at 3. There are also three concordant numbers, three primary consonances, and three consonant chords.", "I.08-010": "To explain the perfect chord and its derivatives, we will put their ratios and note names in three triangles. The largest holds the perfect chord, the principle and root of the others. The two smaller triangles hold the derived chords. Look at the numbers and notes at the large triangle's corners. Whichever corner becomes the base, the result is a consonant chord. Every chord contains C, E, and G. Only their arrangement differs. The numbers behave in the same way: 8 is twice 4 and still gives C; 5 and 10 both give E.", "I.08-011": "DEMONSTRATION", "I.08-012": "The Major Perfect Chord and Its Derivatives.", "I.08-013": "Perfect chord. C 4. E 5. G 6.\nSixth chord. E 5. G 6. C 8.\nSixth–fourth chord. G 6. C 8. E 10.", "I.08-014": "ARTICLE TWO.", "I.08-015": "The Minor Perfect Chord and Its Derivatives.", "I.08-016": "We could demonstrate the minor perfect chord just like the major one. It has the same kind of construction, and inversion gives the same kinds of chords. Only the arrangement of the thirds within the fifth changes. A third that is major in one is minor in the other; the sixths derived from them change in the same way. This does not harm the substance of harmony. On the contrary, it gives harmony all its beauty, because major and minor thirds are equally pleasing. We will therefore show the minor chord and its derivatives more simply. They can still be related to the triangles if desired.", "I.08-017": "DEMONSTRATION.", "I.08-018": "10. 12. 15. | A, C, E. | Fundamental perfect chord.\n12. 15. 20. | C, E, A. | Sixth chord, inverted from the perfect chord.\n15. 20. 24. | E, A, C. | Sixth–fourth chord, inverted from the perfect chord.\nAll other perfect chords and their derivatives taken on other notes differ in no respect from these first two;", "I.08-019": "ARTICLE THREE.", "I.08-020": "The Seventh Chord Formed by Adding a Minor Third to the Major Perfect Chord, and Its Derivatives.", "I.08-021": "We will change the previous chapter's order so that we can begin with the most perfect dissonant chord. A diminished fifth occupies its upper part, yet it seems designed to make consonant chords sound even more perfect. It always comes before them—or, more precisely, a perfect chord or one of its derivatives must always follow it. Its own derivatives have the same property.", "I.08-022": "We will show this chord and its derivatives in four squares because it has four different sounds. Inversion produces the chords shown in the three smaller squares. It also produces other chords through supposition, by placing a sound beneath it. These cannot be inverted, as Book II, Chapter X explains. Their lowest sound is therefore outside the squares.", "I.08-023": "DEMONSTRATION.", "I.08-024": "Fundamental seventh chord: A 20. C♯ 25. E 30. G 36.\nDiminished-fifth chord: C♯ 25. E 30. G 36. A 40.\nSmall-sixth chord: E 30. G 36. A 40. C♯ 50.\nTritone chord: G 36. A 40. C♯ 50. E 60.\nF 16. Lowest sound of the augmented-fifth chord.\nTo find the ratios of the augmented-seventh chord, triple these numbers; 40 will supply the lowest sound of that chord, thus:\n40. 60. 75. 90. 108.\nD, A, C♯, E, G.", "I.08-025": "ARTICLE FOUR.", "I.08-026": "The Seventh Chord Formed by Adding a Minor Third to the Minor Perfect Chord, and Its Derivatives.", "I.08-027": "The previous chord could use C, E, G, B♭ instead of A, C♯, E, G. Both add a minor third above a major perfect chord. Now move that added third below the same perfect chord. Alternatively, add a minor third above a minor perfect chord. Either way gives a new seventh chord. Its only difference from the previous one is the arrangement of the thirds.", "I.08-028": "DEMONSTRATION", "I.08-029": "Which May Be Related to the Squares.", "I.08-030": "10. 12. 15. 18. | A, C, E, G. | Fundamental seventh chord.\n12. 15. 18. 20. | C, E, G, A. | Great-sixth chord, inverted from the seventh chord.\n15. 18. 20. 24. | E, G, A, C. | Small-sixth chord, inverted from the seventh chord.\n18. 20. 24. 30. | G, A, C, E. | Second chord, inverted from the seventh chord.\n8. F. Lowest sound of the ninth chord.", "I.08-031": "Triple these numbers to obtain the eleventh chord's ratios. Its lowest sound will be 20:", "I.08-032": "20. 30. 36. 45. 54.\nD, A, C, E, G.", "I.08-033": "Look at the second chord: its second has the ratio 18 to 20. The ninth chord instead contains the ninth ratio 8 to 18, not the second ratio 8 to 9. Similarly, the second and small-sixth chords contain the fourth ratio 15 to 20. The eleventh chord instead contains the eleventh ratio 20 to 54, not the fourth ratio 20 to 27. We can make the same observations about Article III's small-sixth, tritone, augmented-fifth, and augmented-seventh chords. Remember that both 8 to 9 and 9 to 10 give a second; both 3 to 4 and 20 to 27 give a fourth. A ninth therefore has the ratio 4 to 9 or 8 to 18. An eleventh has 3 to 8 or 10 to 27. The ratios 8 to 18 and 20 to 54 are the same as 4 to 9 and 10 to 27.", "I.08-035": "ARTICLE FIVE.", "I.08-036": "The Seventh Chord Formed by Adding a Major Third to the Major Perfect Chord, and Its Derivatives.", "I.08-037": "This chord arises incidentally from modulation. A ninth is almost always implied. Adding that ninth above the chord is much less harsh than adding a lower sound beneath the seventh chord's fundamental sound to make a ninth. Yet adding the lower sound is the natural method explained in Book II. This follows from the previous chapter's observation: a major third added above a perfect chord sounds less good than a minor third. Despite this, modulation requires us to accept this seventh chord as fundamental. Its inversions have the same names as the chords in the previous article.", "I.08-038": "DEMONSTRATION.", "I.08-039": "18. D. Highest sound of the ninth chord.\n8. 10. 12. 15. | C, E, G, B. | Fundamental seventh chord.\n10. 12. 15. 16. | E, G, B, C. | Great-sixth chord.\n12. 15. 16. 20. | G, B, C, E. | Small-sixth chord.\n15. 16. 20. 24. | B, C, E, G. | Second chord.", "I.08-040": "Triple these ratios to find another lowest sound for the ninth, at 20:", "I.08-041": "20. 24. 30. 36. 45.\nA, C, E, G, B.", "I.08-042": "But the chord is clearly much less tolerable this way than when a minor third is added above it. This upper addition goes against nature and shows that the seventh chord is imperfect. Once the upper sound of the ninth is added, the lowest sound becomes an extra. Article III's squares show this: the sounds inside them can be inverted among themselves, but the lowest sound of the ninth or augmented fifth cannot join in the inversion. We can therefore see that these notes", "I.08-044": "8. 10. 12. 15. 18.\nC, E, G, B, D,", "I.08-045": "represent the previous article's ninth chord, because", "I.08-046": "8. 10. 12. 15. 18. | 8. 10. 12. 15. 18.\nC, E, G, B, D; or F, A, C, E, G,", "I.08-047": "make the same chord. Also, to obtain the eleventh here, we must multiply the ratios of this seventh chord by eight. This is a second proof of its imperfection. The lowest sound will be 45:", "I.08-048": "45. 64. 80. 96. 120.\nB, F, A, C, E.", "I.08-049": "ARTICLE SIX.", "I.08-050": "The Seventh Chord Formed by Adding a Minor Third below the Minor Perfect Chord, and Its Derivatives.", "I.08-051": "This differs from Article III's chord only in moving a major third from the bottom to the top. Minor thirds dominate, making it more tolerable than the previous chord. Its derivatives receive no different names, however, because this chord also comes from modulation.", "I.08-052": "DEMONSTRATION.", "I.08-053": "25. 30. 36. 45. | E, G, B♭, D. | Fundamental seventh chord.\n30. 36. 45. 50. | G, B♭, D, E. | Great-sixth chord.\n36. 45. 50. 60. | B♭, D, E, G. | Small-sixth chord.\n45. 50. 60. 72. | D, E, G, B♭. | Second chord.\n20. C. Lowest sound of the ninth chord.\nWe find the lowest sound of the eleventh at 50 by tripling these ratios, thus:\n50. 75. 90. 108. 135.\nA, E, G, B♭, D.", "I.08-054": "ARTICLE SEVEN.", "I.08-055": "The Diminished-Seventh Chord Formed by Adding a Minor Third to the Harmonically Divided Diminished Fifth, and Its Derivatives.", "I.08-056": "As noted in the previous chapter, this chord comes from adding a fourth proportional number to a harmonically divided diminished fifth. But we cannot derive a chord from one that is neither perfect nor complete. Its principle must be found elsewhere.", "I.08-057": "The fifth comes from the first divisions of the string and is the source of every chord. Its first chord remains equally perfect whether a major or minor third occupies the lower part of the fifth. The resulting seventh chords are also equally fundamental, even though one has a diminished fifth above and the other below. Their division into thirds is enough to win our favor. Those with an added minor third are even more pleasing than those with an added major third. So a diminished fifth does not destroy the foundation. An augmented fifth, however, can be used only through supposition. Harmony treats its lowest sound as an extra, accepted by the ear because the rest of the chord preserves the principle. These observations encourage us to add more minor thirds. After finding the perfect chord, we added a fourth proportional and then a fifth, stopping when further additions would offend the ear. The ear still tolerates three minor thirds together, although they no longer contain a fifth, the principle of all chords. We must find out why this imperfect chord remains tolerable.", "I.08-058": "1. However its sounds are arranged, the chord divides into thirds, with one exception. Inversion introduces an augmented second. It differs from a minor third by only a minor diesis or a lesser semitone. It exceeds a diminished third by the ratio 15552 to 15625. Because it is so close to a third, the ear need not find it offensive.", "I.08-059": "2. The chord fits within an octave, so it can be inverted.", "I.08-060": "3. Take Article III's seventh chord and raise its lowest, fundamental sound by a semitone. The result is the chord we are discussing. This changes only a major third into a minor third. For example, our seventh chord C, E, G, B♭ becomes the diminished-seventh chord C♯, E, G, B♭ when C is sharpened. Invert it to get the augmented-second chord B♭, C♯, E, G. We can also use the notes in the squares of the first seventh chord: moving A to B♭ produces the same kinds of chords. Changing a major third to a minor one does not harm a perfect chord's perfection, although there the change affects only the middle sound. That might also justify accepting the diminished-seventh chord—except that moving its lowest sound destroys the foundation. To preserve the principle, we must understand the original lowest, fundamental sound as implied within its replacement. The rules we establish later make this clear.", "I.08-062": "We call this last chord and its derivatives borrowed to distinguish them from their source chord. They borrow their perfection from a sound that is absent.", "I.08-063": "The next demonstration shows the same chords as Article III's demonstration. Their names remain the same, but here we add the name of the new interval created by moving the fundamental sound. In the diminished-seventh and augmented-second chords, that interval lies between the outside sounds. Those chords therefore use only these names.", "I.08-064": "The diminished-fifth, small-sixth, tritone, augmented-fifth, and augmented-seventh chords keep the same lowest sound in the two demonstrations. Throughout, the only change is A becoming B♭. None of these new chords is fundamental: each borrows its foundation from elsewhere.", "I.08-065": "DEMONSTRATION.", "I.08-066": "108. 125. 150. 180. | B♭, C♯, E, G. | Augmented-second chord.\n125. 150. 180. 216. | C♯, E, G, B♭. | Diminished-seventh chord.\n75. 90. 108. 125. or 150. 180. 216. 250. | E, G, B♭, C♯. | Small-sixth chord with diminished fifth.\n90. 108. 125. 150. or 180. 216. 250. 300. | G, B♭, C♯, E. | Tritone chord with minor third.\n80. F. Lowest sound of the augmented-fifth chord with fourth.\nThe lowest sound of the augmented-seventh chord with minor sixth is found at 200 by tripling the ratios of the augmented-second chord, thus:\n200. 324. 375. 450. 540.\nD, B♭, C♯, E, G.", "I.08-067": "The added fourth proportional makes the diminished-seventh chord seem to come first. Yet we must relate chords formed by supposition to the augmented-second chord, just as we related them elsewhere to the seventh chord. Only then do the interval ratios follow the order set by the natural division of chords into thirds. This begins to show what is really being borrowed. The seventh chord's fundamental sound lends itself to the sound at the bottom of the augmented-second chord and at the top of the diminished-seventh chord. We should now know that this principle can remain among upper sounds only through inversion.", "I.09-001": "CHAPTER NINE.", "I.09-002": "Observations on All the Chords above.", "I.09-003": "We should now see that perfect chords and seventh chords differ only in how their thirds are placed or in a reversal of the thirds' order. They have therefore not been given different basic names. Modulation makes us use particular sounds, and those sounds determine how the thirds forming the chords are ordered. The lower third of a perfect chord determines the modulation by being major or minor. Once that is settled, chords must follow the order of sounds within the octave above that perfect chord's fundamental sound. The perfect chord has great power over modulation, but Article III's seventh chord is independent of it. This seventh is the first of its kind. It stays the same whatever form the perfect chord takes. It belongs exclusively to dominants, and a conclusion cannot be fully felt without it. Every dissonance comes from it. Its major third, inherited from its source perfect chord, forms all major dissonances. The minor third added to make the seventh chord forms all minor dissonances. Inversion produces several chords from it. So does adding a new lower sound beneath its foundation through supposition. It then produces just as many more by lending its foundation to another sound, while keeping exactly the place it must occupy. Other seventh chords get all their perfection from this first one. They have only the minor dissonance, and modulation sets their place. This explains why each derivative of the first dissonant chord has its own exclusive name. The derivatives of other seventh chords share names: they determine nothing themselves, but are determined by modulation.", "I.09-004": "Everything observed in this chapter leads to one conclusion: harmony has only two chords, the perfect chord and the seventh chord. It also has only two dissonances, major and minor. The rest of the book will prove this clearly.", "I.09-005": "Book II will discuss the nature and properties of each interval and chord.", "I.10-001": "CHAPTER TEN.", "I.10-002": "Different Ratios for the Same Chord.", "I.10-003": "We have matched each chord's ratios to the intervals between its notes. One interval can have two ratios. Most of the chords above can therefore also have different ratios if we build them on different notes. See the chromatic system in Chapter V, p. 28. But different ratios do not create new chords. The fifth 27 to 40 is the same fifth as 2 to 3; the same holds for other intervals. The ear cannot detect the difference between these ratios. It comes only from a different arrangement of the whole tones and semitones inside them. The note names do not matter here. We used them only to make the whole explanation clearer.", "I.11-001": "CHAPTER ELEVEN.", "I.11-002": "How Ratios for Divisions Relate to Vibrations and Multiplied Lengths.", "I.11-003": "Take each length produced by a division of the given string, from its number rightward to the string's end. Arrange these lengths so that their vibrations can be distinguished. Assume the strings differ only in length. Their vibration ratios will match the division ratios. We can then divide a string into enough parts to obtain the ratios of dissonances. The same agreement always holds. See Chapter III, Article VI, p. 15.", "I.11-004": "To find length ratios, take the lengths produced by two different divisions. Use a compass to find a common measuring unit for both. Each length contains this unit as many times as the division numbers contain units, but the comparison is reversed. For example, take the lengths marked 2 and 3. String 2 contains three measuring units; string 3 contains two. One comparison is 2 to 3, the other 3 to 2. They would mean the same thing if the first number did not have to represent the lower sound. So reversing a division ratio gives its corresponding length ratio. This is easy for two sounds, but becomes harder with more. In harmony, as with a continuous quantity, each middle sound or term must relate to both extremes. Therefore 4, 3, 2 does not give what 2, 3, 4 gives. The interval 2 to 3 comes first in the latter sequence but last in the former. We must invert the arithmetic proportion as already described elsewhere. Multiply each extreme by the middle term, then multiply the extremes together. The numbers 12, 8, 6 restore the intervals' natural order. Thus the most perfect harmony made by combining consonances is represented in divisions by 1, 2, 3, 4, 5, 6, 8. In multiplied lengths, it can be represented only by 120, 60, 30, 24, 20, 15. This needs more care than the rest.", "I.11-006": "This common measure can immediately reveal the ratios of intervals in the lengths taken to the left of the given string. We can also use the inversion just described. Compare string 3 with string 1. If one part of string 3 contains 1, its other two parts contain 2. String 1, compared with 3, must therefore contain 3. The left-hand lengths give a fifth, in the ratio 2 to 3. Now compare string 3 with string 2. One part of string 3 contains 2, so its other two parts contain 4. One part of string 2 contains 3, and its other part also contains 3. The left-hand lengths therefore give a fourth, 3 to 4. Next compare string 3 with string 4. One part of string 3 contains 4, so its other two parts contain 8. One part of string 4 contains 3, so its other three parts contain 9. This gives the whole tone that is the difference between a fifth and fourth: 8 to 9 for divisions, and 9 to 8 for multiplications. The method is straightforward and can be checked for every kind of interval.", "I.11-007": "END OF BOOK ONE.", "II.01-001": "BOOK TWO.\nThe Nature and Properties of Chords, and Everything That Can Make Music Perfect.", "II.01-002": "CHAPTER ONE.\nThe Fundamental Sound of Harmony and How It Moves.", "II.01-003": "Book I, Chapter III, Article I, p. 5 has already explained the fundamental sound and its place in harmony. Here we will mainly determine how it should move.", "II.01-004": "The part carrying the fundamental sound is called the bass because that sound is always the lowest. Zarlino* explains it this way. The earth supports the other elements; the bass likewise supports, establishes, and strengthens the other musical parts. It is the base and foundation of harmony, which is why it is called bass: base and support. He says that without the earth, nature's beautiful order would collapse. In the same way, without the bass, a musical piece would become dissonant and confused. A bass should therefore move somewhat slowly and by separated intervals, wider than the movements of the other parts. This allows those other parts to move by adjacent steps, especially the soprano, whose proper character is stepwise motion. Yet compare this clear, sound definition of harmony's fundamental part with Zarlino's rules and examples. Contradictions appear everywhere, leaving us constantly in doubt.", "II.01-005": "A principle supporting everything must be firmly established. To lose sight of it even briefly is to destroy it. We will therefore keep the principle just stated and strengthen it with the principle of the whole string. The string's first divisions give consonances that together make perfect harmony. The bass represents this whole string. Its progression must therefore use the consonant intervals found in those first divisions. Each sound will agree with the one before it. Each can also carry the same kind of chord as the first divisions produced, thus representing the whole string that forms the chord's principle and foundation. This explains Zarlino's instruction that the bass should move by separated intervals: those intervals cannot be consonant unless they are separated. His instruction to move slowly is relative to the other parts. Those parts should move diatonically, by steps, so they can make several movements from one consonance to the next while the bass makes only one. When first presenting our rules, though, we will move every part at an equal rate to make things clearer. Do not count the octave as part of the bass progression just defined. The fundamental sound can be several octaves higher or lower without mattering, as long as it stays beneath the other parts. The fifth is the interval most suited to it. Every final cadence or melodic ending has this progression as its main object. Anyone with some feeling for harmony feels compelled to give the bass this movement at a melodic ending, whatever its form. The same applies to the fourth, which represents the fifth. Voices low enough naturally descend a fifth at these endings; voices that cannot do so rise a fourth. This clearly shows the octave's power: either of its two sounds represents it. It also shows the relationship of the fourth and fifth formed by dividing it. The fifth is preferred whenever the voice allows it, but substituting the fourth does not destroy it. To keep listeners in pleasant suspense, the bass can also move through one or more thirds, since two thirds make a fifth. It can likewise use the sixths representing those thirds. Cadences remain reserved for fifths and their representative fourths. The fundamental bass's whole progression must stay within these consonances. Sometimes dissonance makes it rise only a whole tone or semitone. This comes from a license introduced by the interrupted cadence, discussed later. Also note that the ascending whole tone or semitone—not a descending one—is the inversion of the seventh sounding between its two notes. Book III, Chapter XI will show that, except in an interrupted cadence, movements of a third and fourth can be understood as implied there.", "II.01-006": "* Zarlino, Istitutioni Harmoniche, third part, chapter 58, fols. 281 and 282.", "II.01-009": "If this principle holds everywhere, it deserves our confidence. We have not proposed it without being certain it will succeed.", "II.02-001": "CHAPTER TWO.\nChords Assigned to Fundamental Sounds and How They Move.", "II.02-002": "The intervals used for the fundamental bass's movement must also accompany it in the other parts. But those parts need a restraint that does not apply to their guide, the bass. The perfect chord is the first and only chord produced by dividing the string. It should therefore be the only chord belonging to each fundamental-bass sound. We nevertheless cannot exclude the seventh chord. This does not mean its added third is indispensable: removing it would not spoil harmony's perfection. But the seventh adds variety and a certain bitterness that makes the perfect chord's sweetness stronger. We should welcome it rather than reject it. We must count it as fundamental because it preserves the principle in the perfect chord's lowest sound.", "II.02-003": "Each other part carries one sound of these chords. Zarlino has already said that these parts should move diatonically, by steps. The consonant movement of the fundamental bass imposes this condition. Even a little knowledge of interval distances makes us almost involuntarily give the upper parts stepwise movement. This produces a pleasant chord sequence without needing another rule. Nature herself guides us to the perfection proper to her. See Chapters XIX, XX, XXIV, and XXV below, and Book III, Chapters IV and VI.", "II.02-004": "After learning the movements assigned to each part, we may let one part use another's movement. But the original arrangement and sequence of fundamental chords must remain our guide. This especially applies to the seventh. The ear accepts it only on these terms: it must move by steps from the sound before it through to the sound after it, and both those surrounding sounds must be consonant. A perfect cadence shows this. It also shows the proper place of dissonance in harmony. Two bass sounds lead us to a melodic conclusion. The final one is clearly the principal sound, because the whole piece begins on it and is founded on it. It seems natural, then, to make the sound before it less perfect in some way. If both carried perfect chords, the soul would have nothing left to desire after either chord. It would be unsure which sound should provide rest. Dissonance seems necessary because its harshness makes the following rest more desirable. Nature's part in this appears in the necessary choice of the third as the resolution. Only that consonance can make up for the dissonance's harshness. Though imperfect, the third becomes the only thing we desire after the dissonance and gives the perfect chord new charm. This is the origin of the rule for resolving dissonances. Those who failed to recognize a single minor dissonance could not imagine a single consonance that resolves it. Yet the following discussion will make this truth beyond doubt.", "II.03-001": "CHAPTER THREE.\nThe Nature and Properties of the Octave.", "II.03-002": "The octave contains all the sounds that can combine into fundamental chords. Adding it makes them more perfect. The perfect chord and its derivatives still exist without it, but become brighter with it, because natural and inverted chords can then be heard together. Four-part pieces must use it. In five-part pieces it fits perfectly with the fundamental seventh chord. In general, we can always add it to a chord containing only one minor dissonance. In upper parts it must move diatonically, and it readily follows the rules. It also determines modulation, as we will see later.", "II.04-001": "CHAPTER FOUR.\nThe Nature and Properties of the Fifth and Fourth.", "II.04-002": "The fifth is central to every chord. A chord cannot exist without a fifth or the fourth that represents it. We have already discussed these intervals' properties in bass movement. In the other parts, they move much as the octave does.", "II.05-001": "CHAPTER FIVE.", "II.05-002": "The Perfect Cadence, Where the Nature and Properties of All Intervals Meet.", "II.05-003": "A perfect cadence ends a melody so satisfyingly that we want nothing more. The first two chapters have already described its bass, descending a fifth or rising a fourth, and its two chords, the seventh and the perfect chord. But its perfection goes further. The thirds governing these chords determine how all the other intervals move. Only the octave and fifth are exceptions: they were generated first and move independently.", "II.05-005": "We have called the fifth the main object of every chord. The thirds that compose it deserve the same status. The octave generates the fifth by division, then leaves chord construction to it. The fifth generates the thirds by division, then leaves the movement of other intervals to them. Those intervals follow the thirds' nature and properties completely. The major third is naturally lively and happy, so major and augmented intervals share that character. The minor third is naturally tender and sad, so minor and diminished intervals share its character. Zarlino* says that the outer sounds of thirds naturally move toward what best suits their nature. The major seeks to become major—that is, it rises—and the minor descends. Skillful musicians with good judgment plainly recognize this, he says, because the upper part moves a semitone. That semitone is the salt, so to speak, the ornament and cause of beautiful harmony and good modulation. Without it, modulation would be almost unbearable. These two directions determine the movement of every major, augmented, minor, and diminished interval. The general rule is: major and augmented intervals rise; minor and diminished intervals descend.", "II.05-006": "Zarlino seems to propose a semitone as the general rule for interval movement. A semitone is indeed the only suitable movement for major and augmented intervals. Minor and diminished intervals may also descend a whole tone, depending on the modulation. It is surprising that Zarlino praises the semitone so well, then ignores it where it matters most. In the perfect system, the semitone lies between the octave and the sound just below it. The octave provides repose, and a stepwise ascent reaches it only by that semitone. The preceding sound must therefore matter as much to harmony as the octave itself: we pass through one to reach the other. Zarlino says that the major third and major sixth must rise to the octave. This can only come from the observation just made. Yet he forgets to apply the same rule to the tritone. He mentions it briefly but not in his perfect cadence. He gives still less attention to the other major or augmented dissonances derived from the major third containing the sound just below the octave. He says least about the very intervals that follow his semitone rule without exception. We will show this oversight with a perfect-cadence example. The sound preceding the octave forms a major third, the source of every major dissonance that must rise a semitone to the octave.", "II.05-007": "* Third part, chapter 10, fol. 182; chapter 38, fols. 219 and 220.", "II.05-009": "The first bass note in a perfect cadence is called the dominant. It always has to precede the final note and therefore dominates it.", "II.05-010": "Adding a minor third to the dominant's perfect chord produces a seventh. That seventh clashes with both the dominant and its major third. The major third is therefore dissonant against the seventh. The major third is the source of all major dissonances; the seventh is the source of all minor dissonances, without exception.", "II.05-011": "The note that ends the perfect cadence is the tonic. The piece begins and ends on it, and all modulation is determined within its octave.", "II.05-012": "The sound just below the octave is called the leading note. It forms every major dissonance. Whenever we hear one of these dissonances, we feel that the tonic or its octave must come next. The name fits a sound that makes us anticipate the note toward which all modulation is directed.", "II.05-013": "EXAMPLES.", "II.05-014": "Perfect Cadence in the Major Mode.", "II.05-015": "Perfect Cadence in the Minor Mode.", "II.05-016": "The two examples work the same way, except that the minor dissonance descends a semitone in one and a whole tone in the other. The major dissonance always rises a semitone from the major third to the octave. Now remove the fundamental bass and replace it in turn with each other part. This gives all the inversions of the chords, and the harmony remains good. The removed fundamental bass is still implied. Rearranging the parts makes different dissonances audible, but their required movements stay the same. The major dissonance always rises a semitone to the tonic or its octave. The minor dissonance always descends to the tonic's major or minor third. Nothing is more evident.* Zarlino's own diminished-fifth and tritone examples prove it: he shows their inversion without recognizing it.", "II.05-017": "* Third part, chapter 61, fol. 293.", "II.05-018": "Zarlino's Example with an Added Fundamental Bass.", "II.05-019": "Zarlino's Example with an Added Fundamental Bass.", "II.05-020": "Take the two upper parts alone: (A) marks the tritone and (B) the diminished fifth. Compare them with the part labeled Basso. The tritone's note forms a major sixth, rising a semitone to the octave. Compare them with our fundamental bass instead. The tritone's note forms a major third, and the diminished fifth's note forms a seventh. Both move according to our rule. These chords therefore all represent the perfect cadence. Their movements stay the same, and the foundation remains implied. Otherwise the music would be confused and dissonant.a Zarlino believes this when stating it, then forgets it in practice. He saysb the lowest part of a perfect cadence naturally descends a fifth. His example has the upper part rise from a major third to an octave (A).c In another place, while the dominant's major third rises, its fifth descends to the octave (B).d While that fifth descends, the third above it—the seventh above the dominant—descends to the third (C). Combine these three examples and we obtain our full cadence. We will take his Chapter VI example and supply the missing parts:", "II.05-021": "a Third part, chapter 58, fol. 282.", "II.05-022": "b Chapter 5, fol. 251.", "II.05-023": "c Fol. 251.", "II.05-025": "Added Parts. Zarlino's Example. Added Fundamental Bass.", "II.05-026": "Zarlino did not intend this implied harmony. He apparently wanted a perfect chord on the second beat of the whole note that lies a fifth above the fundamental bass. He considered the fourth struck on its first beat dissonant rather than consonant. But how can the final whole note's perfect chord then follow this other perfect chord? The minor third above the earlier whole note makes a seventh against the fundamental bass. If it descends, what will the fifth and octave do? A skilled musician should always add bass figures, especially to a two-part example. Only then can it be judged properly. Without figures, conclusions drawn from it can easily be wrong. Perhaps Zarlino omitted figures because they would expose intervals he wanted to ignore—and apparently wanted others to ignore too.", "II.05-027": "d Chapter 6, fol. 254, measures fourteen and fifteen.", "II.05-029": "If each of the last two notes in the part called Grave is meant to carry a perfect chord, that contradicts harmony's foundation. Our first observations, taken from Zarlino's own reasoning, showed that a bass cannot move diatonically under perfect chords. The example's fourth must therefore be consonant against the fundamental bass: it forms an octave with it. If it were dissonant, the last note could not produce a perfect cadence. The cadence would instead be irregular.", "II.05-030": "EXAMPLE.", "II.05-031": "Zarlino's Example. Added Parts. Fundamental Bass. Irregular Cadence.", "II.05-032": "Which cadence did Zarlino mean? Apparently the perfect cadence. His whole piece centers on C, while this irregular cadence is in A or D. He also never mentions the irregular cadence. When it appears in his examples, it is part of a chord sequence and he does not identify it.", "II.05-034": "Our first example supplies every form of the perfect cadence in two, three, four, or five parts. Choose whichever parts should sound together. Parts that lie above another may be placed below it. The fundamental bass alone cannot naturally change its place, though good taste can permit even this—especially to avoid a perfect conclusion in an upper part while the bass moves stepwise. Harmony is therefore contained in our two chords, the perfect chord and the seventh chord. Every rule rests on their natural progression.", "II.06-001": "CHAPTER SIX.", "II.06-002": "The Interrupted Cadence.", "II.06-003": "Change the movement of any sound in a perfect cadence's first chord, and its conclusion is interrupted. This change produces the interrupted cadence.", "II.06-004": "The interrupted cadence is close to the perfect cadence. Either the chords stay the same or the fundamental bass does. With the same chords, the bass rises by a step instead of descending a fifth. With the same bass, a sixth chord replaces the final perfect chord. These changes affect only consonant sounds: the fundamental, octave, or fifth. They do not change the dissonant sounds' movements. The major third, the basis of every major dissonance, still rises a semitone. The seventh, the basis of every minor dissonance, still descends a whole tone or semitone. Our dissonance rules therefore remain intact. Only one part of the foundation is changed at a time. If the perfect chord is lost, the fundamental bass remains. If the bass changes, the perfect chord supports it. Besides, the sixth replacing the fifth gives a chord derived from the perfect chord. And the seventh, as we have noted, allows the bass a movement corresponding to its own interval. So the foundation still survives. Nevertheless, this cadence requires a license. Either the chord is no longer fundamental or the bass movement no longer comes from consonances. The freedom granted by dissonance alters perfection. But the change is not harsh or unpleasant. It makes perfection more welcome when it returns after a delay.", "II.06-006": "EXAMPLES.", "II.06-007": "Interrupted Cadence in the Major Mode.", "II.06-008": "Interrupted Cadence in the Minor Mode.", "II.06-009": "Compared with the perfect-cadence examples, these differ only by replacing the fifth with a sixth in the parts marked (A). Put part (A) below the fundamental bass. The result is simply a seventh chord followed by a perfect chord, as first proposed. This is the usual form of the interrupted cadence.", "II.06-011": "We may rearrange all these parts and choose two, three, or four of them. Use the fundamental bass as the top part only when good taste allows it. The interrupted cadence is heard only through the change from fifth to sixth: a sixth replaces the fifth of the perfect chord that would end a perfect cadence. All other parts are identical in the two cadences.", "II.06-012": "When part (A) becomes the bass, we prefer to double the third at the octave rather than the bass. The third then represents the true fundamental sound, whose doubling cannot be unpleasant. In a sequence of perfect harmony, however, preferring a doubled third to a doubled fundamental would be a fault. We can still use the bass's octave here instead of the third's, but only with a clear understanding of the result. It is hard to introduce that octave without serious errors. Judgment is needed. Never depart from a principle before understanding it fully.", "II.07-001": "CHAPTER SEVEN.", "II.07-002": "The Irregular Cadence.", "II.07-003": "The perfect cadence moves from dominant to tonic. This one goes the other way, from tonic to dominant, so we call it irregular.", "II.07-004": "Every cadence is formed from fundamental-bass notes that naturally carry perfect chords. In the two previous cadences, we altered the first perfect chord by adding a new sound to create dissonance. The same reason can apply here. We have already seen that dissonance suits a cadence's first note. When this is our only chance to use it, we should seek it rather than avoid it.", "II.07-005": "Does the added dissonance clash with the fundamental sound? We add a sixth, which is consonant with the fundamental but dissonant with its fifth. This may seem to contradict our claim that all dissonances come from the seventh. But a perfect chord with this added sixth is simply the great-sixth chord, an inversion of the seventh chord. See Book I, Chapter VIII, Article IV, p. 39.", "II.07-006": "The added dissonance does not move as a seventh naturally does. It can therefore be called irregular, like the cadence itself. But remember our observation about minor dissonance, whether formed by a seventh or an added sixth. It seems made to soften the imperfection of the third where it comes to rest. That remains true here. The added sixth rises to resolve on the third; the seventh descends to it. Chapter XVIII explains why they differ.", "II.07-007": "The fourth note normally carries a great-sixth chord, and the tonic a perfect chord. We can therefore substitute these two notes and form an irregular cadence from them too.", "II.07-008": "EXAMPLES.", "II.07-009": "Irregular Cadence in the Major Mode.", "II.07-010": "Irregular Cadence in the Minor Mode.", "II.07-011": "Always give the final note a major third if it is to count as a dominant. The modes then differ only in the tonic's third. Here the tonic must come before the dominant.", "II.07-012": "Monsieur Masson does not explain this cadence as we do, but he gives an example of it in inversion. He does not understand the origin of its chords. He calls (A) a tritone, though it is essentially a fourth altered by modulation. More importantly, it is only a sixth against the fundamental bass.", "II.07-013": "EXAMPLE", "II.07-014": "By Monsieur Masson. Our added fundamental bass reveals the inverted irregular cadence.", "II.07-015": "Added Fundamental Bass.", "II.07-016": "The added sixth can always be removed from the perfect chord; good taste alone calls for it. But it adds variety, makes writing in four, five, or six parts easier, and creates pleasing melodies. We should welcome it, not reject it, and praise those who first used it.", "II.07-017": "We discussed these three cadences first to prove that harmony consists only of perfect and seventh chords. All variety comes from their inversions, though dissonant chords can also appear through supposition or borrowing. Their movements always follow those given in the cadences, especially the movements of parts that clash with one another. Once we know a dissonant chord's origin, we can readily tell which chord follows, regardless of the bass arrangement. A consonant chord has more freedom. Later we will learn what modulation means, which notes of a key take derived chords, how to prepare and resolve dissonances, and which bass movements govern all this. We will then see why these three cadences are essential: they contain every kind of dissonance movement.", "II.08-001": "CHAPTER EIGHT.\nImitating Cadences by Inversion.", "II.08-002": "To imitate a cadence by inversion, usually remove the fundamental bass and choose another part as the bass. You can also vary the movement of sounds that do not clash, such as the fundamental and its fifth. Book III explains this. Let each part take its turn as bass or soprano, and every imaginable melody becomes possible. Harmony gains variety when the bass takes another sound of the fundamental chord instead of the fundamental itself. Countless melodies and chord sequences then become available for composing freely. Their inversion keeps the listener alert through constant variety. Writers who noticed inversion's effects did not understand its origin. Their rules and examples show this: every different chord gets a separate example and rule. One says a seventh resolves to a third, fifth, octave, or sixth. Another says a diminished fifth resolves to a third, fourth, tritone, or ninth, moving down, up, or staying still. This makes a science obscure. It treats each part separately when one simple, understandable whole would explain them all. A seventh's dissonance may appear as a diminished fifth, second, ninth, or eleventh, and may resolve through different intervals. But this happens only because the bass moves differently. As it takes different sounds from a fundamental chord, the intervals measured against it take different forms. The chords themselves remain the same, simply rearranged, and their progression stays the same. If an interval seems to change, compare it with its foundation: it has not changed. The fundamental basses placed beneath all our examples prove this. We need only make the relationships clear to the senses, as we hope to do.", "II.09-001": "CHAPTER NINE.\nAvoiding Cadences while Imitating Them.", "II.09-002": "Partly imitating a cadence already avoids its full effect. More specifically, we say a cadence is avoided when its chords are altered where alteration is allowed. There are endless ways to do this, but one simple principle explains them.", "II.09-003": "Add a third to a consonant chord and it becomes dissonant, through the seventh. In a dissonant chord, change the third from the major form natural to dominants to minor. These changes allow a long stretch of melody and harmony without a conclusion.", "II.09-004": "First, our terms are specific: a tonic carries a perfect chord; a dominant carries a seventh chord. A tonic can follow only a dominant with a major third that forms a diminished fifth against its seventh. If the third is not major and the third and seventh form neither a diminished fifth nor a tritone, another dominant must follow. We therefore distinguish tonic dominants, whose seventh chords contain a diminished fifth or tritone, from simple dominants, whose chords do not. The chord's structure shows at once whether we have a cadence or only an imitation. It also shows whether the next note is tonic and what chord each note needs. Here we are discussing only fundamental chords and fundamental-bass movement.", "II.09-005": "The perfect cadence gives a firm rule. Whenever the bass descends a fifth or rises a fourth—the same thing—the first note may, and indeed should, have a seventh chord. If its third and seventh form neither a diminished fifth nor a tritone, the next note cannot be tonic. It must carry another seventh chord. Continue until a diminished fifth or tritone appears between a chord's third and seventh. Its leading note then requires a tonic next. A descending fifth implies a seventh chord on its first note; conversely, a seventh chord implies that movement afterward. Exceptions are an imitation of an interrupted cadence and certain licenses explained later. Only modulation limits how many seventh chords and bass intervals can follow one another.", "II.09-007": "EXAMPLE.", "II.09-008": "Seventh Chords and an Avoided Perfect Cadence.", "II.09-009": "A, B, and C each carry a seventh chord. A–B and B–C move just as C moves to the tonic. They therefore resemble perfect cadences, but the minor thirds in their seventh chords avoid the cadence. At C, the major third introduces a tritone, making the cadence clear and requiring the tonic conclusion. We can postpone the conclusion further by changing key and adding a seventh to the tonic, making it a dominant. If that seventh creates no diminished fifth or tritone, the tonic becomes a simple dominant. If it does, the tonic becomes a tonic dominant. Good modulation permits either choice. The second choice introduces the chromatic genus into harmony, discussed in Book III.", "II.09-011": "The first chord cannot avoid an irregular cadence: its dissonance cannot change between major and minor. Instead, add a sixth or seventh to the second chord. This prepares another cadence, which can again be avoided, and so on.", "II.09-012": "Avoid an interrupted cadence as you would a perfect cadence. But if you change the first note's major third to minor, the next note cannot become a tonic dominant. Making the next note a tonic dominant requires careful judgment in any case, whatever precedes it in this cadence.", "II.09-013": "Even an imitation of a perfect or interrupted cadence can be avoided. Add a sixth rather than a seventh to its second note. The fifth must first be prepared as the previous note's octave or third, because it now acts as the dissonance's upper sound. The result is a great-sixth chord, an inverted seventh chord. It can lead to an irregular cadence, or, through inversion, imitate an avoided perfect or interrupted cadence.", "II.09-014": "EXAMPLE OF ALL THESE CASES.", "II.09-015": "Complete Example: Avoided Cadences and Fundamental Bass.", "II.09-016": "A. A. A. D. E. F. S. T. These perfect cadences are avoided because the first chord has no diminished fifth or tritone between the third and seventh above the fundamental-bass note.", "II.09-017": "B. C. O. P. R. S. Adding a seventh to the second fundamental-bass note—C, P, or S—avoids these interrupted cadences.", "II.09-018": "B. C. R. S. Adding a sixth to the second continuo-bass note avoids these perfect cadences.", "II.09-019": "C. D. This interrupted cadence is avoided in two ways: the first fundamental-bass chord contains neither a diminished fifth nor a tritone, and D's perfect chord receives an added seventh.", "II.09-020": "D. E. S. T. The usual continuo-bass succession for an avoided cadence.", "II.09-021": "F. G. An added seventh on G avoids the irregular cadence. There are some licenses here, explained in Chapter XIII. For now, note that if part Y becomes the bass, the part below it must move to the cue sign Z instead of its simultaneous ordinary note.", "II.09-022": "A. B. G. H. I. L. Change the first note's major third to minor. This introduces a diminished fifth into the next chord, so B, H, and L become tonic dominants rather than tonics. This is the chromatic genus in practice; the next book will explain it. For now, notice an upper part descending by semitones here.", "II.09-023": "E. F. The minor third on E avoids the perfect cadence, as does the added sixth on F. A seventh would be more natural on F, especially if already prepared.", "II.09-024": "N. O. P. Q. These licenses will be discussed elsewhere.", "II.09-025": "M. N. Two perfect chords in succession while the bass moves by a consonant interval.", "II.09-026": "L. M. T. V. Perfect cadences.", "II.09-027": "X. Parts can sometimes move an octave higher or lower to return to their natural range. This must not create consecutive octaves or consecutive fifths.", "II.09-028": "Remove the fundamental bass and let any other part become the bass. This reveals the different progressions produced by inverting fundamental chords. Figures have been provided on every part.", "II.09-029": "So many dissonances in succession would not make very pleasing music. We used them only to fit everything into one short example. Its modulation is not very regular either, but that discussion must wait.", "II.09-030": "Consonant chords are easy to use. Their bass must always move by consonant intervals. Certain changes of key permit an exception, but only for inverted consonant chords and only in one movement between two notes. The study of modulation will explain this later. Dissonances are almost as easy: a fundamental bass immediately shows how they should follow one another. Even without it, we know minor dissonances descend and major ones rise. The chromatic genus and irregular cadence are exceptions, easily identified by our rules. The next book gives short, simple examples of every way to use them. Once the basic rules of harmony are understood, we can create any melody we imagine and easily fit the right chords to it. In two or three parts, choose the consonances and dissonances that best suit the subject or the attractive melody intended for the parts. We should always know which missing sounds would complete the chords. Ignorance of those sounds has led to false rules and serious errors, even among supposedly skilled masters filling out chords or adding continuo figures.", "II.10-001": "CHAPTER TEN.\nChords by Supposition: Another Way to Avoid Cadences while Imitating Them.", "II.10-002": "To understand chords by supposition, first understand chords' limits. All chords come from fifths and thirds, as Book I, Chapters VII and VIII showed. They must therefore divide into thirds, following the fifth's natural division. The octave bounds every sound that can form perfect harmony. Sounds beyond it only repeat sounds inside it. The octave must therefore bound every chord. The perfect chord's lowest sound is harmony's foundation. Adding a third to make a seventh chord does not remove that foundation: the seventh stays within the octave and preserves the division into thirds. Add another third, however, and the foundation becomes confused. Its relation to the fourth third cannot be distinguished from its relation to the corresponding sound inside the octave. The division into thirds also breaks down, since a ninth or eleventh represents a second or fourth. If we ignore that relationship and insist on treating them only as ninths and elevenths, what principle supports them? They exceed the octave, which is every interval's principle—or, as Zarlino calls it, mother, source, and origin.", "II.10-004": "A fifth sound may be added to a seventh chord only underneath it. This is supposition: the added sound lies below the fundamental, which is immediately above it. The chord's principle lies within the fundamental sound's octave, not the added sound's octave. Its progression can then be understood exactly like the earlier chords. The seventh chord above the added bass can still be inverted. But the added sound must always remain at the bottom. The other sounds can exchange places* because they lie within harmony's proper bounds. They move naturally in their mode. The added sound disappears as an extra when it rejoins them. It is therefore only supernumerary: the fundamental harmony exists without it, and the progression remains unchanged.", "II.10-005": "* See Book I, Chapter VIII, Articles III, IV, and V.", "II.10-006": "EXAMPLE.", "II.10-007": "Chords by Supposition: Seven Parts and Fundamental Bass.", "II.10-008": "1. The fundamental bass carries only perfect and seventh chords. It moves as in perfect cadences (B), interrupted cadences (C), or irregular cadences (D).", "II.10-009": "2. In the supposition chords marked 9, 5♯, 7♯, and 4, the fundamental-bass sounds lie above the other bass. If placed below it, the other bass's sounds would have to be removed. Otherwise the harmony would lose its perfection and offend the ear.", "II.10-010": "3. In these chords, the fundamental bass is in unison with the part representing it. That part and the upper parts form only seventh chords, all divided into thirds and moving according to our rules.", "II.10-012": "4. The eleventh chord is marked 4. Its usual full form is very harsh, so the middle sounds are almost always omitted. Keep the two main sounds, fundamental and seventh, and sometimes the minor third or fifth too. Supply a new sound a fifth below the fundamental. It forms an eleventh—not a fourth—with the fundamental's seventh. We can call this chord exceptional in construction because it is not divided like the others. It still follows the rule for supposition chords: it cannot be inverted. Sometimes all its sounds are included nonetheless.", "II.10-013": "EXAMPLE.", "II.10-014": "Eleventh Chord, Tenor, and Bass by Supposition.", "II.10-015": "Here (A) in the bass by supposition lies beneath (A) in the fundamental bass or tenor. The upper parts together make a seventh chord that moves naturally.", "II.10-016": "Compare it with (a) in the earlier example. To preserve stepwise movement there, we did not require the tenor to carry the fundamental-bass sound. The comparison shows the difference in treatment and why we call the chord exceptional in construction.", "II.10-017": "These examples show perfect, interrupted, or irregular cadences underlying the supposition chords. This is another way to imitate cadences while avoiding them. See Book III, Chapter XXXII for more.", "II.11-001": "CHAPTER ELEVEN.\nThe Fourth and Eleventh.", "II.11-002": "We should distinguish the fourth from the eleventh. Until now, the eleventh has not had its own recognized name and has been confused with the fourth. This explains the dispute over whether the fourth is consonant or dissonant. Those guided by ratios could not think it dissonant. Those guided by practice struggled to treat it as consonant. They disagreed because they did not understand one another.", "II.11-003": "First, Zarlinoᵃ treats the fourth as consonant in practice. He gives examples, cites the Greeks, and relies even more strongly on ratios. He says two consecutive fourths produce almost the same effect as two fifths, because the fourth is a perfect consonance. We add that it is also an inverted fifth. He does not say so here, but his examples prove it without his realizing, and his Dimostrationi Harmonicheᵇ mentions it. He also says the Greeks of his own time used fourths in their lowest parts without another consonance underneath as a base. This shows the fourth's full force. Notice that he cannot avoid recognizing a base in harmony, and wants one even when it is inaudible. That base always lies in the fifth's lower sound. Only by understanding it as implied can we prove why inverted chords please the ear.", "II.11-004": "a Third part, chapters 60 and 61, fols. 291, 292, 293, and 294; chapter 5, fols. 177 and 178.", "II.11-005": "b Ragionamento secondo, definition X, fols. 83 and 84.", "II.11-007": "He also calls the eleventh a repetition of the fourth, and the ninth a repetition of the second. Every interval certainly has repeated forms—double, triple, quadruple, and so on—as we have said. But different properties require a distinction. People distinguish a second from a ninth. Why not a fourth from an eleventh, which differ even more? Second and ninth are both dissonant. Fourth is consonant; eleventh is dissonant. A second comes from inverting a fundamental chord. A ninth comes from adding a sound to one. It cannot be inverted, and its preparation and resolution differ from the second's. That is why their names must differ. Similarly, a fourth comes from inverting a perfect chord. As a consonance, it can move freely. An eleventh comes from adding a sound to a seventh chord. It cannot be inverted and requires preparation and resolution. Ratios confirm this too: see Book I, Chapter VIII, Article IV, p. 39. These differences in the chords should be enough to distinguish the intervals. Their relationship when heard alone is not the point. An interval's name identifies a chord that is primary in its kind and contains only sounds within that interval. Seventh, ninth, and eleventh chords work this way. Ninth and eleventh are also the implied names behind augmented-fifth and augmented-seventh chords. A fourth occurs only in an inverted chord, where it represents a fifth, so it is consonant. An eleventh defines a primary chord whose sounds all lie within its compass, so it is dissonant. We write the figure 4 for it only to follow common practice.", "II.12-001": "CHAPTER TWELVE.\nBorrowed Chords: Avoiding Perfect Cadences while Imitating Them.", "II.12-002": "Book I, Chapter VIII, Article VII, p. 41 showed that a diminished-seventh chord and its derivatives borrow their foundation from the lowest sound of a tonic dominant's seventh chord. Compare the next two examples to see this clearly. Only one sound moves differently: the one borrowing its foundation from the seventh chord's lowest sound. It must follow the movement required by the dissonance it creates.", "II.12-003": "See the examples below.", "II.12-004": "EXAMPLES.", "II.12-005": "Perfect Cadence in the Minor Mode.", "II.12-006": "Perfect Cadence in the Minor Mode, Avoided through Borrowing.", "II.12-007": "1. Invert the four upper parts in both examples. They still correspond in the same way. Only the sixth note differs: it borrows its foundation from the dominant.", "II.12-008": "2. Where an ordinary note shows the octave, a cue sign shows the third. In the other example we reverse this. The ordinary note marks the first chord sound's most natural movement; the cue shows an allowed alternative. The underlying harmony does not change. Book III will explain this more fully.", "II.12-010": "3. When these chords are inverted, their lowest sounds remain the same in both examples. The two basses by supposition show this. Each can combine with the four upper parts to form supposition chords. The only difference is that the sixth note borrows from the dominant. These chords are therefore optional choices only in minor keys. Good taste guides composers in applying them to suitable subjects, as we will see later.", "II.13-001": "CHAPTER THIRTEEN.", "II.13-002": "A Rule for Dissonance Movement, Derived from Fundamental-Chord Movement.", "II.13-003": "Dissonances have two kinds, according to the thirds that produce them. They follow those thirds' properties: major dissonances rise, minor ones descend. In a natural chord sequence, we also find that a minor dissonance is preceded by a consonance. That same sound becomes dissonant without moving from its degree. We must therefore specify not only where a dissonance goes next but also what comes before it. These are its resolution and preparation. When the bass descends a fifth—its most perfect movement—the third both prepares and resolves the dissonance. In fundamental harmony, that dissonance is the seventh. When the bass descends a third or seventh, the fifth and octave prepare and resolve it. Yet in natural harmony, the third alone can resolve it. Now reverse the bass's direction and let it ascend by these same intervals. The seventh cannot be prepared. If it still sounds without offending the ear, the rule requiring preparation cannot apply universally.", "II.13-005": "Major and minor dissonances occur together, but they must not be confused. One resolves by rising, the other by descending. The minor likes preparation; the major never requires it. Zarlino recognizes only the tritone as a major dissonance and barely mentions it. Later writers name others, but none explains that all come from the major third above a seventh chord's fundamental. Likewise, the seventh itself produces every minor dissonance. Missing this has kept those writers from revising Zarlino's rules. They still say every dissonance must be prepared, even though experience shows otherwise. De Brossard and Masson provide evidence in passages that Zarlino's examples also support: if the bass is syncopated—formerly forbidden, now freely practiced—the seventh naturally resolves by the octave, or sometimes the fifth or sixth, and so on. (A)", "II.13-006": "The supposedly old prohibition did not apply in Zarlino's time, at least.* He says even the earliest musicians used the diminished fifth as in his next example. Syncopating the bass for a diminished fifth is therefore the same as doing so for a seventh.", "II.13-007": "EXAMPLE.", "II.13-008": "Third part, chapter 30, fols. 209 and 210.", "II.13-009": "Zarlino's Example: Diminished Fifth", "II.13-010": "One fifth may follow another if the second is diminished or augmented.", "II.13-011": "A seventh may also be used if the bass prepares it. (B)", "II.13-012": "(A) De Brossard, Dictionaire de Musique, p. 110.", "II.13-013": "(B) Masson, Traité de Composition, p. 77.", "II.13-014": "EXAMPLE.", "II.13-015": "Seventh Examples A, B, C", "II.13-016": "Two fifths can occur in succession: one perfect, the other diminished, and so on.", "II.13-017": "EXAMPLE.", "II.13-018": "Zarlino gives a sequence like B in the third example, between Canto and Tenore: third part, chapter 61, fol. 294.", "II.13-019": "Examples of Two Fifths", "II.13-020": "All the notes marked C belong to one chord. Showing that we can move freely through one chord's sounds proves nothing here: Masson claims to be discussing two different chords.", "II.13-021": "Returning to our subject, combine seventh examples A and B with fifth example B. Give the seventh examples a natural ending:", "II.13-022": "Combination of the Examples", "II.13-023": "Combining them will show that the different movements have one principle.", "II.13-024": "EXAMPLE.", "II.13-025": "Masson's Basses, Natural Ending, and Fundamental Bass", "II.13-026": "All these parts work well together except pairs making consecutive octaves, such as D–F and G–H. Those were included only to show how different consonant movements produce different melodies without changing the underlying harmony. Any part may even become the bass. All can be inverted and all come from the fundamental bass, which moves from tonic to dominant and back. Other melodies could still be made from this harmony. But every version shows the same point: an unprepared seventh, diminished fifth, tritone, or small-sixth dissonance is possible because the bass reverses its usual direction. Instead of descending a fifth, it rises a fifth at S–T. Here “reversal” means changing direction, not inverting an interval through the octave. Neither major nor minor dissonance is then prepared. Even when the minor dissonance is prepared by every rule, the major is never prepared.", "II.13-027": "EXAMPLE.", "II.13-028": "Prepared Minor Dissonances A and B; Major Dissonance C", "II.13-029": "A and B are prepared minor dissonances. C is a major dissonance and cannot be prepared.", "II.13-030": "Some believe every dissonance must be prepared on a weak beat, without exception. A proves otherwise. Enforcing that rule would destroy one of harmony's finest ornaments: a chain of dissonances that keeps harmony suspended, with consonances accompanying those dissonances preparing the next ones. The rule should apply only to the first dissonance, as at B. Now let the bass rise a third or seventh instead of a fifth. The dissonance cannot be prepared in those cases either.", "II.13-031": "EXAMPLE.", "II.13-032": "Unprepared Seventh; Ascending Third and Seventh", "II.13-033": "At J, the bass rises a third and the seventh is unprepared. At L, it rises a seventh or descends by a step, again leaving the seventh unprepared. Let each part become the bass in turn to derive the movements of the other dissonances it contains.", "II.13-034": "The cue signs show alternative movements for the parts. If used, adjust the other parts to match, keeping the harmonic order shown in the example.", "II.14-001": "CHAPTER FOURTEEN.\nHow Thirds and Sixths Move.", "II.14-002": "Thirds belong to both consonance and dissonance. They are consonant themselves, but produce dissonances. Divide a major third to obtain major and minor whole tones. Add a minor third to either perfect chord to obtain a seventh. Invert the seventh to get a whole tone, or the whole tone to get a seventh, the source of all harmonic dissonances. When no more perfect consonance follows, thirds and their representative sixths have no fixed movement: everything depends on them. But when an octave or fifth follows immediately, it governs their movement, because the other consonances originate from it. The octave is most perfect and wants a major third before it; the major third too is more perfect than the minor. The minor third precedes the fifth, which is less perfect than the octave. Thus the major third rises to the octave and the minor descends to the fifth. This follows their nature. Zarlino correctly says the nearest semitone determines that movement; it gives harmony and melody their ornament. Major sixths follow the properties of major thirds, and minor sixths those of minor thirds.", "II.14-004": "EXAMPLE.", "II.14-120": "A. Major third ascending to the octave.\nB. Major sixth ascending to the octave.\nC. Minor third descending to the sixth.\nD. Minor sixth descending to the fifth.", "II.14-006": "A is a perfect cadence; B inverts it. C is an irregular cadence; D inverts it. The principal cadences therefore contain all our rules. Their thirds and sixths must rise or fall by semitones. A seventh or major sixth may also be added to each cadence's first chord. The thirds then become dissonant against those added sounds, forming diminished fifths or tritones that contain both major and minor dissonances. A third may be consonant by itself but dissonant against the other sounds needed to complete its chord. Its movement must therefore be fixed. The seventh produced by an added minor third descends a semitone. The added major sixth rises a semitone. Both follow their proper character, as the cue signs show", "II.14-008": "Printed Cue Signs within the Sentence.", "II.14-009": "; this led to the rule against rising from a minor third or minor sixth to the octave. These rules come from fundamental harmony. Applied to inversions, however, they have not been followed literally, because most writers apply them wrongly. Zarlino* and others say the minor third should descend to a unison or octave. That is a mistake: it happens only when the underlying harmony is inverted. In that underlying harmony, a fifth or diminished fifth descends to the octave.", "II.14-010": "EXAMPLE.", "II.14-121": "Perfect cadence in which the fifth descends to the octave.\nInverted perfect cadence in which the minor third descends to the octave.\nAvoided perfect cadence in which the diminished fifth descends to the octave.\nInversion of the avoided cadence in which the minor third descends to the octave.", "II.14-012": "Zarlino makes this mistake because he sets rules by looking at only two parts at a time. This happens almost everywhere. In the same passage, he says a major third usually rises to a fifth. Again, this comes only from inverted harmony: in the underlying harmony, the third may rise to a seventh. Even that is not the most natural progression.", "II.14-013": "* Third part, chapter 10, fol. 182.", "II.14-014": "EXAMPLE.", "II.14-122a": "Irregular cadence avoided by adding a seventh to the second note's perfect chord, in which the major third ascends to the seventh.\nInversion of the avoided cadence, in which the major third ascends to the fifth.", "II.14-016": "We could give a perfect or seventh chord to the note whose fifth follows the major third. But this requires a license. Natural harmony requires consonant movement in the fundamental bass, and here that would be absent.", "II.14-017": "Beyond the thirds' usual movements, a major third must descend to the fifth in a major-mode irregular cadence. Here it does not clash with the added sixth. Only the nearest consonance governs its movement, and that is the fifth.", "II.14-018": "EXAMPLE.", "II.14-122b": "Major Third Descending in an Irregular Cadence.", "II.14-020": "The rule does not ban every upward minor third or downward major third. It says only that the major third naturally rises to the octave, and so on.", "II.14-021": "Rules based on fundamental harmony remain valid in derived chords. But an interval named in a rule refers to the original chord, not its inversion. A third, fifth, or octave can become a sixth, fourth, or another interval when inverted. We must treat the new interval as a representative of the original one, rather than apply the rule to its new name. Once the rule is established, modulation guides us. It reveals which underlying chord sequence produces an inversion. The inverted intervals must follow the movement assigned to their originals. Otherwise we might wrongly reject this sequence because a minor sixth rises to the octave.", "II.14-023": "EXAMPLE.", "II.14-123a": "Minor Sixth Ascending to the Octave.", "II.14-025": "In the fundamental harmony, however, this is an octave rising to a fifth, not a sixth.", "II.14-026": "EXAMPLE.", "II.14-123b": "Fundamental bass of an irregular cadence A–B and a perfect cadence B–C.", "II.14-028": "One might also reject this minor third rising to the octave.", "II.14-123c": "Minor Third Ascending to the Octave.", "II.14-030": "But in fundamental harmony, a fifth rises to a third; it is not the minor third.", "II.14-031": "EXAMPLE.", "II.14-124a": "Fundamental bass of a perfect cadence.", "II.14-033": "Modulation matters as much as the interval's fixed position in the fundamental chord. For example, suppose I rise from a minor third to the octave in A or D:", "II.14-124b": "Minor Third and Octave in A or D.", "II.14-035": "This is bad because each bass note really carries a perfect chord, the chord to which the rule applies. But the same movement works in F or B♭. There each bass note carries an inverted perfect chord, a sixth chord, with the perfect chord implied underneath. The rising interval is then a fifth, not a minor third. If this is hard to accept, consider the first example: a minor sixth rises to the octave in F or C, something skilled musicians freely use. In G it would be bad, for the same reasons.", "II.14-036": "If a chord doubles a minor third or minor sixth, one copy may move against its natural direction, as long as the other follows the rule:", "II.14-037": "EXAMPLE.", "II.14-125": "Doubled Thirds and Sixths, Examples A and B.", "II.14-039": "At A the minor third descends correctly. At B the minor sixth also descends, after staying on the same degree to form the following seventh. Their doubled copies must rise, or consecutive octaves would be hard to avoid. The correctly moving interval gives such complete satisfaction that we scarcely notice its doubled copy; it seems only an extra sound. But a dissonance must never be doubled. Thirds must obey that rule whenever they represent dissonance, especially major thirds. A minor third may be an exception only in more than three parts, or when the subject absolutely demands it for a beautiful melody, a fugue, or an imitation that contributes to the music's beauty.", "II.15-001": "CHAPTER FIFTEEN.", "II.15-002": "When to Remove the Seventh from a Ninth Chord.", "II.15-003": "Chapter X may suggest that every ninth chord should include a seventh. But not when the ninth chord stands on a tonic. Here is why.", "II.15-004": "A ninth chord on a tonic requires the leading note beforehand, either in the bass or in the accompanying parts. If the bass has the leading note, it cannot be doubled: its movement is fixed. The doubled note would also rise, causing consecutive octaves even if it moved later than the bass. Once a dissonance sounds, we expect one particular sound next, and it must go there. Holding its duplicate before that same move creates a very offensive suspension. It spoils the satisfaction already supplied by the first resolution. What if the duplicate descends, as a seventh should, while the leading note rises? Then the supposed tonic is no longer tonic; the key changes. This works only in major keys. In a minor key, that note's minor third and seventh would form an augmented fifth. The lower sound of an augmented fifth must be below all the other sounds, but this minor third would instead be above them. Inversion would also give a diminished fourth, which must be excluded from harmony. An augmented fifth is an interval by supposition and cannot be inverted: its chord extends beyond an octave, and its lowest sound must remain below.", "II.15-006": "If the leading note is in an accompanying part or the soprano, it can stay in place and become the seventh above the tonic that follows in the bass. But this is always an augmented seventh. That means the chord is an eleventh chord, not a ninth, and it cannot include the third. If a third replaces the eleventh, a ninth chord becomes implied. The seventh can no longer count as augmented, because that status is possible only in the eleventh chord. It becomes an ordinary seventh and must descend. The key changes here too. A tonic stops being tonic when it carries a ninth or seventh chord. Only a perfect chord or augmented-seventh chord belongs to it.", "II.15-007": "A ninth chord above a tonic must therefore omit the seventh. The seventh could only be augmented here and would clash with the rest.", "II.15-008": "EXAMPLE.", "II.15-009": "Examples A and B: Seventh Removed from the Ninth Chord.", "II.15-010": "Example A works. B fails where the leading note is doubled at C and both copies rise to D. C and F form an augmented fifth; placing C above F would create a diminished fourth. We can tolerate this in a major key by sharpening note F, but then the key changes. The supposed tonic becomes the fourth note, as experience confirms. Its leading note is no longer a leading note: it is an ordinary seventh and must descend, rather than rise to D as an augmented seventh.", "II.16-001": "CHAPTER SIXTEEN.", "II.16-002": "Dissonant Consonances: The Fourth and the Misleading Rules Applied to It.", "II.16-003": "All dissonant chords are built from consonances joined together. The dissonance appears when we compare two sounds that belong to those consonances. A seventh chord combines two fifths and three thirds. Its outside sounds are dissonant because they make neither a fifth nor a third, but a seventh—or a second when inverted.", "II.16-005": "Most musicians make a mistake here. They check only the intervals above the bass, not the intervals between every pair of chord sounds. A sound they call consonant may actually be dissonant. The small-sixth chord has a third, fourth, and sixth above the bass, all consonances. But its third and fourth clash with each other. The great-sixth chord has a third, fifth, and sixth, again all consonances above the bass. Yet its fifth and sixth clash. Which sound is the dissonant one? Relate each chord to its foundation. In the small-sixth chord, it is the third; in the great-sixth chord, the fifth. Both represent the seventh above the fundamental sound of the original seventh chord.", "II.16-006": "EXAMPLE.", "II.16-007": "Seventh, Great Sixth, and Small Sixth Related to the Fundamental Sound.", "II.16-008": "G is always the seventh above fundamental A. Inverting the original seventh chord uses the same sounds. When measured against the foundation, G remains the dissonance. Whether the chord becomes a small-sixth or great-sixth chord, that dissonant sound is prepared and resolved just like its original seventh. The underlying harmony never changes. This makes the proof clear.", "II.16-010": "There is one exception. An irregular cadence adds a sixth to its first perfect chord, creating a great-sixth chord. Here the perfect chord is the basis, not a seventh chord, which is absent from this cadence. The added sixth is therefore the dissonance. See Chapter XVII, Article III, and Chapter XVIII for a fuller explanation.", "II.16-011": "Small- and great-sixth chords have only recently come into use. Some musicians still reject them, refusing what experience offers because of rules that deserve to be called false. Those rules say every fourth is dissonant, yet allow a syncopated bass beneath a fourth as beneath any other dissonance. This causes countless mistakes. To challenge such widely accepted opinions, we must trace everything back to its principle. That investigation will show that our apparently new rules actually follow from the rules we are criticizing. The older rules combine different properties of dissonance that come from different sources and therefore need separate rules. We will explain these in separate articles.", "II.16-012": "ARTICLE ONE", "II.16-013": "THE PRINCIPLE OF DISSONANCE;", "II.16-014": "Which Sound Is Dissonant, and Which Sound Must Be Prepared and Resolved.", "II.16-015": "Consonances and dissonances come from the same principle: the first, fundamental sound. Every interval is generated by its division and defined in relation to it. Third, fifth, and seventh include all other intervals, as Book I showed and Chapter XIX will explain further. They all originate from that first sound. It therefore supplies the principle of dissonance. A seventh exists only by comparing a generated sound with the fundamental. All other minor dissonances—the only kind considered here—come from a seventh or its inversion, a second. Ninths and elevenths, often called fourths, do not contradict this. Remove their chords' extra sound, and only a seventh or second remains dissonant.", "II.16-017": "We can conclude only that dissonance has one principle. The seventh chord's third and fifth cannot supply another. Compared with the seventh, they create no new minor dissonance; they form a third and fifth again. This will matter later.", "II.16-018": "The principle is perfect in itself and generates both consonance and dissonance. It cannot itself be dissonant. The dissonance must lie in the sound compared with it. The preparation and resolution rule proves this: the upper sound of a seventh must be held over in syncopation and then descend. The lower sound, its principle, is not bound by that rule. Invert the seventh to make a second chord. The principle moves above, while the sound governed by the rule moves below. Now the lower sound must syncopate and descend. The rule therefore concerns the dissonant sound alone. A rule requiring the bass to syncopate applies only in this situation. Bass syncopation elsewhere has another explanation. For example, a third or fifth may syncopate while a seventh sounds. That follows the consonances' natural movement, not the dissonance rule. We may also syncopate any consonance for taste; only dissonances are obliged to obey the rule. So a bass held beneath a second is itself the dissonant sound. Its principle is only the second's upper sound, which would be the lower sound of the uninverted seventh. The other accompanying sounds are not its principle. Similarly, a seventh's principle is only its lower sound. Other chord sounds can syncopate by choice or because their movement follows the bass. The lower sound of a second therefore syncopates against the upper sound of that second, not against the fourth or sixth. Otherwise every comparison would create another principle. If we instead call the upper sounds of the second and fourth dissonant, the rule falls apart. The dissonant sound would no longer be the sound that must syncopate. We could choose any sound in uncertainty. The seventh would stop being the basis of all dissonance, and its principle would become confused.", "II.16-020": "EXAMPLE.", "II.16-021": "Syncopations of Consonances and Dissonances: A, B, C, D, E.", "II.16-022": "The fifth syncopates at A because of the natural consonant sequence and the composer's choice of a fifth rather than another consonance. The dissonance rule does not require it. At B, bass syncopation beneath a fourth is simply an inversion of that fifth. At C, the fifth syncopates for the same reasons, but the seventh beside it is required to syncopate by the rule. At D, the seventh obeys the rule while the consonant third does not syncopate. At F, the bass represents the seventh's upper, dissonant sound and therefore must syncopate. The fourth does not: it is consonant and represents chord D's third in fundamental harmony. At D the seventh syncopates against its principle in the bass. At F the lower sound of the second syncopates against its principle in the upper part. It does not do so against the accompanying fourth, just as the seventh at C does not syncopate against the fifth, or at D against the third.", "II.16-024": "Every minor dissonance comes from a seventh or an inverted seventh, a second. Complete chords always confirm this. If the interval is not between a part and the bass, it lies between two upper parts. The rule concerns only the seventh's upper sound, which becomes the second's lower sound when inverted.", "II.16-025": "ARTICLE TWO.", "II.16-026": "The Source Chord of All Dissonant Chords: Its Sounds, Dissonances, and Limits.", "II.16-027": "The seventh produces all dissonances; likewise, the seventh chord produces all dissonant chords.", "II.16-028": "It has four different sounds and one minor dissonance, the seventh. All fit within an octave.", "II.16-029": "A seventh chord is a perfect chord plus a seventh, so the perfect chord always remains inside it. Its fundamental may carry a major or minor third. A major third often creates another dissonance against the added seventh. It then becomes the source of all major dissonances. But the minor dissonance—the seventh—still follows the same rule. We need not stop over the added major dissonance here. In a complete chord, a seventh or second always remains, and we know which sound the rule governs. The third belongs inseparably to the perfect chord and does not prevent the dissonance's natural movement. Even when a major third creates a new dissonance with the seventh, it is not the ultimate principle. That lies in the fundamental sound below both intervals.", "II.16-031": "To test whether all dissonant chords come from the seventh chord, compare its inversions. Do they have the same number of sounds and dissonances? Do they stay within the same range? Do they leave modulation unchanged? If all these match, their origin is certain: the seventh chord is the first dissonant chord given by harmonic ratios. Everyone accepts the second, diminished-fifth, and tritone chords, which meet these conditions. Small- and great-sixth chords do too, so why reject them? An inversion simply puts one of a seventh chord's sounds in the bass. Its third or seventh may become the bass, giving diminished-fifth, great-sixth, second, or tritone chords. Why forbid its fifth as bass, producing a major or minor small-sixth chord? Here the great-sixth and diminished-fifth chords are grouped together because they share the same bass position relative to their source chord. Their difference is major versus minor, as with second and tritone chords. In all cases, a seventh or second contains the minor dissonance. It belongs to the seventh's upper sound or second's lower sound and follows the same prescribed movement.", "II.16-033": "Why reject small- and great-sixth chords? Because Zarlino or other writers did not name them? Because the small-sixth chord contains a fourth? Zarlino also omitted the seventh chord whose major third clashes with its seventh, though he discussed its diminished-fifth and tritone inversions. People still used that seventh chord, just as they gradually discovered and used many others. Appealing to his authority here would contradict that practice. The fourth in a small-sixth chord is consonant for the same reason it is consonant in a second chord, explained in the previous article. The dissonance lies in the upper sound of a seventh or lower sound of a second. The fourth and third together form one of those intervals, depending on their order, and the third—not the fourth—is the dissonant sound. Similarly, the bass is dissonant in the second chord. The fifth against the sixth is dissonant in the great-sixth chord. The eleventh, called fourth, against the fifth is dissonant in the eleventh chord. Examining these relationships corrects the old false idea about the fourth.", "II.16-034": "All these chords can be reduced to a seventh chord arranged in thirds, except the eleventh. That explains the name eleventh. To arrange it in thirds, we must first remove the bass sound. In the chord's natural arrangement, the upper sound forms an eleventh with that bass, not a fourth. The fourth in second and small-sixth chords, however, stays within the octave. Sounds within such an octave can exchange positions freely. The lowest sound of a ninth or eleventh chord cannot: it must always remain below.", "II.16-036": "If a second chord clearly inverts a seventh chord, the second inverts the seventh. We must also accept that the fourth inverts the fifth, and so on. For certainty, examine a derived chord through its fundamental chord, where all its properties can be found. Do not treat each interval in isolation; ask which original third, fifth, or seventh it represents. These form the perfect and seventh chords, and their movements depend only on the lowest sound of those fundamental chords.", "II.16-037": "EXAMPLE.", "II.16-038": "These chords can accompany each bass.", "II.16-039": "Shared Chords for Inverted-Chord Basses, the Fundamental Bass, and Basses by Supposition.", "II.16-040": "The fundamental bass's perfect and seventh chords generate every other chord here. The same dissonance follows the same movement throughout. Each chord has the same number of sounds within an octave, apart from extra bass sounds in supposition chords. These produce a ninth in one case and an eleventh in the other. Changing bass or chord arrangement does not change the modulation. When testing each bass, however, remove its octave from dissonant chords whenever needed to avoid consecutive octaves.", "II.16-042": "The curved link ⌢ marks dissonances prepared by syncopation. The short descending line ╲ shows how they resolve downward. The third in a small-sixth chord, the fifth in a great-sixth chord, and the bass in a second chord all represent the fundamental bass's seventh dissonance. Remove the extra bass sound from a supposition chord, and the same seventh forms its dissonance too.", "II.16-043": "Semicircle: ⌢; short descending line: ╲.", "II.16-044": "ARTICLE THREE.", "II.16-045": "Calling the Fourth Dissonant over a Syncopated Bass Destroys Music's Finest General Rule.", "II.16-046": "Every dissonance must be prepared by a consonance: this rule has no exceptions. But it would fail if a fourth over a syncopated bass were dissonant. When the bass then descends by a step, as it naturally should, that fourth prepares either a diminished fifth or the dissonant fifth of a great-sixth chord.", "II.16-047": "EXAMPLE.", "II.16-048": "Natural Harmonic Succession: Syncopated Bass and Fundamental Bass.", "II.16-049": "This is the most natural harmonic sequence. One might object only that the first syncopation does not start on a weak beat. But that requirement applies only when the sixth–fourth chord contains or implies a second. The second is then the dissonance, whose syncopation must start on a weak beat and end on a strong one—unless another dissonance immediately before it has already been syncopated by the rule. Our statement that every dissonance needs consonant preparation applies only to dissonances that can be prepared.", "II.16-050": "ARTICLE FOUR.", "II.16-051": "Problems in Authors' Rules of Harmony: Their Different Principles and the Errors They Cause.", "II.16-052": "Writers of harmony rules have all abandoned the principle. They give no special status to the first sound or first chord; everything is treated equally. They rank consonances by perfection only to decide which to use when filling out chords. They explain the movement of thirds and sixths only through comparisons. With dissonances, second, seventh, and ninth are all confused. They require preparation, then give contrary rules. They demand consonant preparation and resolution, then contradict that elsewhere. They never explain why some dissonances rise and others fall. Instead of giving the principle, each writer tells us what his own experience has taught him. Experience alone may convince, but hearing does not give the certainty that sight gives in other sciences. Hearing is more easily deceived. A chord pleasing to one listener displeases another. Musicians therefore cling to their own imagination or limited experience, and authority usually wins over reason and experience. But what supports that authority? Who has argued from a solid principle? Who can guarantee perfectly accurate senses in someone claiming complete experience? Musical rule-makers seem guided by neither reason nor experience. Since Zarlino, they have studied intervals separately. Yet the principle lies first in the fundamental sound, then in its chord. To define an interval's properties, we must first define the fundamental sound and the complete chord it requires. Without that chord, harmony is imperfect. Otherwise reason and experience help little: reason loses force away from its principle, and experience can mislead. We cannot understand an interval alone. We must examine all the chords containing it. A sound may descend in one, rise in another; move by step or leap; be consonant or dissonant; require syncopation or forbid it. That explains the obscurity of the rules. For example, “every dissonance must be prepared by syncopation” conflicts with “the bass may syncopate under a dissonance.” Either dissonance can lack syncopated preparation, or the syncopated bass itself is the dissonance. This is the soundest conclusion from the two rules, though perhaps nobody has considered it. Let us explain.", "II.16-055": "1. For melodic effect, one or more dissonances may pass while the bass or another part is syncopated. That is not our subject here.", "II.16-056": "2. A perfect chord's major third remains present when its added seventh syncopates. The seventh is held against both that third and the fundamental. The major third then represents all major and augmented dissonances. Invert the chord so that the minor dissonance—the seventh—is in the bass. If prepared, it must syncopate. We may therefore say the bass syncopates against a major dissonance, though more exactly it syncopates against the fundamental still present in the full chord. Explaining this apparent exception removes doubt. A supposition chord gives another case. Its added bass sound is much more dissonant than the others. It must syncopate when the upper part contains the major dissonance forming an augmented seventh.* De Brossard missed this. Yet the Angelo Berardi table printed in his Dictionary shows that the seventh over the syncopated bass is augmented: only that seventh can naturally resolve to the octave there, exactly as the table indicates. Berardi's treatment of a fourth over a syncopated bass is mistaken too. The fourth is not dissonant in that case.", "II.16-057": "3. Chapter XIII explained that some dissonances cannot be prepared. In inverted harmony only, the bass often syncopates so that a consonance above it is followed by the dissonance. Masson's example on p. 77 shows this.", "II.16-058": "Example by Masson, p. 77.", "II.16-059": "4. The bass may remain syncopated freely if every sound passing above it belongs to the chord at the start of the syncopation. Zarlino's example shows this.", "II.16-060": "* Monsieur de Brossard, p. 133.", "II.16-062": "Third part, chapter 30, fol. 210.", "II.16-063": "Example by Zarlino: Third Part, Chapter 30, fol. 210.", "II.16-064": "These different principles explain when the bass can syncopate. Without them, we cannot tell whether the consonance or dissonance is supposed to syncopate, or where that note should go next. Two clear rules remove the confusion. First, prepare every dissonance that can be prepared with a consonance. Second, let a dissonance that cannot be prepared follow a consonance by an upward or downward move. Both come from the fundamental bass's movement beneath fundamental chords. Everything else is taste. Any chord sound may become the bass. A sound shared by a consonant chord and a following dissonant chord may need to stay in place or syncopate when the dissonance cannot be prepared. Those actions are nearly the same. This is even clearer when the chord does not change and its sounds pass one after another over a stationary or syncopated bass. Since this is freely allowed, a separate rule about bass syncopation is unnecessary. Writers nevertheless made such a rule from these varied observations. They wanted to preserve mandatory syncopation for every dissonance, but almost destroyed it by allowing the bass to syncopate below fourths, sevenths, and so on. Under the first rule, a syncopated bass is the dissonance, so the fourth or seventh is not. They imply this while refusing to acknowledge it. Why make a separate bass rule? Under a second, tritone, or augmented seventh, the bass follows our first rule: the minor dissonance syncopates. Elsewhere bass syncopation is a choice, or follows the natural consonant movements determined by the fundamental bass—just like a syncopated fifth or any other consonance. Treating syncopation too rigidly has led writers far beyond its proper scope.", "II.16-066": "The rules also fail to say clearly enough how each part moves. Statements such as “a sixth follows a fifth” or “a seventh resolves by a third, fifth, or sixth” leave questions unanswered. Does one part stay still? Do both move? Which rises or falls? We remove this uncertainty by first giving precise, clear rules of modulation to guide everything. Then we state that every minor dissonance descends by step and every major dissonance rises a semitone, whatever the bass does. Their origin makes them easy to identify. We discuss this elsewhere, so need add no more here.", "II.17-001": "CHAPTER SEVENTEEN.", "II.17-002": "On license.", "II.17-003": "FIRST ARTICLE.", "II.17-004": "The origin of license.", "II.17-005": "We must derive everything from fundamental-bass movement. Consonant chords allow that bass freedom, but dissonant chords restrict it even while adding a new interval. Dissonance depends on the perfect chord to which it is added; that chord depends on its lowest sound. The same sound therefore supports both. In natural harmony the fundamental bass moves downward when dissonance sounds and resolves, as though seeking support against its harshness. It falls a third or fifth; only the fifth gives an agreeable resolution. The fifth is harmony’s first interval because the octave merely repeats a note. A fall of a seventh or rise of a second begins to introduce license, even if consonance prepares and resolves the dissonance. Falling a seventh still approaches the underlying principle, but the seventh itself comes more from taste than nature. Unlike the perfect chord’s intervals, it does not appear among the harmonic body’s most natural divisions. It is therefore the source of license. People who credit taste alone are more reasonable than critics who reject unfamiliar licenses without listening or reasoning. The descending seventh or ascending second creates the interrupted cadence. This surprises the ear just when a perfect cadence seems ready to satisfy its expectation. The surprise comes from departing from the natural course: that is license. If downward thirds, fifths, and sevenths give prepared resolutions, their reversed movements allowing unprepared dissonance also count as license. So do supposition, borrowing the fundamental sound, and alterations of either fundamental chord. But limiting harmony to its most natural cases would be too restrictive. We should accept all that its principle offers; otherwise we abandon reason and our senses. That principle consists of the thirds, fifths, and sevenths forming fundamental chords and bass movement. All the licenses proposed here come from it.", "II.17-008": "Great masters have lately aimed to please rather than justify every musical choice. They ignore critics who follow one author blindly and let his views limit their reason and experience. These critics accept interrupted cadences but reject progressions made by inverting them. Yet they already accept inversion in sixth, second, tritone, and diminished-fifth chords. Zarlin allows ninth chords but neglects the augmented fifth needed in ninth and seventh chords on a minor key’s mediant. He allows tritone and diminished-fifth chords but forgets the seventh chord underlying them. Discussing another seventh chord, he overlooks small- and great-sixth inversions, although his accepted chords are inversions too. The difference between great-sixth and diminished-fifth chords comes only from whether the underlying seventh chord has a major or minor third. Such teaching gives critics a weak foundation. Ask for reasons and they quote rules. Ask them to listen to pleasing music that appears to break the rules, showing exceptions or misunderstandings, and they refuse. This is the faction opposing the century’s skilled musicians: whatever delights you, they call worthless.", "II.17-009": "Defending good taste against such scholars is fortunate work. Reason can answer them. We will show more than the fact that the best masters use these licenses and experience approves them. We will prove them from a clear, indisputable principle. No need to repeat chapters VI–VII on interrupted and irregular cadences, XIII on unprepared dissonance, or X and XII on supposition and borrowing.", "II.17-011": "SECOND ARTICLE.", "II.17-012": "Licenses drawn from the interrupted cadence.", "II.17-013": "Inverting interrupted cadences gives many licenses. Another is a chain of sixths usually credited only to taste. Zarlin* forbids it because its consecutive fourths become consecutive fifths when inverted, supposedly giving much the same effect. Our rules instead explain the sixths through interrupted cadence and the freedom described in chapter XIII: fundamental bass may rise a third, fifth, or seventh without preparing the dissonance.", "II.17-014": "EXAMPLE.", "II.17-015": "Succession of sixths—interrupted cadences", "II.17-016": "Every measure is an interrupted cadence except the next-to-last. That one would be perfect, but an added sixth at A avoids it. The sixth prepares an irregular cadence; an added seventh at B avoids that and prepares the final perfect cadence.", "II.17-017": "* Terza parte, chapter 61, folios 291 and 292.", "II.17-019": "Swap the upper parts and their fourths become fifths. But inversion greatly reduces the dullness of consecutive fifths. Do not apply to fourths a restriction belonging only to fifths and octaves.", "II.17-020": "THIRD ARTICLE.", "II.17-021": "How one dissonance may resolve through another.", "II.17-022": "We know dissonance prefers consonant preparation and resolution, but can also sound unprepared. Can it also resolve against the general rule? Fundamental chords and bass movement use thirds, fifths, and sevenths. Treat these as fundamental intervals, usable upward, downward, or inverted. Examine which bass movements accept seventh chords; this will show whether a dissonance can resolve through another dissonance.", "II.17-023": "Principles produce rules, not the reverse. A famous author’s opinion is no substitute. Obscurity comes from failing to investigate or distinguish clearly. Authors acknowledge thirds and fifths but forget the seventh, first among dissonances. The fifth divides the octave harmonically; the third divides the fifth. With inversion, the seventh similarly comes from dividing the major third. It also comes from two fourths or a third added to a fifth. Since every dissonance comes from it, either accept it as fundamental or reject all dissonance. Neglecting inversion has hidden harmony’s secrets. Its consistency appears in numbers, divisions, multiplications, string lengths measured either way, intervals, bass movements, and chord progressions. Inversion explains harmony’s enormous variety.", "II.17-025": "Most musicians confuse license with error; Brossard does not even discuss it in his dictionary. But music has an advantage over other practical sciences. Elsewhere the freedoms that beautify an art escape exact rules. In music, one principle explains everything: license inverts what we first learn. We first meet perfect and seventh chords, and bass movements of third, fifth, and seventh or second. Nothing reason discovers beyond them fails to come from them. Everything must therefore rest on those two chords and three intervals.", "II.17-026": "The digression aimed to persuade prejudiced readers. Now recall: dissonance resolves to a third, an imperfect consonance, not the sweetest consonance. A seventh is a third added to a fifth and naturally falls by step. The only fundamental chords are perfect and seventh; bass movement uses their thirds, fifths, and sevenths. Two successive fundamental chords can therefore satisfy all these facts while one seventh resolves to another. This should not shock us. A seventh already resolves to an imperfect consonance and comes from the third itself: the second obtained by dividing a major third is an inverted seventh. Experience shows that the ear accepts this small defect because the underlying principle remains intact.", "II.17-028": "Ascending thirds and fifths are more perfect than the ascending seventh used for this license. Yet they cannot provide this resolution: in those fundamental progressions, the dissonance cannot move naturally.", "II.17-029": "Example of a seventh resolved by another seventh.", "II.17-030": "A seventh resolved by another seventh", "II.17-031": "Any shown part can become bass, but the continuo must never sit above the fundamental bass. Supposition requires its low sound below the fundamental. The added part cannot sound with the two basses, and neither bass should be moved above the other parts.", "II.17-032": "C and D are sevenths above their fundamental-bass notes. The bass moves down a step or up a seventh at A–B. Thus a dissonance resolves through another dissonance.", "II.17-033": "The most pleasing forms are ninth to seventh between C D and F G; seventh to diminished fifth between C D and H I; and second to tritone between H I and C D, with C D placed above H I.", "II.17-034": "Brossard’s dictionary* and Masson show seventh-to-diminished-fifth resolution. Masson also lets a tritone resolve to the fifth above the same note. Put our fundamental A B under his example D, etc., and the result resembles ours. His major dissonance comes in the first seventh chord; ours in the second. Other details differ because he was not working with fundamental bass.", "II.17-035": "When using our fundamental bass, replace note N with its guide-note pitch.", "II.17-036": "L–M gives an irregular-cadence fundamental bass, but the added seventh at M avoids that cadence. We should consider this further.", "II.17-037": "1. An irregular cadence is an original progression when both fundamental-bass notes take perfect chords. Its added sixth is only an extra sound allowed by taste. That added-sixth chord is not fundamental, even though it also inverts a seventh chord. It does not have all the freedom of the original perfect and seventh chords. Those originals can be inverted freely. Extra sounds added to them cannot move just as freely, though the underlying chords keep their properties. In the irregular cadence the added sixth does not clash with the bass. Do not invert it so that its clash with the fifth moves against the bass. The small-sixth inversion is allowed because the dissonance stays between upper parts. Turning it into a seventh chord would give it a different fundamental principle. That does not work here: a seventh cannot resolve over a bass rising a fifth. A cadence means some kind of melodic ending. It requires consonant bass movement under fundamental chords, modified here only by a tasteful license. Keep original and derived chords distinct.", "II.17-038": "* De Brossard, page 131, article 5, note A. Masson, page 115. [Page 98.]", "II.17-040": "2. Add a dissonance to the perfect chord ending a cadence and the ending is interrupted: it is no longer a cadence. If fundamental chords and their bass movements explain the result, they provide its true foundation. The previous example does this. Its fundamental chords may be inverted freely and used with supposition.", "II.17-041": "The added part seems even stranger because its second resolves against the usual rule. But if we accept the other progressions, we must accept this too: fundamental bass governs them all. The license resembles an irregular cadence, where dissonance rises to a third. Still, keep the actual foundation of each progression distinct from that particular cadential license.", "II.17-042": "Experience supports us more strongly than arguments alone. Look at the best masters’ works for further proof.", "II.17-044": "Repeated licenses in the last example are rather harsh. Use them rarely and with expert judgment. Their perfection is even shown by how difficult they are to accompany faultlessly. Composers should study our accompaniment instructions, which specify the chords natural harmony would require.", "II.17-045": "FOURTH ARTICLE.", "II.17-046": "The seventh may also resolve to the octave.", "II.17-047": "The seventh differs from other dissonances. Every consonance can prepare it and almost every consonance can resolve it. The exception is the fourth. That interval resolves a second only when the harmony is an inversion of seventh-to-fifth resolution.", "II.17-048": "Thirds, fifths, and octaves prepare sevenths. In ordinary fundamental harmony, a third resolves them. Interrupted cadences also let a fifth resolve them, giving pleasing variety. Those resolutions accompany a bass falling a fifth or seventh. A falling third is more perfect than a falling seventh, so we should seek a resolution there too. We find the octave, though the result seems to contain hidden consecutive octaves. We will first prove the resolution, then explain why that objection is mistaken.", "II.17-049": "Musicians all allow a ninth to resolve to a third over a bass falling a third. The seventh within that ninth chord must then resolve to an octave.", "II.17-051": "Ninth, seventh, and octave—small example", "II.17-052": "Look at the fundamental chords behind the example. What appears as a ninth is really a seventh, and what appears as a seventh is a fifth. Their movement matches the example. A ninth chord comes from an added low note that supposes a fundamental above it.", "II.17-053": "EXAMPLE.", "II.17-054": "Fundamental bass of two avoided perfect cadences", "II.17-055": "The guide sign shows the extra ninth-chord bass sound. The ordinary note above it shows the fundamental.", "II.17-056": "Consider the whole ninth chord. If ninth-to-third resolution is allowed, seventh-to-octave must be allowed too; otherwise both must be forbidden. Their fundamental origin shows that both movements are natural. Either accept seventh-to-octave resolution or reject the ninth chord.", "II.17-057": "The seventh can also resolve to the octave when the harmony is inverted.", "II.17-058": "EXAMPLE.", "II.17-059": "Inverted bass and fundamental bass", "II.17-060": "The rule against hidden fifths and octaves comes from fundamental harmony, like the other rules. Poor explanations have made it confusing; we must clarify it.", "II.17-062": "The rule aims to prevent awkward movement, especially around dissonance. In consonant harmony, contrary motion easily avoids trouble. But perfect and irregular cadences constantly contain hidden octaves or fifths. Add all the bass’s passing steps and those pairs would actually sound. The ban cannot apply there. It applies to certain inversions of those cadences, where the old bass line would make an unsuitable upper part and the old upper line becomes bass. Yet our existing rule already handles this: upper parts should move by steps when possible, especially with fourths, as in the inversion shown.", "II.17-063": "Hidden octaves and fifths—diatonic progressions", "II.17-064": "Inversion of parts—the fourth", "II.17-065": "So we do not need that separate rule here either.", "II.17-066": "Let each dissonance follow its natural path. The accompanying consonances may move to other consonances as we choose, as long as we keep the proper key movement and resolution chord. A seventh moving to an octave does not then create hidden octaves. The octave already accompanying it, or implied, stays still or moves elsewhere. Any second octave must be traced from that first octave’s own part, not from a different interval. See the example.", "II.17-067": "Seventh resolving to octave—movement of consonances", "II.17-068": "Many more dissonance resolutions follow from this. Book III will discuss them.", "II.17-069": "Always use the chord’s underlying foundation as guide, both for thirds and sixths and for avoiding consecutive fifths or octaves. What looks like a forbidden pair may not sound like one. Masson* and others allow the shown sixth-to-fifth movement. Filling the step from F to D seems to reveal two fifths. But its fundamental bass is D–G, an avoided perfect cadence, and those fifths then disappear. The skilled composer says: a sounding note supposes another; with that underlying note, the apparent fifths vanish, so the passage is good. Such supposition should normally lie between principal beats. Music’s freedom can be overused, sometimes successfully. But when reason and hearing agree, all its variety can be used without harming its perfection. A regular foundation can make written fifths or octaves cease to be such to the ear.", "II.17-070": "Sixth to fifth—in four parts", "II.17-071": "Fundamental bass D, G", "II.17-072": "We needed this longer explanation for people who follow the wording of rules without understanding what they mean.", "II.17-073": "All these consonances can apparently resolve a seventh. But in natural fundamental harmony, its true resolution is still the third. In an interrupted cadence it resolves to a fifth; invert that bass movement and it can resolve to another seventh. Both possibilities come from adding the seventh to a perfect chord and allowing a new bass movement. Resolution to an octave likewise comes only through supposition or inversion. The underlying natural resolution remains to a third.", "II.17-074": "* Masson, page 104.", "II.17-075": "FIFTH ARTICLE.", "II.17-076": "The seventh may be accompanied by the sixth.", "II.17-077": "A sixth sometimes sounds with a seventh, making a very harsh chord. This works only as a passing event: the clashing sounds stay still and belong to the chords on either side. The bass is an added sound admitted by supposition.", "II.17-078": "EXAMPLE.", "II.17-079": "Seventh with sixth—chromatic alternatives", "II.17-080": "ANOTHER EXAMPLE.", "II.17-081": "Sustained sound—pedal point", "II.17-082": "We call this a pedal point.", "II.17-083": "A held note becomes less noticeable when other notes above it move according to natural harmonic rules. The present example does this, as does the added part in the previous article. The same effect occurs in musette and hurdy-gurdy music in France and elsewhere (called “coliers” here; the word is uncertain). Book III’s chromatic rules and Book IV’s pedal-point rules give an idea of them.", "II.17-084": "We could now discuss chromatic writing, melodic dissonances, supposition, and false relations. But the next book explains these simply and clearly, so we leave them for then.", "II.17-085": "SIXTH ARTICLE.", "II.17-086": "Occasions when dissonance seems to be prepared by another dissonance.", "II.17-087": "This article appears under license, but its subject actually follows natural harmony. We insist that prepared dissonance is prepared by consonance, without exception. Since experience seems to show otherwise, musicians often misunderstand. We put the explanation here because this is where they expect such a case.", "II.17-088": "On page 131, Brossard says a syncopated dissonance may lead to a diminished fifth, then to a syncopated fourth apparently prepared by that fifth. Readers who already understand are satisfied; beginners are misled. Strict readers still think every dissonance must be prepared and resolved by consonance and therefore condemn these examples. An apparent exception must be explained, not merely stated. If Brossard had stayed within his book’s stated subject instead of giving practical rules, we would not criticize him here. But his other rules contradict this passage, so we must clear up the confusion.", "II.17-089": "Article III already discussed resolving a dissonance to a diminished fifth. Now consider a diminished fifth apparently preparing a syncopated fourth. Both are the same dissonant note in the same fundamental chord. The bass simply moves among other chord notes while that note stays still. Its interval above the continuo changes; its relationship to the fundamental does not. We add a fundamental bass to Brossard’s example to show this.", "II.17-091": "EXAMPLE.", "II.17-092": "Mr. de Brossard, page 131, at the ninth measure.", "II.17-093": "Brossard’s example with added fundamental bass", "II.17-094": "ANOTHER EXAMPLE.", "II.17-095": "The same seventh prepared by a consonance", "II.17-096": "At A–B, one seventh follows the same seventh. M’s seventh was prepared by the consonance at L. The changing continuo makes it appear first as a diminished fifth, then an eleventh. But its fundamental chord and seventh stay unchanged. The extra bass sound creating the eleventh, or fourth, lies below the fundamental and must be removed when checking the underlying harmony. So no dissonance prepares a different dissonance here. There is only one, prepared by a consonance when preparation occurs. A rule for changing chords does not apply to a bass moving within one chord.", "II.17-098": "Earlier commentators confused underlying principles with their results and could not bring theory and experience together. Our principle works throughout. Perfect and seventh chords, plus their own intervals, explain both natural harmony and license. Fundamental bass descends by thirds, fifths, and optionally sevenths for natural harmony. Their inversions, with supposition and borrowing, explain every usable license.", "II.18-001": "CHAPTER EIGHTEEN.\nObservations on establishing the rules, including how to compose a fundamental bass.", "II.18-002": "FIRST ARTICLE.\nEstablishing the rules.", "II.18-003": "We judge music by listening. Reason is authoritative only when it agrees with the ear. Their agreement is the strongest evidence: hearing satisfies us naturally, while reason satisfies the mind. Use both together in every judgment.", "II.18-004": "Experience gives us an endless variety of chords. Without an underlying principle, we become lost and uncertain. Each listener thinks his own ear cannot fail and trusts himself alone. Reason reduces the problem to one chord. With a little help from experience, it can explain all that chord’s properties. If experience does not contradict reason, let reason lead. A simple principle makes its conclusions especially convincing. Use experience to strengthen the proof.", "II.18-005": "Early speculative writers accept only the perfect chord as a foundation. Zarlin adds practical sixth and sixth–fourth chords, but those already derive from the perfect chord. Dissonances do too: add one sound, and the original perfect chord remains intact inside the result. The numerical addition follows a rule of three or a further multiplication, as Book I, chapter VII, page 29 shows. Reason can therefore determine its use. Musical rules concern usable consonances and dissonances. Consonances all belong to the perfect chord; dissonances to that chord with a seventh added. Those two must be the main foundation of the rules. Our simple principle agrees with expert teaching, practice, and listening experience. That agreement confirms it.", "II.18-006": "Check what Zarlin says about fundamental bass and the movements of parts, thirds, consonances, and dissonances. He overlooks major dissonances, defines interrupted cadence poorly, and omits irregular cadence and inversion, despite teaching inverted chords. He does not distinguish the ninth chord’s origin in supposition. His modal system is unsound, as chapter XXIII will show. His music therefore misses our refinements, and his examples do not support his claims. Ask where his explanations come from and whether they really prove anything. Examine their limits. Then you will see that harmony and melody depend on perfect and seventh chords, especially their shared lowest sound and its movement. Listen to the best composers and test their music with the fundamental bass explained later in this chapter. Only perfect and seventh chords will remain—tonic or dominant—if you can correctly identify the changes of key. In minor keys alone, the sixth note often stands in for the dominant.", "II.18-008": "The deepest foundation is not merely the perfect chord and its added seventh. It is their lowest note, the harmonic center for all other sounds. That is why we use a divided string. Its low sound is the source of the sounds obtained from its shorter divisions, as 1 is the source of all numbers.", "II.18-009": "All chords come from perfect and seventh chords, but those chords depend on the harmonic center and its movement. The intervals are measured from that center. It then moves by those same intervals, determining chord succession. The basic intervals are third, fifth, and seventh. Sixth, fourth, and second invert them; ninth and eleventh extend them through octaves; tritone and diminished fifth alter them. The octave simply repeats, so we leave it aside. The same categories explain chords: inversion, supposition through extended intervals, and borrowing through altered intervals. All lead back to the three basic intervals and the harmonic center.", "II.18-011": "The ear approves the basic chords and every progression following the movement of their fundamental bass, but nothing inconsistent with it. The fundamental may be implied, inverted, supplied by supposition, or borrowed. Reason and hearing agree here without exception.", "II.18-012": "This simple principle is remarkable. Countless chords, beautiful melodies, varied expressions, and well-conveyed feelings all come from two or three intervals stacked in thirds, based on one sound:", "II.18-013": "Fundamental sound. Third. Fifth. Seventh.\n 1. 3. 5. 7.", "II.18-014": "The earlier discussion should already convince us. The following rules will finish the proof.", "II.18-015": "1. Every consonance belongs to the perfect chord. Its fundamental bass moves by consonant intervals, as chapters I–II and Book III, chapter IV explain. This makes the upper parts move diatonically. Almost all consonance rules follow. The only qualifications come from freedoms introduced by dissonance. The main rules, especially those treated by ancient writers as the only rules, remain.", "II.18-016": "These natural progressions avoid consecutive fifths and octaves. Following the prescribed parts, we see perfect consonances usually lead to imperfect ones and vice versa. We also see which perfect consonances may follow each other. Thirds can continue without a fixed limit, so thirds and their inverted sixths move freely. Fourths might seem to inherit the ban on fifths, but experience accepts successive fourths in stepwise movement. Experience wins over that inference.", "II.18-018": "Plainchant uses only stepwise or consonant movement and even forbids major-sixth leaps. This supports our principle. But full musical composition should not be bound by that rule: dissonance adds wonderful expression. Proper modulation is the judge. Modern practice overcomes old difficulties in singing expressive dissonances.", "II.18-019": "2. A falling fifth is the most fundamental and perfect bass movement. A final cadence with it gives complete satisfaction. The fifth returns to a note of the octave from which it arose; rising a fourth does the same. It makes sense to study this cadence closely. This one basic movement will prove enough to complete our rules.", "II.18-020": "Only this basic cadence explains why a major third rises to an octave and a minor third must not. It is where a third can reach the octave by step. But apply the rule to the third above the fundamental, not above any note used as bass in an inversion. The relevant third belongs to a perfect or seventh chord. Rules about sixths confirm this: a sixth follows the third’s behavior only when an inverted chord makes it represent that third. Reduce the chord to its source and this becomes clear. We therefore need no separate sixth rule. The rule covers the fundamental third and anything representing it, including dissonant cases.", "II.18-022": "3. Add a minor third above a perfect chord’s fifth: this makes the first dissonance. It also clashes with the major third already above the root. Thus two thirds produce two kinds of dissonance. Minor dissonance comes from the added minor third; major dissonance from the original major third. This new distinction gives a universal direction: major dissonances rise, minor ones fall. No exception is admitted. It also confirms that harmony’s fundamentals are perfect and seventh chords, since every major dissonance reduces to the major third of a seventh chord and every minor dissonance to its seventh.", "II.18-023": "We have not yet explained why the minor third moves as it does. Its movement underlies minor dissonance. The evidence already given supports the claim; fuller explanation can wait.", "II.18-024": "Chromatic movement and the irregular cadence may seem exceptions. But an irregular cadence’s sixth is an optional extra. Removing it leaves the harmony perfect; removing other dissonances would make harmony dull. In chromatic writing a major dissonance can fall a semitone. Five points explain why this does not overturn the rule. First, its expected upward destination is implied or heard in another part; it is the fundamental, naturally in the bass. Second, major dissonance is not independently dissonant: remove the minor dissonance and the major one ceases to clash. Third, its source, the major third, belongs to the perfect chord; requiring ascent does not absolutely forbid holding it. Fourth, it is the major third of a tonic dominant and becomes incidental to the next key. Fifth, it is treated as remaining on one degree to prepare the following minor dissonance. Hold the bass fixed to see this: a third stays a third, a seventh a seventh. Only the quality changes from major to minor or augmented to just. The note name stays the same too; a flat or natural changes its pitch.", "II.18-026": "Skilled musicians will understand these proofs even without a fully expanded explanation, which would repeat too much. Chromatic writing also has its own properties as a new kind of harmony. Though they seem to depart from the principle, they still depend on it and need only a little clarification.", "II.18-027": "4. Upper parts should move by step, and a minor third cannot rise to an octave. So at a perfect cadence that third must hold still, then fall a step in the next similar cadence. This may explain both the introduction of dissonance and its rules. Holding the minor third turns it into a seventh; it then falls to another third. Hence consonance prepares and resolves dissonance. We derive the rule from perfect cadence for good reason. The old universal preparation rule considers only bass descents by third, fifth, or seventh, the only movements allowing that preparation and resolution; the fifth is primary. Chapter II also traced dissonance to perfect cadence. All rules thus have one source. And in natural fundamental harmony the seventh resolves only to the third, as chapter XVII, article IV showed.", "II.18-029": "The first maker of these rules may have understood harmony deeply through this single principle. Zarlin says early musicians knew only the perfect chord, though he himself lacked some chords used today. Later writers, beginning with him, concentrated on isolated intervals and explained the underlying principle vaguely. Inversions seem to have been discovered gradually by ear. Treating each as a new original chord hid their common source. Rules became full of detours, exceptions, confused terms, and unclear modal distinctions. Compare those rules with our reduction and the unnecessary obscurity becomes evident. The mathematician had proposed the principle, but lacking practical experience could not explain it fully; confused practitioners called him ignorant. Now accept that chords reduce to thirds within an octave,* as experience shows. Only perfect and seventh chords remain original. The sixth contains the perfect chord; the second contains the seventh. Other inversions do the same, leaving their fundamental implied. Ninth and augmented-second chords likewise contain the seventh through supposition or borrowing. These processes account for every chord. Fundamental chords themselves come from the lowest sound, aided by its octave, the first interval it generated. All usable consonance and dissonance follow. Theorists have only partly admitted this truth; most practitioners have resisted it.", "II.18-031": "5. The main rules came from descending bass movements and therefore demanded preparation for every dissonance. Opposite movements require exceptions. Chapter XIII explains them; we need not repeat it.", "II.18-032": "6. Major dissonance comes from a natural major third, so its only necessary precaution is to rise a semitone. Preparation is unnecessary. Minor dissonance can share that freedom in the specified fundamental-bass movements.", "II.18-033": "7. We can leave aside rules for melodic dissonance and syncopation. They depend on taste, though their source is still our principle.", "II.18-034": "8. Modulation connects all these rules and strengthens their common principle. Explaining the connection Zarlin and others missed takes more space, so chapters XXII–XXIV will do it.", "II.18-035": "* Zarlin prescribes this reduction and these limits in Part III of his Istitutioni harmoniche: chapter 3, folio 174; chapter 31, folio 210; chapter 66, folio 323.", "II.18-037": "9. Extra notes in supposition, irregular cadence, or borrowing may seem to need separate rules because our basic ones do not include them. They are simply optional additions that leave the principle untouched. Our other books explain their use. For a clearer check, add a fundamental bass using the following method.", "II.18-038": "SECOND ARTICLE.\nHow to compose a fundamental bass beneath every kind of music.", "II.18-039": "1. Harmony normally registers at the start of a beat, or at the start of each half if the beat divides into two equal parts. All voices and the fundamental bass must agree then. But watch carefully: notes added for melodic effect may occur inside a beat or even at its start without belonging to the underlying harmony.", "II.18-040": "2. Keep the fundamental bass below every other part. Together they must make a perfect or seventh chord. Remove extra and borrowed sounds when needed for this test.", "II.18-041": "3. A ninth or augmented-fifth chord places the fundamental a third above the written bass. An eleventh, also called fourth, or an augmented-seventh chord places it a fifth above. The other notes then make a seventh chord with the fundamental. The octave of an extra eleventh-chord bass sound is also extra, even though the complete arrangement sounds good.", "II.18-043": "4. For a borrowed chord, replace the sixth note with the dominant in the fundamental bass. The sixth forms an augmented second—or inverted diminished seventh—with the dominant’s major third. What remains is a seventh chord above the new fundamental. See point VIII later.", "II.18-044": "5. Identify irregular cadences carefully. Remove the note that would otherwise seem to be a seventh-chord root. Use only the perfect chord left in the other sounds. Points VIII–X return to this.", "II.18-045": "6. Ignore a passing chord combining seventh and sixth, described in chapter XVII, article V. Keep the fundamental bass on the previous note.", "II.18-046": "7. This added bass is only an analytical test. Consecutive octaves or other faults created by adding it do not matter if they are absent from the original parts.", "II.18-047": "8. Knowledge of modulation tells you the key, the function of each note, the correct chord, and any missing or altered fundamental. Borrowed chords occur only in minor. The sixth takes the tonic dominant’s foundation, so the dominant remains fundamental even if supposition is also present. Irregular cadence moves from tonic to dominant or fourth to tonic. Put those notes in the fundamental bass under perfect chords and mentally omit the lower note of the dissonant interval.", "II.18-048": "9. Use consonant bass movements whenever possible. Depart from them only for a seventh resolving to a fifth or seventh, or prepared by an octave. The parts should form only thirds, fifths, octaves, and sevenths above this bass. Some chords omit a sound because the melody favors doubling another. Their underlying identity remains, but the analyst must recognize the omission. Exclude the extra low note of supposition, the irregular cadence’s added note, and the borrowed note replacing the tonic dominant’s foundation. Imagine them absent during the test. In minor, the fifth above the second note is often diminished. Treat it here as a perfect fifth incidentally altered, within a perfect or seventh fundamental chord. Next check:", "II.18-050": "10. Is the minor dissonance, a seventh above the fundamental bass, prepared and resolved correctly? Remember that rising a fourth and falling a fifth are equivalent, as are similar inverted pairs. Sometimes the proof implies a dissonance not actually written, to preserve consonant root movement or the allowed chord types. Its faulty progression must not be blamed on the composer if the fault exists only with the analytical bass. The composer may never have intended that bass to sound. Faults already in the original parts are the composer’s responsibility. Either way, the harmonic foundation must still reduce to perfect and seventh chords.", "II.18-051": "If a second’s upper note or a seventh’s lower note rises while the other note holds, you have an irregular cadence. Treat the rising sound as extra; it must never be the bass. Also check major dissonance: it is the leading note, or major third of the tonic dominant, and clashes only when the minor dissonance is present. It should rise a semitone to resolve.", "II.18-052": "11. Observe these qualifications. First, a dissonance may stay on one pitch as long as the same fundamental chord remains, then resolve correctly. Second, a minor third between the two basses does not concern this test. Third, while one chord remains, a dissonance may move to another chord note, but should normally then reach its original resolution note. If the last sound is itself the major or minor dissonance, it may instead follow its own required resolution. Fourth, major and minor dissonances may exchange their usual consonant destinations. The harmony must remain natural, and each must still move up if required to rise or down if required to fall. Zarlin’s example shows this.*", "II.18-169": "Minor dissonance.\nMajor dissonance.", "II.18-054": "Fifth, in chromatic writing a major dissonance may fall a semitone instead of rising. We treat that as staying on the same degree, as explained earlier.", "II.18-055": "Music that passes this fundamental-bass test is certainly sound in its essential harmony. It may still have faults in the order of consonances, melody, modulation, the lengths of preparation and resolution notes, or the placement of dissonance within the beat. Those are secondary matters and easy to check. Taste supplies most such rules and sometimes tells us to depart from them.", "II.18-056": "* Terza Parte, chapter 30, folio 210.", "II.18-058": "A sounding fundamental bass can be very effective in choral music. In that case all parts must obey the rules strictly. Still, the continuo may form repeated unisons or octaves with it, especially in sixth chords, supposition, and borrowing, without worrying about the fundamental sound in those cases.", "II.18-059": "Earlier writers gave the rules without explaining their foundation. This fuller account aims to make the principle clear enough to remove doubts and disputes.", "II.19-001": "CHAPTER NINETEEN.", "II.19-002": "The preceding chapter continued: melody comes from harmony.", "II.19-003": "At first we might think harmony comes from melody. Each voice has a melody, and combining the voices makes harmony. But someone must first decide where each voice goes so that they fit together. However we organize each part's melody, the parts will hardly make good harmony—perhaps cannot do so at all—unless harmonic rules guide them. Yet teachers begin with writing a melody, intending to make the whole subject easier. A beginner may make progress, but that understanding disappears when a second part must be added. The melody is no longer under our control. As we work out how one part relates to the other, we often forget our first intention or have to change it. If we refuse to change the first part, its restrictions may stop us giving the others the best possible melodies. Harmony therefore guides us, not melody. A skilled musician can plan a beautiful melody that fits the harmony. Where does that ability come from? Nature may certainly have given it. But if nature has withheld that gift, how can the musician succeed? Through rules alone. We must therefore ask where those rules come from.", "II.19-005": "Does the first division of a string give us two sounds that immediately make melody? No. Singing only from octave to octave would not make a very beautiful tune. The second and third divisions, which produce all harmony, give no more suitable material. A tune made only of thirds, fourths, fifths, sixths, and octaves would still not be perfect. Harmony therefore comes first, and melody's rules must come from harmony. We start by taking these harmonic intervals separately and making a fundamental progression. This is not yet melody. We then place the intervals together above one of their own sounds. As they take turns providing the foundation, their progression determines a natural diatonic path. These consonant and diatonic movements supply all the melody we need. Harmonic intervals therefore had to be understood before melodic ones. What we can first teach a beginner as melody consists of these consonant intervals—if that deserves to be called melody. Chapter XXII will show that the ancients also drew their modulation only from melody, although it really comes from harmony.", "II.19-006": "Once we understand consonant progression, adding three sounds above a bass note is no harder than adding one. Compare the instructions: 'You may place a third, fifth, or octave above the bass' and 'You must place the third, fifth, and octave above the bass.' Both require knowing the same intervals. If we know them, using them together is no harder than using them separately. The next instruction says that a part making the third must make the fifth when the bass falls a third. That is exactly how we teach it. Whether a bass progression brings us a third, an octave, or a fifth, we must know what follows that interval for each kind of bass movement. Without noticing, we are therefore teaching four-part composition while explaining only two parts. Every consonance appears in turn, and I must know how each proceeds as the bass moves. I can therefore use them together as easily as separately. If I cannot follow all at once, I can study one at a time. Working through them lets me build complete four-part harmony. From this I gain the knowledge needed for perfection. Our added explanation also makes mistakes avoidable. Several people who previously knew only note values produced harmony as perfect as one could wish after reading our rules twice, if their experience is to be trusted. If a composer can also hear what he has written,* his ear gradually develops. Once he becomes sensitive to the perfect harmony taught by these first steps, he can be sure of success. That success rests entirely on these first principles.", "II.19-008": "Once four-part writing becomes familiar, we can certainly reduce it to three or two parts. But what understanding does two-part writing itself give us, even if we master it? Perfect mastery is almost impossible because this method gives no foundation to guide us. Its teaching remains unproductive. Our memory may not hold everything, and the method can hardly cover every case. Eventually the teacher must say, 'Cætera docebit usus'—practice will teach the rest. When we turn to three or four parts, the explanations are so brief that we seem to need the great masters' own genius and developed taste just to understand them. Zarlin* says four parts can hardly be taught on paper. He leaves them to composers' judgment, saying they can learn from his earlier rules for two and three parts. We take the opposite view. Harmony should be taught in four parts. Everything distinctive about it is found there in only two chords, as we have repeatedly shown. Reducing four parts to three or two is then easy. Zarlin does not completely explain even two or three parts, and says he cannot explain four. Yet he acknowledges that perfect harmony consists of four parts, comparing them to the four elements. (Chapter 58, folio 281. We conclude that earlier harmonic rules have not given complete knowledge, but our proposed principle offers a sure way to that knowledge and leaves nothing out.", "II.19-009": "* This is one reason we give rules for accompaniment.", "II.19-010": "* Terza Parte, chapter 65, folio 320.", "II.20-001": "CHAPTER TWENTY.", "II.20-002": "The character of chords.", "II.20-003": "Harmony can certainly stir different emotions, depending on the chords we use. Chords may be sad, languishing, tender, pleasing, cheerful, or startling. Particular chord sequences can express these same emotions. This subject is far beyond my ability, but I will explain all that experience allows me to.", "II.20-004": "Consonant chords appear everywhere. Use them as often as possible in music expressing gladness and magnificence. Some dissonant chords must still be mixed in. Let their dissonances arise naturally, and prepare them whenever possible. Keep the most noticeable parts, such as the top part and bass, consonant with each other.", "II.20-005": "Prepared minor dissonances can sometimes express gentleness and tenderness quite well.", "II.20-006": "Tender laments sometimes need dissonances made by borrowing or supposition. Prefer minor dissonances to major ones. If major dissonances occur, give them mainly to the middle parts rather than the outer parts.", "II.20-007": "Dissonances by borrowing express languor and suffering very well. Chromatic writing does so especially well; we will discuss it in the next book.", "II.20-008": "Despair, fury, and anything astonishing call for all kinds of unprepared dissonance. Major dissonances should be especially prominent in the top part. Sometimes an unprepared major dissonance can make a beautiful passage from one key to another in music of this kind. But the two keys must not be so far apart that the ear is offended. This takes careful judgment, as does the rest of composition. Piling up dissonances wherever possible is a far greater fault than using only consonances. Use dissonance with great care. If its harshness does not suit the expression, skillfully leave it out—even from a chord normally inseparable from it. Spread the chord's remaining consonances among the parts instead. Remember: every dissonance comes from the seventh, and the seventh is only an added sound above a perfect chord. It does not destroy that chord's foundation. We can remove it whenever we judge that suitable.", "II.20-010": "Melody is just as expressive as harmony. Yet firm rules for melody are almost impossible, because good taste matters more than anything else. Gifted composers must be left the pleasure of excelling here, where almost all the force of feeling lies. Skilled musicians will find nothing new in what we have said. We hope they will not resent our sharing secrets they may have wanted to keep to themselves. Our limited knowledge cannot challenge their command of this final level of perfection. Without it, even the best harmony can seem dull; with it, they can always surpass others. Still, someone who knows how to arrange a chord sequence suitably can draw from it a melody that fits the subject. We will see this later. But taste always starts the process.", "II.20-011": "The ancients seem to surpass us in this respect, if their accounts are true. One musician made Misse cry with his melody. Another made Alexander take up arms. Another calmed a furious young man and made him humane. Many such astonishing effects are reported. Zarlin gives a sensible explanation. Their word harmony often meant simply melody. The effects came chiefly from powerful words, made stronger by the way they were sung, rather than from melody alone. Their melody could not offer the variety that perfect harmony gives us today, since they did not know it. Zarlin also says* that their harmony was a perfect chord over which they sang all kinds of airs without distinction. This was much like the music of our musettes or hurdy-gurdies. They call it Sinfonia.", "II.20-013": "A good musician must also enter fully into the characters he portrays. Like a skilled actor, he must imagine being the speaker. He must picture himself at the events he represents and feel as involved as the people most affected. At least inwardly, he must know how to deliver speech well. He must sense when the voice should rise or fall, and how far. Then he can make his melody, harmony, modulation, and tempo follow that expression.", "II.20-014": "* Terza Parte, chapter 79, folio 356.", "II.21-001": "CHAPTER TWENTY-ONE.", "II.21-002": "On modes.", "II.21-003": "Modern writers know there are only two modes. Yet they cling so closely to inherited rules that they miss the advantages of that discovery. They describe chord choices as arbitrary and leave them to judgment, even when the mode itself provides the guide.", "II.21-004": "A mode is contained in the octave of one sound. That octave holds all the notes needed for its melodies and chords. The ancients looked only at melody. This was their mistake: melody depends entirely on the chords established by the mode.", "II.21-005": "There are two modes because there are two kinds of third. A mode takes its name from the third above its principal sound. A major third gives major mode; a minor third gives minor mode. The words major and minor therefore refer to the third accompanying the fundamental note.", "II.21-006": "The first mode we learned came from the perfect diatonic system. C’s octave contains six other notes; changing their intervals with C changes the mode. The important notes came from C’s perfect chord: E, its third, became the mediant; G, its fifth, the dominant. Musicians found a sixth chord more suitable on the mediant than a fifth chord. But they did not explain why: the sixth chord is an inversion of the tonic’s perfect chord, so the mediant represents the tonic. They also found that the dominant needs a perfect chord with a major third. When it comes immediately before the tonic, it alone receives the seventh dissonance containing a diminished fifth. These two bass notes make the perfect cadence. Yet teachers did not say that diminished-fifth and tritone chords are inversions of this seventh chord. Since that seventh chord precedes the tonic’s perfect chord, its inversions should also precede the tonic chord or its inversions. Experience shows this, but the rules omit it. This principle would make things clearer: whenever this seventh chord or an inversion occurs, a tonic perfect chord or its inversion must follow. These two chords supply every note except the sixth, which is easy to find because it follows the third’s nature. They also tell us the chords needed before tonic or mediant. To find those before dominant, reason from the same rule. A perfect chord is preceded by a seventh chord whose bass lies a fifth above. The dominant normally has a perfect chord; adding a seventh does not change its foundation. So it too should be preceded by a seventh chord a fifth above it. To stay in the same mode, the third of this new chord must be minor. That note is also the seventh above the tonic dominant and the fourth above the tonic. This new seventh chord supplies the sixth note of the mode. We now know both the notes within the tonic’s octave and the chords they need. Those chords come from inverting the fundamental chords containing the notes. Minor differs from major by its minor third and sixth, with qualifications about the sixth left to the next book.", "II.21-009": "With this principle, Masson would not have needed to say,* “When the bass rises a semitone, use a minor sixth then a fifth, or two major sixths,” and so on. He is describing different notes in different modes. Without saying which mode, his rule fixes nothing. In discussing melodic dissonances or supposition, he also lists many notes already belonging to the chord formed by the consonances before or after them. Such dissonances are already implied chord members, so they introduce no supposition. We omit many similar mistakes.", "II.21-010": "Rule writers often defer too much to earlier writers. Their borrowed rules can contradict their own correct statements.", "II.21-011": "The ancients explained the effects of modes and their power over harmony and melody well. But they misunderstood their nature. They gave melody all the credit and restricted it to seven diatonic notes without further distinction. They thought each possible principal note would give a different effect. In doing so, they forgot the perfect system that should have been their model. They copied its consonances: they flattened B to get a fourth above F. Why not also copy its approaches to the tonic? In C, D lies a whole tone above the tonic and B a semitone below. But when E was tonic, they kept F only a semitone above and D a whole tone below. They should have sharpened F and D, just as they had flattened B elsewhere. One might say these differences defined their modes. Experience shows that this is an error. Zarlin’s own comments contradict his rules. He says* the bass is the foundation of the other parts, and* that it naturally falls a fifth in a perfect cadence. His examples show a part rising a semitone to the final note. Other examples add a part falling a whole tone to it. The rising note is the dominant’s major third; the falling note is its fifth. A perfect ending always has tonic after dominant, and the dominant’s perfect chord has a major third and fifth. So these approaches—a semitone upward and whole tone downward—must exist in every mode. Without them the upper parts cannot form the perfect cadence while the bass falls a fifth. A piece must end with that cadence on its main note, or the soul remains unsatisfied. It is absurd to propose modes unable to do this. Zarlin’s rule forbidding a minor third or minor sixth to rise to the octave rests on this same principle. The tonic dominant needs a major third, a semitone below the tonic’s octave, like B below C. Yet the ancient D, E, G, and A modes lack that semitone. They clearly followed melody without considering harmony. Zarlin seems more capable than his predecessors and could have understood, but he deferred to established Church plainchant. It existed long before him and is hard to reform because of custom and cost. Only its keys matching the perfect system suit harmony. People without taste, full of ancient rules they do not truly understand, therefore struggle vainly to harmonize these chants well. Yet sacred music should command our study and labor: music exists only to praise God. Someone who believes this finds it distressing to be unable to use his genius fully on such a great subject. Correct chords can be piled over the chant without technical mistakes, but correct music is not necessarily perfect music. The ancients relied too much on their first discoveries. They composed chant melodies from the perfect system, then based harmony’s rules on those melodies. They should have begun with harmony, which string division shows comes first, and derived melody from it. That would give us easier, more flowing chant than what our churches now use. Their distinction between authentic or principal modes and plagal or collateral modes shows the same blindness.", "II.21-012": "* Chapter III, pages 36, 37, and 38.", "II.21-014": "* Terza Parte, chapter 58, folios 281 and 282.", "II.21-015": "[ * Chapter 51, folios 251 and 252. ]", "II.21-017": "They focused so much on arithmetic and harmonic proportions that they applied to the octave a distinction belonging only to the fifth. A distinction meant for harmony was used almost entirely for melody.", "II.21-018": "Zarlin made a new mode by dividing the octave at the fourth instead of the fifth. But this only rearranges the same sounds: it is inversion. The principal mode and its collateral are therefore the same mode. They have the same tonic, mediant, and dominant. Only the melodic arrangement differs.", "II.21-020": "His example* shows the principal mode first and its collateral second. C, traditionally named “C sol ut,” is tonic in both. E, marked b, remains its mediant; G, marked a, its dominant. The principal melody ranges between two Cs, the collateral between two Gs. This distinction is unnecessary. A melody’s range is limited only by the voices, and ordinary experience tells us those limits immediately.", "II.21-021": "Zarlin’s example: principal mode and its collateral.", "II.21-022": "Dividing the fifth according to its major or minor third is different. Those two modes cannot correspond like principal and collateral modes because their mediants—and therefore sixths—differ. That is what distinguishes their modulation. Seconds, fourths, fifths, and augmented sevenths rising to the octave do not change. Neither does melodic range determine mode: intervals outside the octave are equivalent to those inside. Zarlin reports Plato’s view* that melody comes from harmony. Had he followed it, he would have looked in harmony for modulation’s foundation and found a reliable way to the perfection he claimed. True modulation comes from three sources: the tonic’s perfect chord; the dominant’s chord, adding a seventh when appropriate; and the second note’s seventh chord. These supply the connections of good harmony and beautiful melody. Our earlier rules follow this principle everywhere.", "II.21-023": "* Quarta parte, chapter 13, folio 384.", "II.21-024": "[ * Secunda parte, chapter 12, folio 95. ]", "II.22-001": "CHAPTER TWENTY-TWO.", "II.22-002": "Why we can move from one mode or key to another.", "II.22-003": "Suppose a fundamental bass moves by consonant intervals and we sound only perfect chords above it. Each different bass note can give us a different key. This is because the perfect chord belongs specifically to a tonic, so each of these notes establishes a key. The consonances obtained from the first divisions of the string therefore give us all chords, all melody, and the way to move within one key. They also give us the way to move between keys, as Book III explains. We do not have to decide separately whether the new key should be major or minor: the key we leave governs that choice. Notice how we use the words here. We include mode under key when we are not hearing a change between major and minor on the same tonic. Yet we can change from major to minor, or minor to major, while keeping the same tonic or main note. For example, a cheerful subject may become sad, or a sad one cheerful. This happens in most chaconnes or passacaglias, and often between two successive airs of the same kind. In such cases we can say that the mode changes but the key does not. C remains the tonic in both C major and C minor. To keep the terms distinct, we simply say major key or minor key. In terms of melodic and harmonic movement, a key can change only between major and minor. In terms of its tonic, however, it can be based on the twenty-four different notes of the chromatic system. We cannot choose these freely at every point in a piece. We may choose any note for the beginning and ending, but we can leave it only for a note related to it or to one of its chord notes. When we conclude, we must return through a chain of these connections.", "II.23-001": "CHAPTER TWENTY-THREE.", "II.23-002": "On meter.", "II.23-003": "Meter alone can stir the emotions we have just attributed to music’s other elements. Without it, expression would be weak and ineffective. A sense of regular movement is natural to everyone. It draws us along almost without our consent; only an unusual impairment makes us unable to feel it. Descartes says on page 58 that even animals could dance in time if trained or accustomed to it over a long period. It needs only natural effort and movement. So it is unfair to say someone has no ear simply because they do not know a particular rhythm. They may also be concentrating so hard on dancing, singing, or playing that they cannot attend to the meter.", "II.23-004": "Meter can be derived from harmony’s principle. Its numbers—two, three, and four—also divide the octave arithmetically and harmonically. Since meter means equal movement, we can reduce it to two beats: after the first two movements establish an interval, we naturally repeat it evenly. Walking, tapping a hand, or moving the head shows this. Unless we deliberately go against nature, later movements match the first two. Meter would be easy if every beat had only one note, as in plainchant. It would also be easy if every note inside a beat had equal length. Equal movement is natural. Nor do larger note counts create new proportions: like chord ratios, 4, 6, 8, 10, 12, 15, 16, 20, and so on are built from 2, 3, and 5. Dots, syncopations, and similar patterns, however, require long practice before we feel them naturally.", "II.23-006": "To train the ear, let the pupil choose an even, fairly slow pace. Begin with one sung or played note per beat. Once this is fully comfortable, use two, four, eight, then sixteen notes per beat without changing the pace. Stay with each step until it feels like play. Then practice three and six notes in the same way. Leave dotted rhythms, syncopations, and similar patterns until last. Afterward, repeat everything at faster or slower speeds. Help the pupil feel the first and last beats of a measure and mark them with hand or foot. This needs patience from both teacher and pupil.", "II.23-007": "Some may find this advice irrelevant, but others may appreciate it. Many people abandon music because they think they lack a natural gift, when what they lack is only the habit that practice builds.", "II.23-008": "To read meter, learn the opening numerals and the values of notes and rests. Books by de Brossard, Loullier, l’Affillard, and others explain them very well, and almost any musician can teach them. We give no examples of those basics here: students of composition or accompaniment should already know them. Yet many people have told me that different arrangements of meter numerals confuse them. I propose using only 2, 3, and 4 to distinguish all possible meters.", "II.23-009": "Meters have two, three, or four beats, so those three numerals are enough. Note values can show how slow or fast the beats are. A whole-note beat is naturally slower than a half-note beat; a half-note beat slower than a quarter; a quarter slower than an eighth; and an eighth slower than a sixteenth. Once this is understood, the beat note immediately shows the relative speed.", "II.23-011": "Whole-note beats would be slowest: the Italians’ Adagio or Largo.", "II.23-012": "Half-note beats would be a little faster. They suit tender, graceful music: Andante or Gratioso.", "II.23-013": "Quarter-note beats would suggest lively, cheerful music: Vivace or Allegro.", "II.23-014": "Eighth-note beats would give the fastest movement, Presto. With three beats per measure, sixteenth-note beats could show the extremely fast Prestissimo. With two beats, eighth-note beats can already show that speed. Note values would then distinguish slow, less slow, lively, cheerful, and very fast music. We would only need extra expressive directions such as tenderly, gracefully, detached, connected, or louré where these fit.", "II.23-015": "The opening numeral gives the number of beats. The composer can show each beat’s length by putting its note value just before the clef. Performers then need not add up all the notes that make one beat. The note can also sit at the staff position showing the key, as the next examples demonstrate.", "II.23-016": "EXAMPLES.", "II.23-017": "Four beats.", "II.23-018": "Very slowly.", "II.23-019": "Slowly.", "II.23-020": "Somewhat lively or cheerful.", "II.23-021": "Fast.", "II.23-022": "Two beats.", "II.23-023": "Slowly.", "II.23-024": "Cheerfully.", "II.23-025": "Fast.", "II.23-026": "Very fast.", "II.23-027": "Three beats.", "II.23-028": "Very slowly.", "II.23-029": "Slowly.", "II.23-030": "Cheerfully.", "II.23-031": "Fast.", "II.23-032": "Very fast.", "II.23-033": "Directions such as slowly or lively are unnecessary because the opening note sign already shows the natural speed. Expressive directions can still help. Sad and mournful music naturally uses slow movement; tender and graceful music uses slow or cheerful movement; furious music uses very fast movement. Add such words when the expression requires them.", "II.23-034": "The first four-beat example contains eight quarter notes, two half notes, and a whole note: together they equal four whole notes. A whole-note beat sign at the start saves us doing that calculation. The same idea works when half notes, quarter notes, or other values are the beat.", "II.23-035": "Usually divide a beat into no more than four parts. If the beat is a whole note, four quarters can fill it. Eight eighths are rare, though a few may be used for melodic expression. Only occasional passages divide a beat into eight, and that division is kept in mind. All notes making up the beat must fit inside it, each taking its proper share of time.", "II.23-036": "Faster music uses fewer subdivisions of the beat.", "II.23-037": "For three equal notes in each beat, place a dotted note before the clef. Its value must equal the three notes together.", "II.23-038": "EXAMPLES.", "II.23-039": "Three beats.", "II.23-040": "Very slowly.", "II.23-041": "Slowly.", "II.23-042": "Cheerful.", "II.23-043": "Fast.", "II.23-044": "Two beats.", "II.23-045": "Very slowly.", "II.23-046": "Slowly.", "II.23-047": "Cheerful.", "II.23-048": "Fast.", "II.23-049": "Four beats.", "II.23-050": "Very slow.", "II.23-051": "Slow.", "II.23-052": "Cheerful.", "II.23-053": "Fast.", "II.23-054": "Some music has two, four, or even six unequal beats. These come from splitting each of the previous beats in two, with the first part twice as long as the second. Show this by placing notes for the first two unequal beat values at the start of the measure.", "II.23-055": "EXAMPLES.", "II.23-056": "Two unequal beats.", "II.23-057": "Slowly.", "II.23-058": "Gracefully.", "II.23-059": "Cheerful.", "II.23-060": "Fast.", "II.23-061": "Four unequal beats.", "II.23-062": "Slowly.", "II.23-063": "Loure movement.", "II.23-064": "Cheerful.", "II.23-065": "Fast.", "II.23-066": "Six unequal beats.", "II.23-067": "Slowly.", "II.23-068": "Gracefully.", "II.23-069": "Cheerful.", "II.23-070": "Fast.", "II.23-071": "We usually write the same numerals for unequal beats and for beats containing three equal notes. This causes confusion and can give an air the wrong movement. Unequal beats need a little weight on beats two, four, and six. That gives beats one, three, and five a special grace. The effect differs greatly from conducting the same notes in equal beats. Four unequal beats have the same written arrangement as two beats with three equal notes each; six unequal beats match three such beats; two unequal beats match ordinary three-beat meter. The different opening note signs distinguish them clearly.", "II.23-073": "Six unequal beats are uncommon because they are hard to conduct, though they certainly suit some kinds of expression. Strike beat one. Lower the hand at beat two by moving the wrist. Lower it farther at beat three by moving the arm. Then raise the arm for the remaining beats, as in four-beat conducting.", "II.24-001": "CHAPTER TWENTY-FOUR.", "II.24-002": "The character of modes and keys.", "II.24-003": "As we have said, there are only two modes: major and minor. Either mode can begin on any note in the chromatic system. This gives twenty-four keys. We call the main note of a mode its key.", "II.24-004": "The major mode has the character of a major third. The minor mode has the character of a minor third. But the semitones fall in different places within the octave built on each possible main note, or tonic. This gives the melodic and harmonic movement of these octaves different characters. We should explain those differences.", "II.24-005": "In the major mode, C, D, and A suit glad and joyful songs. F and B♭ suit storms, fury, and similar subjects. G and E suit both tender and cheerful songs. D, A, and E also suit grandeur and magnificence.", "II.24-006": "In the minor mode, D, G, B, and E suit gentleness and tenderness. C and F suit tenderness and lamenting. F and B♭ suit mournful songs. The other keys are used less often. Experience is the safest way to learn their character.", "II.25-001": "CHAPTER TWENTY-FIVE.", "II.25-002": "How this new way of showing meter helps.", "II.25-003": "Skilled musicians may not need this new method, but they cannot deny that it helps beginners greatly. The number at the start of a piece tells how many beats are in a measure. The note before the clef tells how long each beat lasts. Once beginners know these two things, they understand every kind of meter and the differences between them. The many meters no longer overwhelm them. The signs are familiar, few in number, and always placed in the same positions. The pitch position of the note also tells the key of the air. To show whether that key is major or minor, put a sharp above or below this note for major, or a flat for minor.", "II.25-004": "Like this.\nMajor key.\nMinor key.", "II.25-005": "This sign saves musicians from counting the sharps or flats after the clef to work out which notes to sing as “si” or “fa.” Call the note marked with a sharp “ut,” and the note marked with a flat “ré.” These are movable singing syllables, not fixed note pitches. Then any music can be sung in sol-fa without error, even though the order and number of sharps and flats are not shown exactly everywhere. No one then needs to worry about how many ♯ or ♭ signs there are, or count them to find the notes called “si” or “fa.” Seeing whether the sign is a sharp or a flat gives the needed information.", "II.25-006": "Simple numbers show how many beats there are, and note signs show their lengths. A music master can therefore confidently let someone else direct the piece, without fearing that the performance will fail for that reason. Such failures are fairly common. This method avoids them more easily than Mr. Loullier's chronometer, which people have neglected because it is difficult to use. Even so, the chronometer is an ingenious invention. It can specify very accurately the different speeds intended for a composition.", "II.26-001": "CHAPTER TWENTY-SIX.", "II.26-002": "How many measures each air should have, and how it should move.", "II.26-003": "The numbers that tell us how many beats go in a measure also guide the number of measures in a dance air. Two and four are especially important. A cadence is always felt in the fourth measure, often in the second, and rarely in the third.", "II.26-004": "Dance airs usually have two sections. The best sections contain four, eight, twelve, or sixteen measures. Five or six are rare; three is rarer still. A multiple of four works best here. The numbers 7, 9, 11, 13, 14, 15, 17, and so on have no good effect.", "II.26-005": "The examples below list the movement that naturally suits each kind of air.", "II.26-006": "The allemande. Beat.", "II.26-007": "The courante.", "II.26-008": "The sarabande, according to our observations. Beat.", "II.26-009": "The sarabande, according to custom; in this case add: Slowly.", "II.26-010": "The minuet. Beat.", "II.26-011": "The minuet, according to custom.", "II.26-012": "The passepied. Beat.", "II.26-013": "The canary.", "II.26-014": "The French gigue. Beat.", "II.26-015": "The Italian gigue.", "II.26-016": "or", "II.26-017": "or", "II.26-018": "The loure. Beat.", "II.26-019": "The gavotte.", "II.26-020": "The rigaudon. Beat.", "II.26-021": "The bourrée.", "II.26-022": "Rigaudons and bourrées usually carry the same movement marking as a gavotte. French gigues often carry the loure’s marking too—for example, the gigue in the Prologue of the opera Roland. These observations therefore matter more when writing new music than when reading existing music.", "II.26-023": "In very slow airs, each beat may be a half note when there are four beats per measure. With two or three beats per measure, each beat may be a whole note.", "II.26-024": "Each character and emotion has its own suitable movement. Choosing it depends more on taste than on rules.", "II.27-001": "CHAPTER TWENTY-SEVEN.", "II.27-002": "How to set words to music.", "II.27-003": "Beginners should usually set verse rather than prose, following common practice. Verse has a natural cadence. The tune must follow it, and it shows the right movement and where the music should rest.", "II.27-004": "For rhythmically measured airs, choose lines with the same number of syllables or feet. Each line should also have a reasonably complete meaning. Place its last syllable right at the start of a measure's first beat. There are two points to remember. With a feminine rhyme, the next-to-last syllable may take that place instead. Also, if a line does not fully complete the sentence's meaning, avoid a final cadence on its closing syllables whenever possible.", "II.27-005": "EXAMPLE.", "II.27-006": "Chantez (“Sing”): masculine rhyme.\nJe chante (“I sing”): feminine rhyme.", "II.27-007": "Cadences at line endings help beginners greatly. Sometimes they cannot avoid writing something like a perfect cadence before the meaning is complete. They can hide its final effect by changing the bass. Make the bass move by steps through notes belonging to the chords of the perfect cadence's fundamental bass. Or use the bass movement of an irregular or interrupted cadence.", "II.27-008": "Recitative needs more care than an air. When telling a story or recounting events, the tune should copy speech, so the singer seems to speak. Use perfect cadences only where the meaning ends. This calls for all the skills we have described for a good musician. Give long syllables suitably long notes and short syllables shorter notes. Listeners should hear the words' rhythm as clearly as from a skilled speaker. You may still put several long and short syllables on notes of equal length. In that case, place the long syllables at the start of beats, especially the first beat.", "II.27-009": "Operas and other good compositions demonstrate these points. Repeatedly reading and hearing such works often develops taste better than rules do.", "II.28-001": "CHAPTER TWENTY-EIGHT.", "II.28-002": "Design, imitation, and fugue.", "II.28-003": "Words have an expression, whether sad or cheerful. A musical setting must convey it through melody, harmony, and movement. Even without words, a composer imagines a subject that imposes similar limits. The piece's whole plan rests on these three things. First choose a key, mode, movement, and melody that suit the expression. Then fit the harmony to the melody written for that subject. Keep the movement unchanged unless the words require a change. Change key or mode only to vary the melody and harmony. The overall design therefore depends mainly on how the melody continues and develops.", "II.28-005": "Once you have planned a melody, look ahead through the words. Do similar feelings return? Are the same words repeated? Would repeating them help? These are good places for imitation and fugue, both of which contribute to the piece's design.", "II.28-006": "When similar feelings appear in different passages, use similar melody to express them. We call this imitation. Its limits are practical: do not bore the listener by making it too long or repeating it too often. You may imitate the whole melody or only part, according to good judgment. Taste decides which pitches to use, as long as listeners can recognize the intended melodic likeness.", "II.28-007": "When the same words return, or can be repeated, it is good to give them the same melody each time. This creates a more restricted form of imitation called fugue. Book III gives its rules.", "II.28-008": "Imitation may occur in just one part, usually the part called the subject. Fugue must pass from part to part. The first part then seems to follow the part that followed it, making a continuing chain.", "II.29-001": "CHAPTER TWENTY-NINE.", "II.29-002": "Intervals distinguished as major and minor; just or perfect; augmented and diminished.", "II.29-003": "The octave is the source of all intervals and cannot be altered in harmony.", "II.29-004": "The octave divides into a fifth and fourth. These can be altered, but then they lose the perfection of their origin. Their names still tell us their span, not their original nature. Two minor thirds make a diminished fifth; two major thirds make an augmented fifth. Invert the diminished fifth and you get an augmented fourth, or tritone. Invert the augmented fifth and you get a diminished fourth, which cannot be used in harmony for reasons explained elsewhere. Altered intervals therefore represent the thirds that give them their imperfection, rather than retaining their original character.", "II.29-006": "Dividing a fifth gives two different thirds. We must call them major and minor because both remain thirds. Altered fifths and fourths, however, depart from their origin, so those names do not suit them. We call them just or perfect, augmented, or diminished. Their original derivation gives them independent perfection. When altered, their augmented or diminished character comes from major or minor thirds, which form all altered intervals.", "II.29-007": "A major third divides into two different whole tones, also called major and minor. The difference is too small for the ear to notice. In practice, then, there is only one kind of tone, second, and seventh: a tone makes a second, and its inversion makes a seventh. Nevertheless, people customarily call seconds and sevenths major and minor.", "II.29-008": "Dividing a major tone gives major and minor semitones. Their relation to the tone is not like the relation between major and minor thirds. The tone and semitones have different origins, whereas both thirds come from dividing one fifth. A minor semitone separates a major third from a minor third. If another interval can be altered by that semitone, the power to do so must come from those thirds. Fifths, fourths, and tones had no such difference at their origin. The so-called major and minor sevenths differ by that same semitone, just as a fifth differs from a diminished fifth. Yet no one calls a diminished fifth minor, or an augmented fifth major. This shows that major and minor properly belong only to thirds and what directly depends on them. Sixths qualify because they invert thirds; modes qualify because thirds determine them. Altered fifths and fourths instead become augmented or diminished, showing that they have left their proper proportion. They did not originally come from thirds; thirds came from them.", "II.29-010": "Look at intervals within an octave. Proper modulation leaves fifth, fourth, seventh, and second fixed; only third and sixth move. Thus only third and sixth should be called major or minor. Seventh and second should use the same distinctions as fifth and fourth. The seventh does change in minor keys, but only downward, just as the sixth changes upward. Those changes adapt the approach to a principal note of the mode, tonic or dominant. The second does not change. Since second and seventh invert each other, any property assigned to one must also belong to the other.", "II.29-011": "There is another difference: intervals called major or minor can also have augmented and diminished forms.", "II.29-012": "EXAMPLE.", "II.29-013": "Diminished third. Augmented sixth. Minor third. Major sixth. Major third. Minor sixth. Augmented third. Diminished sixth.", "II.29-014": "The example shows four kinds of third and sixth. No other interval has four kinds.", "II.29-015": "EXAMPLE.", "II.29-016": "Unison. Octave. Diminished unison. Augmented octave. Augmented unison. Diminished octave.", "II.29-017": "Fifth. Fourth. Diminished fifth. Tritone. Augmented fifth. Diminished fourth.", "II.29-018": "Seventh. Second. Augmented seventh. Diminished second. Diminished seventh. Augmented second.", "II.29-019": "Call the ordinary seventh minor and the augmented seventh major, and there is no additional augmented form, unlike thirds and sixths. Call a diminished second minor, and no diminished form remains. Seconds and sevenths have only three kinds, like fourths and fifths. Why not name both pairs the same way? Calling them major and minor borrows qualities of thirds and sixths. Brossard tries to justify calling the true augmented seventh major by proposing another augmented seventh, B♭ to A♯. Here it is:*", "II.29-020": "Thus.*", "II.29-021": "Brossard admits that this interval is unused and often confused with an octave. We need examine it only to see his mistake. He calls C to C♯ a diminished second.* But that does not invert his B♭–A♯ interval. An interval and its inversion must use the same note names, as the example and Book I, chapter V’s table show. When only a sharp or flat changes the notes, the basic interval name must stay the same; add major, minor, augmented, or diminished as appropriate. C–C♯ is therefore an augmented unison, not a diminished second. B♭–A♯ is larger than a diminished octave—indeed, effectively an octave, since both names use the same organ key and the same key on most instruments. Possible objections are omitted to keep this short; they are easy to answer.", "II.29-022": "* See Settima in his dictionary.", "II.29-023": "* See Seconda.", "II.29-025": "Brossard’s explanation of the seventh chord and its resolution is no better. He does not say whether he means the augmented seventh,* but gives this use of it.", "II.29-026": "7, 6, 4, 2, 1.", "II.29-027": "He cannot have listened to the chord: it is bad. He would have been more excusable had he flattened the 6 or limited the rule to minor keys. But a rule without stated exceptions must apply generally. To make this one at all general, he needed a fifth instead of the sixth.", "II.29-028": "Some may still want to call sevenths and seconds major and minor, because they can be used that way in practice. But our classification of dissonances follows their source. Major dissonances come from major thirds; minor dissonances from minor thirds. They follow those thirds’ properties. Why call an interval major if it behaves like a minor third? A seventh always descends unless it is augmented. The interval called a major seventh is the same as our augmented seventh, so we must choose the name. Both have ratio 8:15. Our augmented seventh rises, like the major third that forms it; in fundamental harmony it is the tonic dominant’s major third. The so-called major seventh falls, following the minor third’s behavior. We also showed that a ninth is almost always implied with this latter seventh, making that seventh merely a fifth in fundamental harmony. Why not call the basic seventh a just or perfect dissonance, keeping those words within the category of dissonance, and call its alterations diminished and augmented?", "II.29-029": "* See Settima.", "II.29-031": "Fifths and fourths show the same problem. A seventh chord on the second note of a minor key naturally contains a diminished fifth. Does its lower note have to rise a semitone, as in the usual diminished fifth derived from a major third? No. It may stay still—or rather descend a fifth—while the upper note falls. Here the diminished fifth does not govern the chord; the seventh governs its movement. Likewise, a tritone in a small-sixth chord on the sixth note of a minor key does not rise: it stays still. As Book I explained, these intervals replace those that would naturally be present and are admitted for the key’s melodic and harmonic movement. Yet we do not call them minor fifths or major fourths. Those descriptions are forbidden for intervals whose nature is just and perfect. We cannot allow them for a seventh made major only by modulation unless we allow them for every interval.", "II.29-032": "Thirds control modulation. Fifths, fourths, and sevenths may take major or minor forms in the sense just discussed, but only because modulation requires them. They do not determine it. If modes are called major and minor, those names should apply only to the intervals that govern their order and movement.", "II.29-033": "The same reasoning applies to seconds and ninths. A second inverts a seventh. A ninth repeats a second, or represents a seventh in fundamental harmony.", "II.29-034": "The eleventh, called the fourth, always keeps the same interval.", "II.29-035": "END OF BOOK II.", "III.01-001": "BOOK III.", "III.01-002": "Principles of composition.", "III.01-003": "CHAPTER ONE.", "III.01-004": "Introduction to practical music.", "III.01-005": "The scale.", "III.01-006": "There are seven diatonic sounds,* or successive steps of the natural voice: C D E F G A B. Together they form the scale. To keep going, return to the first name after the last and repeat the order. Repeated versions of the same notes are called octaves.", "III.01-007": "Add a final C to practice recognizing the octave: C D E F G A B C. Learn the downward order too: C B A G F E D C.", "III.01-008": "Practice beginning and ending on other notes too, though this goes against the diatonic order. Extend the scale by repeating notes in the next octave. From G, go G A B C D E F G upward, and G F E D C B A G downward. Do the same from other notes.", "III.01-009": "Intervals.", "III.01-010": "Learn to recite the scale both ways from any starting note. Also count the distance from one note to another. For now, count upward only.", "III.01-011": "* See the glossary.", "III.01-012": "These counted distances are musical intervals. Their names come from numbers:", "III.01-013": "2 Second; 3 Third; 4 Fourth; 5 Fifth; 6 Sixth; 7 Seventh; 8 Octave.", "III.01-014": "We put numbers above the names because we will use those numbers as shorthand. Learn that 2 is second, 3 third, 4 fourth, and so on through 8, octave.", "III.01-015": "Choose a starting note and call it degree 1. Count all the notes from it through the destination. The count names the interval. From C, D is second, E third, F fourth, G fifth. From D, E is second, B sixth, C seventh. Practice every possible starting note. You should know immediately that E is A’s fifth, B is E’s fifth, and D is G’s fifth. Use the circular scale below.", "III.01-016": "Circular scale—interval distances", "III.01-017": "Start at C’s 1 in the diagram. Follow the line to D’s 2, E’s 3, and around to 8, the octave C. An octave repeats the same note name. Start on D instead: 1 leads to E’s 2, F’s 3, and onward. Each number shows how far its note lies from the starting note. The little lines form a circle from 1 through 8.", "III.01-019": "Unless we say otherwise, find thirds, fourths, and other intervals upward from the starting note. We assume that starting note is the lower one.", "III.01-020": "Also practice counting downward. G is a fourth below C, just as C is a fourth above G. This simple relationship is useful.", "III.01-021": "Inversion of intervals.", "III.01-022": "An octave starts and ends on what is essentially the same note and contains every scale note. We might therefore expect a note compared with the lower C and upper C to give the same interval. But one C is below it and the other above. We need to explain the difference this creates.", "III.01-023": "Interval inversion—scale and numbers", "III.01-024": "D is a second above lower C, but upper C is a seventh above D. E is a third above lower C, but upper C is a sixth above E. F is a fourth above lower C, but upper C is a fifth above F. G is a fifth from lower C and a fourth from upper C. One interval therefore produces another. The same pattern works from any starting note placed at both ends of the scale. A second from the lower note becomes a seventh to its octave, and so on.", "III.01-026": "Always think of the starting note together with its octave. Compare another note first with the lower starting note, then with the upper octave. The first interval is fundamental or principal; the second is its inversion. C-to-E becomes E-to-C. In numbers, treating 1 and 8 as the same note, we first compare 1–3 and then 3–8.", "III.01-027": "You need remember only three fundamental intervals: third, fifth, seventh. In the chart, each starting note is 1, with its third, fifth, and seventh numbered accordingly. Learn those three intervals from any of the seven possible starting notes. Add that starting note’s octave and they become sixth, fourth, and second. Those three are inversions of the fundamental three.", "III.01-028": "C E G B; D F A C; E G B D; F A C E; G B D F; A C E G; B D F A.", "III.01-029": "Take time over this. Confirm it through your own practice; the rest will then be easier to understand.", "III.01-030": "The staff: the lines on which notes are placed.", "III.01-031": "Notes have different written shapes to show their duration. Their pitch positions go on or between five horizontal lines.", "III.01-032": "STAFF—five numbered lines", "III.01-033": "These five lines make a staff. Each is a line or rule; the gaps are spaces. Number lines from the bottom: lowest 1, highest 5.", "III.01-034": "Clefs.", "III.01-035": "There are three clefs. The examples show their shapes and the note each names.", "III.01-036": "F clef: two alternative signs. C clef. G clef.", "III.01-037": "The line through a clef gets the clef’s note name. Put only one clef at a time at the start of a staff. You can change it later at any point, but the new clef must sit on a line. That line then takes the new clef’s name.", "III.01-038": "F clef is the lowest clef. It usually sits on line 4 or line 3.", "III.01-039": "C clef names the C a fifth above F clef’s F. It can sit on any line except line 5.", "III.01-040": "G clef names the G a fifth above C clef’s C. Usually it sits on line 1 or line 2.", "III.01-041": "A note on the clef’s line has the same name as the clef. For now we use O-shaped notes, because we have not explained note shapes. Some sit on lines; others in spaces. Starting with the clef’s note, count through the scale. Going from bottom line to top means ascending; going back down means descending. Spaces have note names too. The next example shows how this works.", "III.01-042": "EXAMPLE.", "III.01-043": "F clef—F, E, D, C; F, G, A, B", "III.01-044": "C clef—C, D, E, F; C, B, A, G", "III.01-045": "G clef—G, F, E, D; G, A, B, G", "III.01-046": "A note can begin anywhere on the staff, not just on the clef line. Count from the clef to name it. But composing requires instant recognition, so memorize the lines and spaces for each clef position you use. With F clef on line 4: line 3 is D, line 2 B, line 1 G, line 5 A. The space above F is G; the space below is E. Learn the other positions the same way.", "III.01-047": "EXAMPLE.", "III.01-048": "Lines and spaces—note names", "III.01-049": "After learning every name, move the clef to another allowed line and learn the new positions. Repeat with other clefs.", "III.01-050": "You may add lines above or below the staff. Continue the same note order on them.", "III.01-051": "Parts.", "III.01-052": "Harmony combines different sounds that agree. Each voice or instrument producing a sound is called a part. Parts also have special names. The name may not be written, but the clef type or position identifies it.", "III.01-053": "EXAMPLES.", "III.01-054": "4 vocal parts.", "III.01-055": "First upper vocal part.", "III.01-056": "First upper vocal part", "III.01-057": "Second upper vocal part.", "III.01-058": "Second upper vocal part", "III.01-059": "Haute-contre—the highest male voice.", "III.01-060": "Haute-contre", "III.01-061": "Haute-taille—a middle part approaching the preceding one.", "III.01-062": "Haute-taille", "III.01-063": "Basse-taille or concordant—a middle part between the preceding and following ones.", "III.01-064": "Basse-taille or concordant", "III.01-065": "Basse-contre—the deepest, that is, lowest male voice.", "III.01-066": "Basse-contre", "III.01-067": "The first two vocal parts are for female voices only. Higher voices take the first upper part; lower ones take the second.", "III.01-068": "Instrumental parts.", "III.01-069": "Upper instrumental part—alternative G clefs", "III.01-070": "Upper violin, viol, flute, oboe, trumpet, etc. The first clef is ordinarily used for the last three instruments.", "III.01-071": "Haute-contre, taille, and quinte de violon", "III.01-072": "Haute-contre de violon. Taille de violon. Quinte de violon. These three instruments have the same tuning and therefore the same range. Its highest sound is marked by a note in the first part, and its lowest in the third.", "III.01-073": "Instrumental bass ranges", "III.01-074": "Organ, harpsichord, theorbo, bassoon, bass violin, bass viol, bass flute, etc.", "III.01-075": "The six vocal parts have defined ranges, shown by two notes at each clef. Use any notes between those limits. Small guide signs show occasional extensions beyond them. Use these rarely. A composer should usually keep voices near the middle of their range because the extremes strain them.", "III.01-077": "Instruments have different ranges. The violin reaches an octave below its clef and, in principle, has no fixed upper limit. But unless you know the instrument from experience, stay within the printed top note or guide. The notes also show ordinary bass ranges; only the bass viol reaches the lowest marked sound. We do not list every other instrument’s range. Since violin can play music of every general kind, you need not depend on those instruments. Players can tell composers what they need to know about them.", "III.01-078": "Unison.", "III.01-079": "UNISONS—eight clefs, one sound", "III.01-080": "Unison means two notes at the same pitch, like the same note repeated. To keep higher parts above lower ones, we need to compare their staff positions. The example puts the same pitch in every part so all are in unison.", "III.01-081": "Different parts need different sounds, not merely more performers. These identical pitches therefore amount to one part. That is why unison is forbidden in composition. Beginners may use it instead of an octave until they are more skilled.", "III.01-082": "Meter.", "III.01-083": "The simplest composition of meter comes from natural repeated movements. Walking shows how they remain even, unless we deliberately change their natural pattern.", "III.01-084": "Think of each walking step as a beat. Several beats make a measure. Faster or slower walking illustrates faster or slower musical movement.", "III.01-085": "Vertical barlines separate measures. A measure has two, three, or four beats. A hand or foot usually marks them. Strike or lower the hand for beat one, raise it for the last beat, and move it sideways for the middle beats.", "III.01-086": "Barlines separating measures", "III.01-087": "The first beat is called good or principal; the others bad. In a four-beat measure, both first and third are good.", "III.01-088": "Beat counts should simply use numbers: 2, 3, or 4. Instead, people seem to have rejected these clear signs precisely because they are simple and chosen ambiguous ones.", "III.01-089": "C marks four-beat meter.", "III.01-090": "A slashed C marks two-beat meter, etc.", "III.01-091": "Music is already abstract; we should not make it harder. Existing scores use many ambiguous signs, so musicians should know them to interpret those scores. But they need not be the basis of learning. Other authors cover them thoroughly, so we leave them aside. See Book II, chapter XXIII. Once two-beat meter is understood, other movements are easy to learn through aptitude and taste.", "III.01-092": "Put the meter sign just after the clef. If the clef has sharps or flats, they come first. If the movement changes during a piece, put the new sign at the start of the measure where it changes.", "III.01-093": "The shapes, names, and values of notes and rests.", "III.01-094": "Whole, half, quarter, eighth, sixteenth, and thirty-second notes", "III.01-095": "Whole note—one measure. Half note—half a measure. Quarter note—quarter rest, or quarter of a measure. Eighth note—eighth rest, or half a quarter-measure. Sixteenth note—sixteenth rest, or half of half a quarter-measure. Thirty-second note—thirty-second rest, or a quarter of half a quarter-measure.", "III.01-096": "Two whole notes, four whole notes, and beamed eighths", "III.01-097": "Two whole notes. Four whole notes. Eighths, sixteenths, thirty-seconds. Two measures. Four measures. Eighth, sixteenth, or thirty-second notes may be beamed together instead of separated as before.", "III.01-098": "Half notes can be joined by beams like eighth notes. When this is done, their value is halved.", "III.01-099": "Each note shape has a name, printed above it. The labels below show their relative lengths. A whole is twice a half; a half twice a quarter; a quarter twice an eighth; and so on. Read the other way, a thirty-second is half a sixteenth, and a sixteenth half an eighth. One whole can be replaced by two halves, four quarters, eight eighths, sixteen sixteenths, or thirty-two thirty-seconds. It can also replace a mixture totaling the same length. Any mixture is allowed in a measure if every beat is filled correctly.", "III.01-100": "The symbols below the notes are rests. They tell a part to be silent. Use them instead of notes to stop a part or delay its entrance—for an eighth or quarter of a beat, half a measure, a whole measure, or whatever number of beats or measures you choose.", "III.01-101": "Barlines divide the measures, and the meter sign gives their beat count. Notes and rests must fill that count. A whole usually means a full measure and a half note half a measure, but either can instead be chosen as one beat. Other values then change in proportion. A whole still equals two halves, four quarters, eight eighths, and so on. A rest usually lasts as long as its matching note. Whole-measure rests are independent: they serve in two-, three-, or four-beat measures whatever note value fills a beat, except the whole note. Thus two beats may be two wholes, halves, quarters, or eighths, if that value is defined as the beat. One beat may also hold two, three, four, six, or eight equal notes, or mixed values adding to the beat’s length. More notes in a beat require smaller values. A whole note therefore cannot count for less than a beat; other notes follow the same proportions.", "III.01-102": "EXAMPLE.", "III.01-103": "Two beats—a half note for each beat", "III.01-104": "Three beats—a half note for each beat", "III.01-105": "Four beats—varied note values", "III.01-106": "One whole note or two half notes for each beat.", "III.01-107": "Three half notes for each beat", "III.01-108": "You can choose quarters or eighths instead of halves for the beat. In three-beat meter you can also choose sixteenths. These choices show speed, as Book II, chapter XXIII explains.", "III.01-109": "Numbers over the notes label the beats: 1, 2, 3, 4. A beat note may be replaced by any combination of notes and rests with the same total length. You may begin or continue with such smaller or different values as long as the complete beat is accounted for.", "III.01-110": "The dot and the tie.", "III.01-111": "A dot after a note adds half its length. It has the same total duration as that note followed by a half-length note on the same pitch. But two separate notes would require two attacks. To keep one attack, use the dot or connect the two notes with a curved tie.", "III.01-112": "EXAMPLE.", "III.01-113": "Dotted notes", "III.01-114": "Dotted notes equal in value to the two tied notes below them.", "III.01-115": "Tied notes—one articulation", "III.01-116": "Tied notes articulated as one.", "III.01-117": "Whole tone, semitone, sharp, natural, flat, major, minor, augmented, and diminished.", "III.01-118": "A second, the smallest interval introduced earlier, can be a whole tone or semitone. E–F and B–C are semitones. The other neighboring notes in the scale are whole tones apart.", "III.01-120": "Semitones are the smallest intervals needed in practice. Where the scale does not already have one, a sign can raise or lower a note by a semitone to create one. Such signs can also widen E–F or B–C into whole tones.", "III.01-121": "These signs are called sharp, natural, and flat.", "III.01-122": "Sharp is written ♯, natural ♮, and flat ♭. Each sign must be placed to the left of the note, as in the following example.", "III.01-123": "A sharp raises a note a semitone, and a flat lowers it a semitone. A natural sometimes acts like a sharp, but also cancels a previous sharp or flat and restores the note’s ordinary form.", "III.01-124": "Accidentals do not change note names. Singing teachers make one exception for beginners: they call sharpened notes “si” and flattened notes “fa.” These are movable singing syllables, not fixed pitches. The notes then move diatonically like “si” and “fa” in the scale. A composer needs to understand the intervals more than to practice singing them. Focus here on how ♯, ♮, and ♭ change intervals by a semitone.", "III.01-125": "EXAMPLE.", "III.01-126": "Sharp, natural, and flat", "III.01-127": "ANOTHER EXAMPLE.", "III.01-128": "Whole tones and semitones—alterations A, B, C, D", "III.01-129": "F♯ at A is a semitone higher than F. E–F♯ is therefore a whole tone, like D–E, leaving only a semitone from F♯ to G. D E F♯ G thus follows the same pattern as G A B C, with B labeled D. B♭ at C is a semitone lower than B. In descending C B♭ A G, C–B♭ is a whole tone and B♭–A a semitone. This matches descending G F E D. The naturals on the next F at B and B at D restore their normal pitches.", "III.01-130": "Intervals can keep the same name while differing by a semitone. We then call them major/minor or augmented/diminished. C–E has a semitone more than D–F, so the first is a major third and the second a minor third. E–C has a semitone less than F–D, so it is a minor sixth. The same idea applies to other intervals with the same name. We will explain augmented and diminished more fully later.", "III.01-131": "Sharps and flats usually show these differences. A sharp on an interval’s lower note, F, normally makes the interval minor; on its upper note, G, major. A flat on the lower note, H, makes it major; on the upper, J, minor. Augmented goes with the major side, diminished with the minor side.", "III.01-132": "EXAMPLE.", "III.01-133": "Major, minor, diminished, and augmented intervals", "III.01-134": "Compare each top note with the bass note directly below it. This gives the major or minor interval labeled in the example.", "III.01-135": "Accidentals above or below a bass note do not change that bass note. They describe major or minor intervals above it, explained later.", "III.01-136": "Compound intervals.", "III.01-137": "Notes above an octave repeat the note names within it. You can therefore identify an interval by names without counting every octave. C below the F clef to G above the G clef spans nineteen degrees. But G is still C’s fifth. Knowing this and that G is above C is enough. Extra distance matters only for keeping upper parts above the bass and within their normal ranges.", "III.01-139": "EXAMPLE.", "III.01-140": "Simple and compound octaves, fifths, and thirds", "III.01-141": "Normally compare all parts with the lowest one. The example shows octaves, fifths, and thirds repeated through two, three, or four spans. We could call some fifteenths or twenty-seconds, but for now simply recognize C as the octave, G as the fifth, and E as the third.", "III.02-001": "CHAPTER TWO", "III.02-002": "The fundamental bass.", "III.02-003": "The main difficulty in composing harmony or melody lies in what we call the fundamental bass, especially at this stage. For now, it must move by consonant intervals: thirds, fourths, fifths, or sixths. Each bass note may rise or fall only by one of these intervals. Prefer the smaller move. Instead of going up a sixth, go down a third; instead of going down a sixth, go up a third. Rising a third and falling a sixth amount to the same thing. So do rising a sixth and falling a third; rising a fifth and falling a fourth; and rising a fourth and falling a fifth. We therefore need remember the interval in only one direction. The opposite move gives the same result.", "III.02-004": "EXAMPLE.", "III.02-005": "Bass movement: up or down", "III.02-006": "As we have said, the note name alone identifies the interval we want. The third of C is E. For this bass movement, E may be above or below C; the same applies to other intervals. Remember this whenever we say that the bass rises a third, fourth, fifth, or sixth. We also allow it to fall a sixth, fifth, fourth, or third respectively. If we say it falls a third, it may instead rise a sixth, and so on. This rule applies only to bass movement.", "III.02-007": "The octave is not on our list of consonant bass movements. An octave only repeats note 1, so staying on 1 has the same effect as moving to its octave above or below. Still, sometimes the bass must fall an octave to give the other parts room. In particular, this keeps them above the bass, where they belong.", "III.03-001": "CHAPTER THREE.", "III.03-002": "Begin four-part composition with the perfect chord.", "III.03-003": "A chord is several sounds arranged to be heard together. Each sound is written as a note in one of the parts.", "III.03-004": "For now, we need only the perfect chord. Put one note in the bass. Put its third, fifth, and octave in the other parts.", "III.03-005": "Use the scale from chapter I to find these intervals. Any note can be the bass. Call that bass note 1, like this:", "III.03-006": "C E G C C; 1. 3. 5. 1. or 8.; 1. 2. 3. 4. 5. 6. 7. 8.", "III.03-007": "We write 1 or 8 because the octave has the same note name as the bass. Count to the right, following the numbers around the circles that contain the scale.", "III.03-008": "Any part can take the third, fifth, or octave. The third may be above the fifth or octave, and the fifth may be above the octave, as convenient. All must stay above the bass. You may lower the bass as far as needed to leave room for the other parts. As you gain skill, however, keep each part in its natural range. The tenor goes above the bass; the haute-contre, a high voice part, above the fundamental; and the top part above the haute-contre.", "III.04-001": "CHAPTER FOUR.", "III.04-002": "On the succession of chords.", "III.04-003": "The bass moves by consonant intervals, but the upper parts move diatonically, from one note to its nearest neighbor. C can move to D or B, or stay on C, as it often will. The same rule applies to other notes. Here is how to proceed.", "III.04-005": "1. Choose the tonic, the note on which the bass begins and ends. It governs the other notes in its octave. With C as tonic, use only C, D, E, F, G, A, and B in every part. Do not add sharps or flats.", "III.04-006": "Put C in the bass and its perfect chord above it. Keep track of which upper part has the octave, which the fifth, and which the third.", "III.04-007": "2. If the bass moves up a third at A or a fourth at B, the part that had C’s octave—here the tenor—takes the fifth above the new bass note.", "III.04-008": "The haute-contre had the third above C. It now takes the octave above the new bass note.", "III.04-009": "The top part had C’s fifth. It now takes the third above the new bass note.", "III.04-010": "3. If the bass rises a fifth at C or a sixth at D, the tenor moves from octave to third; the haute-contre from third to fifth; and the top part from fifth to octave.", "III.04-011": "4. You do not have to memorize every route separately. Each upper part has only three choices: stay still, rise one diatonic step, or fall one diatonic step. These choices work whatever the bass does. If staying still gives a third, fifth, or octave above the new bass, stay still. If not, moving one step up or down will produce one of them.", "III.04-012": "If two parts land on the same note and leave a chord member missing, one of those parts had two possible stepwise choices. Reverse that part’s direction. For example, when the bass rises a fourth, the part on the fifth can fall to the octave or rise to the third. Here it must rise. When the bass rises a fifth, the part on the octave has a similar choice; here it must fall to the third above the new bass.", "III.04-014": "EXAMPLES.", "III.04-015": "Upper part. Haute-contre. Tenor. Fundamental bass.", "III.04-016": "A: rise a 3rd or fall a 6th.\nB: rise a 4th or fall a 5th.\nC: rise a 5th or fall a 4th.\nD: rise a 6th or fall a 3rd.\nRoutes between measures, marked below the bass:\nD: rise a 6th or fall a 3rd.\nC: rise a 5th or fall a 4th.\nB: rise a 4th or fall a 5th.\nA: rise a 3rd or fall a 6th.", "III.04-017": "Only six changes need remembering: 8–5 or 8–3, marked E and F; 3–8 or 3–5, G and H; 5–3 or 5–8, J and L. Bass up a third at A or fourth at B: use 8–5 at E, 5–3 at J, and 3–8 at G. Bass up a fifth at C or sixth at D: use 8–3 at F, 3–5 at H, and 5–8 at L. Thus each part’s current interval tells us its next interval for the chosen bass movement. Continue through the piece. If you cannot write all parts together, work out one part at a time.", "III.04-019": "Always include third, fifth, and octave in the three upper parts. For the first chord, any part may take any of them. After that, each follows the rule for its current interval. The rule applies both within a measure and across the barline. The same bass movement always calls for the same interval changes above it. The A movement in the first measure and at the end of the example therefore works the same way. So do the B, C, and D movements marked above and below the bass. Do not expect one particular voice always to show the same pattern: its role changes between third, fifth, and octave. The pattern belongs to whichever part currently has that interval.", "III.04-020": "After arranging the chords for the first two bass notes, apply the same process from bass note two to three, three to four, four to five, and onward. Each bass movement must be one of the allowed consonant intervals. That interval determines the movement of the other parts.", "III.04-021": "The 1 above or below each bass note shows that every chord contains 1 3 5 8.", "III.04-023": "You can now write your own bass. Begin and end on C. Between them, use any consonant movements you like, keeping C, D, E, F, G, A, and B unaltered by sharps or flats. But do not put B in the bass; our examples avoid it too. Write the first perfect chord. Then move each upper part according to its current interval and the bass’s next movement.", "III.04-024": "EXAMPLE.", "III.04-025": "Upper part. Haute-contre. Tenor. Fundamental bass. Rise by 5. 6. 4. 6. 6. 4. 4. 4. 3. 5. 3. 5. 3. 5. 5. 4. 5. 4.", "III.04-026": "Begin with two beats per measure. A beat can be a half note or quarter note; our examples use whole-note beats.", "III.04-027": "Up a sixth equals down a third. Up a fourth equals down a fifth. Remember these equivalences.", "III.04-028": "Imagination and taste decide the bass’s shape. You may first copy this bass and check whether your upper parts agree with ours. Then invent other basses. For an ending, the last bass note must follow a note a fourth below or fifth above it. Thus G must come before the final C.", "III.05-001": "CHAPTER FIVE.", "III.05-002": "Rules to follow.", "III.05-003": "1. Do not write two octaves or two fifths in succession. Check the figures: one part should not show 8 8 or 5 5. Our present method lets us avoid this fault without special effort. There is an exception in four-part music. Two successive octaves or fifths are allowed when the two parts move in opposite directions: one rises while the other falls.", "III.05-004": "Examples: two octaves and two fifths with the parts moving in opposite directions.", "III.05-005": "8. 8. 5. 5. 8. 8. 5. 5.", "III.05-006": "2. Avoid having a part rise from a minor third to an octave. We could not see this rule in the earlier examples, because major and minor had not yet been introduced. The dissonance we discuss next will make us follow the rule without needing to think about it separately.", "III.06-001": "CHAPTER SIX.", "III.06-002": "On the seventh chord.", "III.06-003": "FIRST ARTICLE.", "III.06-004": "Once you understand the consonant intervals used in perfect chords and bass movement, look at how they relate. Ignore the octave for a moment: it repeats the bass, called 1. A perfect chord has three different notes, 1 3 5. There is a third from 1 to 3 and another from 3 to 5. Add one more third above 5 and you get 1 3 5 7, the seventh chord. Its only difference from a perfect chord is the added seventh.", "III.06-005": "The added seventh is dissonant, so we call the whole chord dissonant. We may add the octave to make five parts, or to help upper parts move by steps. The octave often takes the fifth’s place. Either is acceptable: let the parts follow their natural stepwise movement. The third, however, should almost always remain in the chord.", "III.06-006": "For now, use seventh chords only where the bass both arrives and leaves by rising a fourth or falling a fifth.", "III.06-007": "Prepare and resolve the seventh with consonant intervals. The part that forms the seventh against the bass must make a third before and after it. The first third stays on the same pitch to become the seventh. The seventh then falls one diatonic step to become the following third.", "III.06-008": "Put the first seventh on a measure’s first beat. Prepare it on the previous measure’s second beat. First seventh means one that has no seventh chord immediately before it. Once the bass reaches a seventh chord by rising a fourth or falling a fifth, keep moving in those intervals until the tonic, C. Put sevenths on each bass note except C and F. C needs a perfect chord to act as tonic. F would have to move to B, which we are not allowed to use in the bass. E is also excluded because its seventh chord would require B just before it. At this stage, then, use seventh chords only on A, D, and G.", "III.06-009": "EXAMPLE.", "III.06-010": "Upper part. Haute-contre. Tenor. Fundamental bass. Rise by 3. 4. 4. 4. 4. 4. 6. 5. 5. 3. 4. 4. 3. 4. 4. 4. 5. 4.", "III.06-011": "The upper parts always show 3 7 3: the seventh between two thirds. At C, its first occurrence is prepared on the second beat, or second note, of a measure.", "III.06-012": "3 7 3", "III.06-013": "Resolving the seventh down to the third changes another part’s expected movement. Normally, a fifth rises to a third when the bass rises a fourth. But that part may also fall to the octave. With a seventh present, it must take this route because the seventh itself must fall to the third. We cannot change the seventh’s resolution, so we change the fifth at A. This is why we sometimes replace the fifth of a seventh chord with the octave: it keeps the upper parts moving by steps. Chapter IV gave the related rule: if two parts reach the same note, change whichever part can move up or down to another chord interval.", "III.06-014": "The part making a fifth can instead make another fifth if it moves opposite to the bass, as the previous chapter allowed. This may fill out the chord, restore the parts to their natural ranges, or improve the tune. Guide B shows the octave we avoided because another part already sings it at L. A composer guided by melody rather than harmony decides such matters by taste.", "III.06-015": "SECOND ARTICLE.", "III.06-016": "The seventh is the first dissonance and, in a sense, the source of all the others. Every consonance can prepare and resolve it. Its other resolutions come from the one already described, so we will leave them for later. For now, learn two more preparations. To prepare it by the fifth, let the bass fall a third. To prepare it by the octave, let the bass rise a diatonic step. When the bass rises that step, all the upper parts fall except the one becoming the seventh. That part stays still for preparation, then falls to the third.", "III.06-017": "A sixth can also prepare the seventh. We will discuss that later because we are currently studying only fundamental harmony: bass, third, fifth, seventh, or 1 3 5 7.", "III.06-018": "Only the first seventh may change the bass movement given in the first article. Only this first seventh can therefore be prepared by a fifth or octave. Every later seventh lies between two thirds. Whatever prepares a seventh, its resolution is always the third.", "III.06-019": "EXAMPLE.", "III.06-020": "Upper part. Haute-contre. Tenor. Fundamental bass. Rise by 4. 6. 4. 4. 3. 6. 6. 4. 4. 2. 4. 4. 4. 4.", "III.06-021": "Turn the page for the continuation of this example.", "III.06-022": "CONTINUATION OF THE PRECEDING EXAMPLE.", "III.06-023": "Rise by 3. 3. 5. 6. 4. 4. 4. 2. 4. 4. 5. 4.", "III.06-024": "We can now use seventh chords on E as well as A, D, and G. The bass can fall a third for preparation by the fifth, or rise a second for preparation by the octave. At C, two parts rise an octave together to return to their natural ranges. They may do this only if they do not make consecutive fifths or octaves with each other. Rules for an upper part against the bass also apply to any other pair of parts. We had not needed to mention this because the arrangement used so far avoids the problem.", "III.06-025": "If two parts can rise an octave, one certainly can. At J the bass rises an octave rather than staying on the same note. But an upper part preparing a dissonance must stay on the same pitch; it cannot make that octave leap.", "III.06-026": "Ignore the sharp on F for now. Beginners do not need to use sharps or flats until they have learned more.", "III.06-027": "The bass sometimes goes beyond its normal range, and the tenor lies above the haute-contre. We allowed this to keep the upper parts moving diatonically, our main concern at this stage.", "III.06-028": "All later teaching depends on these first principles. Learn them thoroughly and the rest becomes easier.", "III.07-001": "CHAPTER SEVEN.", "III.07-002": "Points about dissonance.", "III.07-003": "Dissonance makes composition easier rather than harder. When the bass rises a second, fourth, or sixth, some note in an upper part can stay where it is. It was consonant with the first bass note; it becomes a seventh above the second. Use this whenever you can. It often prevents a part from rising from a minor third to an octave, or, after inversion, from a minor sixth to an octave. We will discuss that elsewhere. But check what happens next: the following bass note must have a third onto which the seventh can resolve. If it does not, use the perfect chord instead.", "III.07-004": "EXAMPLE.", "III.07-005": "A. B. C. D.", "III.07-006": "I cannot use a seventh over B in the first version. The fifth over A prepares it, but it cannot resolve onto the third over C. Replace C with D, however, and the seventh over B works well: it resolves naturally onto D's third. Apply the same reasoning elsewhere. Remember that a tonic acting as tonic cannot carry a seventh chord. We are discussing only fundamental harmony here.", "III.08-001": "CHAPTER EIGHT.", "III.08-002": "Key and mode.", "III.08-003": "We called the bass's starting and ending note the tonic. It governs how the other notes in its octave move. If we choose C, we cannot add sharps or flats to C, D, E, F, G, A, or B without changing our original premise. The scale shows those notes in that order within C's octave. The French word ton is normally used for an interval, such as a third; here it chiefly means the key based on a chosen note. That note names the key and is called its tonic. It determines all the diatonic intervals—the whole tones and semitones—between neighboring notes from the tonic up to its octave. Moving through them in this way is called modulation. We must now distinguish key from mode.", "III.08-004": "Mode depends on the third above the tonic. A third is either major or minor, so there are only two modes. We usually combine the ideas of mode and key by saying major key or minor key.", "III.08-005": "Give C a major third and we call the result C major, rather than the key of C in the major mode. Give it a minor third and we call it C minor. All modulation belongs to one of these two kinds. The deciding factor is the third above the tonic. What we learn within C's octave represents every major key. The difference between major and minor is small, so we will wait until major is fully understood before studying minor.", "III.08-006": "To apply what we learn in C to every key, we need names for notes' positions rather than only their pitches. Tonic, for example, can mean any note. D, E, F, or G can be tonic just as C can. Once we choose a tonic, every other note is named in relation to it. The tonic is first; counting from it gives the second, third, fourth, fifth, and so on. In C, D is second, E third, F fourth, and so on.", "III.08-008": "Names used in any key, shown here in C.", "III.08-009": "C. Octave.\nB. Leading note.\nA. Sixth note.\nG. Tonic dominant.\nF. Fourth note.\nE. Mediant.\nD. Second note.\nC. Tonic note.", "III.08-010": "Three notes besides the tonic have special names: mediant, dominant, and leading note. The mediant and dominant help make the tonic's perfect chord. They also have special properties that distinguish them from the other notes.", "III.08-011": "Mediant means the middle note. It divides the distance from tonic to dominant into two thirds. It also decides the mode: a major third gives major mode, and a minor third gives minor mode.", "III.08-012": "The tonic dominant gets its name because it always comes immediately before the tonic at an ending. In the earlier examples, G, the dominant of C, came before every appearance of C, especially the final one.", "III.08-013": "The leading note gets its name because whenever it sounds in a part, the tonic immediately follows. It therefore makes us hear which key we are in. In C, the mediant is E, the dominant G, and the leading note B. In every key, these notes stand at the same intervals from the tonic as E, G, and B do from C. Only the mediant of a minor key differs: its third is minor rather than major.", "III.09-001": "CHAPTER NINE.", "III.09-002": "How to proceed harmonically when the bass moves diatonically.", "III.09-003": "C’s octave makes it easy to identify major and minor thirds and sixths. E, for instance, is C’s major third. Book IV, chapter II lists these intervals.", "III.09-004": "A note with a perfect chord may be considered a tonic; one with a seventh chord a dominant. But distinguish the tonic dominant from ordinary dominants. Its third must be major; other dominants often have minor thirds. In C there is only one tonic, C, so only C may take a perfect chord.", "III.09-005": "G is the only tonic dominant in C. Only G can therefore take a seventh chord with a major third.", "III.09-006": "In a sense there are only two chords: perfect and seventh. All others come from them. So far we have used them with a particular kind of bass movement. If we change that movement, the chord notes need not change. We only move a note up or down an octave. These new arrangements need new names to distinguish them from their sources.", "III.09-007": "List of consonant chords derived from the perfect chord.", "III.09-008": "1 always means the bass. Other numbers measure distance from it. 8, 10, and 12 repeat 1, 3, and 5 in another octave. If 8 repeats 1, then 10 repeats 3 and 12 repeats 5.", "III.09-009": "We can reduce numbers while keeping the same interval distances. 4 5 6 becomes 1 2 3: the distance from 4 to 5 equals 1 to 2. Likewise, 6 8 10 12 becomes 1 3 5 7. Reducing the first number to 1 identifies the bass of the perfect or seventh chord. All consonant and dissonant chords come from those two.", "III.09-010": "We leave 8 out of the chord lists because it simply repeats bass note 1.", "III.09-011": "Figures placed above or below bass notes to indicate every sound in a chord.\n\nThe perfect chord consists of:\n C. E. G.\n 1. 3. 5.\nThis chord always occurs on the tonic and sometimes on its dominant.", "III.09-012": "Chords derived from the perfect chord by inversion.", "III.09-013": "6. The sixth chord consists of:\n E, G, C, inverted from C, E, G,\n 1. 3. 6. 6. 8. 10.\n 1. 3. 5.\nThis chord always occurs on the mediant.\n\n6.\n4. The sixth–fourth chord consists of:\n G, C, E, inverted from C, E, G,\n 1. 4. 6. 4. 6. 8.\n 1. 3. 5.\nThis chord occurs only on the dominant, but more rarely than the perfect or seventh chord.", "III.09-014": "List of dissonant chords derived from the seventh chord.", "III.09-015": "7. The tonic dominant’s seventh chord consists of:\n G, B, D, F.\n 1. 3. 5. 7.", "III.09-016": "Chords derived by inversion.", "III.09-017": "Slashed 5. The diminished-fifth chord consists of:\n B, D, F, G. inverted from G, B, D, F.\n 1. 3. 5♭. 6. 6. 8. 10. 12.\n 1. 3. 5. 7.\nThis chord occurs only on the leading note.\n\n6♯. The small-sixth chord consists of:\n D, F, G, B. inverted from G, B, D, F.\n 1. 3. 4. 6. 4. 6. 8. 10.\n 1. 3. 5. [7 illegible]\nThis chord ordinarily occurs on the key’s second note.\n\n4♯. The tritone chord consists of:\n F, G, B, D. inverted from G, B, D, F.\n 1. 2. 4♯. 6. 2. 4. 6. 8.\n 1. 3. 5. 7.\nThis chord occurs only on the fourth note.", "III.09-018": "The tonic’s perfect chord can be transferred only to its mediant or dominant. It becomes a sixth chord over the mediant and a sixth–fourth over the dominant. Knowing those notes in a key therefore tells you their chords. Still, the dominant more naturally takes a perfect chord than a sixth–fourth, and especially takes a seventh chord just before the tonic. The difference between perfect and seventh chords is only one added note. You may remove it and play the perfect chord wherever the seventh chord was required. But know which note you remove and why. The seventh chord generates all dissonant chords. You need to understand both its notes and what chord follows it, because these determine the behavior of its derivatives.", "III.09-020": "A dominant’s seventh chord can lead not only to the tonic itself but to the tonic chord’s inversions over mediant or dominant. The dominant can even change from a seventh chord to a sixth–fourth while staying on the same bass note, if there is time and the composer wishes. The tonic’s inversions receive the same approach as the tonic; the dominant seventh’s inversions must likewise lead directly to tonic harmony or an inversion. So study a chord’s notes, its natural movement, and its possible arrangements. Moving an upper note to the bass changes its name so we know which note is lowest. Mediant and dominant can represent the tonic through inversions of its perfect chord. Likewise any note of the dominant seventh can become bass before tonic harmony, provided the other chord notes accompany it. In C, G, B, D, or F before C or E must be accompanied by the other three notes of G B D F. We leave G out as a destination here because G’s seventh chord is our starting subject.", "III.09-021": "A dominant may take a perfect chord or seventh chord, and the seventh still contains the perfect chord. Therefore both receive the same approach. Every seventh-chord bass note has its own dominant, a fifth above or fourth below. D is consequently G’s dominant. When D leads to G in that relationship, it needs a seventh chord: D F A C, following the same pattern as G B D F. Any of D, F, A, or C used as bass directly before G must carry that set of notes. Any of G, B, D, or F before C must likewise carry G B D F. Dissonant harmony is thus a chain of dominants. The basic chain is easy; the earlier examples show it. The difficult part is relating it to bass lines that choose different notes from each perfect or seventh chord. That can demand all our attention. Restrict the problem to one octave and it becomes easier: learn how consonant harmony is approached, since dissonant harmony is approached the same way. Use scale-position names rather than fixed pitches so the reasoning works in every key. Once all you need to identify is the tonic, the difficulties quickly disappear.", "III.09-023": "The tonic takes a perfect chord, and the mediant a sixth chord. The dominant takes a perfect chord unless it comes directly before the tonic. Then add F to G B D, making its seventh chord.", "III.09-024": "In a stepwise bass, the second note lies between tonic and mediant. There it can take only the small-sixth chord D F G B.", "III.09-025": "The leading note rising to tonic takes B D F G, the diminished-fifth chord. If it descends instead to a note outside the tonic chord, treat it as the dominant’s mediant. It is the dominant’s third, so give it B D G, a sixth chord inverted from G B D.", "III.09-027": "When the fourth note rises to the dominant, use the same kind of approach as leading note to tonic. Both destinations need equivalent preparation. G governs C, and D similarly governs G. In C, the fourth note F therefore takes F A C D, the great-sixth chord inverted from D F A C.", "III.09-028": "The name great sixth marks a small difference from the diminished-fifth chord. Its fifth is perfect, not diminished. This follows from the underlying thirds: G–B major, D–F minor. The two chord arrangements are otherwise alike; both place the third of a seventh chord in the bass. Later we explain why derived chords get different names here while fundamental chords do not.", "III.09-029": "When the fourth note falls to the mediant, give it F G B D, the tritone chord.", "III.09-030": "The sixth note before dominant or mediant takes A C D F, a small-sixth chord derived from D’s seventh chord; D is G’s dominant. This parallels the second note’s small-sixth chord before tonic or mediant.", "III.09-031": "Compare these rules with the chord list to see the complete pattern. A dominant can be treated like a tonic because both receive the same chord approaches. In a stepwise bass, identify which notes belong to those tonic and dominant chords, then check what follows each. One bass note can belong to two different fundamental chords. The next note tells you which chord to choose. Keep the full three-note perfect chord or four-note seventh chord in mind when supplying the upper accompaniment.", "III.10-001": "CHAPTER TEN.", "III.10-002": "The continuo bass.", "III.10-003": "Do not confuse the stepwise bass movement we now discuss with the consonant bass movement shown earlier under perfect and seventh chords. Those two chords are the fundamental ones. To show this, we will add a fundamental bass beneath later examples. It will carry only perfect chords or seventh chords. The ordinary bass, which we call the continuo bass, may carry any kind of chord. The whole forms perfect harmony together. The fundamental bass will therefore check all our compositions. It will show that the different chords come only from movement opposed to its own, as we have explained. Measured from either bass, however, the chords are essentially unchanged. The difference is simply that we can put any note of a fundamental chord into the bass. The complete collection of chord notes stays the same, and their prescribed movement in the fundamental chords does not change.", "III.11-001": "CHAPTER ELEVEN.", "III.11-002": "Bass progression as the simultaneous determinant of chord progression; how to relate a derived chord to its foundation.", "III.11-003": "Tonic, mediant, and dominant can move freely when carrying consonant chords, provided the bass stays in the key. We are using only C major’s notes, C D E F G A B, so this is straightforward.", "III.11-004": "Dissonant chords restrict bass movement. This includes the dominant seventh and all its inversions—in fact, every chord other than a perfect chord or its inversions. A dissonant bass note governs another note. If its chord is not a seventh chord, it comes from one. Find that fundamental seventh chord and you know what harmony follows, regardless of the actual bass note.", "III.11-006": "A dissonant chord always has two neighboring notes or numbers: 3 4 [F G], 5 6 [C D], and so on. In a seventh chord, move the bass up an octave to reveal 7 8 [F G]. A second gives 1 2 [C D]. Choose the higher of the pair as fundamental bass. The lower becomes its seventh. This reduces the chord to 1 3 5 7, as the page 202 list shows. Fundamental G must move next to C. If the actual bass lacks C, it must contain a note of C’s perfect chord—or seventh chord if we are in another key. Fundamental D similarly leads to G or its derivatives. After a seventh chord, the fundamental bass always falls a fifth.", "III.11-007": "A bass that breaks this succession must be changed. Check either the chords required by each scale note and its movement, or the fundamental bass. The latter carries only perfect or seventh chords; each seventh-chord root then falls a fifth. This rule helps both check an existing bass and write a new one. Leave exceptions such as interrupted and irregular cadences for later.", "III.11-008": "Before the example, remember to look forward. A chord leading naturally to a perfect chord is chosen according to what follows, not what came before. The progression usually goes between tonic and dominant, treating dominant as another tonic. Thus, in stepwise movement, the same approach patterns work for both. Here are the general rules.", "III.11-010": "1. A bass note rising a whole tone or semitone to a perfect chord takes a great-sixth or diminished-fifth chord.", "III.11-011": "EXAMPLE.", "III.11-012": "Great-sixth and diminished-fifth chords before the perfect chord.", "III.11-013": "Only the bass differs between these two chords. The upper notes stay the same whether the bass rises a whole tone or semitone. The composer may choose either, even if the semitone lies outside the original key. Treat the dominant as a tonic, and you may approach it as one. Sharpening the fourth note gives it a leading note. The size of the ascending step distinguishes the usual approaches: a whole tone to dominant, a semitone to tonic. Even if a semitone makes the dominant sound fully like a tonic, the music may return to its original key afterward. A perfect chord leaves us free to move on as we wish.", "III.11-015": "2. A bass note descending to a perfect chord takes a small-sixth chord.", "III.11-016": "EXAMPLE.", "III.11-017": "Small-sixth chord; mediant guide notes.", "III.11-018": "The guide notes show that the bass can go instead to the mediant of either perfect-chord note. The harmony stays the same, but the mediant takes a sixth chord.", "III.11-019": "Here we cannot distinguish a second note, nor a tonic from a sixth note or dominant. Tonic and dominant perfect chords require the same approach, so major mode does not distinguish them here. Minor does: the sixth falls only a semitone to dominant, whereas the second lies a whole tone above tonic. Also, dominant always has a major third while minor tonic has a minor third. If major mode leaves the dominant uncertain, simply treat it as a tonic and fit the preceding chords to its key. The next notes will reveal its actual role.", "III.11-020": "EXAMPLE.", "III.11-021": "Bass progressions, references A, B, C, D, F, G.", "III.11-022": "The move from the opening note to A leaves A’s role uncertain: tonic or dominant. That does not affect the required chords. But A–B leads to a tonic, proving A is dominant. B–C is likewise unclear until D identifies C as dominant. F also identifies G as dominant. In every key the note just below tonic is a semitone away; the note just below dominant is a whole tone away.", "III.11-024": "In minor, descending from tonic toward dominant or at least the sixth note may put the next lower note a whole tone below tonic. The tonic is still easy to recognize by its minor third, since dominant must have a major third.", "III.11-025": "3. A note a third above or below tonic or dominant takes a sixth chord when moving to either of them.", "III.11-026": "EXAMPLE.", "III.11-027": "Sixth chords leading to tonic or dominant.", "III.11-028": "Because the bass leads to perfect chords at B, D, G, and L, it needs sixth chords at A, C, F, and J.", "III.11-029": "4. The mediant’s sixth chord contains the tonic’s perfect chord, so the mediant represents tonic. The fourth note falling to it takes a tritone chord. A great-sixth chord is also possible, but we explain that elsewhere.", "III.11-030": "EXAMPLE.", "III.11-031": "Tritone on the fourth note descending to the mediant.", "III.11-032": "Compare these five examples. The same fundamental chord notes are rearranged as the bass moves differently. Fourth rising to dominant: great sixth. Fourth falling to mediant, representing tonic: tritone. Leading note rising to tonic: diminished fifth. Second or sixth falling to tonic or dominant: small sixth. Each comes from the seventh chord that governs the next bass note. The fundamental bass under the complete octave example makes this clear. A leading note functions as such only while rising to tonic. If it descends, treat it as the dominant’s mediant, and temporarily treat dominant as tonic to avoid mistakes.", "III.11-033": "General example of the octave, ascending and descending.", "III.11-034": "General octave example—five parts.", "III.11-035": "The fundamental bass is added only to show that perfect and seventh chords account for all the harmony and follow their natural progression. Do not check strict voice-leading rules between this analytical bass and the other parts. Check only that the harmonies match the figures. The voices’ actual movement belongs to the continuo bass, whose stepwise progression is the subject here.", "III.11-036": "1. The ascending passages J–L and B–M and descending passages N–K and O–U all lead to dominant or tonic. Only those two notes naturally take perfect chords in a key. Notes a third above them act as their mediants when descending to them; the tonic mediant keeps its identity in any direction. A perfect chord follows the dissonant chord that governs it. Thus the small-sixth, great-sixth, diminished-fifth, and tritone chords all come from the seventh chords shown in the fundamental bass. The small sixth on second, diminished fifth on leading note, and tritone on fourth come from the tonic dominant’s seventh at D, followed by tonic. The great sixth on fourth and small sixth on sixth come from the second note’s seventh at A and C, followed by the tonic dominant it governs. Ordinary sixth chords on mediant, sixth, and leading note occur because those notes are a third above or below the next tonic or dominant.", "III.11-038": "2. The sixth note at B seems to need a small-sixth chord to match fundamental B’s seventh. We leave out one of its dissonant sounds. First, either version is acceptable. Second, the next bass note is the leading note, a major dissonance. Dissonances should not be doubled. A small-sixth chord here would send its third down onto that same leading note and double it. Finally, our sixth-chord rule still applies because the bass is heading to a perfect-chord note a third away.", "III.11-039": "3. Suppose fourth note R in the continuo were replaced by second note A or C, or sixth note T, just before dominant L or K. The fourth note in the harmony would then need a sharp, as at S. Perfect chords like to be approached through their leading notes. There is an exception in minor keys. The sixth falls a semitone to dominant, and the dominant’s own leading note cannot sound there, whatever the preceding bass note. If it did, the dominant would become tonic, with the true key clarified only afterward. Our example shows how later notes reveal whether an apparent tonic is really dominant. The tritone chord therefore comes from the seventh chord on that dominant, marked D in the fundamental bass.", "III.11-041": "4. At F, G, and H, the stepwise continuo bass makes the upper parts depart from their normal movement. They must do this to avoid consecutive fifths or octaves, return to their proper ranges above the bass, or include every chord note.", "III.11-042": "Upper parts are required to move by steps only when the bass moves by consonant leaps. If the bass changes its method, they may too. Breaking stepwise movement can also make a melody more varied. We could rearrange the upper parts’ order and movement without mistakes, but that is for later.", "III.11-043": "5. The example has several unprepared sevenths, contrary to our first rule. We will explain those later. For now, follow the chord order shown through the octave. Later we will see that after consonant harmony, movement is free within modulation’s rules.", "III.11-044": "6. The previous book said that when a fundamental bass rises a tone or semitone, a third and fourth are implied. Inserted Y between Z and A shows them. Z’s fifth prepares the seventh, and the third prepares A’s seventh. The basic chords do not change. Without Y, the second Z–A uses the same note names as the seventh A–X.", "III.12-001": "CHAPTER TWELVE.", "III.12-002": "More rules from the previous example.", "III.12-003": "When a bass note needs a seventh chord, you may leave out the seventh unless a consonance in the previous chord has prepared it. But if that consonance is a major third or major sixth, it is better to raise it a semitone. If the chord is an inversion derived from a seventh chord, you may leave out either of the two sounds creating the dissonance. They are easy to find: they always lie next to each other, as chapter XI explains.", "III.12-004": "You may repeat a bass note as often as good taste allows. Give it the same chord, or change its chord as we learn how to do so.", "III.12-005": "You may also move to a different bass note while keeping a chord that changes only its name. Start with a seventh chord. Move the bass to its third and you can use the diminished-fifth chord; move to its fifth and you can use the small-sixth chord; move to its seventh and you can use the tritone chord. All contain essentially the same harmony. Apply the same principle in similar cases. The next example shows this.", "III.12-006": "The same chords in different inversions.", "III.12-007": "Suppose a bass note is a third above the next bass note, and that next note takes a perfect or seventh chord. The first note should usually take an inversion of the following chord. At A, the sixth chord comes from the following perfect chord. At B, the great-sixth or diminished-fifth chord comes from the following seventh chord.", "III.12-008": "When the bass changes its place within a chord without changing the harmony, the upper parts may stay still if the chord is consonant. A dissonant chord must still contain all four different sounds. One way is to add the octave of the note being left at D, if that octave was absent from the earlier chord on the same fundamental-bass note. Another is to remove the octave of the current note at J and replace it with the octave of the note being left at C.", "III.13-001": "CHAPTER THIRTEEN.", "III.13-002": "The perfect cadence.", "III.13-003": "A melody ending on the tonic after its dominant makes a perfect cadence. Put the tonic on the measure's first beat so the ending is clearly felt. The dominant before it should carry a seventh chord, or at least a perfect chord. The seventh may be implied rather than played. See the example.", "III.13-004": "Perfect cadence: arrangements and fundamental bass.", "III.13-005": "The perfect cadence tells us which bass notes need perfect chords. Wherever the melody feels at rest, a perfect chord must sound. We feel that rest not only in the cadence's usual bass movement, but also when the bass follows one of its accompanying parts. The example shows these arrangements. Each part has figures showing the chord it would take as bass. A perfect chord can follow either a great-sixth chord or a diminished-fifth chord. As long as we stay in the same key, the melody can rest only on the tonic or dominant. This gives us a clear guide. Whatever route the continuo bass follows, we can hear and identify its points of rest and the chords that must come before them. The figures on each part show what these are for its particular movement. Any part can become the bass; the remaining parts then accompany it.", "III.13-006": "Next we will clarify this by looking at the leading note: its force at a cadence, how it identifies dissonances, and how it governs the order of chords.", "III.14-001": "CHAPTER FOURTEEN.", "III.14-002": "The leading note and how dissonances resolve.", "III.14-003": "When a dissonant chord contains the leading note, it points to a melodic ending. The tonic's perfect chord must follow, either with the tonic in the bass or in a derived form. Without the leading note, a dissonant chord does not determine an ending. Another dissonant chord must follow it, and the chain continues until the leading note appears. It then brings an ending, or something resembling one—for example, an arrival on the mediant instead of the tonic. Our earlier seventh-chord examples show this. One seventh chord follows another until we reach the tonic dominant, where the leading note sounds.", "III.14-004": "There is an exception. A great-sixth chord on the fourth note can move to the dominant's perfect chord. That great-sixth chord is dissonant even though it does not contain the leading note.", "III.14-005": "For now, identify the leading note in a dissonant chord by finding a diminished fifth or tritone. It may lie between upper parts or between a part and the bass. But those two notes must also be the major third and seventh of a fundamental seventh chord. Its root must be the tonic dominant; otherwise the rule fails. In C, the notes are B and F. Their order makes either a diminished fifth or a tritone. B is G's major third, and F is its seventh; G is the tonic dominant.", "III.14-006": "EXAMPLE.", "III.14-007": "Tritone and diminished fifth: leading notes and guide notes showing resolution.", "III.14-008": "The perfect-cadence example showed the same relationship. Choose any part as bass, and the other parts form its chord. A diminished fifth or tritone will still be present. The interval's name changes only because the same two notes change position.", "III.14-009": "The guide-note signs after these intervals show where they naturally move. The perfect-cadence example shows the same movement with ordinary notes. This gives us a firm rule for the movement of every dissonance. We call that movement resolution.", "III.14-010": "We divide dissonances into major and minor, just as we divide thirds.", "III.14-011": "A major dissonance is formed by the leading note. The leading note naturally rises a semitone to the tonic, as the examples show. Every major dissonance must therefore rise in the same way.", "III.14-012": "If you know the key, look for the note a semitone below the tonic. When that note appears in a dissonant chord, it is the major dissonance. If you do not know the key, work back to the chord's foundation. The major dissonance is always the major third of a tonic dominant carrying a seventh chord. So that major third can be treated as a major dissonance. The same applies to the leading note under its diminished-fifth chord, the major sixth above the second note of the key, and the tritone above the fourth note.", "III.14-013": "A minor dissonance is formed by the note a seventh above the fundamental bass. It resolves by falling one diatonic step. The seventh and diminished fifth belong to this class.", "III.14-015": "If a dissonant chord has no major dissonance, it contains only the minor one. But whenever a major dissonance is present, the minor one is present too. Both still follow their prescribed movements.", "III.14-016": "This explains all the different resolutions at once. The dissonant notes do not change their own required movements. What varies is the bass: it may move to any note of the chord that should naturally follow. Always refer chords to their foundations to understand this.", "III.15-001": "CHAPTER FIFTEEN.", "III.15-002": "The eleventh, usually called the fourth.", "III.15-003": "A dissonant chord usually comes just before a perfect cadence. People have called it the fourth,* but eleventh would be a better name. Here it differs from a perfect chord only because the fourth replaces the third. It appears only over a bass note that should naturally take a perfect or seventh chord. One of those chords then follows on the same bass note. The fourth resolves by falling one diatonic step to the third it replaced. This makes it a minor dissonance. Like other minor dissonances, it comes from the seventh above the fundamental sound. We will explain why when discussing supposition. For now, the example shows all its preparations and resolutions.", "III.15-004": "* See Book II, chapter XI.", "III.15-005": "EXAMPLE.", "III.15-006": "Preparing the eleventh or fourth with the 3rd, 4th, 5th, diminished fifth, 6th, 7th, or 8th.", "III.15-007": "We still write 4 for the eleventh, following custom. The example shows it prepared by every consonance, and even by a diminished fifth or seventh. Look at each pair joined by the curved mark ⌢. The preparation always falls on a measure's last beat; the dissonance sounds on the next first beat.", "III.15-008": "Learn these preparations carefully in C. Their differences come only from different bass movements. The same patterns work in every key. This dissonance does not quite belong at this point in our discussion. Still, it almost always comes immediately before a perfect cadence, and some authors treat the two together. We have followed their example here.", "III.16-001": "CHAPTER SIXTEEN.", "III.16-002": "On the irregular cadence.", "III.16-003": "An irregular cadence* usually moves from tonic to dominant. A perfect cadence does the reverse, from dominant to tonic. The perfect cadence falls a fifth; the irregular one rises a fifth. An irregular cadence can also move from the fourth note to the tonic, because falling a fourth is equivalent to rising a fifth. Both bass notes naturally take perfect chords. But adding a sixth to the first chord makes the ending clearer and produces a pleasing flow of harmony and melody.", "III.16-004": "Adding that sixth creates the great-sixth chord. The fourth note naturally takes this chord when it comes just before the tonic dominant. Use that same chord on the fourth note, but move next to the tonic’s normal chord: this makes an irregular cadence. Another irregular cadence moves from tonic to dominant with an added sixth in the tonic’s chord.", "III.16-005": "* See Book II, chapter VII.", "III.16-006": "EXAMPLE.", "III.16-007": "Irregular cadences A and B.", "III.16-008": "(A) Irregular cadence from the tonic to its dominant.\n(B) Irregular cadence from the fourth note to the tonic.", "III.16-009": "The added sixth clashes with the fifth, so the sixth is the dissonance. It cannot fall onto the fifth; it must rise to the next chord’s third. The previous example marks this with ╱ between the first chord’s sixth and the following third.", "III.16-011": "Invert the chord with its added sixth and we gain an easy way to write four or five parts over several successive bass notes. One part can keep moving in sixths with the bass without breaking any rule. The fundamental bass verifies the harmony.", "III.16-012": "EXAMPLE.", "III.16-013": "Part always making the sixth; continuo bass and fundamental bass.", "III.16-014": "See this example in the Supplement", "III.16-015": "(A) (B) Irregular cadences in which the sixth is added to the perfect chord on note A.", "III.16-016": "All six parts could play together except at J, where the fundamental bass rises a second to a note carrying a seventh. One part there makes two consecutive fifths with the fundamental bass and would need changing. Focus on the two parts that move in sixths both upward and downward. The added sixth lets us easily add three other parts to them. The entire progression still uses only three different chords.", "III.16-017": "At C, the tonic’s perfect chord becomes a sixth chord when its mediant is in the bass. At D, it becomes a sixth–fourth chord over its dominant. At F, the tonic dominant’s seventh chord becomes a small-sixth chord over the second note. At G, it becomes a tritone chord over the fourth note.", "III.16-018": "At H, the fourth note takes a perfect chord with an added sixth. Over sixth note L, this becomes a small-sixth chord. This chord does not always form an irregular cadence, however. When it does not, its source is the seventh chord on second note J, where its natural movement is shown.", "III.16-019": "Before musicians understood the small- and great-sixth chords heard so effectively here, adding even two parts correctly to the pair moving in sixths was almost impossible. Now we can easily add three, and even add the fundamental bass. Study inversion carefully: take any note of the required fundamental chord as bass and put the remaining notes above it. Keep the harmony consistent with either of the two cadences just discussed, or with the natural fundamental-bass movements shown at the start of this book. A bass may move freely after a consonant chord, but the movement chosen limits which chord can follow. If you cannot easily identify the fundamental bass, look at each note’s place in the key. We are still working only in C. Learn the chord appropriate to each note and each movement, and supply it correctly. With practice you can judge between two possible chords on one note. In the example, the fourth note may take a tritone chord or a great-sixth chord. It may also take both, but the great-sixth must come first. These choices apply when it moves to the mediant or tonic. Curved marks above and below the parts identify these passages: H C; G C; H G.", "III.16-021": "H C; G C; H G.", "III.16-022": "If the bass moves like a fundamental bass, give each note a fundamental chord. One exception is the move from the sixth note to the mediant: an inverted irregular cadence fits especially well there.", "III.16-023": "EXAMPLE.", "III.16-024": "Figured bass A–N; cadence H–J and its fundamental bass.", "III.16-025": "Second note A gets a seventh chord because the move from A to B is a fundamental-bass movement.", "III.16-026": "B also gets a seventh chord. Its seventh has been prepared by the minor third over A. Keep that note still instead of raising it to the octave, which is strictly forbidden. There is an exception when the note is doubled in more than three parts: one copy may rise if the other stays still and follows the rule. At B the leading note sounds, so it must rise to the tonic, and the tonic’s perfect chord must sound. The bass does not contain the tonic there, only its dominant. I therefore give the dominant at C a sixth–fourth chord to represent the tonic’s perfect chord.", "III.16-028": "Fourth note D falls to the mediant. I could give it either a great-sixth chord or a tritone chord.", "III.16-029": "Mediant F must take a sixth chord because no other chord can resolve the dissonance before it. Its move to sixth note G is a fundamental progression, but resolving the dissonance comes first.", "III.16-030": "Inverted irregular cadence between H and J. See the fundamental bass below.", "III.16-031": "L must take a great-sixth chord. It contains the same notes as M’s seventh chord a third below, following chapter XII’s explanation.", "III.16-032": "M takes a seventh chord for the same reason as A.", "III.16-033": "M, N prepare the eleventh, which in turn prepares the following perfect cadence.", "III.17-001": "CHAPTER SEVENTEEN.", "III.17-002": "Related bass movements that keep the upper harmony the same.", "III.17-003": "The tonic, mediant, and dominant can carry chords made of the same notes. So when a bass would naturally move to the tonic, you may replace the tonic with either the mediant or dominant. When it would move to the mediant, you may use the tonic instead. Similarly, a dominant taking a seventh chord can be replaced by its third, fifth, or seventh. If it takes only a perfect chord, use its third or fifth instead.", "III.17-004": "See the following example.", "III.17-005": "EXAMPLE.", "III.17-006": "Arrivals on the tonic, mediant, and dominant.", "III.17-007": "Do not apply the last four arrivals, or the next four, to the dominant. They would make it sound like a tonic.", "III.17-008": "EXAMPLE.", "III.17-009": "Tonic preceded by dominant A, fourth note B, leading note C, or second note D.", "III.17-010": "Our examples start on the tonic, but they could start on the mediant or dominant too. The guide notes show these choices.", "III.17-011": "Guide notes for starting notes: silent alternatives.", "III.17-012": "This does not refer to the start of a piece. A piece must begin with the tonic. Fugues and similar writing can break this rule, but we have not studied those yet.", "III.17-013": "When the second note comes directly before the tonic dominant, it acts as that note’s dominant and needs a seventh chord. You can replace it with its third or fifth. Its seventh is rarely suitable as a replacement because it is the tonic. At this stage, a tonic acting as tonic can take only a perfect chord.", "III.17-014": "See the Supplement", "III.17-015": "EXAMPLE.", "III.17-016": "Dominant preceded by the second note or its derivatives.", "III.17-017": "You can now exchange these bass notes as long as the succession of harmonies stays the same. Check this by relating the chords to their fundamental bass.", "III.17-018": "See the following example.", "III.17-019": "EXAMPLE.", "III.17-020": "Second note, tonic dominant, and substitutions A–F.", "III.17-021": "The second note acts as dominant of the tonic dominant and supplies the fundamental bass for the other examples.\nAt A, the second note replaces the tonic dominant.\nAt B, the fourth note replaces the second note, while the second note at C replaces the tonic dominant.\nAt D, the fourth note replaces the second note; at F it replaces the tonic dominant.", "III.17-022": "Substitutions through leading note G and sixth note H.", "III.17-023": "After the fourth note, leading note G replaces the tonic dominant.\nThe same substitution with a different movement.\nSixth note H replaces the second note when that second note acts as dominant of the tonic dominant. The tonic dominant is again represented by its 3♯, the leading note G.", "III.17-024": "When the bass moves by steps, the dominant often takes a sixth–fourth chord more suitably than a perfect chord. This is especially true on a weak beat.", "III.17-025": "Together with the material from the start of this book, this briefly covers all bass movements used in the most natural harmony. Some dissonances remain to be discussed, but their possible movements are tightly limited. Once you fully understand what we have covered, their use will be easy to learn.", "III.18-001": "CHAPTER 18.", "III.18-002": "How to prepare dissonances.", "III.18-003": "When we explained how to prepare and resolve a seventh, we also meant to explain all dissonances, because the seventh is their source. We divided dissonances into major and minor. Only minor dissonances must follow every rule of the seventh. Major dissonances come from the leading note, although that note also belongs to a seventh chord. The leading note needs no preparation. So none of the major dissonances needs it either: see Book Two, Chapter XIII. A seventh, however, must be prepared by a consonance. The same is true of every minor dissonance. If we stay in the key we are treating, we can therefore sound a dissonance when its note was a consonance in the previous chord. We can also do this when moving between keys, once we know how to connect them pleasantly. Remember two earlier points. One note can serve several dissonances in succession if the chords containing it are fundamentally the same chord. Also, a seventh or diminished fifth can prepare an eleventh, even though both are dissonances. A note that has already formed a dissonance can therefore form another in a chord that seems different in some respect, as long as we do not change key in that situation.", "III.18-004": "We said that only a third, fifth, or octave could prepare a seventh. That rule refers to the bass's fundamental progression. Its most natural movements are down a third, a fifth, or a seventh. Going up a second is equivalent to going down a seventh; other intervals have similar relationships. Usually choose the smaller of two related intervals for the bass. For instance, prefer up a second to down a seventh, and apply the same principle elsewhere. Chord inversion changes what these intervals are called. We can place any note of a fundamental chord in the bass. The chord then receives a different name because its notes form different intervals above the new bass note. In one place, a sixth or fourth will therefore prepare a seventh instead of a third or fifth. In another, a third, fourth, fifth, sixth, or even octave will prepare a diminished fifth. The diminished-fifth chord, like every other dissonant chord, represents the seventh chord. So any consonance can prepare a dissonance without error, provided we do not deliberately avoid the natural movement. Here is an example. Replace the tonic in the bass with its mediant or dominant, using the chord derived from the tonic's perfect chord. Suppose the tonic's octave, fifth, or third is to prepare a seventh. That octave becomes a sixth above the mediant or a fourth above the dominant. The fifth and third change in corresponding ways. Our first rule for sevenths therefore covers every minor dissonance. The same reasoning applies after a tonic's perfect chord, whether its bass is the tonic, mediant, or dominant. Instead of sounding the seventh that one of the perfect chord's consonances must prepare, we may sound a diminished fifth, tritone, great-sixth chord, small-sixth chord, and so on. This happens because we have put another note of the seventh chord in the bass in place of its fundamental note.", "III.18-006": "EXAMPLE.", "III.18-007": "Preparing dissonances — first series", "III.18-008": "Continuation of the previous example.", "III.18-009": "Preparing dissonances — continued", "III.18-010": "1. At A, an octave prepares the seventh in fundamental harmony. At D, the bass is the mediant, so that octave becomes a sixth above it. At F, the bass is the dominant, so the octave becomes a fourth.", "III.18-011": "The octave, sixth, and fourth can therefore prepare the seventh. At G, in a great-sixth chord, the fifth represents the seventh and is prepared by an octave. The cue signs above the mediant and dominant show two other preparations for this fifth: the sixth and fourth above those notes. Read the other cue signs in the same way.", "III.18-012": "At H, the third in the small-sixth chord represents the seventh. An octave, sixth, or fourth prepares it.", "III.18-013": "At J, the second is prepared in the bass. A third comes before it in the upper part.", "III.18-014": "2. At B, the fifth prepares the seventh in fundamental harmony.", "III.18-015": "At L, the fifth of the great-sixth chord represents the seventh. A fifth, third, or octave prepares it.", "III.18-016": "At M, the third of the small-sixth chord represents the seventh. A fifth, third, or octave prepares it.", "III.18-017": "At N, an octave prepares the second, or the fourth marked by a cue sign does so.", "III.18-018": "3. At C, the third prepares the seventh in fundamental harmony.", "III.18-019": "At O, the fifth of the great-sixth chord is prepared by the third above the fundamental note to which the seventh is added.", "III.18-020": "At P, a fourth prepares the same fifth. This fourth is above the note that forms the seventh of the fundamental bass. That note must carry the second chord.", "III.18-021": "At Q, prepare the second as at J.", "III.18-022": "At R, the same fifth is prepared by a sixth above the dominant of the fundamental bass note. Notice the general rule: the dominant of any note can always stand for that note. It then carries an inversion of the perfect or seventh chord that the other note should have carried. The resulting inversion is a sixth–fourth or small-sixth chord.", "III.18-023": "At S, an octave prepares the same fifth. It is the octave of the note that forms the third, or mediant, of the fundamental bass note.", "III.18-024": "At T, a third, sixth, or octave prepares the third of the small-sixth chord. The preceding seventh resolves to a sixth above the same note above which the seventh sounded.", "III.18-025": "We have not yet discussed the second. Before we say more, remember that it prefers only the kind of preparation just described.", "III.18-026": "Every way of preparing a dissonance comes from the preparation of the seventh. The main difficulty is recognizing which bass notes belong to the chord of the fundamental note. Concentrate fully on this. Otherwise everything remains doubtful and we have no firm guide. Remember that the first dissonant chord must always follow a consonant chord. That consonant chord is the perfect chord of the tonic, the dominant, or the fourth note of the key. A sixth chord on the mediant of any of those three notes can represent its perfect chord. A sixth–fourth chord can also represent it, but only on the tonic's dominant.", "III.18-027": "In music for only two or three parts, we often play only the consonant notes of a chord that also contains a dissonance. Unless we follow the bass progression and know the key, our rules are useless. We must therefore make every effort to understand them. We give the rules in C alone because understanding that key is enough for all the others. After that, we only need to learn to distinguish the keys.", "III.18-028": "A piece must begin with a consonant chord. A dissonant chord therefore comes only after a consonant one. But another dissonant chord often follows it. We have said that a consonant chord cannot come after a dissonant one unless the leading note can be recognized in that dissonant chord. Otherwise, as the rules for the seventh show, dissonant chords keep following one another. This can be hard to recognize in two- or three-part music. A dissonant chord always contains at least two consonances: the third and fifth, or their inversions, the sixth and fourth. An octave may occur too. We may therefore move between dissonant chords without realizing it. If we want to understand what we are doing, we must not neglect these basic principles. Complete understanding should give us our greatest satisfaction.", "III.19-001": "CHAPTER 19.", "III.19-002": "When dissonances cannot be prepared.", "III.19-003": "Suppose the fundamental bass goes up a third, fifth, or seventh instead of down by those intervals. We then find that the seventh can no longer be prepared. Yet these progressions seem to compel us to sound it. The diatonic octave progression in Chapter XI shows this: we go from the tonic to the dominant, then immediately back to the tonic. See also Book Two, Chapter XIII. All masters accept this, and it does not offend the ear.", "III.19-004": "If the bass rises a third and then immediately falls a fifth, we also cannot prepare the seventh over the note reached by the rise.", "III.19-005": "EXAMPLE.", "III.19-006": "Rising a fifth or third — unprepared seventh", "III.19-007": "Example A shows the equivalent of a rising fifth. It begins on the mediant, which stands for the tonic. Example B shows why a rising third in the fundamental bass prevents preparation of the seventh. The note that makes a seventh with the second bass note cannot make a consonance with the first bass note.", "III.19-009": "We could put a major third above the second bass note in Example B. The key would then change. This happens very often, especially in inverted harmony, as shown here.", "III.19-010": "EXAMPLE.", "III.19-011": "Inverted harmony — parts exchanging roles", "III.19-012": "Each part can act either as the upper part or as the bass. This shows how a diminished fifth, tritone, or seventh can appear without preparation.", "III.19-013": "For a bass rising a seventh or falling a second, where the seventh cannot be prepared, see Book Two, Chapter XIII.", "III.19-014": "An unprepared dissonance is allowed only after a consonant chord. If the preceding chord is dissonant, preparation is required without exception, under the rules already given.", "III.19-015": "Do not include the leading note among the prepared or unprepared dissonances discussed here. These rules concern only minor dissonances. The major dissonance that comes from the leading note is outside these latest rules. In fact, a minor dissonance often sounds unprepared for the sake of that major dissonance. This happens when the fundamental bass rises a third or fifth and then falls a fifth. That final fall produces a perfect cadence. Such a cadence requires the leading note to have sounded in the chord over the note from which the bass falls a fifth. Important consequences follow from this. We will discuss them after explaining how to move from one key to another.", "III.20-001": "CHAPTER 20.", "III.20-002": "A precise list of bass progressions for the different dissonances used.", "III.20-003": "The rules for dissonances must always come from the fundamental bass and the fundamental seventh chord. We will see that the seventh chord underlies every dissonant chord we use. The bass can follow different paths through the notes of that seventh chord. The upper parts then form different intervals above it, so we must give the chords names that match those intervals.", "III.20-004": "We extend the first rule for sevenths in only one way here. Each note of the key receives a seventh chord while the bass rises by fifths or falls by fourths.", "III.20-005": "The first seventh may be prepared by any consonance, or left unprepared, according to the preceding chapters. After that first seventh, we must follow the rule: the third must always prepare and resolve the seventh.", "III.20-006": "See the following example.", "III.20-007": "EXAMPLE.", "III.20-008": "A sequence of sevenths in four parts", "III.20-009": "All the parts keep moving down. The sevenths alternate between two accompaniments: a third and fifth, or a third and octave. The combinations are 1. 3. 5. 7. and 1. 3. 7. 8.", "III.20-010": "Five parts would make this harmony more complete, as the next discussion will show.", "III.20-011": "Some sevenths here do not have their natural proportion. Examples are the sevenths on C and F, which our first rules specifically prohibited. In this sequence of dissonances, that should no longer cause difficulty. These intervals result from the modulation, where we are not allowed to add a sharp or flat to any note. Later, other false intervals will arise from these. Their form results from the circumstances, so we must write them as if they were correct. We cannot avoid using them if we want to stay in the key where we began. They do not offend the ear at all, because the ear is already occupied with the notes belonging to this modulation.", "III.20-012": "Use the tenor part, marked A, as the bass. Its note aligned with the first seventh now carries a small-sixth chord. The next note carries a seventh chord. This gives a new bass progression and seemingly new chords. The following example shows it, with the same part again marked A.", "III.20-013": "Now use the haute-contre, or high-tenor part, marked B, as the bass. The note aligned with the first seventh carries a second chord. The next note carries a great-sixth chord. This produces another bass progression. See the following example, where the part is again marked B. A second chord and a tritone chord contain the same intervals, with one difference: the fourth is perfect in the second chord and augmented in the tritone chord. The name tritone comes from the augmented fourth's three whole tones. The distinction between these two chords has the same cause as the distinction between a great-sixth chord and a diminished-fifth chord.", "III.20-015": "The same distinction also applies to major and minor small-sixth chords, although we do not give them two different names. All these differences come from a seventh chord with either a major or a minor third above its bass. We do not use different names for those two forms. We do, however, reserve one form for the tonic dominant alone: its major third forms a diminished fifth or tritone with its seventh. The other dominants can take the form with a minor third, where the third and seventh form neither a diminished fifth nor a tritone. These other dominants must follow one another until the tonic dominant arrives. Their derived chords follow the same rule.", "III.20-016": "The next example shows every chord produced by these different bass progressions. Each part can be used as an upper part or a bass. The exceptions are the fundamental bass and the part below it: both can serve only as basses.", "III.20-017": "Turn the page to see the example.", "III.20-018": "EXAMPLE.", "III.20-019": "Six parts usable as basses, with fundamental bass and supposition", "III.20-020": "1. The first four basses follow the most natural progressions in relation to the fundamental bass. The fifth and sixth borrow their progressions from those first four.", "III.20-021": "The fifth bass combines material from the first and fourth basses. All three carry the mark ∞.", "III.20-022": "The sixth bass takes its progression from the second and third, which have the cross †. Each measure in the fifth or sixth bass contains one note from each of its two source basses. That is how we can recognize the borrowing. Notes at the same pitch degree have the same chord figures in the different basses. Some notes in the fifth and sixth basses should carry seventh chords, but we have not marked all of them with 7. This shows that a perfect chord alone is possible there: the seventh may be left out. If we omit it, we must also avoid the octave in the chords on the preceding notes, because that octave would prepare the seventh.", "III.20-023": "2. In the first four basses, the first and second parts are a third apart, as are the third and fourth. The last two descend while the first two stay on their notes. They keep taking turns like this to the end. A minor dissonance naturally descends, so at least the parts that form it must move down. In this kind of harmonic sequence, the consonance a third below must move the same way. Remember that a sixth above is equivalent to a third below, as in this example:", "III.20-024": "A third below or a sixth above", "III.20-025": "This restriction on the consonance's movement applies only in relation to the fundamental bass. The consonant note may stay where it is and become a dissonance if the bass moves ahead of it:", "III.20-026": "As follows:", "III.20-027": "At A and B, the bass falls a third rather than a fifth. The consonant note C lies a third below the dissonance F. It stays on the same degree and becomes the dissonance D.", "III.20-028": "A consonant note held until it becomes dissonant", "III.20-029": "3. To hear the other parts together, leave out the fifth and sixth basses. To hear the fifth and sixth instead, leave out the four upper parts, or at least the first and third. With the latter choice, however, unisons or octaves will occur repeatedly and will not sound pleasing.", "III.20-030": "4. Consider the first four basses on their own. The top three contain every note of the chords figured on the fourth. We can choose another of these parts as the bass. Move it down an octave so it lies below the others, or move the others up an octave. The other parts will always contain the chords figured on the chosen bass. Now choose the fifth bass: above it, play only the second, third, and fourth parts. The first resembles the fifth too closely. If the sixth bass is chosen, play only the first, second, and fourth above it. In that case change the one note in the first measure that produces two consecutive octaves.", "III.20-031": "This one example teaches how all dissonant chords are built, how their dissonances move, and how different bass progressions change the chords. As we can see, inversion alone produces all these differences.", "III.20-032": "5. Taken separately, the fifth and sixth basses sound pleasing. They can even be syncopated:", "III.20-033": "As follows:", "III.20-034": "The fifth and sixth basses with syncopation", "III.20-035": "Or with the parts inverted.", "III.20-036": "The two syncopated basses inverted", "III.20-037": "Adding two more parts here is fairly difficult. Inversion introduces a kind of supposition that demands a strong knowledge of harmony. For now, practise only what is written: two parts, without adding others.", "III.20-038": "A part used as bass must start and finish on the tonic. At the ending, its dominant must come before that tonic. Only a very small change is needed in the other parts. Make that change agree with the way those parts move when heard above the fundamental bass.", "III.21-001": "CHAPTER 21.", "III.21-002": "The second chord.", "III.21-003": "Invert a seventh interval and it becomes a second. In the same way, the second chord is an inversion of the seventh chord.", "III.21-004": "EXAMPLE.", "III.21-005": "The second and seventh intervals and their chords", "III.21-006": "The inversion also reverses how these dissonances are prepared and resolved.", "III.21-007": "Minor dissonances are normally prepared and resolved in the upper part. The second works the other way: its minor dissonance lies in the bass. The bass must prepare and resolve it, following the movement required for a minor dissonance. Sound the bass note on the second beat. On the first beat of the next measure, form a second above that note. Then move the bass note down. As long as the bass follows this pattern, each note can receive the chords shown in the next example. Continue until the major dissonance appears; a consonant chord follows it.", "III.21-008": "There is an important qualification. In a harmonic progression like this one, a major dissonance may appear without forcing us to respond to it. The bass may keep following the same degrees and pass through the mediant without closing there. The close is then reserved for the tonic, which arrives one or more measures later, either directly or through its derived forms. The next example shows this. The major dissonance does not follow its natural movement here, so it is treated as minor. This is allowed only because the modulation calls for delaying the close. Even so, after the leading note it is always better to stop on the tonic's perfect chord or the mediant's sixth chord.", "III.21-010": "A seventh prepared and resolved in the upper part.", "III.21-011": "Preparing and resolving the seventh in the upper part", "III.21-012": "A second prepared and resolved in the bass.", "III.21-013": "Preparing and resolving the second in the bass", "III.21-014": "At A and B, the second is prepared and resolved in the bass in the same way that the seventh is prepared and resolved in the upper part. Comparing the fundamental bass shows that both examples use chords containing the same notes.", "III.21-015": "The basses in the two examples move almost alike: both descend by step and repeat each note at the same pitch. How do we choose between their chords? Look at the barline. In one example, the two repeated notes are inside the same measure. In the other, the barline separates them. If your bass matches one of these patterns, you can always use the chords shown with that pattern. Follow this rule and you will not go wrong.", "III.21-017": "Some bass lines in the previous chapter carry chords that do not follow these patterns. That is because those lines are representing upper parts only. In other cases, stay with our rule if you want to write correctly.", "III.21-018": "The second must be prepared by the third. Yet in the upper part it may be prepared by any consonance. The bass, for its part, must always be syncopated in this situation.", "III.21-019": "Different bass progressions can make any consonance appear to prepare or resolve a dissonance. To check your work, put a fundamental bass below the composition. Against that bass, a minor dissonance always forms a seventh. You will see that only an octave, fifth, or third prepares it, and only a third resolves it. If this is not so, your composition is neither correct nor regular.", "III.21-020": "Again, the first dissonance may be prepared by the octave, fifth, or third of the fundamental note if a consonant chord precedes it. The dissonances that immediately follow must instead be prepared by that note's third, rather than another consonance. This gives the most natural harmonic sequence. Sometimes, however, we seek variety by preparing a seventh with the fundamental note's fifth or octave, even in the middle of a sequence of sevenths or after several of them. The only reason for doing this is to vary the melody or harmony. Use it rarely, or at least with good judgment. The same rule applies to every minor dissonance when we examine its foundation, where the seventh is always the governing interval.", "III.21-021": "The rule that a seventh resolves only to the fundamental note's third does not mean that a fifth or even an octave can never resolve it. Those are licences. Use them only after mastering the rest completely. We will therefore leave them aside for now.", "III.22-001": "CHAPTER 22.", "III.22-002": "Keys and modes in general.", "III.22-003": "Once you are sure of the explanation of keys and modes in Chapter VIII, you need only learn what follows.", "III.22-004": "ARTICLE 1.", "III.22-005": "Major keys.", "III.22-006": "Any note can be the tonic of a major key. Its octave must then follow the same pattern as C's octave. Sharps and flats raise or lower intervals by a semitone wherever needed to create that pattern. We need to know how many signs to put, normally after the clef. They tell us to raise or lower every note on the degrees they mark. Take D as an example. F is a minor third above D, but C's third is major. Make F sharp, and D now has a major third, just as C has E as its major third. Similarly, F needs B♭ for its fourth. Put a flat on B in the key of F to make its pattern match C's.", "III.22-007": "These examples show all the transposed major keys. Their octave movement follows the pattern of C's octave.", "III.22-008": "Major keys with sharps", "III.22-009": "Major keys with flats", "III.22-010": "These eleven major keys, plus C, make twelve. The octave system contains only twelve chromatic notes. See Book One, Chapter V.", "III.22-011": "Sharps are placed in this order: F, C, G, D, A, E, B, and so on. One sharp must therefore be F. Two are F and C. Three are F, C, and G. Continue by counting upward by fives, starting with F, the first sharp, and proceeding to the last.", "III.22-012": "The leading note tells us how many sharps a major key needs, because the last sharp always falls on that note. D major needs two sharps before the clef. Its leading note is C♯, and a sharp cannot be put on the C line until one has been put on F, the place of the first sharp. E major needs four sharps because its leading note is D♯. Apply the same reasoning to other keys. Another method is to count by fives from the major key with one sharp. That key is G. The sequence G, D, A, E, B therefore takes 1, 2, 3, 4, 5 sharps.", "III.22-013": "For flats, count upward by fours, starting with B: B, E, A, D, G, and so on. A major key's fourth note determines how many flats it needs. F's fourth is B♭, so F major needs a flat on the B line. Use the same method for the other keys. The series of major keys with flats begins on F. Count by fours from there, just as you counted by fives for sharps, to find the number required.", "III.22-014": "ARTICLE 2.", "III.22-015": "Minor keys.", "III.22-016": "D's octave is the usual model for all minor keys.", "III.22-017": "See the following example.", "III.22-018": "EXAMPLE.", "III.22-019": "D — Octave; C♯ — Leading note; B♭ — Sixth note; A — Tonic dominant; G — Fourth note; F — Mediant; E — Second note; D — Tonic.", "III.22-020": "Going up, the minor key differs from the major only in its third: minor in the minor key, major in the major key. Going down, however, restore the flat to B and remove the sharp from C, the leading note.", "III.22-021": "EXAMPLE.", "III.22-022": "The D-minor octave progression", "III.22-023": "Follow these progressions in any minor key and you cannot go wrong.", "III.22-024": "These examples show all transposed minor keys. Their octave movement matches the D octave just shown.", "III.22-025": "A minor", "III.22-026": "Minor keys with sharps", "III.22-027": "These two keys are the same key.", "III.22-028": "Minor keys with flats", "III.22-029": "There are twelve minor keys here too, including D. D and A are both written without sharps or flats.", "III.22-030": "E is the first minor key with a sharp before the clef. To find the number for the other minor keys, count by fives from E. E, B, F♯, C♯ take 1, 2, 3, 4 sharps, and the pattern continues. B minor is second, so it needs two sharps. The key's second note also tells us the number, because that note carries the last sharp.", "III.22-031": "G is the first minor key with a flat before the clef. Count by fours: G, C, F, B♭, E♭ need 1, 2, 3, 4, 5 flats. This gives the number for each key. Its minor third carries the last flat and therefore also tells us how many are needed.", "III.22-032": "Memorize how many sharps or flats each major and minor key needs. You need this both to put them before the clefs and to add or remove them beside individual notes when the key changes during a piece. This knowledge does more than let you choose a key for composition. It also helps you recognize the keys you move into and show those keys clearly to the performers.", "III.22-033": "Use ‘ut’ as the tonic name in every major key: its octave then follows the C model. Use ‘ré’ as the tonic name in every minor key: its octave follows the D model, both up and down. These are names for the transposed tonic, not a claim that every tonic has the fixed pitch C or D. The intervals and chords are the same in every major key, and likewise in every minor key. Remember that any part must make the required change according to whether it is rising or falling.", "III.22-034": "For every key's octave, going up and down with the required sharps and flats, see Book Four, Chapter VI.", "III.23-001": "CHAPTER 23.", "III.23-002": "How to move from one key to another, also called modulating.", "III.23-003": "1. Treat every note carrying a perfect chord as a tonic. Our first perfect-chord examples can therefore be understood as showing a different key on each note. They are also the models for this chapter. A natural move from one tonic to another must cover a consonant interval. After starting a piece in one key, we may move to a key a third, fourth, fifth, or sixth above or below it. The first tonic then becomes the new key's mediant, dominant, fourth note, or sixth note. We can keep linking keys in this way.", "III.23-004": "2. Besides the possibilities just given, a major key's tonic can sometimes become a seventh degree, or even a second degree. It can never become a leading note. A minor key's tonic has only the second-degree option in this additional case.", "III.23-005": "Here “seventh” means the note a whole tone below the octave. It does not mean the leading note, a semitone below the octave, which naturally belongs to every key.", "III.23-006": "3. In the middle of a piece, we may make the dominant of a major key the new tonic. Its key should normally be major too. Sometimes it can be made minor, if done judiciously. But if the starting key is minor, its dominant can become only a minor key.", "III.23-007": "You may go beyond these rules if you can judge what you are doing. Even then, always be wary of losing your way. The most skilled musicians must share that concern.", "III.23-008": "4. Whatever the starting key, keep the music moving within it for at least three or four measures. Stay longer if your invention and good taste call for it.", "III.23-009": "5. Prefer moving to the key of the starting key’s dominant rather than to another key. The original tonic becomes the fourth degree of the new key. An irregular cadence can make this change.", "III.23-010": "6. On changing key, immediately identify its principal note: the tonic. Think of it as ‘ut’ or ‘ré,’ using the relative tonic names of the major and minor models. This determines how every note within its octave should move and which chords belong there. Sharps and flats make the new key's intervals match the C and D models. For example, moving from C to G major means sharpening every F in every part. F♯ then plays the role of leading note in G that B plays in C. If the new key is G minor instead, sharpen F only when it rises. Flatten E when it falls: E is G's sixth degree, and it must follow the pattern of D's sixth degree, which becomes flat in descent. Also flatten B, so G has a minor third like D's. Apply the same reasoning to other notes and keys.", "III.23-011": "7. Repeating a key too often is not pleasing to the ear. The starting key is the exception: we may return to it from time to time. Do not immediately return to another key you have just left. Suppose you begin in C, visit another key, and return to C. That return is allowed. But it would not be good to revisit the other key after leaving it for C or for some third key. Prefer a new key instead. Move judiciously through the keys, then gradually return through those closest to the starting key. You can then finish in that key so naturally that it seems never to have been left. If the piece has visited several other keys, spend a little longer moving within the principal key near the end than you did at the beginning.", "III.23-012": "8. From a major key, prefer the key of the sixth degree to the key of the mediant. From a minor key, prefer the mediant's key to the sixth degree's. The less desirable option is still allowed. Remember also that the mediant and sixth degree count as major in a major key and as minor in a minor key.", "III.23-013": "9. To choose major or minor for the destination key, use this test: its tonic, third, and fifth must come from the notes in the octave of the key just left. There is a broader rule too. Unless a long piece requires some departure, every tonic's perfect chord used during the piece should be made from the notes of the starting key's octave, without adding new sharps or flats to alter them. In C, for example, E, F, G, A, and sometimes D can form their thirds and fifths from the notes already used in C's modulation. Major can therefore lead to minor, and minor to major. The third must agree with the diatonic order of the original key, or at least the key being left. From C major to A, choose A minor, because C is A's minor third. Use the same test elsewhere. In minor keys, apply the rule to the descending octave only: the leading note then loses its sharp and becomes natural. This also allows the corresponding change in major keys by putting a flat on the leading note. Our earlier permission for a tonic to become a second degree requires a whole tone between the tonic and its second. This last kind of modulation was mentioned in the second article.", "III.23-015": "10. Make the move between keys so gradual that the ear hardly notices. The order of procedure just given will help you do this.", "III.23-016": "11. When changing key, the last note in the old key must have a consonant chord. It can therefore be the tonic, mediant, or dominant. Sometimes it can be the sixth degree carrying a sixth chord. For now, though, concentrate on going from a tonic to its dominant. Make that dominant the new tonic, then follow the routes in the next example. Spend a few measures in the key of each note to which the bass moves.", "III.23-017": "EXAMPLE.", "III.23-018": "Routes between keys — starting at the first or second measure", "III.23-019": "You may begin the bass with either the first or the second measure. Stay longer in the starting key than in the key of the next note. Spend even less time in later keys. Sometimes only one, two, three, or four notes of a later key are used before moving on. Taste decides this more than rules do.", "III.24-001": "CHAPTER TWENTY-FOUR.", "III.24-002": "More Rules from the Previous Chapter.", "III.24-003": "Cadences are the first means of learning to change key. They create a resting point within a piece. After this, you may move into any key you want and sound another cadence there, continuing in this way. After the perfect chord that ends every cadence, you are free to move to any chord.", "III.24-004": "Sometimes you repeat the tonic note where the cadence ended. Give the repeated note a chord suited to the key you want to enter.", "III.24-005": "Give the repeated note a seventh chord or a sixth–fourth chord to make it a dominant, A.", "III.24-006": "Give it a tritone chord or a great-sixth chord to make it the fourth note, B.", "III.24-007": "A sixth chord makes it the mediant, C, or the sixth note if it rises to the leading note, D.", "III.24-008": "The small-sixth chord makes it the sixth note when it descends to the tonic dominant, F. Sometimes it makes it the second note, G.", "III.24-009": "Instead of repeating the tonic, you may raise it a semitone. Give the raised note a diminished-fifth chord. It then becomes the leading note, H.", "III.24-010": "If the tonic note has a major third, it can become a dominant without changing anything, J.", "III.24-011": "Turn the page for the next example.", "III.24-012": "EXAMPLE.", "III.24-013": "Cadences and changes of key — first line", "III.24-014": "Cadences and changes of key — second line", "III.24-015": "Cadences and changes of key — third line", "III.24-016": "Cadences and changes of key — fourth line", "III.24-017": "You may simply give a perfect chord to every note marked (6/5) with a B above it. The irregular cadence that sounds a mediant can become a sixth note, just as a sixth note can become a mediant. Part of this could already be seen at T in the previous example.", "III.24-018": "EXAMPLE.", "III.24-019": "A as sixth note or mediant — S and T", "III.24-020": "A is the sixth note of C. It becomes the mediant of F at S.", "III.24-021": "A, the mediant of F, becomes the sixth note of C at T. In both cases the chord stays the same. A note that can serve either as mediant or sixth always lies between two keys a fifth apart. It divides the fifth into two thirds: for example, A lies between F and C.", "III.24-022": "You may also change key through 7, 7 and 6, 2, 4♯, 6/5, and barred 5. Let one or more bass notes move with these kinds of chords. Then introduce a tritone or diminished fifth to establish the key you want to enter. This interval must consist of the major third and seventh of a tonic dominant.", "III.24-023": "EXAMPLE.", "III.24-024": "Modulation through dissonant chords — three systems", "III.24-025": "The dissonance that brings you into a new key must always be prepared by a consonance in the final chord of the key you are leaving.", "III.24-026": "This helps you compose a bass to suit the chords you want to use. We shall now reverse the approach. You may compose a bass freely, and its progression will show us which chords belong to it.", "III.25-001": "CHAPTER TWENTY-FIVE.", "III.25-002": "How to Choose Chords for Bass Notes in Any Progression.", "III.25-003": "ARTICLE ONE.", "III.25-004": "First, watch for cadences and anything that brings a melody to a close. Beginners can hardly avoid using these frequently in their bass, especially to change key. Such endings are easy to spot: they always fall on the first beat of a measure. Even a little developed taste lets you hear them immediately. Notes on that first beat where the melody comes to some kind of rest must always have a perfect chord. They are therefore treated as tonic notes.", "III.25-005": "2. After a tonic note, if the bass moves through consonant intervals, you may give each note a perfect chord until the note followed by a diatonic interval. There is an exception. A note a third above or below another note with a perfect chord can take a sixth chord instead, and this is even preferable. Conversely, if the first note must have a perfect chord, the next note a third above or below must have a sixth chord. But this applies only if another consonant step does not follow that second note. Consonant progressions naturally require a perfect chord or seventh chord on each note. This will be explained further.", "III.25-006": "In this situation, the note that can take a sixth chord is always the mediant or the sixth note. If you fear making a mistake, you may simply give each of these notes a perfect chord.", "III.25-008": "EXAMPLE.", "III.25-009": "A. B. C. D. E. G. H. J. Sixth note. Second note.", "III.25-010": "In C, the note a third above C and below the following dominant must take a sixth chord, A.", "III.25-011": "B. A note a third above the dominant, or equivalently a sixth below it, could have a sixth chord. Yet the diminished-fifth chord fits better. This note is the leading note of C, and we remain in that key until C. A diminished-fifth chord differs from a sixth chord only by its added diminished fifth. Likewise, a seventh chord differs from a perfect chord only by its added seventh. We could have added that seventh to the dominant just before the note with the diminished-fifth chord. This follows Chapter XI.", "III.25-012": "Four notes rise successively in thirds from the tonic. The mediant has a sixth chord. The dominant has a sixth–fourth chord at C instead of a perfect chord. Why? A flat on B establishes another key. The bass shows this through the diminished fifth between B-flat and the following E. E, the lower sound of that diminished fifth, becomes the leading note. The B-flat chord must therefore fit the key this leading note prepares. B-flat does not belong to C, the key we are leaving. The dominant of C also adjusts its chord to the next one. Without leaving C, it takes a sixth–fourth chord whose notes make up the tritone chord on B-flat. If this dominant had a perfect chord, its third would have to be minor to avoid a false relation. A false relation means sounding, in successive different parts, two notes with the same name but distinguished by an added sharp or flat. For example, after B sounds in one part as G’s major third, B-sharp or B-flat cannot sound in another part. More will be said elsewhere. The sixth–fourth chord at C thus makes the harmony fit the next chord more closely. A perfect chord with a minor third would also work there. Even a small-sixth chord could be used, with a diminished-fifth chord on the note just before it, since E and the following B-flat form a diminished fifth. Such an interval in the bass determines the key absolutely: its lower sound is always the leading note, as already stated. The same rule applies to a tritone, but its upper sound is the leading note. There is an exception. If the bass next rises a fourth or falls a fifth, this diminished fifth or tritone might contain no leading note. Each bass note may instead act as a dominant moving toward the tonic dominant. The notes forming the diminished fifth or tritone are immediately followed by that tonic dominant: see G, H, J. This happens only between the second and sixth notes of minor keys, which form diminished fifths or sharp fourths with one another.", "III.25-014": "Our earlier rule would give a sixth chord to the note at D. Its sixth would have to be minor to fit the key of the notes before and after it. But B loses its flat immediately afterward. We must fit what follows rather than what precedes. A perfect chord at D is therefore better: it avoids a false relation with the next harmony and also follows our rule for consonant bass movement.", "III.25-015": "The note at F takes a diminished-fifth chord for the reasons just given: it forms a diminished fifth with the previous note. Remember this when changing key. Fit the chords to the new key rather than the old one, especially if a note can take two chords and the choice would otherwise make no difference.", "III.25-017": "ARTICLE TWO.", "III.25-018": "Imperfect Cadences.", "III.25-019": "Other bass progressions relate to the natural progression of a perfect cadence. These are called imperfect cadences. See Book II, Chapter VIII.", "III.25-020": "Imperfect cadences resemble the perfect cadence in harmony, not in bass movement. To see this, put together all the notes of the perfect cadence. Then take each part’s movement separately and use it as the bass. The chords differ only in the arrangement of their notes.", "III.25-021": "EXAMPLE.", "III.25-022": "Minor dissonance. C. Major dissonance. A. Fundamental bass.", "III.25-023": "To hear these parts together, omit A and C. They resemble the highest part too closely: the note that resolves the minor dissonance there does not suit an octave doubling in this situation. Alternatively, omit the highest part and play A and C. The example combines them only to show their different movements. Dissonant parts have a fixed direction; the others may rise or fall. The fundamental-bass note appears in the three lowest parts. It may stay on the same degree or fall a third, as well as making its natural fall of a fifth. When it falls a third at A, its chord normally loses the seventh, because the effect resembles two consecutive octaves. Strictly speaking, however, this is tolerable, especially in four parts.", "III.25-024": "Chapter XI’s octave example gives all these movements with the same chords used here. To check, make any chosen part the bass. Do not put the two lowest parts above the others. The remaining parts sound well in any arrangement. A chord figured in one part is supplied by the other parts.", "III.25-025": "Most earlier examples contain these imperfect cadences. Their last notes do not always fall on the first beat, because they occur within diatonic movement. That movement cannot establish a perfect conclusion.", "III.25-026": "ARTICLE THREE.", "III.25-027": "How to Identify the Key of an Imperfect-Cadence Progression.", "III.25-028": "Diatonic movement can lead to several keys. To identify which key it leads to, consider the following points.", "III.25-029": "1. First look to the leading note. Here is how to recognize it in the bass.", "III.25-030": "Once we know the opening key, we know its leading note. The key uses only certain notes within its octave, following the pattern of C major or D minor. Altering one of those notes with a sharp or flat certainly changes the key.", "III.25-031": "The first new sharp marks a leading note. If two or three sharps occur in succession, take the last as the leading note. A sharp on F therefore makes F the leading note and indicates G as the key. If G also receives a sharp, F-sharp loses that role. G-sharp becomes the leading note and indicates A as the key. Follow the order F, C, G, D, A, and so on, and you cannot go wrong. Ignore any flats mixed with these sharps. If there is no sharp, use the flat to identify the new key. The leading note is the note that would receive the next flat if another were added. For instance, with B-flat and no sharp, E is the leading note, because E would receive the next flat. With E-flat, A is the leading note. Follow the flat order B, E, A, D, and so on: the next unflattened note after the flattened one is always the leading note. Article One also showed how diminished fifths and tritones reveal the leading note in the bass. The note that could take the next flat is exactly a tritone above or a diminished fifth below the note with the last flat. To avoid confusion, never use the natural sign here.", "III.25-033": "2. The bass may never reach the leading note, so a key change may escape detection by that test. Diminished fifths or tritones often occur between a minor key’s second and sixth notes—or rather from the sixth to the second—without identifying the key in that way. This applies when there is no sharp; a sharp always decides. First ask whether the key suggested by these intervals or other signs has the required relationship to the key being left. Next, after the resting point created in some degree by diatonic movement, ask whether the following note belongs more closely to one key than another. Pay special attention when consonant motion follows the last diatonic note. This often leads to final cadences that establish the key.", "III.25-034": "EXAMPLE.", "III.25-035": "Leading note of A. Leading note of D. Key of A. Leading note of G. Leading note of B♭. Leading note of F. Leading note of D. Leading note of G. Leading note of F. Leading note of C. Key of F. Leading note of C. A. B. C. D. F. G. H. J. L. M.", "III.25-036": "The first leading note is easy to recognize. From A, a diatonic passage runs to B, where it is interrupted and the rule of sevenths applies. The interruption leads to a cadence on C. Therefore the diatonic notes, starting at A’s dominant, must fit C. Nothing after that dominant keeps us in A. We give the repeated dominant a sixth–fourth chord to make its harmony fit the next chords more closely. Also, G becomes natural at B and stops being a leading note. No sharp or flat appears before the C cadence. This shows that C begins to establish itself at A. Favor the coming key over the present key, especially when the chords can fit it without difficulty. Here no sharp, flat, consonant progression, or resting point requires another route.", "III.25-038": "G-sharp no longer applies. The next C-sharp points to a new key. At C there is a rest in the melody, followed by a consonant interval requiring a seventh on that note. This sends us back to A: the rising-fourth progression ends on A.", "III.25-039": "F-sharp points to a new key because no other sharp follows.", "III.25-040": "The flat at F makes us give the previous note a minor third, so the harmonies agree better. Flats on B and E tell us that A should be the leading note. Next, E loses its flat and becomes the leading note itself: B remains flat, and there is no sharp.", "III.25-041": "The diminished fifth between the notes at D could indicate a leading note. The note taken as leading note rises a semitone at J, its natural movement. But consonant intervals begin at L, where F ends. These require perfect chords or seventh chords on the following notes, depending on the bass intervals. They also lead us to choose the key established by the next leading note. Still, the rules for movement by thirds would allow this:", "III.25-042": "Proceed thus. D. L. J.", "III.25-043": "That would keep F until D, followed by the leading note. Good taste may guide either choice. Since good taste enjoys variety, it always urges us to leave a key that has lasted too long when we can.", "III.25-044": "The diminished fifth above D’s leading note does not resolve in the next chord. It becomes the sixth above the note at G, while the chord’s foundation stays the same. Immediately afterward it resolves downward to the sharp sixth of the neighboring note. The diatonic motion there makes us fit the harmony to the key indicated by the next leading note.", "III.25-046": "We have not yet discussed the augmented-second chord at G. You may ignore it for now.", "III.25-047": "H becomes a leading note for two reasons. First, it moves by a semitone to the following note in the next measure. Second, its diminished-fifth chord is the same harmony as the seventh chord required by the immediately following note, which rises a fourth. Also, all sharps have gone and B remains flat, so E is the leading note. Next, sharps and flats disappear. Only B can be the leading note, establishing C. Give the notes of C their required chords through to the end. At M, however, a rising fourth requires a seventh chord on C and a perfect chord on F, because another consonant interval follows F. A perfect chord always makes its bass note a tonic, so F becomes tonic again. But the B-flat belonging to F disappears immediately. With no sharps or flats left, B returns as leading note. C was interrupted only briefly for variety, because the consonant bass movement made this possible.", "III.25-048": "To finish: let consonant progressions decide. Fit diatonic passages to the consonant progression that follows, rather than the one before them. If the leading note is unclear, keep the chord sequence prescribed by the octave in Chapter XI. Begin that sequence from the last consonant chord, on the last note moving by a consonant interval. A rising semitone may suggest that its first note is the leading note. But check whether sharps follow or notes lose their flats; these are stronger clues. A rising semitone can also connect a major key’s mediant to its fourth note, or a minor key’s second note to its mediant, or its dominant to its sixth. In that last case the sixth descends immediately afterward. Thus a consonant progression, sharp, flat, or particular chord sequence must settle the matter.", "III.25-050": "When consonant motion follows diatonic motion, the shared note that ends one and begins the other must have a perfect chord or sixth chord. A note requiring the perfect chord will have been approached from its leading note by a rising semitone. Alternatively, it will be the dominant, approached by a rising whole tone. A mediant is approached by a rising semitone in minor and a rising whole tone in major. When these notes are approached downward, the tonic always follows a descending whole tone. The dominant follows a descending semitone in minor or a whole tone in major. These differences must help identify the key, because you already know how a new key must relate to the old one. Its major or minor character comes from the third and fifth, using notes belonging to the old key. Besides, a leading note will almost certainly appear before or after, and the next consonant passage will almost certainly lead to a conclusion that identifies the key. Conclusions are determined by fourths or fifths, with this exception: two or three diatonic notes may follow, rising or falling, and the melody may rest on the last before another consonant or disjunct progression starts.", "III.25-051": "EXAMPLE.", "III.25-052": "A. B. C. D. F. G. H.", "III.25-053": "The bass falls a fifth at A, but the first note must not have a seventh. The second note should have neither a perfect chord nor a seventh chord. The next diatonic passage, where the melody rests, decides this.", "III.25-055": "The melody rests on the third note after B. I therefore fit B to that note’s key. The note before B must then take the chord required by this key, not the chord suggested by consonant movement. B must have neither a perfect chord nor a seventh chord.", "III.25-056": "The second note at C takes a chord suited to the key of the next note, where the melody rests. Before its proper small-sixth chord, I give it a seventh chord. The seventh is prepared by the previous chord and resolves pleasantly to the sixth over the same bass note. The next chapter will discuss this further.", "III.25-057": "At D and F I follow the rule for movement by thirds. To choose more confidently, give the perfect chord preferably to notes on the first beat. Notes on the last beat then take a sixth chord. Still, both notes may have perfect chords, as at G.", "III.25-058": "The final consonant interval suggests a conclusion. Its key governs the chords of every diatonic note leading to it from H onward.", "III.25-059": "ARTICLE FOUR.", "III.25-060": "How to Tell Whether Diatonic Movement Will Rest on the Tonic or Dominant.", "III.25-061": "To tell where the melody will rest, remember these distances. From tonic to dominant, the bass rises a fifth or falls a fourth. From dominant to tonic, it rises a fourth or falls a fifth. If the diatonic passage goes beyond this range, check whether the leading note appears in the bass. If it does, it identifies the tonic. If it does not, the melody will certainly rest on the dominant.", "III.25-062": "EXAMPLE.", "III.25-063": "Progressions leading to the dominant, in which the leading note does not appear. Progressions leading to the tonic, in which the leading note appears. A. B.", "III.25-064": "At A the bass rises a whole tone, identifying the dominant. At B it rises only a semitone, identifying the tonic.", "III.25-065": "A diatonic passage may begin on any note of the key. Several clues must reveal that note’s place in the present key or a possible replacement key: the consonant interval from the preceding note, the resting point immediately afterward, the whole tones and semitones in the passage, and the consonant or disjunct motion that interrupts it. As the previous article’s last example shows, a consonant interval before the passage is less decisive than one after it. Still, the whole-tone and semitone pattern alone is enough to clarify matters. Learn where the semitones lie in each mode, ascending and descending. Remember that diatonic passages normally break off only after a tonic, mediant, or dominant. Sometimes they stop after another note. Even then, the next consonant movement and the rules already given should prevent mistakes. We know what rising or falling thirds, fourths, and fifths require. We also know how the same chord often appears over two notes moving by successive thirds or otherwise, according to what follows. Attend to all these points. Make modulation your first concern; compare chords with the bass’s movement, check everything against a fundamental bass, and watch for the leading note, which helps wherever it appears. Then mistakes become difficult. Once you know the chord on one note, follow the octave’s order from there until diatonic movement ends. See Chapter XI. Later you will learn how to add harmonic variety.", "III.26-001": "CHAPTER TWENTY-SIX.", "III.26-002": "How to Use Sevenths on Every Note of a Key in Diatonic Movement.", "III.26-003": "Only the tonic must always have a perfect chord. Every other note can receive a seventh chord, but the context matters. When notes rise a fourth onto a perfect or seventh chord, treat them all as dominants; each may have a seventh chord. In diatonic movement, however, the bass note with the seventh must last two beats or be played twice. These are much the same thing: on the second beat, give it the sixth chord required by the following note. Always prepare the seventh in this case, except for the first one, which may be unprepared if the bass progression allows.", "III.26-004": "EXAMPLE.", "III.26-005": "A. B. C.", "III.26-006": "A, B. I could have fitted these diatonic chords to the key established by the ending that follows. But we may also stay in the previous key. Its tonic at B then takes a chord suited to the new key on its second beat.", "III.26-007": "C naturally takes a great-sixth chord. That chord could follow the seventh chord given here. Instead of resolving the seventh to the sixth above the same bass note, however, we resolve it to the fifth above the next note. The next note’s small-sixth chord and C’s great-sixth chord are fundamentally one chord. Thus, once a dissonance sounds, do not leave it until it can resolve. The bass note for its natural resolution may be absent. In that case, ask whether the next bass note can support the same sounds that should have formed the resolving chord. The next discussion explains this.", "III.27-001": "CHAPTER TWENTY-SEVEN.", "III.27-002": "How One Dissonance Can Continue Through Chords on Different Notes and Resolve on Seemingly Foreign Notes.", "III.27-003": "A seventh chord contains four different notes, each of which can precede the same note. Place these four notes one after another in the bass. Their chords look different but share the same foundation, as Chapter XII explains. If a dissonance cannot resolve in the next chord, ask whether it can continue as part of that chord. Keep doing this until it can resolve.", "III.27-004": "EXAMPLE.", "III.27-005": "Examples A, B.", "III.27-006": "Example A includes the major dissonance; B has only the minor one. At A the second note naturally takes a small-sixth chord. Its third and fourth form a dissonance, resolved by lowering the third. The next bass note cannot support that resolution. Instead, the same sounds form its tritone chord. The dissonance still cannot resolve there, and continues until C, where it descends to C’s third. G with its seventh chord provides the foundation of all four apparent chords. Whenever you find a dissonance, identify the chord’s foundation. Then look for the bass note on which it can resolve. If the bass contains only notes of the dissonant chord, resolution is impossible. It must reach a note belonging to the resolving chord, where a minor dissonance can fall or a major one rise. To find that note, reason from the foundation: this chord’s root is dominant to a note a fourth higher. Find that higher note in the bass, or another note of its perfect chord. If the melody does not rest there, a note of its seventh chord will also do. Sometimes only the dominant of that target note appears—the same bass foundation as the current dissonant chord. Unless repeated, this dominant must then last at least two beats. On the second beat it can take the chord derived from its target note. A few minor exceptions appear in Chapter [number obscured], on licenses.", "III.27-008": "Suppose a note has a seventh chord, although its position before the next note or in the octave calls naturally for a different chord. If it is too short to sound that proper chord as well, the next bass note must be able to take the same underlying chord. Its chord must contain the sounds that should have formed the first note’s natural chord.", "III.27-009": "See the next example.", "III.27-010": "EXAMPLE.", "III.27-011": "Continuo bass. Fundamental bass. A. B. C. D.", "III.27-012": "At A and D, the key’s second note naturally takes a small-sixth chord. Its sounds appear in the tritone chord after A and the seventh chord after D.", "III.27-013": "The descending sixth note at B naturally takes a small-sixth chord. Its sounds appear in the next note’s great-sixth chord.", "III.27-014": "The seventh above the dominant resolves to the sixth above that dominant when it repeats at C. A dissonance can therefore resolve to different consonances. A minor dissonance resolves correctly by falling to a consonance above either the same bass note or the next one. A major dissonance resolves by rising to a consonance.", "III.27-015": "Consider one more point. The natural chord sequence may suggest giving a note an inversion of the next note’s chord. Ask instead whether it could take a chord dominant to the next one. That dominant chord would be much better than repeating the same underlying harmony. This is especially true when a consonance in the previous chord can prepare the dominant chord’s dissonance.", "III.27-016": "Harmony proceeds as a chain of tonics and dominants. Understand their derived chords well enough to make each chord dominate the next. The perfect chord and its derivatives dominate nothing: any chord may follow them if it obeys the rules of modulation. Every dissonant chord, however, dominates the next one, as in the examples of 7, 7 and 6, 2, 4♯, 5, and barred 5. We need careful judgment to recognize derived chords and arrange them properly. Yet the rules already given for each chord and bass progression are enough to solve these difficulties.", "III.27-018": "Example of Choosing a Chord According to the Chord That Follows.", "III.27-019": "A. B.", "III.27-020": "The second note at A naturally takes a small-sixth chord. This is derived from the seventh chord on the tonic dominant that follows immediately. For more variety, however, notice that the second note itself dominates that dominant. Give it the chord required for that role instead. After B, the dominant is delayed by an intervening note. That note can only take a chord derived from B’s seventh chord. B should therefore have a seventh chord, especially since a consonance in the previous chord prepares the seventh.", "III.27-021": "So far, all our rules concern harmony. They limit each part’s melody, except the bass on which the harmony is built. Master this knowledge before turning to melody. We shall discuss melody after the licenses, which add variety and can further enrich harmony.", "III.28-001": "CHAPTER TWENTY-EIGHT.", "III.28-002": "Licenses, Beginning with the Interrupted Cadence.", "III.28-003": "An interrupted cadence stops a perfect cadence from reaching its expected ending. Sound a seventh chord on the tonic dominant. Instead of moving naturally to the tonic, raise the bass just a whole tone in major or a semitone in minor. The seventh resolves to the fifth above this new bass note. See Book II, Chapter VI, on interrupted cadences.", "III.28-005": "EXAMPLE.", "III.28-006": "Interrupted cadence in the major key. In the minor key.", "III.28-007": "The final perfect chord doubles the third at the octave instead of the bass. This goes against the natural order, but results from the bass’s irregular movement rather than the other parts. The minor dissonance still falls and the major one rises to resolve. The doubled third represents the fundamental sound that would naturally be heard. In major, you may instead descend to the bass’s octave rather than rise to the third, as the cue sign shows. In minor, follow the example exactly.", "III.28-008": "Now invert the chords of the interrupted cadence to see how we can use them.", "III.28-009": "EXAMPLE.", "III.28-010": "Major key. Minor key. Fundamental bass.", "III.28-011": "Put each of these bass lines below the others in turn. You will hear the different chords shown by the figures. This gives pleasing harmonic and melodic sequences over an ascending or descending diatonic bass.", "III.28-012": "See the next example.", "III.28-013": "EXAMPLE.", "III.28-014": "D. F. G. H. J. Continuo bass. Fundamental bass. A. B. C.", "III.28-015": "When this part is the bass, omit D and change F’s last two notes. When F is the bass, make the same change to this part.", "III.28-016": "This part cannot be the bass.", "III.28-017": "If this part is the bass, keep it moving diatonically to the end, preferably upward rather than downward.", "III.28-018": "Omit D when this part is the bass. D forms an irregular cadence against B and C in the fundamental bass. That cadence cannot be inverted with a seventh chord or second chord on its first note.", "III.28-019": "Adding a sixth to B’s perfect chord avoids the perfect cadence from A to B. This prepares an irregular cadence. An added seventh at C avoids that cadence too, allowing the perfect cadence at the end.", "III.28-020": "See Book II, Chapters IX and X.", "III.28-021": "Omit the fifth from B’s chord and A to B becomes an interrupted cadence, like H to J in part G.", "III.28-022": "The continuo bass limits the upper parts’ motion. When one of those parts becomes the bass, you may alter its motion. This freedom means changing consonant movement into diatonic movement without changing the underlying harmony. Adjust the other parts, now above it, to fit.", "III.28-024": "The second note of an interrupted cadence may take a sixth as the bass rises a whole tone or semitone. If so, do not give the first note a seventh chord: that seventh could not resolve.", "III.28-025": "You can interrupt a cadence’s ending by adding a dissonance to its last note. Prepare and resolve that dissonance according to the fundamental bass, which must always guide you against errors. At C, however, the dissonance cannot be prepared, yet it is good: the fundamental bass falls a fourth there, or equivalently rises a fifth.", "III.28-026": "Licenses include the irregular cadence and dissonances that cannot be prepared, such as when the fundamental bass rises a third, fifth, or seventh. They also include everything obtained by inverting those progressions. Yet these supposed licenses are inseparable from good harmony itself. That is why we discussed them in the order we considered easiest for beginners.", "III.29-001": "CHAPTER TWENTY-NINE.", "III.29-002": "The Augmented-Fifth Chord.", "III.29-003": "Some chords introduced by license remain to be discussed. First is the augmented-fifth chord. It can occur only on the mediant of a minor key.", "III.29-004": "This is really a tonic dominant’s seventh chord, with a fifth sound added a third below it.", "III.29-005": "EXAMPLE.", "III.29-006": "Seventh chord; augmented-fifth chord. Tonic dominant. Added sound.", "III.29-007": "Look for the chord’s foundation in the tonic-dominant chord, not in the added sound. Our original rules therefore still hold. The seventh chord on the tonic dominant follows its usual course: the major dissonance rises, the minor one falls, and all resolve into the tonic’s perfect chord. The added sound either becomes a note of that perfect chord or descends to the tonic.", "III.29-009": "EXAMPLE.", "III.29-010": "Preparation and resolution of the augmented fifth.", "III.29-011": "Prepare this chord with a seventh chord on the dominant of the tonic dominant. The second note, acting here as a dominant, rises just a semitone instead of a fourth to the tonic dominant. The other parts sound only the tonic dominant’s seventh chord. That chord then resolves in the usual way already described.", "III.29-012": "Sometimes this chord interrupts a cadence. The tonic dominant rises a semitone to the added sound. This sound was the sixth note but becomes the mediant of a new key. The new leading note, forming the augmented fifth, brings about the key change.", "III.29-013": "EXAMPLE.", "III.29-014": "Interrupted cadence, change of key, and cue signs.", "III.29-015": "In four-part writing, you may put the cue-sign notes in the top part instead of one of the corresponding notes in the other parts.", "III.29-016": "The chord from which this one is derived can also prepare it.", "III.29-017": "EXAMPLE.", "III.29-018": "Preparation through the derived chord; four alternatives.", "III.29-019": "Some composers prepare it with the fifth above the same bass note, or the minor sixth above the note a semitone below. They also use chords derived from the seventh chord on that lower note. These approaches are somewhat bold.", "III.30-001": "CHAPTER THIRTY.", "III.30-002": "The Ninth Chord.", "III.30-003": "The previous chord had an augmented fifth; this one has a perfect fifth. More precisely, the third above its fundamental sound is now minor rather than major. Take a dominant’s seventh chord with a minor third, then add a note a third below the dominant: this makes the ninth chord.", "III.30-004": "EXAMPLE.", "III.30-005": "Augmented-fifth chord. G, E, C♯, A: dominant. F: added sound.", "III.30-006": "Ninth chord. G, E, C, A: dominant. F: added sound.", "III.30-007": "Every chord by supposition comes from a dominant’s seventh chord. This includes the ninth, augmented fifth, eleventh, and augmented seventh; the last two will be discussed in the next chapters. This point matters because it immediately shows how to prepare and resolve these chords. A fundamental bass reveals that all of them follow our rules for sevenths.", "III.30-008": "See the next example.", "III.30-009": "EXAMPLE.", "III.30-010": "Ninths and augmented fifths; continuo bass and fundamental bass.", "III.30-011": "If the fundamental bass sounds below, omit every continuo-bass note carrying a ninth or augmented fifth. Otherwise, the fundamental-bass notes must be above the notes marked 9 or 5♯. In supposition, the fundamental sound can be heard only above the added sound that substitutes beneath it.", "III.30-012": "Bass notes marked 9 and 5♯ may either stay or fall a third, as shown by the cue signs. The ninth resolves to the octave over a stationary bass, or to the third over a bass falling a third. In that second case the seventh would resolve to the octave. We shall see this elsewhere.", "III.30-014": "Some allow a ninth to resolve to the fifth while the bass rises a fourth. The resulting harmony is unsuitable, however, so we leave that choice to people of good taste.", "III.30-015": "Example: Ninth Resolving to the Fifth.", "III.30-016": "Ninth resolving to the fifth; alternative resolution through cue signs.", "III.30-017": "A better option is to resolve the ninth to the sixth while the bass rises a third. The underlying harmony then stays the same. See the other example’s cue signs.", "III.30-018": "A minor dissonance by supposition always requires preparation. You may use a ninth when a consonance in the previous chord prepares it and the bass rises a second or fourth. Then resolve it as the example shows, keeping to good modulation.", "III.30-019": "A seventh can always accompany a ninth, but add it only if a consonance in the previous chord prepares it. See also the discussion in Book II, Chapter XVII.", "III.30-020": "Minor dissonances by supposition, such as the ninth and the eleventh discussed next, may also be prepared by an ordinary dissonance, such as a seventh or diminished fifth. The seventh, however, is suitable only for preparing the heteroclite eleventh. These dissonances belong to the same fundamental chord. Chapter XII already showed that one note may form several dissonances in succession if all come from the same fundamental chord.", "III.30-021": "Turn the page for the next example.", "III.30-022": "EXAMPLE.", "III.30-023": "Successive dissonances; continuo bass and fundamental bass.", "III.30-024": "The continuo notes at A take chords derived from the fundamental chords shown by the fundamental-bass figures. The same applies at B. A dissonance by supposition may follow another dissonance. Yet a dissonance must have a consonance before and after it. To keep that rule intact, the successive dissonances on the same degree cannot really be separate dissonances. They all come from the original seventh. Its fundamental chord stays unchanged until these apparent dissonances resolve into a consonance. The example shows this, and this is what actually happens.", "III.30-025": "See Chapter XV for preparation of the heteroclite eleventh by the diminished fifth, and so on.", "III.31-001": "CHAPTER THIRTY-ONE.", "III.31-002": "The Eleventh Chord, Called the Fourth.", "III.31-003": "The eleventh chord has five sounds: [D, A, C, E, G: 1. 5. 7. 9. 11.]. Its added sound is a fifth below the seventh chord’s foundation:", "III.31-004": "A, C, E, G.\n 5. 7. 9. 11.\n 1. 3. 5. 7.", "III.31-005": "This chord is rarely used because it sounds extremely harsh. Its 7, 9, and 11 are three minor dissonances. Yet using it is easy: three consonances in the previous chord stay in place to prepare those dissonances. Do not resolve all three together. All must descend, since they are minor, and simultaneous resolution would create consecutive fifths between parts. Resolve the harshest—the eleventh and ninth—first. Resolve the seventh afterward.", "III.31-007": "EXAMPLE.", "III.31-008": "Eleventh chord and successive resolution; cue signs.", "III.31-009": "The continuo moves as it does when preparing a ninth: the same motion prepares the ninth and eleventh here. To resolve the eleventh, it is best to keep the bass still and then sound a seventh chord. The bass can also rise a third, as the cue sign shows. That produces a great-sixth chord derived from the seventh chord that would sound over the stationary bass.", "III.31-010": "The upper cue signs show the fifth sounds that are sometimes left out of the eleventh chord, especially in four-part writing. You may substitute this fifth sound for another, provided it is consonant or, if dissonant, prepared.", "III.31-011": "Here we mean the complete, true eleventh chord. Because it is so harsh, we remove most of its sounds, producing the form discussed in Chapter XV. This is why that form may be called heteroclite. The change makes the chord much easier to tolerate. The full chord is rarely used, although skillful use can create pleasing suspensions in harmony and melody.", "III.31-012": "EXAMPLE.", "III.31-013": "Heteroclite eleventh; suspensions A and resolutions B.", "III.31-014": "The usual figure is simply 4 for the heteroclite form. For the full chord, add 9: [4/9] or [9/4]. A seventh sometimes accompanies the heteroclite form; then use [7/4] or [4/7].", "III.31-015": "Chords by supposition simply delay the sounds that would naturally occur. At A and B, A’s sounds delay B’s expected sounds. You will find the same thing wherever these chords appear. Compare them with the continuo bass, not the fundamental bass, which always represents perfect harmony.", "III.32-001": "CHAPTER THIRTY-TWO.", "III.32-002": "The Augmented-Seventh Chord.", "III.32-003": "This chord differs from the eleventh chord only because the third above its fundamental sound is major rather than minor.", "III.32-004": "EXAMPLE.", "III.32-005": "Augmented-seventh chord. G, E, C, A: fundamental sound. D: added sound.", "III.32-006": "Eleventh chord. G, E, C, A: fundamental sound. D: added sound.", "III.32-007": "[Handwritten note: see the Supplement.]", "III.32-008": "This chord occurs only on the tonic. A perfect chord on that same tonic must come before and after it.", "III.32-009": "EXAMPLE.", "III.32-010": "Augmented seventh; suspensions A and resolutions B.", "III.32-011": "The sounds at A delay those at B. The marks [diagonal lines] show the natural movement of A’s sounds.", "III.32-012": "When the bass falls a whole tone or semitone, the sound forming the augmented seventh is often left out.", "III.32-013": "EXAMPLE.", "III.32-014": "Chord figured with 2; continuo bass and fundamental bass.", "III.32-015": "Another example; continuo bass and fundamental bass.", "III.32-016": "The figure is 2 because the chord is prepared like a second chord. But it contains both a fifth and a fourth, so the fourth must be treated as a dissonance by supposition. The chord is therefore an eleventh or augmented-seventh chord with one sound removed: the sound heard immediately afterward in the bass at D. That sound does not suit octave doubling.", "III.33-001": "CHAPTER THIRTY-THREE.", "III.33-002": "The Augmented-Second Chord and Its Derivatives.", "III.33-003": "The augmented-second chord and its derivatives are called chords by borrowing. The tonic dominant gives its place as foundation to the sixth note, in minor keys only. This produces the augmented-second chord and its derivatives. Thus:", "III.33-004": "instead of", "III.33-005": "Seventh chord. G, E, C♯, A.", "III.33-006": "we find", "III.33-007": "Augmented-second chord. G, E, C♯, B♭.", "III.33-008": "The augmented-second chord comes by borrowing from the tonic dominant’s seventh chord. This description is justified because the sixth note takes the tonic dominant’s place, while the other sounds of the seventh chord stay unchanged. Both major and minor dissonances keep their natural movements. In the middle of a piece, you may freely choose either bass note to accompany the tonic dominant’s seventh-chord sounds. But you cannot then choose any continuation you like. The harmony must follow exactly the course required by that seventh chord. The tonic’s perfect chord must follow either choice.", "III.33-010": "EXAMPLES.", "III.33-011": "Minor dissonance C; major dissonance B or leading note; D; tonic dominants A; mediants F; tonics G.", "III.33-012": "Chords by borrowing; sixth note A; tonic dominant; cue sign H; mediants F; tonics G.", "III.33-013": "Chords by borrowing contain two major and two minor dissonances. The extra, foreign dissonances come from replacing the tonic dominant with the sixth note. The minor dissonances always fall. The foreign major dissonance does not always rise, as a leading note would have to. At cue sign H, it may rise. It must rise if the minor dissonance C or A is in the bass.", "III.33-015": "The examples differ only because the sixth note replaces the tonic dominant at A. Their dissonances follow the same course, and the modulation is unchanged.", "III.33-016": "Replacing the dominant with the sixth note creates the augmented-second chord. It also changes every derivative of the tonic dominant’s seventh chord in the same way.", "III.33-017": "The leading note normally takes a diminished-fifth chord. Replacing its 6 with 7♭ creates a diminished-seventh chord, solely through this same change, B.", "III.33-018": "Likewise, the fourth note’s tritone chord takes a minor third instead of its second, C.", "III.33-019": "The second note’s small-sixth chord takes a diminished fifth instead of its fourth, D.", "III.33-020": "The mediant’s augmented-fifth chord takes a fourth instead of its third, F.", "III.33-021": "The tonic’s augmented-seventh chord takes a minor sixth instead of its fifth, G.", "III.33-022": "To hear the difference more clearly, use only the four upper bass lines. Make each one the bass in turn, placing the others above it.", "III.33-023": "The two lower bass lines cannot become upper parts because they carry chords by supposition. Hear each separately with the four upper parts. The two lower basses would not sound well together.", "III.33-024": "Let the new minor dissonance descend alone. The tonic dominant’s seventh chord then remains in its natural form.", "III.33-025": "EXAMPLE.", "III.33-026": "Descent of the new minor dissonance; six chords.", "III.33-027": "The leading note may also rise alone, but only in invertible chords. The last two are chords by supposition and do not allow this. After rising, the leading note must return to its place in the tonic dominant’s seventh chord.", "III.33-028": "EXAMPLE.", "III.33-029": "Ascent and return of the leading note; four chords.", "III.33-030": "As stated earlier, all these borrowed chords and the augmented-fifth chord belong only to minor keys. Each always belongs to one particular bass note. Chapter XXXV explains this further. For other licenses, see Book II, Chapters XIII and XVIII.", "III.34-001": "CHAPTER THIRTY-FOUR.", "III.34-002": "Chromatic Movement.", "III.34-003": "Chromatic melody moves through semitones, upward or downward. Its harmonic effect is wonderful. Most of these semitones lie outside the diatonic pattern, so they repeatedly create dissonances that delay or interrupt endings. They also make it easier to include every sound of a chord without disrupting the upper parts’ diatonic movement.", "III.34-004": "Chromatic movement is used only in minor keys. Descending chromatic parts are harder to understand than ascending ones.", "III.34-005": "ARTICLE ONE.", "III.34-006": "Descending Chromatic Movement.", "III.34-007": "Begin in a key by making any part descend in semitones. You may continue in that key, in its dominant’s key, and more particularly in the key of its fourth note. The original tonic then becomes a dominant. Each tonic can similarly become the dominant of the next key. Do not move too far from the starting key: return as soon as an opportunity appears.", "III.34-008": "The first way to understand chromatic movement clearly is to follow tonics as they become dominants in turn.", "III.34-009": "Move from tonic to dominant, then return to the tonic and turn it into a dominant. Continue using Chapter XXI’s rule of sevenths. Let the upper parts descend by as many semitones as possible. Each chromatic note forms a third, seventh, or sometimes diminished fifth above the fundamental bass, which still takes a seventh chord. Only one thing differs from our usual rules: the leading note may descend a semitone here instead of making its required ascent. The note it should rise to is still understood in the chord. This liberty is allowed only because of the chromatic movement.", "III.34-010": "EXAMPLE.", "III.34-011": "Descending chromatic movement; fundamental bass of sevenths.", "III.34-012": "[Handwritten note: see the Supplement.]", "III.34-013": "The ♮ signs beside the 7s turn previously major intervals into minor ones. You can see this in the parts.", "III.34-014": "Make each part the bass in turn and leave out the fundamental bass. First you will find a 7–6 sequence like the one derived from fundamental sevenths, but with this chromatic alteration. Then you will see tritones and diminished fifths replacing 2 and [6/5]. Through chromatic movement, these intervals resolve one another. Except at the ending, the leading note falls instead of rising.", "III.34-015": "Here is another chromatic treatment over a tonic that is held or stays on the same bass note.", "III.34-016": "EXAMPLE.", "III.34-017": "Pedal point; chromatic movement over a held tonic.", "III.34-018": "This can be called a pedal point.", "III.34-019": "The leading note is almost always present in chromatic movement. You may therefore use any chord containing the major dissonance, including those just shown. The augmented-second chord and its derivatives are also available. The augmented-fifth chord is especially useful for interrupting a cadence: see Chapter XXX’s example, where the leading note descends a semitone. You now know how all augmented or diminished chords by borrowing or supposition are built. Use them wherever a leading note can appropriately occur. But do not avoid ordinary perfect or seventh chords and their derivatives when they come naturally. Keep the upper parts diatonic as far as possible.", "III.34-020": "[Handwritten note: page 274.]", "III.34-021": "ARTICLE TWO.", "III.34-022": "Ascending Chromatic Movement.", "III.34-023": "Chromatic movement may also rise. It then lacks the sadness of descending movement, and its harmony fits the fundamental bass perfectly.", "III.34-024": "EXAMPLE.", "III.34-025": "Ascending chromatic movement; fundamental bass; interrupted cadence A; borrowing B/C.", "III.34-026": "B. Although this is the fundamental note, it cannot sound while C borrows its place as foundation.", "III.34-027": "A. Interrupted cadence.", "III.34-028": "EXAMPLE", "III.34-029": "Two Parts Rising and Falling at the Same Time by Semitones.", "III.34-030": "Turn the page for the example.", "III.34-031": "The Three Upper Parts May Change Places, Each Becoming the Bass.", "III.34-032": "Contrary chromatic movements; continuo bass and fundamental bass.", "III.34-033": "All these chromatic semitones involve only the sixth and seventh notes of the current key. In minor, lower the leading note a semitone when descending and raise the sixth a semitone when ascending. These notes can therefore pass through both forms, whether rising or falling.", "III.34-034": "To be fully convinced of these rules, compare them with the recap in Book II, Chapter XVIII. It includes every chord, its different continuations, and all the melodies that can be used.", "III.34-035": "Also read our observations on how the rules are established. They will be very useful.", "III.34-036": "Chapter XLIV gives a chromatic example in which chords by supposition and borrowing sound very effective.", "III.35-001": "CHAPTER THIRTY-FIVE.", "III.35-002": "How to Put Everything So Far into Practice.", "III.35-003": "ARTICLE ONE.", "III.35-004": "Bass Progression.", "III.35-005": "First write the most beautiful bass melody you can imagine. Use a familiar key that leads to other familiar keys, following Chapter XXIV. Include perfect cadences as often as possible: they provide the bass’s natural movement, which should favor consonant intervals over diatonic ones. Use interrupted and irregular cadences only when you recognize them and feel where they fit. An interrupted cadence pleasantly varies a key that has too many perfect cadences. An irregular cadence lets the melody rest on the tonic dominant or even the tonic, keeping the listener in pleasing suspense. Also include bass movements that support harmonic sequences derived from these cadences, as the examples show. Remember the progressions of 7, 7 and 6, 2 and 6, barred 5, 4♯, 2♯, 9, 11, 5♯, and 7♯.", "III.35-006": "Give each bass note and each chord one beat. In four-beat meter, for example, divide a whole note into four quarter notes to make four beats.", "III.35-007": "If you doubt your ability to write a good bass and lack a natural gift for inventing varied, pleasing melodies, follow this approach. Move freely among the notes of a key, choosing smaller intervals over larger ones: rise a third rather than fall a sixth, for example. The leading note must go next to the tonic, except in chromatic movement. Make a final cadence before changing key. Proceed similarly in the new key, then continue from key to key as Chapters XIII, XIV, XV, XVI, XXIV, and XXV explain. End perfect, interrupted, and irregular cadences on the first beat. If the first cadence lands elsewhere and you want to keep the melody, shift the bass’s starting beat. Start on beat two or three instead of one, or on one instead of two or three, and so on. If the problem occurs later in the piece, add or remove one or two notes as needed. Cadences should also be felt every two or four measures. You may break that last rule when good taste calls for it or when the words require it; the words then guide you.", "III.35-009": "ARTICLE TWO.", "III.35-010": "Using Consonant and Dissonant Chords.", "III.35-011": "Use a perfect chord to begin and end, and for every cadence inside a piece. It and its derivatives—the sixth and sixth–fourth chords—can also appear in diatonic bass movement. Such passages mix consonant and dissonant chords. See Chapter XI’s octave and Chapter XVI’s sixths. Prepare and resolve all dissonances by the rules. Once you know chord sequences thoroughly, this takes little effort. Dissonances may also be unprepared after the tonic’s perfect chord only, on the tonic or its derivatives, if the key remains the same. A key change is nevertheless possible when the bass rises a third and then falls a fifth.", "III.35-012": "EXAMPLE.", "III.35-013": "Rising third, then falling fifth; key changes A and B.", "III.35-014": "[Handwritten note: see the Supplement.]", "III.35-015": "When the bass rises a third, then falls a fifth and changes key, major changes to minor at A, or minor to major at B. The lines connecting notes,", "III.35-016": "thus, [lines converge from the two notes on the left toward the one on the right],", "III.35-017": "show that the right-hand note’s dissonance is unprepared. They also show how the upper part must move here.", "III.35-018": "You may invert these fundamental progressions as you choose.", "III.35-019": "Keep the upper parts diatonic for now. Depart from this only to complete a chord, move a part back above the bass, or return it to its natural range. Even then, avoid consecutive octaves or fifths unless inverted.", "III.35-020": "When parts rise or fall together, place them a third or sixth apart. Use fourths as little as possible, and never octaves or fifths. Thus two parts a third or sixth apart may keep that relationship in the next chord and continue doing so.", "III.35-021": "For now, regard it as always good when one part moves diatonically up or down while another moves by a consonant interval. A more exact explanation will follow.", "III.35-022": "The same chord sequence applies in every key. Identify the key, then give each note the chord belonging to its position. The second note, mediant, dominant, and so on always hold the same positions and take the same chords.", "III.35-023": "ARTICLE THREE.", "III.35-024": "Major Dissonances from the Leading Note, and Their Bass Notes.", "III.35-025": "1. Use the tritone only on the fourth note when it next falls to the mediant or tonic.", "III.35-026": "2. Use the diminished fifth only on the leading note when it next rises to the tonic or, sometimes, the mediant.", "III.35-027": "3. A small-sixth chord with a major sixth belongs only to the key’s second note. With a minor sixth it usually belongs to the sixth note.", "III.35-028": "4. A major third and seventh forming a tritone or diminished fifth occur together only over the tonic dominant. These four dissonances are the commonest.", "III.35-029": "5. The augmented seventh occurs only on a tonic that stays in place to prepare and resolve it.", "III.35-030": "6. As explained elsewhere, the augmented fifth belongs only to the mediant of a minor key.", "III.35-031": "7. The augmented second belongs only to the sixth note in minor, which must then fall.", "III.35-032": "8. The diminished seventh belongs only to the leading note, which must then rise.", "III.35-033": "9. Other derivatives of these last two dissonances use the same bass notes as the corresponding chords in which only the dominant is replaced by the sixth note. This applies only in minor keys.", "III.35-034": "ARTICLE FOUR.", "III.35-035": "Minor Dissonances.", "III.35-036": "1. A note requiring a perfect or seventh chord may first take the heteroclite eleventh, called the fourth, if its proper chord follows immediately. Do not apply this to the first or last note of a piece. Preparation will then be assured if you observe two points.", "III.35-037": "First, do not use the eleventh when a perfect chord follows its own derivative, since both are the same underlying chord.", "III.35-038": "Second, give a sixth to the note that rises a third to the note where you want the eleventh.", "III.35-039": "2. A seventh without a major dissonance is preferably prepared by an octave, fifth, sixth, third, or sixth. Even the fourth may prepare it when that fourth is a consonance in a tonic dominant’s sixth–fourth chord. The choice depends on the bass movement.", "III.35-040": "3. Prepare the ninth with a third or fifth, depending on the bass motion. A diminished fifth may also prepare it.", "III.35-041": "4. Prepare the eleventh with a fifth, or rarely a seventh. Its heteroclite form may be prepared by any consonance, a seventh, or a diminished fifth.", "III.35-042": "5. When a second is prepared in the bass, any consonance may precede it in the upper part while the bass stays still. Resolve every dissonance as previously explained.", "III.35-043": "In any dissonant chord, you may remove one of the two sounds creating the dissonance and use just a perfect chord or one of its derivatives.", "III.35-044": "ARTICLE FIVE.", "III.35-045": "Which Consonances to Double First.", "III.35-046": "Use this order of preference: octave, fifth, fourth, third, sixth. Prefer the octave to the fifth, and so on. An octave is already a doubling. In a consonant sixth chord, doubling the third or sixth at the octave is as good as doubling the bass.", "III.35-047": "ARTICLE SIX.", "III.35-048": "Meter and Beat.", "III.35-049": "Without rhythmic movement, music loses its grace, and beautiful melodies cannot even be invented. Writing chords is not enough. Their parts need melodic movement that makes caesuras, sections, cadences, long and short syllables, and the proper beats for dissonance clear. All must be felt at the first instant of a measure’s first beat. See Chapter I and Book II, Chapters XXVI, XXVII, XXVIII, and XXIX.", "III.35-051": "ARTICLE SEVEN.", "III.35-052": "Syncopation.", "III.35-053": "In meter’s natural order, each note starts and ends within one beat. A note beginning exactly on a strong beat may nevertheless stay on the same pitch as long as taste allows, whether held continuously or not. But if it begins elsewhere and half its value continues into the next strong beat, the displaced accent strikes the ear: this is syncopation. It can appear in four forms.", "III.35-054": "First, a barline divides the note’s duration into equal halves, thus:", "III.35-055": "First form of syncopation; meters in 2, 4, and 3.", "III.35-056": "Second, tie two equal successive notes on the same pitch with a semicircle above or below them: [upper arc] or [lower arc]. Their sound must continue without a break.", "III.35-057": "EXAMPLE.", "III.35-058": "Second form of syncopation; tied notes.", "III.35-059": "Third, a note or rest lasting half the first beat precedes another note that continues into the next beat.", "III.35-060": "EXAMPLE.", "III.35-061": "Third form of syncopation; notes A, B, C, D, F, G, H, and J.", "III.35-062": "A, B, C, D, F, G, H, and J are syncopated notes.", "III.35-063": "Fourth, repeat two equal notes on the same pitch instead of tying them. The first falls on a weak beat and the second on a strong beat. This may fit the words or make the tune livelier or more cheerful.", "III.35-064": "EXAMPLE.", "III.35-065": "Fourth form of syncopation; repeated notes.", "III.35-066": "A syncopated note must begin on a weak beat or in the second half of the first beat. It must also divide equally across that beat and the next. Instead of one note, use two notes each worth half its duration. Repeat them, or tie them with a semicircle to sustain one continuous sound. When tied, they are performed like one note with their combined duration.", "III.35-067": "The most skilled masters agree that composers should freely choose among these forms of syncopation. They serve both harmony and melody. In harmony, they introduce prepared dissonances. In melody, they increase expression without changing the kind of interval sounding across the two syncopated notes or the one held note.", "III.35-068": "EXAMPLE.", "III.35-069": "Syncopation in harmony and melody.", "III.35-070": "Figures such as 3 and 6, showing only consonances, mark syncopation used for melodic effect. A consonance followed by a dissonance shows syncopation serving harmony.", "III.35-071": "For melody, bass and upper part may syncopate together or separately. For harmony, the bass can syncopate only in second, tritone (4♯), or augmented-seventh chords.", "III.35-072": "In strict harmonic syncopation, make the preparation, dissonance, and resolution equal in duration whenever possible. Only triple meter is excepted, because it has two weak beats. There, the preparing or resolving consonance may last twice or half as long as the prepared dissonance.", "III.35-073": "If dissonances occur in succession, only the first can follow the rule of preparation on a weak beat and sounding on a strong beat.", "III.35-074": "If the dissonance cannot be prepared, syncopation no longer applies. As far as possible, move diatonically from the preceding consonance through the dissonance to its resolving consonance, using equal note values. Equal values matter less here than in syncopation. Nor is stepwise motion into an unprepared dissonance a universal rule, especially for sevenths, diminished fifths, and all major dissonances.", "III.36-001": "CHAPTER THIRTY-SIX.", "III.36-002": "Composing in Two Parts.", "III.36-003": "Fewer parts mean stricter rules. A freedom allowed in four-part music may become an error when fewer parts are used.", "III.36-004": "1. Now distinguish perfect and imperfect consonances.", "III.36-005": "The octave and fifth are perfect consonances. Do not write consecutive octaves or fifths here, even if inverted.", "III.36-006": "The fourth is also perfect, but it is not very suitable in two-part music. We shall simply explain how to use it.", "III.36-007": "Thirds and sixths are imperfect consonances. You may repeat or mix them freely as long as you keep good modulation.", "III.36-008": "When moving between a third and sixth, if both parts move by consonant intervals, make them move in opposite directions: one up, the other down.", "III.36-009": "Alternate perfect and imperfect consonances as much as possible.", "III.36-010": "Moving from perfect to perfect, perfect to imperfect, or imperfect to perfect generally requires one part to move diatonically while the other moves by a consonant interval. Contrary motion is advisable even then.", "III.36-011": "EXAMPLE. Successive Perfect Consonances.", "III.36-012": "Succession of perfect consonances", "III.36-013": "Any other way of placing two perfect consonances in succession is bad.", "III.36-014": "The A measures resemble each other; so do the B measures.", "III.36-015": "2. While one part stays still, the other may move through any number of consonant intervals, provided the two parts always sound in agreement.", "III.36-016": "3. These transitions are all good: octave to third; fifth to third or sixth; sixth to third; third to sixth.", "III.36-017": "4. Octave to fifth is good with contrary motion, except when the bass descends diatonically.", "III.36-018": "5. Octave to sixth is good. If both parts move by consonant intervals, use contrary motion. When the bass falls a third, however, everything is good.", "III.36-019": "6. Sixth to octave is good except if the bass rises diatonically, the upper part falls diatonically, or both move by consonant intervals.", "III.36-020": "7. Sixth to fifth is good except if the upper part rises diatonically, the bass falls diatonically, or both move by consonant intervals.", "III.36-021": "8. Fifth to octave is good except if the bass rises diatonically or both parts move by consonant intervals.", "III.36-022": "9. Third to octave is good unless the bass falls diatonically. When the bass rises a fifth, use contrary motion.", "III.36-023": "10. Third to fifth is also good. Use contrary motion when the bass rises a second, third, or fourth. The bass must rise a fourth rather than fall a fifth; otherwise the progression is bad.", "III.36-024": "11. The next example shows every consonance that may come before or after a fourth.", "III.36-025": "Consonances that may precede and follow the fourth", "III.36-026": "Cue signs show the consonances and dissonances that may follow the fourth. Figures between the parts do the same. Figures below the bass show which chords to use.", "III.36-027": "In A and B the cue signs offer two different chords: tritone or great sixth. Use one or the other, never both together.", "III.36-028": "Other progressions are not good. These rules especially depend on preferring smaller intervals. Rising a sixth is equivalent to falling a third, so choose the falling third. Apply the same principle to other equivalent motions. Good taste may call for the opposite, but only where the rules’ substance remains intact.", "III.36-029": "These rules work in every key, whether the thirds and sixths are major or minor.", "III.36-030": "Keep all the other four-part rules too, including the natural movement of major and minor thirds and the movement of dissonances. They apply everywhere.", "III.36-031": "Once you understand good modulation, you will follow almost all these rules with little effort.", "III.37-001": "CHAPTER THIRTY-SEVEN.", "III.37-002": "False Relations.", "III.37-003": "To avoid false relations within one part, use diatonic or consonant motion. A diminished fifth, seventh, or fourth is also allowed downward, but not upward. Once good modulation is secure, however, any known interval within an octave may be used. Be more cautious with intervals not listed above. Italians also use the descending diminished third, such as E-flat to C-sharp. We leave that choice to the composer.", "III.37-004": "With a perfect understanding of modulation, you cannot make false relations between two parts.", "III.37-005": "EXAMPLE.", "III.37-006": "False relations — major and minor modes", "III.37-007": "A shows a major mode; B shows a minor one. A key cannot be half major and half minor. Nor may you change between major and minor on the same tonic until you have made a perfect cadence in the mode in which you began. Even then, proceed cautiously. Knowing modulation well makes these rules almost unnecessary, so we need say no more.", "III.38-001": "CHAPTER THIRTY-EIGHT.", "III.38-002": "Writing a Melody Above a Bass.", "III.38-003": "Begin by writing the bass in one key whose modulation you understand. You also know how consonances and dissonances follow one another and how dissonances are prepared and resolved. Writing a correct melody above that bass should then be straightforward.", "III.38-004": "For more freedom of invention, first identify each bass note’s chord. Then choose a sound from each chord to make your melody. A perfect chord offers the third, fifth, or octave. A seventh chord also offers the seventh, if you want it and can use it correctly. Prepare the seventh, except when the bass rises a third or fifth while the upper part falls diatonically, or rises and then falls diatonically. See Chapter XIX. If the seventh cannot fall diatonically to a consonance in the next chord, omit it or change the bass. There is an exception: the next bass notes may all belong to the same seventh chord, with a later note finally supporting its consonant resolution. Keep the seventh on its pitch until then, unless an intervening bass note doubles it at the octave. In that case, lower the seventh a third, then raise the new note to the consonance that would have resolved the seventh. Alternatively, lower the seventh to the leading note if it belongs to the same chord. The downward-third option forms a sixth above the bass note that doubles the seventh; the leading-note option forms a tritone.", "III.38-005": "EXAMPLE.", "III.38-006": "Seventh unprepared or prepared by the third", "III.38-007": "A. I start on the fifth, although the octave or third was possible. The fifth is better here because it lets the next seventh enter unprepared, as explained above.", "III.38-008": "B. Hold the seventh until C, where the bass doubles it at the octave. Then lower it a third and raise it to its expected resolving consonance. Strictly speaking, it could instead have descended to the cue sign.", "III.38-009": "D. A third prepares the seventh. Hold it until F, where its octave enters the bass. It can then descend to the leading note at F, which belongs to the same chord.", "III.38-010": "To see whether a seventh can stay while the bass moves, examine the intervals. The bass notes must form a third, fifth, diminished fifth, or octave in relation to the seventh; alternatively, the seventh must form a third, fifth, or diminished fifth above one of those bass notes. The same reasoning works for other dissonances when you trace their foundation. Otherwise, the known limits of consonant and dissonant motion keep you from error.", "III.38-011": "We have seen an upper note stay while the bass moves through one chord’s notes. The reverse also works: hold the bass while the upper part moves through the notes of its chord.", "III.38-012": "One bass note may support several chords. A third, fifth, sixth, or other interval shared by those chords may sound in either. If an interval is missing from one chord, do not use it there.", "III.38-013": "If your taste is still developing, write figures for the chords you know belong to the bass. Choose chord notes for the melody, staying within the rules. Those rules often favor certain notes because of what comes before or after them.", "III.38-014": "In two parts, the upper part should always finish on the octave, rarely on the third, and never on the fifth.", "III.38-015": "GENERAL EXAMPLE.", "III.38-016": "General example — upper part, continuo bass, and fundamental proof", "III.38-017": "The upper part was written against the continuo alone. Against the fundamental bass it has many faults, but these concern voice movement, not the underlying harmony. The fundamental bass is included only as proof of the perfect harmony supplying the melody’s sounds.", "III.38-019": "A. I move freely through the chord’s notes.", "III.38-020": "I move from the fifth to the sixth at B. I could instead have held the previous pitch, making a fourth, because the fourth belongs to B’s small-sixth chord. Moving to the third was also possible.", "III.38-021": "B, C, D, E. Four sixths follow one another because each belongs to its chord. I could instead have chosen another interval in each chord.", "III.38-022": "F, G. The leading note goes to the mediant instead of the tonic. This obeys the rules for consonant motion. The mediant also represents the tonic and belongs to its chord.", "III.38-023": "H. The fourth belongs to the second chord. I then move to the sixth at J and the second at K, where it belongs to the tritone chord.", "III.38-024": "L’s sixth prepares M’s seventh. It resolves downward to N’s sixth, the leading note, which rises as required to the tonic at O. I move to that tonic’s third at P before sounding the second at Q.", "III.38-025": "At P, Q, R, S, T, seconds are prepared and resolved in the bass. The upper part precedes them with a third at P and a sixth at R. An octave, fifth, or fourth could do the same. Any chordal consonance may come before or after the second. At T it is followed by a fourth from the small-sixth chord. Keep the required bass motion unchanged.", "III.38-026": "The third is best for preparing and resolving a second, so use it often. At T we replace it with a fourth that would clash with it. That fourth must go to the note where the third would have descended if both had sounded, as at V. Here is the general rule. Suppose another note replaces the upper note that should resolve a dissonance, and the two would form a seventh or second. Move the substitute to the note that should have followed the missing note. The missing note would have formed a minor dissonance with the substitute. This situation occurs between third and fourth in a small-sixth chord, or fifth and sixth in great-sixth and diminished-fifth chords. If the third or fifth should resolve a dissonance and then fall diatonically, its replacement—the fourth or sixth—must go to that expected destination.", "III.38-028": "The rest follows the same principles. At M the key changes: instead of raising the leading note to the tonic’s octave, we make it the seventh above the tonic. That tonic becomes a fourth note through the great-sixth and tritone chords at N and O. At J we return to C because the consonant bass passage ending at U identifies C as tonic. To prepare that key, remove the sharp from F at D. B-flat then announces F. Finally, a sharp restoring B to its natural state establishes C again.", "III.38-029": "Compare the upper part and continuo, one at a time, with the fundamental bass to clarify these points. Each fundamental-bass note has a perfect or seventh chord. From it, the continuo and upper part choose a third, fifth, octave, or seventh, then follow the movement rules already given. Notice G, H, J, K, L, and similar passages: when the continuo moves diatonically, the upper part often follows the fundamental bass’s motion. Thus consonant movement in one part often requires diatonic movement in the other, and diatonic movement often requires consonant movement in the other.", "III.39-001": "CHAPTER THIRTY-NINE.", "III.39-002": "Figured Melody, or Supposition.", "III.39-003": "What has previously been called supposition we call figured melody. Its rules follow.", "III.39-004": "Complete harmony must be clear on every beat. A beat is felt at its starting instant, whether the hand moves down or up. Between one beat’s start and the next, you may insert as many notes as invention and taste allow.", "III.39-005": "ARTICLE ONE.", "III.39-006": "Figured Melody Using Consonant Intervals.", "III.39-007": "If the inserted notes move by consonant intervals, use only notes of the current beat’s chord. Land on a note of the next beat’s chord, and continue this way to the end.", "III.39-008": "EXAMPLE of a Figured Upper Part.", "III.39-009": "Figured melody through consonant intervals — upper part", "III.39-010": "Every upper note belongs to the chord shown by the bass figures.", "III.39-012": "The composer may divide a two-beat measure into four beats. At A, two different chords divide one note’s duration into two beats. Depending on the tempo, several chords may therefore fit within one beat. Conversely, one chord may last for one measure or several measures.", "III.39-013": "EXAMPLE of a Figured Bass.", "III.39-014": "Figured bass and fundamental bass — conditional cue signs C, D", "III.39-015": "Numbers below the figured-bass notes show their intervals against the fundamental bass. Numbers above them show their chords.", "III.39-016": "You may start with a fundamental bass and write the figured bass above it, much like a figured upper part. There is an important difference. Do not avoid matching the two basses’ notes. Instead, use the fundamental bass’s root notes in the figured bass as often as possible, even at the very start of a beat.", "III.39-017": "Fit the upper part to whichever part accompanies it. If both basses are to sound, the upper part must obey the rules against both. At C and D it makes two fifths with the fundamental bass, so replace those notes with the cue-sign notes.", "III.39-018": "Alternatively, write the figured bass first. Identify its beats, then add a fundamental bass below that obeys all the rules for fundamental-bass motion and chords. Next write an upper part, using more or less figuration than the figured bass.", "III.39-019": "Some figured-bass notes fit two chords. Look to the next beat to decide between them. The fundamental bass can also guide the choice.", "III.39-020": "Aim for variety. Avoid repeating the same passages too often.", "III.39-021": "You may add figuration to all beats or only some. Sometimes figure just half a beat, in the bass, upper part, or both, while following the rules.", "III.39-022": "EXAMPLE.", "III.39-023": "Two figured parts — variety of beats", "III.39-024": "Let one part begin first and another enter two or three beats later, or even one or two measures later, according to taste. More parts may enter in the same way.", "III.39-026": "Begin anywhere in the measure, even on the last quarter of a beat. You may also let a part rest for a while. If it is the bass, stop it for at most one or two measures. A continuo bass must always be understood, even when only one part sounds.", "III.39-027": "Use quarter rests and the other rest signs explained in Chapter I to mark these silences.", "III.39-028": "A dot after a note continues that note. It usually belongs to the harmony with the other parts because it nearly always falls on a strong beat. The dot lasts half the preceding note’s value. If that means half a beat or less, the note after it is included only for melodic effect.", "III.39-029": "ARTICLE TWO.", "III.39-030": "Figured Melody Using Diatonic Intervals.", "III.39-031": "Any number of notes may pass between beats. If they move diatonically, only the first must belong to the chord. But if the last note leaps by a consonant interval to the next beat, it too must belong to the current beat’s chord.", "III.39-032": "If a beat is slow enough to split into two equal beats, divide its notes into equal portions too. Make the first note of each portion belong to the chord sounding beneath it.", "III.39-033": "Taste sometimes calls for an exception. The first note of a diatonic beat may lie outside the chord. It then acts as a kind of coulée—a sliding approach—to a chord note reached immediately afterward, before the beat ends.", "III.39-034": "EXAMPLE.", "III.39-035": "Figured melody through diatonic intervals", "III.39-036": "This two-beat meter is divided into four almost throughout. The first eighth note of each pair always belongs to the chord.", "III.39-037": "At A, the first of the final two eighth notes is outside the chord because it belongs to a diatonic passage connecting the beats. The first two eighths do not belong to that passage and are chord notes.", "III.39-038": "Divide B into four, giving each note a chord. The tonic must have its natural chord as soon as it follows the leading note. If the tonic came immediately in the next measure and the melody rested there, B would not need this division. But the melody instead rests on the dominant. We therefore hear an irregular cadence from B’s last eighth to the next note.", "III.39-040": "C’s first and third eighths lie outside the chord. They slide into the second and fourth, which belong to it. The fourth must be a chord note because it moves by a consonant interval to the next beat. F and D contain similar sliding approaches.", "III.39-041": "D’s dot continues the preceding note. Its figured tritone chord lasts for the dot’s full value. The tritone resolves only on the following beat.", "III.39-042": "We have explained this in a way that replaces the very abstract rules used until now.", "III.39-043": "The freedom to figure melodies and invert chords creates music’s immense variety.", "III.40-001": "CHAPTER FORTY.", "III.40-002": "Writing a Fundamental Bass Below an Upper Part.", "III.40-003": "If you cannot yet sense the bass while composing a melody, use a fundamental bass to find the best bass for the finished upper part. Every melody has a natural bass that fits better than any other and comes to mind before we seek it. Even a little feeling for perfect harmony lets us naturally sing a cadence’s bass when hearing its upper part. This reveals the key. Following perfect and irregular cadences reveals key changes; interrupted cadences have the same upper motion as perfect ones. A fundamental bass, using only perfect and seventh chords, identifies the key even faster.", "III.40-004": "EXAMPLES. Upper-Part Movements in Cadences.", "III.40-005": "Perfect or irregular cadences in major and minor keys", "III.40-006": "These cadences are all based on C, though they also fit other keys.", "III.40-007": "A rises from leading note to tonic in major or minor. In minor, however, the same movement could go from the second note to the mediant, as F shows.", "III.40-008": "B falls from the second note to the tonic in major or minor. In minor it could also fall from the fourth note to the mediant, as G shows. These first two cadences therefore closely connect C major and A minor. In general, both work in a major key and the minor key a minor third below it: C major/A minor, F major/D minor, G major/E minor, and so on.", "III.40-009": "C, D, F, and G may be perfect or irregular, depending on the bass. A rise of a fourth to the tonic makes a perfect cadence. A fall of a fourth to the tonic or dominant makes an irregular one. Mentioning the dominant means these patterns can belong to keys besides C. C and D can be irregular in D; D can also be irregular in F. F and G can be perfect in E-flat; G can also be irregular in A-flat. H, J, L, and M are the actual irregular cadences on C’s dominant. But H can also be perfect or irregular in B-flat; J irregular in A minor; L perfect in D; and M irregular in B-flat major, G minor, or E-flat major or minor. We can use this freedom to interpret an upper-part cadence in different ways.", "III.40-011": "1. Use C major or D minor if you know them better than other keys. The melody must start on the octave, third, or fifth. Then inspect its first cadence, usually in measure two or four, to check the key. If you began with C, E, or G—the chord tones of C—a first cadence ending on D does not mean D is the key. For D, the opening should have been D, F, or A. If the melody needs sharps or flats to make certain semitones, those signs identify the key as Chapters XXIV and XXV explain. An opening C may be A’s minor third, F’s fifth, or C’s octave. Sharps, flats, and cadences settle the key. If the tune follows natural taste, its final note alone should identify the tonic.", "III.40-012": "2. Once the key is certain, interpret every suitable cadence within it. Compare foreign cadences with the previous example, using the rules below.", "III.40-013": "1. Against the fundamental bass, the upper part must always be a third, fifth, octave, or seventh.", "III.40-014": "2. Prefer fundamental-bass motion in this order: descending fifth, fourth, third, seventh. Rising a second is equivalent to falling a seventh, and so on. If a descending fifth does not fit the upper part, try a fourth, third, or seventh in that order of preference.", "III.40-016": "3. To practice fundamental bass thoroughly, keep the upper part unfigured. Figuration confuses beginners. Give each upper note at least one beat.", "III.40-017": "4. Start with dance types such as gavottes and sarabandes. Their cadences usually occur every two measures, making decisions easier. Book II, Chapters XXV–XXVIII, gives their tempo, number of measures, suitable verses, and guidance for setting words.", "III.40-018": "5. If a cadence is foreign to the key, ask whether it ends the melody; the words can help. If it does, the key changes, usually to the old key’s dominant, mediant, fourth, or sixth. Compare with the previous example. A cadence ending like this:", "III.40-019": "Thus — cadences in F, G, D, E, and A", "III.40-020": "is a perfect cadence in one of those keys, just as this one", "III.40-021": "Perfect cadence in C", "III.40-022": "is one in C. Other correspondingly related cadences work the same way. If the melody has not fully ended, however, let the bass follow its natural movement, preferring the most perfect progressions whenever possible.", "III.40-023": "6. Keep the bass note while the melody forms its third, fifth, or octave. Change it if you can do so without disrupting the bass’s natural movement; variety is a major source of harmonic beauty.", "III.40-025": "7. Treat the first beat as the main beat. Move a bass note earlier or later if it fits a nearby first beat better. There are two cases. First, if a note after the first beat could already sound on it, bring it forward. Second, if a weak-beat note would immediately repeat on the next first beat and nothing can go between, avoid that early repetition. Keep the previous first-beat bass if possible, or choose another note different from the next first-beat note.", "III.40-026": "EXAMPLE.", "III.40-027": "First beat preferred — examples H and J", "III.40-028": "H is better: the second measure’s second-beat note fits its first beat too, so put it there.", "III.40-029": "ANOTHER EXAMPLE.", "III.40-030": "Another example — held or varied bass", "III.40-031": "In A I cannot keep the same bass note through the first measure, although I can change it as in B: another note can fit between the first measure’s second beat and the next measure’s first beat. In C and F, do not use the first measure’s second bass note, because that note must appear on the next first beat. At D, repeat the previous first-beat note, which still fits the second beat. At G, choose a different note because the first does not fit the second beat.", "III.40-033": "8. Often divide an upper note into equal halves and place two different compatible bass notes beneath it. This keeps the bass consonant and allows the best progression from the second bass note to the next one.", "III.40-034": "EXAMPLE.", "III.40-035": "Dividing an upper note and progressing the bass", "III.40-036": "Dividing the note also helps place the key’s best bass notes on strong beats. In order of preference these are tonic, dominant, fourth, sixth, and sometimes second. Use the mediant rarely and the seventh never on any beat. If the seventh cannot be avoided, the key has changed; accidentals or foreign cadences show this.", "III.40-037": "9. Put the first prepared dissonance on a principal beat. If several follow, this rule concerns only the first. An unprepared dissonance requires a three-note diatonic upper motion: down through three degrees, or up and immediately down. Meanwhile the bass rises a third or fifth and then falls a fifth. The middle upper note is the dissonance.", "III.40-039": "EXAMPLE.", "III.40-040": "Unprepared seventh and cadence cue signs", "III.40-041": "The bass may rise a fourth here instead of a fifth, avoiding the dissonance. This converts perfect and irregular cadences into one another. A–B is perfect. Replace A with the cue-sign pitch and it becomes irregular with B.", "III.40-042": "The cue signs above the first bass note show further choices. Put that first note at either cue-sign pitch.", "III.40-043": "Only the seventh is dissonant against the fundamental bass. The other dissonances come from inversions, using another note of the fundamental bass’s seventh chord as bass. Follow Chapters XVII, XVIII, XX, XXI, XXII, and XXVI.", "III.40-044": "An unprepared seventh can sometimes work even after an upper-part leap. Hold the bass note that sounded before the seventh. This is good if the upper part immediately falls diatonically and the bass can rise a fourth to form a third with it after the seventh.", "III.40-045": "Turn the page for the example.", "III.40-046": "EXAMPLE.", "III.40-047": "Upper-part leaps — examples A, B, J and C, D, F", "III.40-048": "A to B is a leap. If the first bass note stayed, B would make a seventh. But B does not descend afterward, and that bass could not rise a fourth to make a third with J. Change the bass as shown, choosing its best progression. C, D, F supplies the conditions missing at A, B, J. This was also called supposition or dissonance for melodic effect. In fact the dissonant harmony is already present at the first upper note; the bass stays to receive the seventh later. Sound the complete seventh chord on the first bass note under C to hear this. After the seventh, the upper part may therefore visit other notes of that chord. It must eventually return to the third, or at least the octave, of the bass note reached by the rising fourth at G.", "III.40-049": "EXAMPLE.", "III.40-050": "Dissonance for melodic taste — examples G and H", "III.40-051": "The bass may rise one degree instead of a fourth, making an interrupted cadence. This belongs only to a borrowed or inverted bass, not the fundamental bass itself. Use it according to taste inside a piece, provided it creates no consecutive fifths with the upper part.", "III.40-053": "10. If the same kind of cadence repeats in one key, find an internal cadence that does not fully end the melody and could belong to another key. Use that foreign cadence for variety. Repeated identical cadences make an air dull. If the upper melody should stay unchanged, vary the bass, especially at cadences without a final conclusion.", "III.40-054": "For major, use the related minor key a minor third below. For minor, use the major key a minor third above. Only the bass need change; the melody may stay the same.", "III.40-055": "EXAMPLE.", "III.40-056": "Same upper part — cadences in C and A", "III.40-057": "A and B are perfect cadences; C and D are irregular. Their upper parts naturally fit both C major and A minor. In either key, reinterpret the same melody’s cadence in the other. The same works for D minor/F major and G major/E minor, and other pairs with that relationship.", "III.40-059": "This way of moving a cadence between keys also helps when you want a definite key change.", "III.40-060": "An interrupted cadence works in either case too.", "III.40-061": "11. Irregular cadences work well inside an air and can often end the first of two sections, though not as a habit. Favor measures two, six, and ten for them. Perfect cadences fit measures four, eight, and twelve better. If a perfect cadence occurs in measure six or ten, an interrupted cadence may replace it.", "III.40-062": "12. A cadence transferred to another key may call for a less perfect bass progression instead of the usual preferred one. Use judgment and discretion.", "III.40-063": "13. When inventing freely, composers may not notice whether a melody uses figuration, ties, or continuous stepwise movement. With figuration, beginners may confuse harmonic notes with notes added only for melodic effect. With leaps, they may fear consecutive fifths or octaves against the fundamental bass. But the melody is then borrowing the fundamental bass’s natural movement. A different bass is therefore needed to fit it. Use the fundamental bass to identify the chords, then choose chord notes for a new bass that agrees with the existing melody in harmony and motion. Consecutive fifths and octaves do not harm the harmonic foundation itself. They are forbidden to avoid dry, tedious monotony. Our original rules described the natural movements of bass and upper part. Once the melody borrows the bass’s motion, the bass cannot keep that same course. New rules must govern their interaction so the second part fits the first. Yet these rules still rest on the original ones: natural part order avoids consecutive fifths and octaves, resolves all dissonances correctly, and prepares them or leaves them unprepared according to the best bass progression.", "III.40-065": "We often change the bass’s natural route to avoid its frequent strong endings. Use another note of each cadential chord in the bass instead of its natural root. This keeps the melody and harmony suspended as the subject requires. A full conclusion belongs only where the meaning is complete. The next chapter explains further.", "III.41-001": "CHAPTER FORTY-ONE.", "III.41-002": "Writing a Continuo Bass Below an Upper Part.", "III.41-003": "Strictly speaking, the fundamental bass should be the true continuo bass. Custom instead calls the bass chosen by good taste to fit the other parts the continuo. We use that name to distinguish it from the fundamental bass.", "III.41-004": "Developed taste naturally senses the best bass for any air, as the previous chapter began by saying. But this gift needs knowledge to avoid errors, and knowledge needs taste to reach perfection. Being free to choose among chord notes does not tell you which choice is best. Variety is our only rule for good taste. Aim for it while observing these points.", "III.41-005": "1. Now avoid consecutive octaves and fifths. Follow the rules for consonances and dissonances in Chapters XIV, XVIII, XX, XXI, and XXX exactly.", "III.41-006": "2. After writing the fundamental bass, study the upper part: its design, character, tempo, and special features. Give the new bass the same expression. Where the melody does not need a final cadence, avoid one by choosing other suitable notes from the fundamental chord. They must fit the upper part according to the consonance and dissonance rules. Prepare dissonances when required and resolve each seventh-chord note by its prescribed movement. Seek variety between the parts. A sixth followed by a consonance or dissonance need not recur every time. Another bass route might give a tritone resolving to a sixth, a diminished fifth to a third, or a seventh to a sixth, third, or fifth. You can also use only the seventh chord’s consonant intervals: octave, fifth, third, or their inversions, sixth and fourth. Use supposition or borrowed chords when diatonic bass movement leads to them. Diatonic movement is the most singable, so prefer it whenever possible, especially away from endings. Prepare every minor dissonance by supposition in the syncopated upper part while the bass rises. If the bass falls, it must leap. For every chord with a major dissonance, follow the precautions given in the octave or Chapters XI, XXII, XXXI, XXXIV, and XXXV for augmented fifths, augmented sevenths, tritones, and augmented seconds. Prepare a second through syncopation in the bass. At a true melodic ending, follow the fundamental bass. This produces a bass with both skill and taste.", "III.41-008": "EXAMPLE.", "III.41-009": "Continuo bass beneath an upper part — eight measures", "III.41-010": "In measure four, the cue signs show how to turn C’s perfect cadence into an irregular cadence in A. Variety actually calls for this choice here.", "III.41-011": "The fundamental bass has equal progressions at A and B in measures one and two. I save the more cadential progression for measure two, where cadences normally occur. This one is irregular; measure four’s is perfect. In measure one I make the continuo move diatonically while fitting the melody. In measure two I continue that motion: the second beat forms a seventh against the fundamental bass, resolving to its third and still fitting the upper part. Continue diatonically until the perfect cadence, then follow the fundamental bass. Afterward, seek diatonic motion again. The last note of measure four can stay, making a third against the fundamental bass and an octave against the melody. In measure five it makes a sixth against the melody and a seventh against the fundamental bass. Measure six supplies a ninth. Only at the final ending do I follow the fundamental bass’s motion again. The continuo’s intervals against the fundamental also determine its chords. A correct fundamental bass carries only perfect and seventh chords. Notes a third, fifth, or seventh from it therefore take the corresponding derived chords. The upper part could be figured by the same method if used as bass. This explains the ninth figure on measure six’s first note: it is a third below, or sixth above, the fundamental note. It can belong only by supposition. Since the fundamental carries a seventh chord, the continuo must take a ninth chord, even though the melody does not sound the ninth. Its fifth belongs to that chord, and the implied ninth is properly prepared and resolved.", "III.41-013": "Explaining every possible continuo variation this way would never end. Study the treatise’s examples carefully, using each to clarify the questions that concern you. Consult skilled masters’ works too. You will soon overcome these difficulties.", "III.42-001": "CHAPTER FORTY-TWO.", "III.42-002": "Useful Comments on the Previous Chapter.", "III.42-003": "1. You can write a bass below another part without first writing a fundamental bass. Our precise rules for consonant succession are enough. Alternate perfect and imperfect consonances whenever possible. Avoid successive perfect consonances if you can. Imperfect ones may follow each other, but too many would destroy variety. Keep the bass diatonic as much as possible, with occasional consonant motion. Consonant motion is essential at the main cadences.", "III.42-004": "2. Use the chord sequences given by the rules of the octave, 7 and 6, 2 and 6/5, 9, and the others. They tell which chord should follow each chord. See Chapters XI, XXI, XXII, XXVII, XXVIII, and XXIX.", "III.42-005": "3. For variety, consult Chapter XVII’s examples of different bass movements under one melody. Among their four parts, find a pair of notes moving like a pair in your upper part, then another matching pair elsewhere, and continue. Check carefully that the mode or key relationships agree. Compare scale positions, not note names. The examples use C, but mediant-to-dominant or sixth-to-fourth motion can take the same chords in any key.", "III.42-007": "Review Chapters XIV and XVIII on dissonance preparation and resolution before using dissonances.", "III.42-008": "See also Chapters XXIV and XXVI, Articles I–III: how to change keys, identify them, and find chords for any bass progression. This combined knowledge resolves the many doubts that constantly arise.", "III.42-009": "Once comfortable with these subjects, learn how to use licenses at suitable moments. Add figuration to the upper melody and, if desired, the bass. Keep track of principal beats and each beat’s harmonic note so you can write accurate bass figures. If a chord’s foundation is unclear, add a fundamental bass beneath the two parts. It will reveal errors and identify the continuo’s chords. A third, fifth, or seventh relative to the fundamental allows only its corresponding chord. A continuo note a third or fifth below the fundamental creates supposition; check that it obeys the rules.", "III.42-010": "Once the bass figures are correct, adding two or three parts is easy—unless the upper melody or bass is too elaborate for the extra parts to fit regularly. More parts therefore require the bass to follow the fundamental more closely. Still, our examples show stepwise ascending and descending octave basses in four or five parts, using ordinary chords, different sixth chords, 7 and 6, 2 and 6/5, 9, and others. Next we examine the rules for several parts.", "III.43-001": "CHAPTER FORTY-THREE.", "III.43-002": "Guidelines for Writing in Two, Three, and Four Parts.", "III.43-003": "For the best two- or three-part music, compose all parts together. Each needs a flowing, graceful melody. A skilled composer usually hears the effect of the accompanying parts while writing one part.", "III.43-004": "1. One part usually carries the main beautiful melody, called the subject. But its beauty suffers if the other parts are not also melodically attractive in proportion. Only in recitative should they merely supply harmony. In other two- or three-part music, their melodic quality should be nearly equal. It is rightly said that a singing bass promises beautiful music.", "III.43-005": "Fewer parts require more varied chords. Apply this rule most strictly in two-part music.", "III.43-006": "2. In three parts, fill out chords as much as possible. Always include a third or sixth between at least two parts. Use octaves sparingly unless the design,* fugue, or melody calls for them. Perfect cadences especially allow them, since each part usually ends on the tonic.", "III.43-007": "* Design and fugue are discussed in the last chapter.", "III.43-008": "EXAMPLE.", "III.43-009": "Three-part composition", "III.43-010": "Four or more parts can form choruses, quartets, quintets, and so on. The final chapter includes a quintet or canon. A chorus may have many singers on each part; a quartet or quintet usually has one. Giving every part a beautiful, natural melody at once is hard. At least give that quality to the bass and top part, especially in choruses. You may also place the melody in any part or pass it between parts. Prefer the highest voice—or highest instrument if no voices are present—because penetrating sounds naturally attract attention. The bass is a separate consideration: it must take priority and remain our guide.", "III.43-011": "Try hard to give every quartet or quintet part a beautiful melody, however difficult that is. Fugue may have been invented mainly for these pieces. They have little charm without it. When the fugue returns in different parts, it pleasantly surprises listeners and redirects attention from less melodic parts to the one carrying the fugue. This is a skillful way to focus attention on the strongest feature. Taste controls the fugue’s melody, its accompaniment, and rests used where a part would otherwise be ungraceful. Choose these well to succeed; the next chapter explains. Choruses alone can please without fugues because their leading parts’ beautiful melodies hold attention sufficiently. Duets and trios can do so too.", "III.43-012": "You may write more than five parts, but only great masters should attempt it. They know how to double consonances, move them in opposite directions, and vary the texture with more or less figured melodies.", "III.44-001": "CHAPTER FORTY-FOUR.", "III.44-002": "Design, Imitation, and Fugue.", "III.44-003": "In general, musical design is the subject of the composer’s plan. A skilled composer first chooses tempo, key or mode, melody, and harmony suited to that subject. See Book II, Chapter XXX. Here “design” means more specifically a melody that recurs through a piece, to fit the words or satisfy taste or imagination. It takes the form of imitation or fugue.", "III.44-004": "Imitation simply repeats a melodic passage wherever desired, in any part, without additional rules of regularity.", "III.44-005": "Fugue also repeats a melodic passage in chosen parts, but follows stricter rules, given below.", "III.44-006": "Imitation may repeat one measure, several measures, or the entire air, in any or all parts at any pitches. Fugue requires the melody to alternate between the main upper part and bass, although another part may carry the subject instead of the top part. With more parts, it is better still for every part to take its turn. The pitches must also follow rules rather than free choice.", "III.44-007": "1. While still learning, prefer tonic and dominant for the subject’s opening and ending. Keep its melody within the key’s octave. Notes outside that span count as equivalent to their octave counterparts inside it.", "III.44-008": "2. Tonic at one part’s opening or ending must answer dominant in the other. Apply the same relationship throughout the octave. The second note above tonic corresponds to the sixth above dominant. A third, fourth, or fifth above or below tonic similarly corresponds to that distance above or below dominant, according to the melody’s direction. The whole subject must preserve the correspondence required at its beginning and end.", "III.44-010": "3. The diatonic routes between tonic and dominant contain different numbers of notes. In the longer route, either of two neighboring notes may answer a note required by the shorter route, especially inside the subject. Descending tonic to dominant has only sixth and seventh between them. Descending dominant to tonic offers fourth, third, and second. Choose among these the notes nearest the final tonic to reproduce the earlier melody as closely as possible. If the longer route came first, adapt the shorter route to it. Prefer a close match near the ending rather than the opening. The example clarifies this.", "III.44-011": "First example. Second example. Third example. A. C. D. or.", "III.44-012": "Fourth example. B. F. Fifth example. G. H.", "III.44-013": "Sixth example. J. L. M. N. P. Q. R. T. or.", "III.44-014": "In example one, the sixth or seventh answers the mediant at A.", "III.44-015": "In example two, the sixth answers the mediant at C.", "III.44-016": "In example three, the seventh answers the mediant at D.", "III.44-017": "In example four, dominant B or fourth note F answers the tonic at B and F.", "III.44-018": "In example five, the mediant answers the seventh at G or sixth at H.", "III.44-019": "In example six: mediant answers seventh L or sixth N; second answers sixth J or dominant P; dominant answers second M or tonic Q; tonic answers fourth R.", "III.44-021": "Choosing correctly among the five notes from tonic up to dominant takes care when answering a melody within the four from dominant up to tonic. This five-versus-four difference remains whether the subject rises or falls. Sometimes borrow the second or fourth note to create five notes on the dominant-to-tonic upward route, or the equivalent tonic-to-dominant downward route. Earlier writers neglected these points, so experience should supply the explanation.", "III.44-022": "1. At the subject’s start and finish, tonic must answer dominant and dominant tonic. Inside it, substitute fourth for dominant or second for tonic when this makes the melody match better. Second up to dominant and fourth down to tonic then each span four degrees, matching dominant up to tonic or tonic down to dominant. Conversely, second down to dominant and fourth up to tonic span five, matching dominant down to tonic or tonic up to dominant. The match is only approximate because each mode has fixed diatonic steps. Do not add new accidentals to alter them, except in minor: flatten the descending sixth and sharpen the ascending leading note. You may sometimes also sharpen a minor key’s mediant or any key’s fourth when it answers the leading note. See T in example six. Those notes must form major thirds or major sixths with the bass.", "III.44-024": "When inventing a fugue melody, imagine its bass and answer at the same time. The answer creates variety. You may then begin with either melody.", "III.44-025": "3. After finding the bass, add two or three possible accompanying parts. They and the bass should follow roughly the same movement under the subject and answer. A correctly imitated bass carries the same chords in both. These accompanying parts can then help create several simultaneous fugues or a canon, discussed later.", "III.44-026": "4. Several basses may fit a fugue melody, which may itself work best in the bass. Inversion lets us choose different basses or use an upper-type melody as bass. Alternating these accompaniments is especially attractive in fugue, where the accompanying parts provide the variety. We said the bass could stay nearly the same with matching chords only to explain correct melodic imitation. Matching chords alone prove that relationship.", "III.44-027": "5. Tonic and dominant guide the choice of notes between them, since subjects normally end there. Still, match the answer’s intervals to the subject where possible, especially inside it: a third answers a third, fourth a fourth, and similarly fifth, sixth, or seventh. Give up exact matching for diatonic motion or important scale notes. Favor what comes next over what came before, and the tonic/dominant opening and ending over exact intervals. Thus fourths often answer fifths or vice versa. If a consonant leap leads into diatonic motion toward the tonic, reproduce that stepwise passage toward the dominant in the answer. A passage toward the dominant must instead be answered toward tonic, especially if it forms a cadence. Final cadences must use tonic and dominant. Internal ones may use fourth instead of dominant or sometimes second instead of tonic.", "III.44-029": "Subjects usually begin and end on tonic, dominant, or mediant. A mediant takes a sixth or seventh in response, as example five showed. Look ahead rather than backward and compare the chords over the subject’s and answer’s basses. This largely prevents mistakes.", "III.44-030": "EXAMPLE.", "III.44-031": "First melody. Answer. First melody. Answer. FUNDAMENTAL BASS. CONTINUO BASS.", "III.44-032": "The continuo shows that any suitable bass can preserve this correspondence by carrying the same chords under both melodies. The fundamental bass is still the best demonstration.", "III.44-033": "6. The subject must last at least half a measure. If it exceeds four measures, start the answer during measure four. Even then, a fairly lively tempo is needed to make such a long unaccompanied melody pleasing.", "III.44-034": "7. Begin on any beat, but normally end on beat one; beat three in four-beat meter can serve similarly. Another ending beat usually reflects a feminine rhyme, in actual words or an imagined text, or simply fancy. Taste-based rules sometimes yield to novelty. An unexpected ending can please when used wisely, and may then end on a note other than tonic or dominant.", "III.44-036": "EXAMPLES.", "III.44-037": "First melody. Answer.", "III.44-038": "First melody. Answer.", "III.44-039": "8. Match the subject as fully as possible. Keep the same number of whole notes, half notes, and other values in the corresponding beats at every entry.", "III.44-040": "9. Parts may enter in unison or at the octave, but entries at the fifth or fourth are even more pleasing. Any part may introduce or repeat the subject. To change key, move each note to the same scale position in the new key. Preserve its relationship to tonic, the note values and their numbers, and the opening and ending beats.", "III.44-041": "10. Entries may wait until the subject finishes, or overlap it if the design permits. Overlap works very well if the other features remain unchanged. See example six.", "III.44-042": "11. Inversion creates harmonic variety and enriches fugue too. Turn every rising interval downward and every falling interval upward, keeping everything else unchanged as in Article IX.", "III.44-043": "EXAMPLE. First melody. INVERTED FUGUE. or. Inverted answer. Same.", "III.44-044": "12. Different subjects may sound together or one after another. Avoid starting them on the same beat or in the same measure, especially the first time. Give them opposite motion and different characters: whole notes in one, halves or quarters in another, as you choose. If entire subjects cannot combine, combine at least portions of them. The example explains.", "III.44-045": "QUINTET. Laboravi (I have labored). Continuo bass. Fundamental bass.", "III.44-046": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-047": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-048": "CONTINUO BASS. FUNDAMENTAL BASS. For the proof.", "III.44-049": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-050": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-051": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-052": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-053": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-054": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-055": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-056": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-057": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-058": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-059": "CONTINUO BASS. FUNDAMENTAL BASS.", "III.44-060": "The example uses four different subjects; music rarely has more at once. One or two often suffice, especially since inversion adds greatly to the result.", "III.44-061": "The answer in “Raucæ factæ sunt” usually ends on the second note rather than tonic. Tonic would be better, as in the bass’s entry. But the second is acceptable, especially when other simultaneous subjects can fit only that note. Harmony or taste may sometimes require interrupting the exact subject. This can be a skillful source of variety, but only after the entries are familiar enough.", "III.44-062": "Remember that extra notes may pass between beats for melodic effect. Identify them by checking the fundamental bass: they do not belong to its harmony.", "III.44-063": "The fundamental bass is only proof: throughout the piece, the harmony reduces to perfect and seventh chords and their rules. Do not check its voice-leading against the other parts. Check only the chord foundations. Voice-leading rules apply among the five upper parts and continuo. The fundamental bass contains those foundations and nearly all the progressions behind our rules. The other parts form its octave, fifth, third, or seventh, except in irregular cadences and supposition or borrowed chords, already explained in Book II.", "III.44-064": "There are as many possible fugues as melodies, so taste must choose among them. Keep the rules for openings, endings, and answers. With several subjects together, always choose one as a guide. Take a pleasing subject, add three or four parts, and find other subjects within them. Avoid subjects that start and end together with identical rhythms; they become dull accompaniments to one another. Follow the rules before the last example. Prose naturally creates variety because its phrases rarely have equal lengths. Regular verse needs more effort: stagger subjects’ starts and finishes, and add suitable runs. Keep everything clear. Each entry must stand out without hiding another. Before a part takes a subject, let it rest when appropriate, but rest only on a consonance. The subject’s first appearance should not simply continue earlier melody. Later this may work, once every part has presented it at least once.", "III.44-066": "You may present every entry of the first subject before introducing the second and third, mixing earlier subjects with new ones. Or present all subjects separately before combining them. Introducing different subjects simultaneously is risky: listeners may notice one and forget another. Distinguish their designs, directions, and entry “tones” within the measure so both remain clear. Sometimes a part sings two subjects as one continuous melody, which later separates into two. This is very pleasing. The next part should enter at their dividing point, though a shift of several beats or even more than one measure is allowed.", "III.44-068": "Keep the same delay between successive entries. If the first answering part waits one measure, each later part should wait one measure after the part before it. Exceptions are possible, especially once every part has entered. The third entry may come one measure earlier or later, but not a quarter or half measure, or more than one measure. If the second waited two measures, the third may wait one or three. The same applies to later entries at the third part’s unison or octave. Tonic/dominant and second/sixth answers do not always fit after identical delays. What combines after one or two measures in one form may fail in the other. Strictly enforcing the original delay would limit invention too much; countless designs might become impossible.*", "III.44-069": "If all parts rest to highlight a new subject, do not make the melody sound completely finished. Keep listeners wanting the continuation. Use an interrupted or irregular cadence for this silence. A perfect cadence must at least be in a foreign key, as in the examples.", "III.44-070": "Fugue is an ornament governed by taste. General rules alone cannot ensure success. Music expresses many feelings and events, creating new situations beyond rules. Harmony reveals the available routes; taste chooses them. Develop that taste by repeatedly studying and hearing the best composers in this genre.", "III.44-071": "* See “Raucæ factæ sunt” and “Defecerunt oculi mei” in the previous example.", "III.44-073": "A perpetual fugue, or canon, uses a whole air repeated very regularly by every part.", "III.44-074": "The commonest canons use unison or octave entries to suit voice or instrument ranges. Write a melody, then add any number of parts. Join their melodies into one flowing air. One part begins; the next enters as soon as the first finishes the original melodic section. Others follow in turn. At the end, the first restarts and the others follow, provided their original entries were correctly timed. See the adjacent example.", "III.44-075": "1. 2. 3. 4. 5.", "III.44-076": "Once one of these five melodies is invented, the others are easy to add. The real difficulty is joining them into the smoothest air taste permits. Here is that air.", "III.44-077": "CANON. Da capo (from the beginning). Awake, endless sleeper, Relindindin, Relididin, Relididin, A-", "III.44-078": "You can recognize all five melodies in the canon, with a few added small notes for melodic effect. Each part starts when the preceding part reaches the note or beat bearing this mark: [repeat sign].", "III.44-080": "Repeat sign: marks each part’s entry.", "III.44-081": "Continue as long as you wish. The first part restarts at the end, and the others follow.", "III.44-082": "Canons may also enter at the fifth or fourth. Every part must reproduce the same melody exactly. Plan the whole air and add accidentals wherever the natural scale steps would prevent an exact match. Follow the melody, regardless of modulation. This is much harder: each entry starts in a new key a fifth or fourth away, depending on the canon. The previous canon allowed unlimited parts. Here we think four is the maximum; no four-part example of this kind has yet appeared.", "III.44-083": "CANON AT THE FIFTH. Ah! Far from laughing. Ah! Far from laughing, We-", "III.44-084": "Ah! Far from laughing, Let us weep, let us weep. Ah!… A.", "III.44-085": "At A, if the octave is beyond the voice, repeat the previous pitch instead.", "III.44-086": "“At the fifth” means upward. A fifth up equals a fourth down; allow the latter, especially to fit voices’ ranges.", "III.44-087": "The four parts are written out together so the result can be judged, although the simple instruction would be: enter a fifth above the previous part after two complete measures. The ending cue signs [cue sign] may not lie on the staff line matching the return point [repeat sign]. Still restart at the cue-sign pitch. Imagine a new clef—or, more accurately, a new key, which is what happens—while keeping the returned melody’s modulation unchanged. Continue as long as desired.", "III.44-088": "Cue sign indicating the pitch at which to restart.", "III.44-089": "Repeat sign for the canon at the fifth.", "III.44-090": "CANON AT THE FOURTH. With wine, let us fall asleep, let us fall asleep…", "III.44-091": "The last two canon types require thorough mastery of inversion. Avoid fifths, fourths, and elevenths wherever possible.", "III.44-092": "With some developed taste, mastering modulation and fundamental harmony brings quick and complete success in composition. All variety comes from inverting that fundamental harmony, while its modulation stays unchanged.", "III.44-093": "End of Book Three.", "IV.01-001": "BOOK FOUR.", "IV.01-002": "Principles of Accompaniment.", "IV.01-003": "CHAPTER ONE.", "IV.01-004": "Recognizing Intervals on the Keyboard.", "IV.01-005": "To understand what follows, you must know the first chapter of the previous book up to its discussion of clefs and vocal ranges. That last discussion is not needed for accompaniment.", "IV.01-006": "A harpsichord or organ contains all the sounds used in musical compositions. Play its keys one after another. From left to right, pitches rise; from right to left, they fall.", "IV.01-007": "Each key gives a different sound. A wider gap between keys makes a larger interval; a smaller gap makes a smaller interval. The smallest is a semitone. It lies between neighboring keys with no playable key between them, such as E and F. F to G is a whole tone because the sharp key lies between them. Count both white and black keys: each neighboring pair is one semitone apart.", "IV.01-008": "Turn the page for the example.", "IV.01-009": "EXAMPLE.", "IV.01-010": "SEMITONE.\nC to C♯.\nC♯ to D.\nD to E♭.\nE♭ to E.\nE to F.\nF to F♯.\nF♯ to G.\nG to G♯.\nG♯ to A.\nA to B♭.\nB♭ to B.\nB to C.\n\nWHOLE TONE.\nC to D.\nD to E.\nE to F♯.\nF to G.\nG to A.\nA to B.\nB♭ to C.\nC♯ to D♯.\nE♭ to F.\nF♯ to G♯.\nG♯ to A♯.\nB to C♯.\n\nC to E♭: one and a half whole tones.\nC to E: two whole tones.\nC to F: two and a half whole tones.\nC to F♯: three whole tones.\nC to G: three and a half whole tones.\nC to A♭: four whole tones.\nC to A: four and a half whole tones.\nC to B♭: five whole tones.\nC to B: five and a half whole tones.\nC to its octave: six whole tones.", "IV.01-011": "Whole tones and semitones come in different kinds, but purely practical players need not distinguish them.", "IV.01-012": "Start from D, or any note you choose, instead of C. Count semitones from key to neighboring key to find the number of whole tones or semitones between your starting note and any other.", "IV.01-013": "Accompaniment requires a strong knowledge of the keyboard and music. We assume that readers who use these principles already have it. They can identify intervals on the keys by the same counting method used on the scale. See Book III, Chapter I.", "IV.01-014": "C, D, E, F, G, A, and B are used far more often than other notes. Music treats these seven as the notes from which compositions are made. Our rules will therefore use the seven natural keys. Consider the sharps and flats between them only when the desired interval requires them.", "IV.01-015": "To find a second, third, fourth, fifth, and so on, count your starting natural key as 1. The next natural key upward is 2 and makes a second. Key 3 makes a third, key 4 a fourth, and so forth. Learn this carefully. Accompaniment depends mainly on knowing these intervals. Always count upward from the starting note or foundation, never downward.", "IV.01-017": "EXAMPLE.", "IV.01-018": "Figures. Names of intervals.\n2. Second: C to D, D to E, E to F, etc.\n3. Third: C to E, D to F, E to G, etc.\n4. Fourth: C to F, D to G, E to A, etc.\n5. Fifth: C to G, D to A, E to B, etc.\n6. Sixth: C to A, D to B, E to C, etc.\n7. Seventh: C to B, D to C, E to D, etc.\n8. Octave: C to another higher C, etc.", "IV.01-019": "Unison, First Degree or Fundamental Sound; Second; Third; Fourth; Fifth; Sixth; Seventh; Octave.", "IV.01-020": "Ninth or Second; Tenth or Third; Eleventh or Fourth; Twelfth or Fifth; Thirteenth or Sixth; Fourteenth or Seventh; Fifteenth or Octave; Sixteenth or Ninth or Second; Seventeenth or Tenth or Third; Eighteenth or Eleventh or Fourth.", "IV.01-021": "All harmonic intervals are contained within an octave. Larger intervals repeat them. Note names show this: a third, tenth, and seventeenth have the same upper note name; the same applies to other intervals. Once you know G is the fifth of C, you may play any G above that C. Repeat this exercise from every key, not only C, until intervals are familiar from any starting point.", "IV.02-001": "CHAPTER TWO.", "IV.02-002": "Distinguishing Major and Minor, Perfect, Augmented, and Diminished Intervals.", "IV.02-003": "Thirds and sixths can be major or minor.", "IV.02-004": "Fifths and sevenths can be perfect, augmented, or diminished.", "IV.02-005": "Fifths and sevenths can be perfect, augmented, or diminished.", "IV.02-006": "Seconds and fourths can be perfect or augmented.", "IV.02-007": "Neither the diminished fourth nor the diminished second belongs in accompaniment or harmony.", "IV.02-008": "Some writers call seconds, sevenths, and ninths major or minor, but this is improper. If the prescribed size of one of these intervals varies by a semitone, ignore that difference for now.", "IV.02-009": "For now, learn to distinguish thirds and sixths and their major and minor forms. Sharps and flats on notes will identify augmented and diminished intervals. Once you know which key forms a third, fourth, fifth, or sixth above another, count the tones or semitones between them. That tells you whether the interval is major, minor, perfect, augmented, or diminished.", "IV.02-010": "Whole Tones and Semitones in Each Interval.", "IV.02-011": "2. Second: one whole tone or one semitone; C to D, E to F, etc.\n2♯. Augmented second: one and a half tones; B♭ to C♯, E♭ to F♯, etc.\n3♭. Minor third: one and a half tones; C to E♭, D to F, E to G, etc.\n3♯. Major third: two tones; C to E, G to B, D to F♯, etc.\n4. Fourth: two and a half tones; C to F, D to G, F to B♭, etc.\n4♯. Augmented fourth, called tritone: three tones; F to B, C to F♯, etc.\n5/. Diminished fifth, called false fifth: three tones; B to F, E to B♭, etc.\n5. Fifth: three and a half tones; C to G, B to F♯, etc.\n5♯. Augmented fifth: four tones; C to G♯, D to A♯, etc.\n6♭. Minor sixth: four tones; C to A♭, D to B♭, etc.\n6♯. Major sixth: four and a half tones; D to B, E to C♯, etc.\n7♭. Diminished seventh: four and a half tones; C to B♭, G to F, etc.\n7. Seventh: five tones; C to B♭, D to C, etc.\n7♯. Augmented seventh: five and a half tones; C to B, D to C♯, etc.\n9. Ninth: the same keys as the second, except that it should naturally lie an octave higher.", "IV.02-012": "Some differently named intervals contain the same number of tones here. Theory distinguishes them more precisely, but practical playing does not need that knowledge. Later we will see the only practical distinction, involving a ♯ or ♭.", "IV.02-013": "EXAMPLE.", "IV.02-014": "Seconds.", "IV.02-015": "Augmented Seconds.", "IV.02-016": "Minor Thirds [Row without a Printed Title].", "IV.02-017": "Major Thirds.", "IV.02-018": "Fourths.", "IV.02-019": "Tritones.", "IV.02-020": "Diminished Fifths.", "IV.02-021": "Fifths.", "IV.02-022": "Augmented Fifths.", "IV.02-023": "Minor Sixths.", "IV.02-024": "Major Sixths.", "IV.02-025": "Diminished Sevenths.", "IV.02-026": "Sevenths.", "IV.02-027": "Augmented Sevenths.", "IV.02-028": "Ninths.", "IV.02-029": "Now practice finding every kind of interval above every keyboard note. Learn them so thoroughly that, from any note you think of, you can instantly name and play its minor or major third, sixth, tritone, perfect, diminished, or augmented fifth, seventh, and so on. This is necessary for accompaniment.", "IV.02-030": "1. Start with each key's thirds and fifths. Fourths and diminished fifths lie between them. Augmented fifths and sixths are just above the fifth. Sevenths are below the octave. Seconds and ninths are above the starting note or its octave.", "IV.02-031": "2. Counting natural keys may give the correct interval name but the wrong size. Find the note name first, then sharpen or flatten it. B's fifth is F by name, but B–F lacks the required tones. Use F♯ instead. F's fourth is B by name; counting the tones shows that B♭ is needed. Treat other intervals the same way.", "IV.02-033": "3. The fifth and fourth are two unchanging consonances, besides the octave. If the starting key is sharp or flat, its fifth and fourth must be treated likewise. In this naming system F counts as flat, because all flats are called “fa”; B counts as sharp, because all sharps are called “si.” Here “fa” and “si” are the musical naming syllables.", "IV.02-034": "Three dissonances can also be called unchanging: seventh, second, and ninth. The seventh naturally sits a whole tone below the octave; the second a whole tone above. Some situations are exceptions, but we will discuss them later.", "IV.02-035": "4. Keep the note name required by the interval. F's major third is A, so its minor third must be A♭, not G♯. The same keyboard key may usually be called G♯, but here it is A♭. G cannot make a third with F.", "IV.02-036": "Every note therefore has a sharp and a flat. B's major third is D♯, not E♭, even though both use the same key. G♯'s major third is B♯, not C, and its major sixth is E♯, not F. The interval's counted position always determines the note name. This explains why an augmented second and a minor third use the same keys. So do 7♭ and 6♯, 5♯ and 6♭, and the diminished fifth and tritone. D's tritone is G♯, but its diminished fifth is A♭, though they share a key. Remember: a fourth needs four note positions, as D–G; a fifth needs five, as D–A. Apply this to every interval.", "IV.02-038": "EXAMPLE.", "IV.02-039": "Same Keys. Likewise. Likewise. Tritone or Augmented Fourth; Diminished Fifth; Diminished Fifth; Tritone; Diminished Fifth; Tritone.", "IV.02-040": "Same Keys. Likewise. Likewise. Augmented Second; Minor Third; Diminished Seventh; Major Sixth; Augmented Fifth; Minor Sixth.", "IV.02-041": "For an easy diminished interval, begin on a sharp key rather than a flat. For an augmented interval, do the reverse.", "IV.02-042": "In practice, the diminished fifth and tritone divide an octave into equal halves, as shown next.", "IV.02-043": "Diminished Fifth. Tritone.", "IV.02-044": "Once you know one interval, this helps you find the other. Use either of its two keys as the starting degree.", "IV.02-045": "The major third and minor sixth have the same kind of relationship.", "IV.02-046": "Also the minor third and major sixth.\nThe fourth and fifth.\nThe second and seventh.\nAnd the augmented second and diminished seventh.", "IV.02-047": "EXAMPLE.", "IV.02-048": "Major Third; Minor Sixth; Minor Third; Major Sixth; Fourth; Fifth; Second; Seventh; Augmented Second; Diminished Seventh.", "IV.02-049": "Once you have found any interval, move its starting key an octave higher. This gives the related interval. Become fully familiar with everything explained here before going on.", "IV.03-001": "CHAPTER III.", "IV.03-002": "Hand position and fingering.", "IV.03-003": "In practice, the first degree or fundamental sound is the bass. Play it with the left hand. The right hand plays the notes that form intervals with that bass. Usually it plays three or four of them together; from now on, we will call this group a chord. Whenever the following instructions say “chord,” they mean the notes played by the right hand.", "IV.03-004": "1°. Play the left-hand notes one at a time. Use successive fingers rather than using the same finger for different notes in succession. Follow the numbered fingerings provided.", "IV.03-005": "2°. Do not use the right-hand thumb except in the particular cases explained later. If a small hand forces you to use it, this greatly slows the development of the habits that are as important to practical playing as knowledge is.", "IV.03-006": "3°. The right hand plays at least three notes at once. Use the index finger for the lowest note and the little finger for the highest. Use either the middle or ring finger for the middle note, according to the printed fingering. Follow those numbers exactly: thumb = 1, index finger = 2, then count onward to the little finger = 5.", "IV.03-007": "4°. Strike the chord by moving the fingers rather than the whole hand. The fingers should move independently, from the joints where they meet the hand.", "IV.03-008": "5°. Start the first finger exactly with the bass. Let the others follow so quickly that the chord seems to sound together. It is actually a slight arpeggiation, like three or four thirty-second notes played in rapid succession.", "IV.03-010": "6°. Do not lift all your fingers at once, unless a change is so quick that you have no better option. The first finger moves alone, gliding from one key to the next in time with the bass. The others follow immediately. Keep fingers from hanging in the air: leaving one key and touching the next should happen as one action, with no noticeable gap.", "IV.03-011": "7°. Let your fingers move naturally. Do not force them. Speed comes from good habits.", "IV.03-012": "These points matter. Chords are closely connected, and their sequences usually follow similar patterns. Your fingers therefore learn when to move closer together and when to spread apart. This makes accompaniment more graceful and helps you master it sooner. If you lift the whole hand for each chord, you must often look away from the score to find the next one. Fingers that stay on the keyboard could find it for themselves.", "IV.03-013": "These hand-position rules mainly concern the harpsichord. For the organ, change only the following: play every note of a chord simultaneously; keep a key held if it belongs to both the current and next chord; and connect the sounds as smoothly as possible.", "IV.04-001": "CHAPTER FOUR.", "IV.04-002": "Finding Chords on the Keyboard.", "IV.04-003": "We begin with a chord table. Figures name intervals, but also remind you which notes make up a chord. A single accompaniment figure usually means three, four, or five sounds. Memorize the intervals that accompany each figure so you recognize the whole chord at sight. Asked what goes with a seventh, answer immediately: a third and fifth. Learn the same information for every chord below.", "IV.04-005": "The Most Necessary Chords.", "IV.04-006": "[No figure] The perfect chord is usually unfigured. It contains: 3. 5. 8.\n6. The sixth chord is accompanied by: 3. 8.\n6/4. Another sixth chord, called sixth–fourth, accompanied by: 8.\n6. Another sixth chord, called small sixth, accompanied by: 3. 4.\n6/5. Another sixth chord, called great sixth, accompanied by: 3.\n7. The seventh chord is accompanied by: 3. 5.\n4. The fourth chord is accompanied by: 5. 8.\n2. The second chord is accompanied by: 4. 6.\n4♯, or 4. The tritone chord is accompanied by: 2. 6.\n5/, or 5♭. The diminished-fifth chord is accompanied by: 3. 6.", "IV.04-007": "Figures show the main intervals. The others are rarely written, so memorize them.", "IV.04-008": "A lone ♯ calls for a major third; a lone ♭ for a minor third. Alone above or below a note, either sign indicates a perfect chord with that kind of third.", "IV.04-009": "A ♯ beside a figure raises its interval by a semitone; a ♭ lowers it by a semitone.", "IV.04-010": "Stacked figures belong to one chord. Figures side by side indicate separate chords in succession.", "IV.04-011": "Turn the page for the example.", "IV.04-012": "The Perfect Chord and Its Fingering.", "IV.04-013": "Perfect Chord: Successive Positions and Fingerings.", "IV.04-014": "Perfect Chord: Four Groups of Transposed Positions.", "IV.04-015": "Perfect Chord: Five Groups of Transposed Positions.", "IV.04-016": "Perfect Chord: Five Groups of Transposed Positions.", "IV.04-017": "Further Perfect-Chord Positions: Three Groups.", "IV.04-018": "Further Perfect-Chord Positions: Three Groups.", "IV.04-019": "Further Perfect-Chord Positions: Two Groups.", "IV.04-020": "The second and fifth fingers take the outside notes, so only the middle fingers are numbered. We will keep doing this except where the thumb replaces finger 2. Use the first three chords' finger arrangements for all the others. Finger 1 is the thumb; 2, 3, 4, and 5 continue toward the little finger.", "IV.04-021": "Before going on, practice every perfect chord up and down the whole keyboard, as shown for C's octave. Play each chord's notes as an even arpeggio from end to end. The first note of a new chord must come at the same pace as the last note of the previous one.", "IV.04-023": "Start ascending chords with finger 2 and descending chords with finger 5. When accompanying, always start with finger 2, or the thumb if needed.", "IV.04-024": "Sixth Chord with Third and Octave.", "IV.04-025": "Right Hand: Chords. Left Hand: Bass. Sixth Chord; Two Possible Bass Positions.", "IV.04-026": "Play any perfect chord. Keep the upper chord unchanged and move the bass up a third or down a sixth—the same result. The original perfect chord becomes a sixth chord above the new bass.", "IV.04-027": "Sixth–Fourth Chord with Octave.", "IV.04-028": "Right Hand: Chords. Left Hand: Bass. Sixth–Fourth Chord; Two Possible Bass Positions.", "IV.04-029": "Use the same method, but move the bass up a fifth or down a fourth.", "IV.04-030": "Seventh Chord with Third and Fifth.", "IV.04-031": "Right Hand: Chords. Left Hand: Bass. Seventh Chord by Moving the Bass, or 7 Added to the Perfect Chord.", "IV.04-032": "Move the bass down a third or up a sixth to find this chord as before. Or keep the perfect chord and simply add a seventh. Its accompanying intervals are the same, except that the octave is optional rather than specified. Add or omit the octave as appropriate. With the octave included, use the four fingers without the thumb.", "IV.04-034": "Tritone Chord with Second and Sixth; Second Chord with Fourth and Sixth.", "IV.04-035": "Right Hand: Chords. Left Hand: Bass. Tritone and Second.", "IV.04-036": "Lower the bass by a whole tone. To make a tritone chord, start with a perfect chord whose third is major. To make a second chord, use a minor third.", "IV.04-037": "Fourth Chord with Fifth and Octave.", "IV.04-038": "Right Hand: Chords. Left Hand: Bass. Fourth and Fingering 4.", "IV.04-039": "Take a perfect chord and move its third up to the fourth. If the octave lies between the other notes, always play it with finger 4.", "IV.04-040": "These examples show the later chords in only one keyboard position. Practice them from every note and across the entire keyboard, just as with perfect chords. Keep the same fingering everywhere.", "IV.05-001": "CHAPTER FIVE.", "IV.05-002": "Useful Observations on All Chords.", "IV.05-003": "Accompaniment, like all harmony, has only two kinds of chord: consonant, the perfect chord; and dissonant, the seventh chord.", "IV.05-004": "Play a perfect chord. It produces all the consonant chords and has only three different sounds: bass, third, and fifth—for example C, E, G. Another C an octave above does not add a different sound; it repeats the first.", "IV.05-005": "C, E, G make a perfect chord when C is the bass. Put E in the bass and play C and G in the right hand: a sixth chord. Put G in the bass and play C and E: a sixth–fourth chord. These are all the consonant chords. Add the bass note's octave in the right hand to complete them. To see it quickly, hold any perfect chord in the right hand and play each of its notes an octave lower in turn with the left. You will hear all three chords.", "IV.05-006": "EXAMPLE.", "IV.05-007": "Right Hand: Chords. Left Hand: First Bass, Second Bass, Third Bass.", "IV.05-008": "The same chord is perfect over bass one, a sixth chord over bass two, and a sixth–fourth chord over bass three. The three basses use the chord's three notes.", "IV.05-009": "A seventh chord contains four different sounds. Put each in the bass in turn to find every dissonant chord used in harmony, apart from exceptions we will discuss later.", "IV.05-011": "EXAMPLE.", "IV.05-012": "Right Hand: Chords. Six Alternative Left-Hand Basses.", "IV.05-013": "This bass has seventh chords above it.", "IV.05-014": "These are great-sixth or diminished-fifth chords. Which one appears depends on whether the first bass's third is minor or major.", "IV.05-015": "These are small-sixth chords, major or minor depending on the first bass's thirds.", "IV.05-016": "These are second or tritone chords. Again, the first bass's thirds determine the difference.", "IV.05-017": "These are ninth or augmented-fifth chords, again differing because of the first bass's thirds.", "IV.05-018": "These are eleventh chords, called fourths, or augmented-seventh chords. The difference follows the same pattern, and so on.", "IV.05-019": "Do not focus on the first chord; it is incidental.", "IV.05-020": "Leave the last two basses' chords aside for now.", "IV.05-021": "Choose any perfect or seventh chord. For a seventh chord, add the bass's octave. Hold the right-hand chord while the left hand tries each of its notes as bass. This gives the chords in the examples. For a perfect chord, its third in the bass makes a sixth chord; its fifth makes a sixth–fourth chord. For a seventh chord, its third in the bass makes a great-sixth or diminished-fifth chord; its fifth makes a small-sixth chord; its seventh makes a second or tritone chord. You can also work backward. If you have any of those dissonant inversions, add the bass's octave to the chord. Are your fingers spaced in thirds? Then the lowest finger plays the note that should go in the bass to reveal the original seventh chord. If not, two fingers will be adjacent. Use the higher of those two notes as the bass. See Book III, Chapter XI. Consonant chords are easier to identify. Put the right-hand chord in a position with fingers spaced in thirds. The note under finger 2 would support the perfect chord if placed in the bass.", "IV.05-022": "Study these relationships carefully. They make chords much easier to understand and play, especially when you can instantly predict the result of moving the bass up a third, fifth, or seventh. Remember: up a seventh is equivalent to down a second; up a third to down a sixth; up a fifth to down a fourth; down a third to up a sixth, and so on.", "IV.06-001": "CHAPTER SIX.", "IV.06-002": "Keys and Modes.", "IV.06-003": "Good accompaniment needs a secure knowledge of keys and modes. Read Book III, Chapters VIII and XII. Then practice the octave exercises below until they feel easy. Chords are shown in several keyboard positions, with fingerings for both hands. Below the first two basses, an added fundamental bass proves that only perfect and seventh chords underlie the music. The varied chords above the stepwise ascending and descending bass all come from the chords figured on that fundamental bass. Each note is named to make the relationship clear. A note with a derived chord lies a third, fifth, or seventh above the note carrying its original perfect or seventh chord. Such chords normally belong to the same scale degrees in every key.", "IV.06-004": "The fundamental bass is only for the explanation. Do not use it in practical accompaniment. The chord positions follow the rules relative to the continuo bass, not the fundamental bass. Play the continuo bass with your left hand.", "IV.06-005": "If the explanation is unclear, practice the chords for now. Later material will help make it understandable.", "IV.06-006": "Keys and Modes: Chords for Every Note as the Bass Moves by Steps Up and Down an Octave.", "IV.06-007": "C Major. Three Right-Hand Positions; Continuo Bass and Fundamental Bass.", "IV.06-008": "D Minor. Three Right-Hand Positions; Continuo Bass and Fundamental Bass.", "IV.06-009": "Some use “first degree,” “second degree,” and so on instead of “tonic note,” “second note,” and so on. The terms mean the same thing.", "IV.06-010": "Master one key before starting another. Practice all three keyboard positions with the given fingering. Then you will be ready wherever your hand lies and will not need to lift it.", "IV.06-011": "Notice the shared note that almost always connects one chord to the next. It makes them much easier to play.", "IV.06-012": "Add the continuo bass's octave wherever it is missing. This reveals how its chords relate to the fundamental bass's chords.", "IV.06-013": "The major- and minor-mode examples include fingerings and each note's role in the key. They apply to all other keys. Only the keyboard positions differ. Understand these first two examples and you understand the theory of every major and minor key by matching major with major and minor with minor.", "IV.06-014": "A sixth chord following a perfect chord by step sometimes doubles its third or sixth instead of the bass. This makes the hand position easier and avoids consecutive octaves. Use the thumb in that case.", "IV.06-015": "EXAMPLE.", "IV.06-016": "A Minor.", "IV.06-017": "G Major.", "IV.06-018": "G Minor.", "IV.06-019": "F Major.", "IV.06-020": "D Major.", "IV.06-021": "A Major.", "IV.06-022": "C Minor.", "IV.06-023": "E Minor.", "IV.06-024": "E Major.", "IV.06-025": "B♭ Major.", "IV.06-026": "B♮ Minor.", "IV.06-027": "B♮ Major.", "IV.06-028": "F Minor.", "IV.06-029": "E♭ Major.", "IV.06-030": "F♯ Minor.", "IV.06-031": "F♯ Major.", "IV.06-032": "C♯ Minor.", "IV.06-033": "C♯ Major.", "IV.06-034": "G♯ Minor.", "IV.06-035": "A♭ Major.", "IV.06-036": "B♭ Minor.", "IV.06-037": "E♭ Minor.", "IV.06-038": "D♯ Minor.", "IV.06-039": "The last two keys use the same keyboard keys with different note names. Other keys can also have two names. C can be written B♯, and C♯ as D♭; every note in the octave then changes its name too. This is uncommon, so a brief explanation should suffice. Anyone may study both naming systems for the keyboard. That knowledge is essential for handling the greatest difficulties.", "IV.06-040": "Keep your eyes on the music while accompanying. Look at your fingers only when necessary. Practice teaches this. A trained ear becomes better than the eye at detecting mistakes, and these octave exercises teach your fingers to find chord shapes naturally. Hand position and fingering matter more than you may think; do not neglect them.", "IV.06-041": "After mastering the octave exercises, practice naming every chord silently without looking at the score or your hand. If possible, identify its source too: “This comes from the perfect or seventh chord on this note; next I usually move to this chord, which comes from that one.” Use every helpful approach to learn quickly and thoroughly. Knowing the chord sequence through each key's octave puts you past nearly all the difficulties. The sequence itself is the same in every key.", "IV.06-043": "If studying every key becomes tedious, continue after the first sixteen or eighteen. Return to the others when you want complete certainty.", "IV.07-001": "CHAPTER VII.", "IV.07-002": "How to order the chords within each key’s octave.", "IV.07-003": "Start by treating any note with a perfect chord as a tonic. Within a key, only the tonic and dominant have this privilege. You can treat the dominant as a tonic for this purpose even when it carries a seventh chord. This helps you quickly find the chords that should come before the tonic or dominant: they are nearly always the same.", "IV.07-004": "1°. When the bass rises a fourth or falls a fifth to the tonic, a seventh chord must come first. These two bass movements are equivalent. The same rule applies when moving to the dominant.", "IV.07-005": "EXAMPLE.", "IV.07-006": "Bass rises a fourth to the tonic; bass rises a fourth to the dominant.", "IV.07-007": "2°. A step down to the tonic needs a small-sixth chord before it; a step up needs a diminished-fifth chord. Apply the corresponding rule when approaching the dominant by step.", "IV.07-008": "EXAMPLE.", "IV.07-009": "Stepwise approaches down and up to the tonic, and up and down to the dominant.", "IV.07-010": "When the dominant has a perfect chord, add a ♯ to the sixth in the preceding chord. This makes that small-sixth chord like the one used before the tonic in the same bass movement. You then need to hear what follows to know whether the arrival note is the dominant or tonic. If the dominant instead carries a seventh, you can identify it at once.", "IV.07-011": "There is one difference in these upward stepwise approaches. The tonic follows a diminished-fifth chord, but the dominant follows a great-sixth chord. Only the bass differs: it rises a semitone to the tonic and a whole tone to the dominant. The other notes have the same arrangement, as the example shows. Use this to tell the leading note from the fourth degree, and the tonic from the dominant.", "IV.07-012": "EXAMPLE.", "IV.07-013": "The leading note rises a semitone to the tonic; the fourth degree rises a tone to the dominant.", "IV.07-014": "The seventh, small-sixth, great-sixth and diminished-fifth chords used before the tonic and dominant only look different. All come from the seventh chord; their form depends on the bass movement. So a bass note that rises a fourth or falls a fifth to the next note needs a seventh chord. If it moves by step instead, use a chord derived from the seventh chord. This assumes the arrival note carries a perfect chord or seventh chord. Read the figures to check: beginners should always use a figured bass.", "IV.07-015": "EXAMPLE.", "IV.07-016": "Bass rises a fourth or falls a fifth; bass moves down by step; bass moves up by step.", "IV.07-017": "Each bass uses the same chord notes. The diminished-fifth, small-sixth and great-sixth chords contain the notes of the seventh chord whose bass rose a fourth. Their names change with the bass movement, but all derive from that one chord.", "IV.07-018": "To identify major or minor differences within these chords—for example, between the diminished-fifth and great-sixth chords—follow the bass movement or the music’s key relationships. A given key allows only certain notes or keyboard keys. When the key changes, sharps or flats beside the figures show it.", "IV.07-020": "A note lends its perfect chord or seventh chord only to its third, fifth or seventh. Therefore a sixth chord or sixth–fourth chord derived from a perfect chord needs the same preceding chord as the perfect chord itself. The earlier octave examples showed this: the mediant needs the same approach as the perfect chord.", "IV.07-021": "EXAMPLE.", "IV.07-022": "Chords before the mediant.", "IV.07-023": "It is fairly easy to move from a consonant chord to another consonant chord or to a dissonant one. Moving between dissonant chords needs more attention. Most often, this uses the seventh-chord progression shown in the next-to-last example. The following example gives the different chord sequences that can come from it.", "IV.07-024": "See the next example.", "IV.07-025": "EXAMPLE.", "IV.07-026": "The seventh chord’s bass, and five other basses using chords derived from it.", "IV.07-027": "Use these chords with any of the basses. You may keep all four upper notes except the leading note labelled A: remove it when that note is in the bass. Another approach is to remove the octave of whichever note you play in one of the five lower basses. This will do until a more detailed rule is given.", "IV.07-028": "If one note’s perfect or seventh chord must come before another note’s chord, then that second chord must come after the first. Learning either relationship teaches the other. Remember these progressions both as “what comes before?” and “what comes after?”, for the basic chords and their derived forms alike.", "IV.07-029": "Check the earlier octave examples. The upward route from mediant to dominant uses the same chords as the upward route from sixth degree to tonic. The downward route from seventh degree to dominant uses the same chords as the downward route from mediant to tonic. Everywhere, the mediant takes the same approach as the tonic. The next details explain this.", "IV.08-001": "CHAPTER VIII.", "IV.08-002": "General rules.", "IV.08-003": "Stay in one key for now. Remember that only the tonic and dominant take the perfect chord. Set aside the seventh that may be added to the dominant chord.", "IV.08-004": "Before a whole-tone rise to a perfect chord, use a great-sixth chord. Before a semitone rise, use a diminished-fifth chord. You may instead use a seventh chord on that rising bass note only when a figure clearly calls for it.", "IV.08-005": "Use a small-sixth chord before a step down to a perfect chord, or a step up to the mediant.", "IV.08-006": "Before a step down to the mediant, use a tritone chord, or sometimes a great-sixth chord.", "IV.08-007": "Use a sixth chord in three cases: before a step up to a great-sixth or tritone chord; before a step down to a small-sixth chord; and before a leap of a third up or down to a perfect chord.", "IV.08-008": "A perfect chord may be used on notes that move by consonant intervals. For a leap of a third, either a perfect chord or a sixth chord may sometimes fit the first note. Follow the figure to choose.", "IV.08-009": "If the bass rises a fourth or falls a fifth, you may add a seventh to the first note’s perfect chord. If it rises a fifth or falls a fourth, you may add a sixth instead. These rules assume that the arrival note has a perfect chord or seventh chord. All the earlier rules rest on these two.", "IV.08-010": "These rules also give us the following conclusions.", "IV.08-011": "After a great-sixth or tritone chord, you may move down by step to the mediant. That also allows a fourth down to the tonic, or a step up to the dominant with a sixth–fourth chord. The reason is that the same notes form the tonic’s perfect chord, the mediant’s sixth chord and the dominant’s sixth–fourth chord. However, an upward move to the dominant after a tritone chord is rare. Later examples will clarify this. Also think of every rule in both directions: if one chord must come before another, it must—or at least may—be followed by that chord, with the required bass movement. The octaves in Chapter VI provide nearly all these rules.", "IV.08-012": "Example: seventh-chord progressions and their inversions.", "IV.08-013": "Seventh chords in minor keys: three right-hand positions and two bass choices.", "IV.08-014": "The same upper chords have two bass options. One bass moves up a fourth or down a fifth and takes a seventh chord each time. The other moves down by step; each repeated bass degree takes first a seventh chord and then a small-sixth chord. This follows the earlier rules.", "IV.08-015": "At (A), three different sixth chords show the possible ways to approach the first seventh chord. They apply only to that first seventh, with the bass moving as shown.", "IV.08-016": "Transpose this pattern into every minor key. To use it in major keys, remove the flats after the clefs, then transpose the pattern as needed. We have included one more flat than is customary for this minor key. It marks the minor sixth, which belongs to every minor key. We should have marked it throughout the book, but followed customary notation instead.", "IV.08-018": "Practice the sequence in every key and in all three keyboard positions shown. Do the same with every later example. For the previous example, notice the alternating finger pattern: two fingers move down while one stays; then that one moves down while the first two stay. Continue alternating to the end.", "IV.08-019": "Further chord sequences come from these. The next example is major. To make it minor, add the previous example’s flats to the key signature. Keep the final leading note unchanged in both major and minor.", "IV.08-020": "Each chord now gains one note. Two fingers stay while two move down; then the second pair stays while the first pair moves down. Alternate to the end. Do not use the thumb.", "IV.08-021": "Turn the page to see the example.", "IV.08-022": "EXAMPLE.", "IV.08-023": "Four-note chords in three positions, with five bass choices.", "IV.08-024": "Practice both textures: four parts in all, with three notes in the right hand, and five parts in all. Use the first for inverted chords. Use the second for seventh-chord sequences that do not mix in other chords, except great-sixth chords or the chords by supposition discussed later. To turn the last example into four parts, remove the upper note that doubles each bass note at the octave. But keep that doubling with the bass that rises a fourth or falls a fifth. As explained, practicing that version is just as useful as practicing the other.", "IV.08-025": "The chords connect so closely in this sequence, which holds the most natural harmony together, that the hands often learn it before the mind understands it. The fingers can seem to anticipate thought, as long as you follow the finger placement already explained.", "IV.08-026": "You can easily write out the pattern in the three keyboard positions and all the required keys, so we give only one example.", "IV.08-027": "The small-sixth, great-sixth, diminished-fifth, tritone and seventh chords you have just seen follow the earlier rules. No further explanation is needed here: seventh chords take the same approaches as perfect chords. The next chapters add some further points about seventh chords and chords of the second.", "IV.09-001": "CHAPTER IX.", "IV.09-002": "Which chords follow a seventh chord when the bass stays on the same degree.", "IV.09-003": "FIRST ARTICLE.", "IV.09-004": "After a seventh chord, the same bass note must support a sixth in its next chord. Several different chords contain a sixth, so we need to explain which to use.", "IV.09-006": "All these chords contain a sixth, so any may follow a seventh chord over an unchanged bass: small-sixth, great-sixth, diminished-fifth, sixth, sixth–fourth, tritone or chord of the second. To choose, look at the next bass note after the repeated notes. The same applies if a single long note takes both chords. Use the following method when figures are missing or wrong, which happens very often.", "IV.09-007": "A composer is free to keep the same chord over repeated bass notes. Usually, however, if there are two repeated notes and the first starts the measure, it takes a seventh chord. The second then takes one of the chords listed above. Choosing requires a clear understanding of the key and its harmonic movement. Focus on one key and remember these rules. Tonic and dominant normally have perfect chords; the dominant may also add a seventh. The second degree takes a small-sixth chord, and so does the sixth degree when moving down. The mediant takes a sixth chord; so do the sixth degree moving up and the seventh degree moving down. The fourth degree takes a tritone chord moving down or a great-sixth chord moving up. The leading note, or seventh degree, takes a diminished-fifth chord moving up. Your bass note must be one of these degrees, so its place tells you which chord follows its seventh chord. A step up or down to the next note also tells you the natural preceding chord. These clues prevent mistakes. If the repeated note is the dominant, its only option containing a sixth is the sixth–fourth chord. After that, you need only recognize key changes during the piece; that is not the hardest task.", "IV.09-008": "EXAMPLE.", "IV.09-009": "A seventh resolves to a sixth over the same bass: second degree, mediant, fourth degree, sixth degree, dominant and leading note; A.", "IV.09-010": "Three clues identify which sixth-containing chord follows the seventh: the bass note’s degree, the next note’s degree, and the chord needed on that next note.", "IV.09-011": "The rule always works for an ascending bass that moves by step. For a descending bass, if each note lasts long enough for two chords—or the figures call for two—use the previous chapter’s rule. Before stepping down to a seventh chord, always use a small-sixth chord.", "IV.09-012": "At (A), the bass steps up from a perfect chord to a seventh chord. Use an octave instead of a fifth with that seventh. Keep the finger that doubled the previous bass at the octave: its note now forms the seventh. The other two fingers move down by step.", "IV.09-013": "A stepwise bass move after a seventh chord can depart from these rules only by moving immediately to the next note, before there is time to play the usual second chord on the original bass note. If the bass moves up, the new chord must be a perfect chord or another seventh chord, as explained in the previous chapter. If it moves down, it must be another seventh chord. Often the new bass supports exactly the notes that the expected second chord would have used over the old bass. The finger movement therefore still follows our rule. Book III, Chapters XXVI and XXVII explain this.", "IV.09-015": "SECOND ARTICLE.", "IV.09-016": "For these chord rules, treat a note and its altered form as the same bass degree. This applies to C–C♯, C♯–C, B–B♭ and B♭–B, for example. Choose as if the bass repeated C or B, using the earlier rules, but adjust the chord notes to fit the key and harmonic movement.", "IV.09-017": "After a seventh chord, a leaping bass must never rise a fifth or fall a fourth. If it falls a third, rises a sixth, rises a third or falls a sixth, look one note beyond the arrival note to decide the chord on that arrival.", "IV.09-018": "EXAMPLE.", "IV.09-019": "Altered notes returning to naturals, and movement by thirds; A, B and C.", "IV.09-020": "Sharpened notes moving down to naturals, and natural notes moving up to sharps, still allow the normal chord sequence. To choose quickly, think this way: if the sharp does not belong naturally in the descending line, work out the chord as though the sharp were absent. If the sharp belongs naturally in the ascending line, treat the note as sharpened when choosing. One exception is that a composer may put a perfect chord on a note that rises a semitone, as at (A). A great-sixth chord would also have been possible there, using the same upper notes as the diminished-fifth chord over the sharpened form of (A).", "IV.09-021": "At (B), the bass falls a third after the seventh chord. Look at the following note to choose B’s chord. Since that next note needs a perfect chord and B steps down to it, B needs a small-sixth chord. An upward step to the perfect chord would instead require a great-sixth or diminished-fifth chord. Apply the same reasoning elsewhere.", "IV.09-022": "If the bass rises a third after a seventh chord, the new chord usually derives from the old one. At (C), the diminished-fifth chord is the previous seventh chord rearranged.", "IV.09-023": "Remember: a third up is equivalent to a sixth down, and similarly for the other intervals.", "IV.09-024": "The previous chapter already covered a fifth down after a seventh chord, so it is not discussed here.", "IV.10-001": "CHAPTER X.", "IV.10-002": "The chord of the second.", "IV.10-003": "Our earlier statement that the first of two repeated bass notes may take a seventh chord applies only when it is not on the last beat of the bar. If you do use a seventh there, the same bass note on the next bar's first beat must take the chord of the second. The chord of the second, rather than the preceding seventh, then determines the rule. That seventh is only an incidental way to approach it; a perfect chord or any sixth chord could also come before it. The central rule is this: when the second of two repeated notes is on the first beat, give it the chord of the second. Normally, the first repeated note, on the previous bar's last beat, takes the great-sixth chord. See the bass of seconds and Book III, Chapters VIII and XXI.", "IV.10-005": "These notes, held or repeated at the same degree across two bars, are called syncopated. See Book III, Chapter XXXV, Article VII. In the bass, this kind of syncopation occurs only with chords of the second or augmented-fourth chords, 4♯.", "IV.10-006": "The first syncopation may approach its chord of the second from a perfect chord, a seventh chord or any sixth chord. With several syncopations in a row, however, a great-sixth chord normally comes before and after each chord of the second. The tritone chord, 4♯, can sometimes replace the chord of the second, especially in the last syncopation. After the final chord of the second, choose the next chord by looking at the chord that will follow it. Always take your guidance from what comes next rather than what came before.", "IV.10-007": "You may sometimes alternate chords of the second with small-sixth chords, but this is very rare.", "IV.10-008": "For these rules, treat every four-beat bar as two two-beat bars. This helps you avoid mistakes.", "IV.10-009": "Accompanists need practical command of these rules even more than theoretical knowledge. Practice the earlier examples as much as possible. Transpose them into different keys and learn to play them in all three keyboard positions. This prepares you to accompany both figured and unfigured basses.", "IV.11-001": "CHAPTER XI. Chords of the sixth.", "IV.11-002": "A bass often moves by scale steps while taking sixth chords throughout. Follow the next example to learn this easily.", "IV.11-003": "EXAMPLE.", "IV.11-p403": "A sequence of sixth chords, with choices marked “or”.", "IV.11-005": "Chapter VIII already allows the great-sixth chord to move to a sixth chord on the mediant, a sixth–fourth chord on the dominant, or a perfect chord on the tonic. So this example introduces nothing new. [The supplement corrects the original punctuation to make these relationships clear.] Practice the sequence anyway: it occurs very often. With the added flat observed, it works in every minor key. Remove the flats and it works in every major key.", "IV.11-006": "When the fourth degree (A) descends to the mediant (B), or even to the tonic (C), it may take a great-sixth chord, a tritone chord, or both one after another. If you use both, the great-sixth chord must come first.", "IV.11-007": "The last rule comes from the irregular cadence. We could discuss perfect, imperfect and interrupted cadences here too, but our other rules already include them. Take a seventh chord followed by a sixth–fourth chord on the key's dominant: this is an imperfect cadence. A perfect cadence normally goes from dominant to tonic, as the octave examples in Chapter VI show. The sixth–fourth chord on the dominant therefore stands for the perfect chord that should normally have appeared on the tonic after the dominant seventh. The bass can also move from the dominant to the mediant without changing the basic harmony of those two chords. Another example is Chapter VIII's rule allowing the bass to rise by step from a seventh chord to a perfect chord or another seventh chord: this comes from the interrupted cadence. Still, read Book III, Chapters XIII, XVI, XXV and XXVIII, for the fuller discussion of these cadences. They help explain inversion, identify keys, show which notes can or must take particular chords, and explain how different bass movements reveal these relationships.", "IV.12-001": "CHAPTER XII. The augmented-second chord and the chords derived from it.", "IV.12-002": "The 2♯ figure indicates the augmented-second chord. Add a tritone and a major sixth above the bass. This chord is used only on the sixth degree of a minor key.", "IV.12-003": "Begin with the seventh chord on the key's dominant. Keep its upper notes, but move the bass up a semitone to the sixth degree. For example, if the dominant is E, play E's major third, fifth and seventh with the right hand. With the left hand, play F instead of E. Do the equivalent for every other key's dominant.", "IV.12-004": "EXAMPLE.", "IV.12-p404": "A minor, D minor and G minor: dominant, then sixth degree.", "IV.12-006": "Moving the dominant bass note to the sixth degree produces a corresponding change in every chord derived from its seventh chord. The next example shows this.", "IV.12-007": "Chords derived from the 2♯ chord.", "IV.12-p405": "One upper part with six different bass choices. Use one bass at a time.", "IV.12-009": "The notes of this chord remain arranged in thirds, wherever you play them on the keyboard.", "IV.12-010": "On the sixth degree descending to the dominant, the usual chord is the small-sixth chord. It differs from the augmented-second chord only in using a third instead of the augmented second.", "IV.12-011": "The fourth degree usually takes the tritone chord. Here, add a minor third rather than a second.", "IV.12-012": "The second degree usually takes the small-sixth chord. Here, use a diminished fifth in place of the fourth.", "IV.12-013": "The leading note usually takes the diminished-fifth chord. Here, use a diminished seventh instead of the sixth.", "IV.12-014": "The mediant sometimes takes the augmented-fifth chord. Here, use a fourth in place of the third.", "IV.12-015": "The tonic sometimes takes the augmented-seventh chord. Here, use a minor sixth in place of the fifth.", "IV.12-016": "For more on this, see Book III, Chapter XXXIII.", "IV.12-017": "The small-sixth, diminished-fifth, tritone, augmented-fifth and augmented-seventh chords all derive from the dominant's seventh chord. As the example shows, moving its bass to the sixth degree can change each of them. Practice every one in every minor key, alternating between its two possible forms of accompaniment. Also notice which scale degrees can take these chords. This will help you understand them more accurately.", "IV.12-018": "Study the chords shown by the last two basses only after reading the next chapter, which explains them.", "IV.12-019": "When playing the chords in this last example, leave out the bass's octave in every case.", "IV.13-001": "CHAPTER XIII. Chords formed by supposition.", "IV.13-002": "The two chords formed by supposition are the ninth chord and the eleventh chord. The augmented-fifth and augmented-seventh chords come from them. The only difference concerns the third in the underlying seventh chord: it is minor in one case and major in the other.", "IV.13-003": "Each of these chords is built from five different notes.", "IV.13-004": "ARTICLE I.\nThe ninth chord.", "IV.13-005": "The printed text equates the ninth interval with the third; the supplement corrects “third” to “second.” The ninth chord is different: add the third, fifth and seventh above the bass, giving 1. 3. 5. 7. 9. Write only the figure 9.", "IV.13-006": "To find this chord, keep the previous chord under your fingers and add a third above the bass note marked 9. If one of your existing notes is a fourth above that bass, move just that finger down to the third and keep everything else. This may leave the chord incomplete, but that is acceptable. When the bass rises by step from a seventh chord to a ninth chord, move the fingers as in the seventh-chord rule of Chapter VIII. The example shows this between F and B.", "IV.13-007": "EXAMPLE.", "IV.13-p406": "Ninth chords, with reference letters A, B, C, D, E and F.", "IV.13-009": "(A) Add the third to the previous chord. (B) Two fingers have moved down from (A), as the seventh-chord rule requires. After this kind of ninth chord, the right hand normally follows that same rule.", "IV.13-010": "(C) Move the finger holding the fourth to the third; keep the other fingers where they are.", "IV.13-011": "(D) The same action.", "IV.13-012": "ARTICLE II.\nThe augmented-fifth chord.", "IV.13-013": "Build it like a ninth chord, but make the fifth augmented. Its figure is 5♯. Use it only on the mediant of a minor key. It often produces an interrupted cadence.", "IV.13-014": "ARTICLE III.\nThe augmented-seventh chord.", "IV.13-015": "Add a fifth, ninth and eleventh to this chord's bass and augmented seventh: 1. 5. 7. 9. 11. Mark it 7♯. It occurs only on the tonic.", "IV.13-016": "ARTICLE IV.\nThe eleventh chord, also called the fourth chord.", "IV.13-017": "Start with the same construction as 7♯, but use an unaugmented seventh. The usual figures are 4, ⁴₉ or ⁹₄. A plain 4 means the chord already used in the final cadences of the octave examples. Adding 9 gives a different form with five notes. For convenience, however, the right hand often plays only three of them; with the bass, that makes four.", "IV.13-018": "You can find this chord easily: it uses the same keyboard notes as the chord before it.", "IV.13-019": "See the example on the next page.", "IV.13-020": "EXAMPLE.", "IV.13-p408a": "Eleventh chord, with the extra note indicated by cue A.", "IV.13-022": "The cue marked (A) shows the note to add to this ⁹₄ chord.", "IV.13-023": "If the bass is about to move down by step, this chord sometimes includes a fifth and a second. Under the fingers, it then has the same shape as the diminished-fifth or great-sixth chord required on the next, lower bass note.", "IV.13-025": "EXAMPLE.", "IV.13-p408b": "A fourth–second chord, then either a great-sixth or diminished-fifth chord.", "IV.13-027": "The figure should be ²₄, but the usual figure is ⁵₂.", "IV.13-028": "For these chords, see Book III, Chapters XXIX, XXX, XXXI and XXXII.", "IV.14-001": "CHAPTER XIV. How the preceding chords relate to one another.", "IV.14-002": "The right-hand shape for a perfect chord also supplies the consonant sixth and sixth–fourth chords. Likewise, the shape for a seventh chord supplies all the dissonant types: small sixth, great sixth, diminished fifth, tritone, second, ninth, eleventh or fourth, augmented fifth and augmented seventh. There are some specific details to watch.", "IV.14-003": "Dissonant chords are classified as major or minor according to the third in their underlying seventh chord.", "IV.14-004": "Chord sequences usually follow the same pattern. A minor dissonant chord normally leads to another minor dissonant chord. This continues until a major dissonant chord appears, usually leading to a consonant chord. Chapter VIII's rule of sevenths teaches successive dissonant chords. The octave and sixth-chord rules in Chapters VI and XI teach how to mix dissonant and consonant chords. The chord patterns agree closely across these rules, and they also help with chords by supposition. If you use four right-hand fingers for a supposition chord, follow the seventh-chord pattern until the major dissonant chord points to the ending.", "IV.14-006": "These progressions become easy when you know which fingers move. Usually the right hand uses four fingers: two move down and two stay. If the chord is stacked in thirds, move the two highest fingers. Otherwise, find the pair of neighboring fingers: move the lower of that pair together with the finger below it. If no finger lies below the neighboring pair, move the highest and lowest fingers. The moving notes are the fifth and seventh of a seventh chord, the seventh and ninth of a ninth chord, or the ninth and eleventh of an eleventh chord. Even if you use only three fingers, move the two playing those intervals and keep the third still.", "IV.14-007": "There are exceptions. In an interrupted cadence, or a related chord sequence such as H, three fingers may have to move down. Keep the higher finger of a neighboring pair in place; if there is no neighboring pair, keep the lowest finger in place. Another pattern moves only one finger while the other three stay: either the lower finger of a neighboring pair, or the highest finger if there is no neighboring pair. This corresponds to a bass descending by thirds with seventh chords on every note.", "IV.14-008": "See the next example.", "IV.14-009": "EXAMPLE.", "IV.14-p410": "Progressions H and J, with one upper part and three bass choices.", "IV.14-011": "You can add a seventh to a perfect chord. A note that seems to require only the perfect chord may therefore take a seventh chord instead. The choice depends on the composer's taste and understanding.", "IV.14-012": "Learn this sequence and its different basses even though it occurs much less often than the others. Complete preparation avoids surprises. Rarely add the bass's octave to major dissonant chords; it can fit only in seventh, small-sixth and great-sixth chords. Practice these chords in four parts: three notes in the right hand plus the bass. Chords by supposition have five parts without the bass's octave. Never add that octave to them.", "IV.14-013": "The ban on adding the bass's octave to dissonant chords makes accompaniment more regular. Otherwise, consecutive octaves or fifths would be unavoidable; composition strictly forbids them. That is why we often double the third or sixth in a sixth chord instead of doubling the bass at the octave. Still, an accompaniment that does not follow this rule is not necessarily bad: its basic purpose is simply to make all the chord's notes heard. But perfection is always better where possible. Our chord arrangements let you learn sequences that avoid almost all these faults without having to think about each one.", "IV.14-015": "To see how chords relate, study Chapters V, VIII, XI and XII, and the discussions in Books II and III. We must still explain how preparing and resolving dissonances connects their successions.", "IV.15-001": "CHAPTER XV. Preparing and resolving dissonances: finding the key and the chords for its notes.", "IV.15-002": "Calling a dissonant chord major or minor refers only to a particular interval inside it. We will now call that interval the dissonance, instead of speaking of the whole chord.", "IV.15-003": "The earlier rules make dissonance preparation easy enough for accompanists. Books II and III provide more if needed. Those rules also make resolution almost as easy, but the following explanation will help you understand it better.", "IV.15-004": "To see the difference between major and minor dissonances, play the seventh chord on the key’s dominant. The dominant’s major third supplies every major dissonance; its seventh supplies every minor dissonance.", "IV.15-p411": "The minor and major dissonances within a seventh chord.", "IV.15-007": "FIRST ARTICLE.\nMajor dissonance.", "IV.15-008": "A major dissonance always comes with a minor one. When the major is present, focus on it. If a dissonant chord has no major dissonance, focus entirely on the minor.", "IV.15-009": "The major dissonance is always the current key’s leading note. This is the major third of the key’s dominant. Any dissonant chord containing it comes from the dominant seventh chord. The chord or leading note therefore tells you the key. If you already know the key, you can find the chord and its major dissonance at once: the leading note lies a semitone below the tonic, or below the tonic one, two, three or more octaves higher.", "IV.15-010": "At the start of a piece, the key tells you its leading note. A later key change is always signalled by a sharp used alone as a figure, beside another figure, or on a bass note: it marks the new leading note. The opposite signal is a flat added to the old leading note, or the removal of its sharp, in either bass or upper chords. That note is no longer the leading note, so find the new one. Once you know the key, Chapter VI’s rule of the octave tells you all its chords, including the major-dissonant chord. A bass degree may temporarily take a different chord, as in the rules about sevenths. It soon returns to its normal chord, or that chord appears over the next bass note instead. A different bass route therefore does not change the chords. If one new sharp gives way to another, follow the order of sharps and take the last as the leading note. See Book III, Chapter XXV, Article III for the fuller explanation. Every accompanist must know this thoroughly.", "IV.15-011": "Resolve the major dissonance by moving its finger up a semitone. This always works. Its chord resolves to the tonic’s perfect chord, though sometimes that arrival chord must also include a seventh.", "IV.15-012": "EXAMPLE.", "IV.15-p413": "Major dissonances: one upper part with nine bass options and the stated bass changes.", "IV.15-014": "The same two upper chords work with the basses below, showing all the major-dissonant chords. The leading note forms the major dissonance and is the dominant’s major third. It always rises a semitone to the tonic.", "IV.15-015": "The normal resolution is from the dominant seventh chord to the tonic’s perfect chord. All the other bass options derive their chord sequence from this.", "IV.15-016": "Here the bass goes from dominant to mediant, with the same chords.", "IV.15-017": "The bass stays on the dominant while the same chord sequence proceeds.", "IV.15-018": "The fourth degree has a tritone chord and moves to the mediant or tonic. The upper chord sequence stays the same.", "IV.15-019": "The mediant has an augmented-fifth chord. It stays or moves to the tonic; the chord sequence is unchanged.", "IV.15-020": "The second degree has a small-sixth chord and moves to the mediant or tonic, using the same chord sequence.", "IV.15-021": "The tonic first has an augmented-seventh chord, then stays in place to regain its perfect chord.", "IV.15-022": "The leading note always takes the diminished-fifth chord. It moves to the tonic or mediant while the same chord sequence continues.", "IV.15-023": "Here the sixth degree takes the dominant’s place, so remove the dominant from the first chord. The bass then moves to the dominant or mediant with the same chord sequence. To work out how inversions of this augmented-second chord affect the other bass options, replace the dominant with the sixth degree in the first chord. While the sixth degree replaces it, the dominant cannot also be the bass.", "IV.15-025": "Resolve an augmented-second chord or one of its derivatives by moving only the major dissonance up and holding the other notes. Alternatively, move only the minor dissonance down. See Book III, Chapter XXXIII.", "IV.15-026": "The chords in the previous example always belong to the same named scale degrees, in every key. For example, 5♯ occurs only on the mediant.", "IV.15-027": "Apply this minor-key example to keys generally. The exception is that major keys do not use the 5♯ chord, the 2♯ chord or the latter’s derivatives.", "IV.15-028": "The minor dissonance could have been explained alongside the major, because it is present too. Its line to the next note shows that it always moves down. A diminished fifth or tritone will illustrate the relationship.", "IV.15-029": "EXAMPLE.", "IV.15-p414": "How the major and minor dissonances move in a diminished fifth and a tritone.", "IV.15-031": "The diminished fifth and tritone invert into one another, and their resolutions do too: a third at (A), a sixth at (B). The major dissonance always moves up and the minor always moves down. F and B therefore resolve to E and C. In any key, the leading note forms the major dissonance and rises to the tonic. When that major dissonance is present, the fourth degree forms the minor dissonance and falls to the mediant. Try this in every key.", "IV.15-033": "SECOND ARTICLE.\nMinor dissonance.", "IV.15-034": "Every minor dissonance comes from a seventh. Without a major dissonance beside it, there is no fixed scale degree that must form or resolve it: any degree can carry a seventh chord. To find the key, let the fingers continue their familiar dissonant-chord sequence until a major dissonance appears and identifies it. Sometimes a consonant chord reached after a great-sixth chord identifies the key first. Normally that combination belongs to a particular degree, as Chapters VI–IX explain. But an upward move from a great-sixth chord to a perfect chord does not always establish the key. The chapter on sevenths shows a bass rising to a perfect chord, falling a third and making another similar rise. Its final progression makes the key certain: these basses end on the dominant or tonic, with a diminished-fifth chord before that tonic.", "IV.15-036": "The previous example already shows how to resolve the minor dissonance. In chords by supposition, at least two minor dissonances must move down. A fully filled eleventh chord, also called a fourth chord, has three minor dissonances; otherwise it has only one. When all three are present, normally move down only the two harsher ones, the ninth and eleventh, and hold the seventh. Some pieces require the opposite, but less often.", "IV.15-037": "The earlier example lists the major dissonances. Minor dissonances are the second, diminished fifth, seventh, ninth and eleventh (also called the fourth), plus the third in a small-sixth chord and the fifth in a great-sixth chord.", "IV.15-038": "A chord of the second differs from the others because its dissonance is in the bass. Move the bass down to resolve it.", "IV.15-039": "When two fingers lie side by side in a dissonant chord, the lower note is the minor dissonance. In a chord of the second, only the bass is adjacent to the second above it. In other chords with no adjacent fingers, the top finger carries the minor dissonance and must move down.", "IV.15-040": "In an irregular cadence, the great-sixth chord’s dissonance is its sixth rather than its fifth. The sixth moves up by step while the fifth stays.", "IV.16-001": "CHAPTER XVI. Chromatic motion.", "IV.16-002": "Chromatic motion occurs only in minor keys. It uses the sixth and seventh scale degrees moving by semitones, upward or downward, either in the bass or within the chords.", "IV.16-003": "Chapter XI, Article II, already gave an idea of this movement. Here is the further point: a major dissonance normally rises a semitone, but in this case it falls a semitone. It moves to the flattened form of the same note, or back to that note's natural key on the keyboard. To obtain this effect, add that lowered note to the consonant chord that would normally follow the major dissonance. The added note lies directly below the note that would have become the tonic after the leading note. This follows the preceding chapter's explanation that a seventh can be added to the perfect chord resolving the major dissonance.", "IV.16-004": "Chords formed by borrowing or supposition are also common in this harmony. That makes an unfigured bass difficult to play without mistakes.", "IV.16-005": "EXAMPLE.", "IV.16-p417": "Chromatic example across two connected systems, marked A, B, C, D, F, G, H and J.", "IV.16-007": "The entire chord sequence follows our rules.", "IV.16-008": "Although the leading note descends in one part, other parts follow the progression of sevenths between A, B and C, or its inversion between F and G. The movement from C to D comes from the interrupted cadence.", "IV.16-009": "Between H and J, the ninth holds back the octave that immediately follows it.", "IV.16-010": "The rest follows roughly the octave patterns of Chapter VI, except that thirds change from minor to major or from major to minor. In every chord made by supposition or borrowing, notice which notes replace the ones normally expected. Once your fingers know these chord sequences, they can often act before you have to reason them out. Pay particular attention to intervals that change from major to minor on the way down and from minor to major on the way up.", "IV.16-011": "To recognize each new key in this example, use the sharps to identify its leading note.", "IV.16-012": "A natural sign attached to a note or bass figure cancels an earlier ♯ or ♭ and restores the natural note. Some writers use a sharp or flat to cancel the previous alteration, but this is less consistent: 7♭ normally means a diminished seventh, while 7♯ means an augmented seventh.", "IV.17-001": "CHAPTER XVII. Review of the different chord sequences.", "IV.17-002": "Learn each key’s harmonic movement thoroughly. Try to identify the key from every chord you play.", "IV.17-003": "Consonant chords alone often leave the key unclear. If the first dissonant chord still does not identify it, the major dissonance must be missing. Other clues then help: the bass movement tells you the next chord, and the minor dissonance wants to move down. This uncertainty mostly occurs in sequences like the seventh-chord progression of Chapter VIII or its derivatives. A major dissonance almost always ends that progression and identifies the key at once. Thorough knowledge and practice of these sequences prevent mistakes, so we will review them.", "IV.17-004": "Study the review that follows.", "IV.17-005": "Fundamental bass rises a third: dissonance A cannot be prepared. | Bass falls a fourth, as in Chapter VIII. | Fundamental bass falls a third: the third prepares the dissonance and the octave resolves it. | Bass falls a fifth. | Bass rises a second: the octave prepares the dissonance and the fifth resolves it. | Bass falls a fifth with chromatic movement. | A sixth added to perfect chord C prepares an irregular cadence, then rises to resolve on the third. | Final cadence.", "IV.17-p419": "Review: one upper part with nine bass choices, labelled A–R.", "IV.17-007": "A curved mark ⌒ links a dissonance to the consonance preparing it. A horizontal line — does the same in chromatic motion, where that preparing consonance also forms the major dissonance. A sloping line ╲ or ╱ points to the consonance that resolves it.", "IV.17-008": "Every bass uses the same upper chords. The fundamental bass determines their sequence, so many of the alternative bass movements are unusual for those chords. Well-written music rarely contains progressions like these, especially at D, F, G, H, J, K, L, M and N. If you encounter them, use the following methods.", "IV.17-009": "1°. If you set aside the problem of consecutive octaves or fifths, add the octave to the first dissonant chord and let the fingers move naturally, as shown.", "IV.17-010": "2°. To avoid those consecutive intervals, use the normal three right-hand notes and leave out the octave doubling of the alternative bass in dissonant chords. If a chord is still awkward, keep the octave and omit a dissonant note instead. This turns the chord into a consonant one. For a seventh, small-sixth or great-sixth chord following another dissonant chord, the possible reductions are these: a seventh chord becomes a perfect chord; either sixth chord becomes a simple sixth chord; a small-sixth chord may also become a sixth–fourth chord; a great-sixth chord may also become a perfect chord. Use both the natural stepwise motion of the fingers and the rules for which chord follows which bass movement. For example, a major small-sixth chord should lead to a perfect chord when the bass steps down. If a seventh or great-sixth chord appears instead, reduce it to a perfect chord, as at M. Similarly, a diminished-fifth or great-sixth chord should lead to a perfect chord when the bass steps up. If a great-sixth or seventh chord follows instead, reduce it to a perfect chord, also as at M.", "IV.17-012": "A sixth–fourth chord can follow a small-sixth chord with a step down in the bass, or a great-sixth chord with a step up. If the following chord is another small-sixth chord, you may reduce it to that sixth–fourth chord. But if the first small-sixth chord contains the leading note, reduce the next small-sixth chord to a simple sixth chord instead.", "IV.17-013": "The natural chord after a tritone chord with a step down in the bass is a sixth chord. The same is true after a major small-sixth chord with a step up. So reduce a following small-sixth or great-sixth chord to a simple sixth chord in these progressions, as at N, F, G, H and R. F, G and H in bass 7 do not actually follow the specified bass movement, but familiar finger habits still find the chords. The same reasoning applies to a small-sixth chord after a seventh chord with a descending step, as at D in bass 6.", "IV.17-014": "3°. Suppose the bass moves by step and two successive chords are the same kind, or do not follow the normal rule. If you keep them unreduced, move the upper chords opposite to the bass: down against an ascending bass, up against a descending bass. Use this at P–Q or P–M–Q, unless you reduce M in bass 3 to a perfect chord. Reducing one chord means the next need not be reduced, especially with stepwise bass movement. However, keep the lowest or highest finger in place if its note also belongs to the next chord. Exceptions occur when the bass steps up from a seventh chord to a diminished-fifth or great-sixth chord, or from a ninth chord to a seventh chord. The next example shows them.", "IV.17-015": "EXAMPLE.", "IV.17-p422": "Contrary motion involving seventh, diminished-fifth, great-sixth and ninth chords.", "IV.17-017": "A dissonance adds a note to a consonant chord; the consonant chord alone contains harmony’s foundation. If the added dissonance makes accompaniment awkward, leave it out. Play the consonant chord that should follow and that the fingers naturally reach. This works only if it contains only the notes that properly accompany the dissonance, and if you have mastered all the examples. It solves many problems caused by bass figures that list only the intervals in the composer’s music, without considering the rest of the accompaniment.", "IV.17-018": "Do not use this reduction for chords of the second, supposition chords or borrowing chords. It is rarely suitable for seventh chords either.", "IV.17-019": "4°. Chords B–B contain consecutive fifths between their parts. Finger placement makes these hard to avoid, just as when the bass rises from a perfect chord to a sixth chord.", "IV.17-020": "5°. Basses 8 and 9 use chords by supposition. Include as many of their notes as you can. Add the bass’s octave to the chord just before them and follow the earlier rules; this will reliably prepare the hand.", "IV.17-021": "6°. In an uninterrupted sequence of dissonant chords, the right-hand fingers keep moving down. This applies whether the chords are all sevenths or a mixture of types. Once a leading note appears, move upward—at least the finger on that leading note must rise.", "IV.17-023": "EXAMPLE.", "IV.17-p423": "A dissonant-chord sequence continuing across two systems.", "IV.17-025": "The ninth chords shown by the figures also contain sevenths. Each seventh must move to a sixth, even when no 6 is printed. The 8 after the 9 may look like a call for a perfect chord, but the sixth is still needed to resolve the seventh, just as the octave resolves the ninth. Let the fingers slide down to neighboring keys, their usual movement after minor dissonances, and they will find this naturally.", "IV.17-026": "A similar case occurs when a note has only a 5 figure but could take a seventh or ninth chord before the bass steps up, as in Chapter IX’s first example. A 5 followed by 6 on one note, then a step up, may be confusing. Add the seventh or ninth already under the fingers to the perfect chord indicated by 5: they will sound very well. Choose the chord indicated by 6 from the chord you are holding, or more reliably from the bass note’s scale degree. The Chapter IX example shows this. You may also add a ninth to a chord marked only 7 when that ninth is already under a finger from the preceding chord.", "IV.17-028": "7°. A dissonance may become part of another dissonance before it resolves; see Book III, Chapters XII, XV and XXVII. One bass note can also support several different chords in a row, as many examples have shown. The following pedal point is another case.", "IV.17-029": "EXAMPLE.", "IV.17-p424": "A pedal point across two systems, showing both pedal bass and fundamental bass.", "IV.17-031": "A pedal point continues only as long as its bass note stays the same. Here it ends at A, then starts again immediately.", "IV.17-032": "The fundamental bass shows that the pedal point obeys the harmony rules. In borrowing chords, remember that the sixth degree takes the dominant’s place. In supposition chords, the fundamental bass must lie above the pedal bass.", "IV.17-033": "The notes marked B involve double supposition. The first naturally requires an augmented fifth; the second requires the irregular eleventh chord. But a long-held bass note tends to fade from attention while we listen to the moving chords. If those chords progress regularly, the sustained bass can be treated like a point, or a zero in arithmetic. That is also why a sixth and seventh may sound together here.", "IV.17-034": "EXAMPLE.", "IV.17-p425": "A sixth and seventh together over a pedal, with the fundamental bass showing the harmony.", "IV.17-036": "Remove the pedal bass and read the chords with the fundamental bass. Their harmony follows the rules. It must be judged that way.", "IV.17-037": "For another way to combine a sixth and seventh, see Book II, Chapter XIX.", "IV.17-038": "Hurdy-gurdy and musette tunes grow, in a sense, from this pedal-point idea. Understanding it explains the different bass patterns of that kind.", "IV.17-040": "Thoroughly learn and practice the chord inversions—or, more precisely, the changed bass progressions—in all our examples. The fundamental basses show that different bass movements create the different chord names. With practice, the fingers recognize the many relationships between chord sequences and often help when memory fails. Their natural movement is down to a neighboring key after a minor dissonance, up after a major one. You need not consciously name each interval: the seventh, ninth, eleventh, diminished fifth, third of a small-sixth chord and often fifth of a great-sixth chord move down, and the finger finds its next key. The tritone and augmented second similarly move up. When two fingers lie together, the lower one always moves down, except in an irregular cadence.", "IV.18-001": "CHAPTER XVIII. Essential rules for accompanying well.", "IV.18-002": "1°. Before you start playing, identify the piece's key, mode, meter and tempo. Check for changes of mode, meter or clef later in the piece. Read the bass figures carefully, including any ♯ or ♭ signs attached to them. Use the bass's movement to work out what is needed when figures are missing. In short, apply all the rules already given.", "IV.18-003": "2°. Match the accompaniment to the character of the voices and the music. Express the spirit of the words; without words, follow the melody's own expression. Match your volume to the singers or instruments. Do not drown them out, but do not leave them unsupported either. Where appropriate, the left hand can double the right-hand chords, except for their dissonances. Or you can leave out octaves, and sometimes particular dissonances, depending on the situation.", "IV.18-005": "3°. If the harpsichord or theorbo's sound fades, you may play the same chord again. Prefer the first beat of the bar, and place it with the last syllable of a word. A repeated chord in the middle of a word—or even a phrase—can make the meaning harder to hear. The organ does not need this: its sounds are “contained” [a printing error corrected to “continuous” in the supplement].", "IV.18-006": "4°. Keep the chords near the middle of the keyboard whenever the bass allows it. If you must move them to another register, try to shift while keeping the same chord, or at least after a consonant chord, never after a dissonant one. This is not always possible: the composer may unexpectedly send the bass up or down two octaves. When changing position, look or feel for a key that belongs to both the chord you hold and the chord you need. If moving upward, replace the finger on that key with the lowest finger; if moving downward, use the highest finger. Do this without lifting the whole hand. One finger takes another's place and carries out the shift. You can then keep looking at the score. Also remember the earlier instructions for arpeggiating chords.", "IV.18-007": "To accompany an unfigured bass, you need the rules of composition as well as all the accompaniment rules given here. Even then, success is difficult unless your ear, taste and fingers can act ahead of conscious reasoning. The best preparation is frequent practice of the earlier principles, until your ear becomes accustomed to good, sound harmony.", "IV.19-001": "CHAPTER XIX. How to figure a continuo bass and read its chord symbols.", "IV.19-002": "Any of a perfect chord's three intervals can identify it in the bass figures. Usually no figure is written, unless a ♯ is needed to show a major third or a ♭ to show a minor third.", "IV.19-003": "A standalone ♯ means a major third; a standalone ♭ means a minor third. Attached to a number, either sign changes that interval by a semitone from its natural form.", "IV.19-004": "Identify each chord with the figure that gives it its name. For example:", "IV.19-006": "Do not add ♯ or ♭ just to identify an interval already major or minor by nature in the current key. If a sign is required, prefer ♮. The tritone figure is the one customarily accompanied by ♯.", "IV.19-007": "If you change a chord's usual construction, add the figure showing that change beside its identifying figure.", "IV.19-008": "EXAMPLE.", "IV.19-010": "For any chord containing a major dissonance, use a figure that also identifies the dissonant interval.", "IV.19-012": "Many continuo basses do not follow this consistent system. Their figures can mislead players who rely on figures alone. These cases show why our rules are needed.", "IV.19-013": "Some writers use several figures when one would do. This makes things confusing.", "IV.19-014": "A figure next to a note identifies its chord. If the figure is placed later, and that note can take a perfect chord, begin with the perfect chord. Change to the figured chord on the second, third or fourth beat, depending on how far after the note the figure appears.", "IV.19-015": "A long note may take a new chord each beat, or keep one chord for two beats. If the spacing of the figures does not make the timing clear, decide by ear.", "IV.19-016": "An augmentation dot continues the preceding note. A figure placed over or under that dot tells you to change chords during the time added by the dot.", "IV.19-p429": "The chord figure 6 begins at the augmentation dot.", "IV.20-001": "CHAPTER XX. Which bass notes should receive chords.", "IV.20-002": "Play a chord at the beginning of each beat. However, one bass note may support the same chord across several beats or bars.", "IV.20-003": "You can divide a one-beat note into two time-units and play two different chords over it. You could divide it further, but the chord changes would become too rushed.", "IV.20-004": "An ornamented or moving bass may play several notes within a beat. Put the chord on the first note of the beat. By playing one chord per beat, the right hand effectively keeps time.", "IV.20-005": "At a fairly fast tempo, if one chord fits several beats in a row, wait until its sound has faded completely before repeating it. Repeating the same chord too often becomes tedious.", "IV.20-007": "A moving or ornamented bass can be hard to figure, because some of its notes do not belong to the chord that needs to sound. Our rules help: use the chords that should naturally follow one another. Suppose the bass moves by step through a series of 7 or 2 chords, with none of the intervening sixth chords required by the rules. Even if each dissonant chord begins on a beat, split that beat into two equal halves. On the bass note starting the second half, play the chord that belongs between those dissonant chords. Well-trained fingers will often find this automatically from the earlier principles. The bass note under that chord may be unexpected, and its figure may be missing or unfamiliar. In that case, trust the fingers' natural chord movement rather than the potentially misleading bass note.", "IV.20-008": "EXAMPLE.", "IV.20-p430": "A moving bass with three upper parts: first page of one continuous example.", "IV.20-p431": "The same moving-bass example continues across two systems.", "IV.20-011": "When the bass descends by step, the small-sixth chord should come before the seventh chord. With two bass notes at the same degree, the great-sixth or diminished-fifth chord should come before the chord of the second. These rules still apply when the relevant bass note arrives after the start of the beat. They also apply when the chord is unfigured, as at A and D, or its figures are hard to interpret, as at B and C. Insert the small- or great-sixth chords between the seventh or second chords as required. Let one or two fingers move down after the minor dissonance while the others stay. Use the same approach in other progressions with similar difficulties.", "IV.20-013": "Keep a sharp or flat from one chord if it can also serve the next, unless a new figure explicitly cancels it. Because that alteration belongs to the current key, it may form a diminished or augmented fifth. In this situation, prefer that fifth to a perfect one. Treat other intervals the same way. The composer should indicate any required exception; if not, the ear must decide.", "IV.20-014": "END.", "IV.20-015": "Appointment as the King’s sole music printer.", "IV.20-016": "Royal letters patent, issued at Fontainebleau on 5 October 1695, bear the signature LOUIS and, on the fold, “By the King, Phelypeaux.” They carry the great seal in yellow wax. Further letters called “Suranation,” issued at Marly on 28 May 1715 and signed in the same way, confirm them. All were verified and registered in Parlement on 7 June 1715. They authorize J B-Christophe Ballard—the King's sole music printer and music copyist to the royal chapel—to print music, arrange for it to be printed, sell it and distribute it. This covers vocal and instrumental music by any author. Without Ballard's permission, all other printers, booksellers, engravers, type-founders and persons are forbidden to engrave, cast or counterfeit his musical notes, type, decorative initials or other inventions. They may not undertake or commission this music printing anywhere in the kingdom or its dependent lands and lordships, even under contrary letters. Violators face confiscation of the books or copies, musical type and other printing equipment, plus a fine of six thousand livres. The full letters give further details. The King directs that this extract, printed at the beginning or end of a book, be accepted with the same authority as the original.", "supplement-001": "SUPPLEMENT\nContaining changes to two chapters and several necessary corrections.", "supplement-002": "BOOK I.", "supplement-003": "Page 3, ninth line from the bottom: A D C E B should read A D C E B.", "supplement-004": "Page 8, line 5: replace “ces” (these) with “ses” (its/their).", "supplement-005": "Page 9, line 13: after “L’accord parfait” (the perfect chord), add a footnote clarifying what follows: “See chapter VII and chapter VIII, article I, pages 35 and 36.”", "supplement-006": "Page 14, lines 22–25: replace “majeure ou mineure” with “majeur ou mineur” (major or minor; correct the French grammatical gender).", "supplement-007": "Page 15, line 5: replace “nombre 1” with “nombre” (number), removing 1. On the same page, third line from the bottom, also remove the numeral 1.", "supplement-008": "Page 19, line 11: replace “aussi” (as much/also) with “plus” (more).", "supplement-009": "Page 21, second paragraph, line 1: replace “si nous trouvons des Accords” (if we find chords) with “si nous trouvons dans la suite des Accords” (if we subsequently find chords). Add this footnote: “See the demonstrations in chapter VIII to understand what we assert here.”", "supplement-010": "Page 22, first paragraph, line 3: replace “chapter VI, articles VII and VIII” with “chapter VIII, articles VI and VII.” The demonstration at the foot of the page should be as follows.", "supplement-011": "2 — 3 — 4 — 5 — 6 — 1\nWhole tone: 3 to 4. Major semitone: 4 to 5. Minor semitone: 5 to 6.", "supplement-012": "Page 24, line 2: replace “s’épuiser” (be exhausted) with “se puiser” (be drawn from).", "supplement-013": "Page 25: replace “double” with “doublée” (doubled).", "supplement-014": "Page 27, line 18: begin a new paragraph with “l’on peut pousser,” etc. (“one can extend,” etc.). Fourth line from the bottom: replace “dont on sert” with “dont on se sert” (which one uses). Last line: replace “Systême” (system) with “Systême Chromatique suivant” (following chromatic system).", "supplement-015": "Page 28: “Systême Chromatique” (chromatic system) suffices; remove the additional words “Chromatique suivant.” In the first line after the system, replace “le” with “ce” (the → this).", "supplement-016": "Page 34, chapter VIII, line 2: replace “avoir” with “a” (to have → has). Line 5: replace “on a fait” with “on fait” (one has made → one makes).", "supplement-017": "Page 36, line 1: replace “comme majeur” with “comme le majeur” (as major → as the major). Line 9: replace “donc le dernier” with “donc ce dernier” (therefore the latter → therefore this latter).", "supplement-018": "Page 40, line 3: replace 20 with 10.", "supplement-019": "Page 41, line 6: replace “occupant” (occupying) with “octuplant” (multiplying eightfold).", "supplement-020": "Page 47, last line: replace “par ce moyen” (by this means) with “par le Moyen” (by the Mean).", "supplement-021": "Page 48, paragraph, line 10: replace “elle contiendra” with “contiendra” (remove the pronoun before “will contain”). Line 12: replace “que les longueurs” with “que ces longueurs” (than the lengths → than these lengths).", "supplement-022": "BOOK II.", "supplement-023": "Page 52, second paragraph, next-to-last line: replace “see below, chapters XIX, etc.” with “chapters XVIII, XIX, and XXI.”", "supplement-024": "Page 53, line 7: do not divide the words “toute la piéce de Musique étant fondée sur lui” (the whole piece of music being founded upon it) with a comma. Instead, put the entire phrase between two commas or parentheses.", "supplement-026": "Page 54, chapter V, line 3: begin a new paragraph at “Nous devons avoir déja,” etc. (“We should already have,” etc.).", "supplement-027": "Page 55, first paragraph, lines 12–14: delete “Que leur extremitez aiment naturellement à se porter vers la partie qui approche le plus de leur être ; de sorte” (“That their extremes naturally tend toward the part closest to their nature; so that”).", "supplement-028": "Page 56, second paragraph: replace the passage beginning “La Septiéme qui provient,” etc., with: “The seventh produced by a minor third added to the dominant’s perfect chord forms a dissonance not only with the dominant but also with its major third. Thus the major third itself forms a new dissonance against the added seventh. This major third is the source of all major dissonances, and this seventh the source of all minor dissonances, without exception.”", "supplement-030": "Page 57: arrange the example as follows.", "supplement-466-major": "Perfect cadence in major mode—correction to page 57.", "supplement-466-minor": "Perfect cadence in minor mode—correction to page 57.", "supplement-033": "Page 58: slash the example’s figure 6 instead of attaching a sharp. This same error occurs wherever I intended a chord of the kind that this figure denotes. Admittedly, authors have not yet used this distinction in their published works.", "supplement-034": "Same page, references at the bottom: replace “(b cap. 5, f. 251.)” with “(b cap. 51, f. 251.).”", "supplement-035": "Page 59, footnote reference: replace “cap. 6” with “cap. 52.” Line 6: replace “chap. VI” with “Chap. LII.” Delete the example’s top part entirely.", "supplement-036": "Page 62: arrange the example as follows.", "supplement-467-major": "Interrupted cadence in major mode—correction to page 62.", "supplement-467-minor": "Interrupted cadence in minor mode—correction to page 62.", "supplement-039": "Pages 64–67: delete chapter VII and replace it with the following chapter.", "supplement-040": "CHAPTER SEVEN, revised.\nOn the irregular cadence.", "supplement-041": "A perfect cadence goes from dominant to tonic. This one goes the other way, from tonic to dominant, or from fourth note to tonic. That is why we call it irregular.", "supplement-042": "We now introduce a dissonance not previously discussed, though skilled musicians often use it well. It adds pleasing variety, supports graceful melodies, and is especially useful in four or more parts. Those who first tried it deserve praise.", "supplement-044": "The added sixth is consonant with the bass, but dissonant with the fifth above that bass. It must resolve upward. We will explain why.", "supplement-045": "A perfect chord with this added sixth is a great-sixth chord. Normally it is an inversion of a seventh chord.* Here, however, treat it as an original chord. In other situations it follows the properties of its seventh-chord source.", "supplement-046": "* See Book I, chapter VIII, article IV.", "supplement-048": "EXAMPLE.", "supplement-468-major": "Irregular cadence in major mode—revised chapter VII.", "supplement-468-minor": "Irregular cadence in minor mode—revised chapter VII.", "supplement-051": "Always give the ending note a major third. Then it functions as dominant and the opening note as tonic. Major or minor mode is shown only by the opening tonic’s third, which may be either kind.", "supplement-052": "Masson gives an inverted example of this cadence without explaining it as we do. He does not recognize the chords’ source. What he calls a tritone at A is a fourth altered to fit the modulation—and, against the fundamental bass, it is really a sixth.", "supplement-053": "EXAMPLE BY MR. MASSON,", "supplement-054": "in which the added fundamental bass shows the irregular cadence in inversion. a", "supplement-468-masson": "Masson’s example with added fundamental bass.", "supplement-056": "Zarlin says nothing about this cadence. Masson and Brossard call it imperfect. Brossard instead uses irregular for a cadence ending outside the mode’s essential notes:b tonic, third, and fifth. That label tells where a cadence is used, not what kind it is. It does not help choose among different cadences, since it describes them all equally. It really calls the modulation irregular when the ending leaves the original mode’s main notes.", "supplement-058": "a Masson, Nouveau Traité de Musique, page 99.", "supplement-059": "b Mr. de Brossard’s dictionary, under irregolare.", "supplement-061": "Brossard translated the old definition without allowing for changed practice. Ancient modulation was much more restricted. They called both foreign cadences and certain melodic ranges irregular, though range depends on the voice. Zarlin’s music suggests that they stayed in their first mode throughout. Ending a cadence outside it was improper or even wrong. We know that skillful movement between modes improves harmony by adding variety. The ancients used many rules to hide their limited understanding; modern discoveries make those rules unnecessary. Brossard’s own account of old and new modes should have led him to qualify his definition.", "supplement-062": "Perhaps we should avoid arguing about names and follow accepted usage. But usage is not settled. Performers often mix up technical words and seem to enjoy confusing opponents. Writers too choose names by preference rather than reason. If tradition is the guide, start with Zarlin. He calls inverted perfect cadences Cadenze fuggite.* In French, imperfect fits them better than interrupted. Inversions do not interrupt a perfect cadence as modern interrupted cadences do. Likewise his irregular describes things we regard as regular. Our name fits a genuine reversal: perfect cadence’s bass falls a fifth and seventh resolves downward; irregular cadence’s bass rises a fifth and sixth resolves upward. An imperfect cadence only removes or inverts the fundamental bass. Though the two adjectives are similar, imperfect is closer to perfect than irregular here.", "supplement-064": "Enough about names. Let us discuss the substance.", "supplement-065": "Expert composers use this dissonance successfully. It sounds as pleasing as the perfect cadence’s dissonance and helps both melody and harmony. Since writers have scarcely explained it, we will add reasons to the evidence of listening and practice.", "supplement-066": "Different dissonance names serve practical convenience. There is really one basic dissonance, with all others derived from it. We call it a seventh, but hear it most clearly as a second, its inversion. Harmonic ratios produce consonances first, then this dissonance through division of the major third. That completes their harmonic sequence of divisions.", "supplement-067": "* Zarlino, Terza Parte, chapter 52, folio 254.", "supplement-069": "No diatonic note used in music fits between notes a second apart. They are therefore as close as possible. If sounds were solid objects, we might say they touch and collide. This matches our language about dissonance offending the ear or clashing colors offending the eye. The word syncope already suggests collision: Greek syn means together, copto means I strike. Brossard saysa a syncopated note strikes the beat and the conductor’s hand. But that is a secondary effect. The note first clashes with another sound; the clash is then felt in the beat and the hand marking it.", "supplement-071": "The effect resembles these two rules for solid bodies, stated by Reverend Father Pardie:b", "supplement-072": "A moving body encountering another body at rest gives it all its motion and itself becomes motionless.", "supplement-073": "A hard body striking an immovable body rebounds with all its motion.", "supplement-074": "Prepared dissonance resembles the first case; unprepared dissonance the second.", "supplement-075": "EXAMPLE.", "supplement-470-parfaites": "Perfect cadences—prepared and unprepared dissonance.", "supplement-470-irregulieres": "Irregular cadences—prepared and unprepared dissonance.", "supplement-078": "Consonances are in the first upper part; dissonances in the second.", "supplement-079": "a Mr. de Brossard’s dictionary, under Syncope.", "supplement-080": "b Reverend Father Pardie, page 147, proposition XVIII, and page 153, proposition XXIII.", "supplement-081": "Figures show the intervals each upper part forms with the bass. Diagonal lines ↘ ↗ show dissonance moving down or up. B marks prepared dissonances; F marks unprepared dissonances.", "supplement-082": "Watch B, the prepared dissonance. It stays still while consonance A moves against it. A then stops, and B moves to C, the place A itself could have gone. It is as if A handed its movement to B. In the other case, consonance D stays immovable. Dissonance F strikes it and returns to G, where it began, like a rebounding body.", "supplement-083": "The nearest consonance therefore governs the dissonance’s movement. Its degree of perfection also matters.", "supplement-084": "In perfect cadence, the octave represents the fundamental. At A and D it drives the seventh B and F downward. In irregular cadence, the fifth takes the active role and drives the sixth upward. The fifth is less perfect than the octave, just as irregular cadence is less perfect than perfect cadence. So 7 moves away downward from 8; 6 moves away upward from 5. Both resolve to the third, C or G, which generated them and softens their harshness. See chapter II, page 53.", "supplement-085": "The example gives the best treatment of prepared and unprepared dissonance, even without all possible chord-filling notes. Harmony begins with the perfect chord. Any added sound is dissonant* against its nearest consonance, and that consonance determines where it moves. The dissonance has no independent properties: it needs the consonance belonging to the foundation. Therefore the sixth added at an irregular cadence must rise. It is always major in this situation. The arrangement parallels the seventh forced downward in perfect cadence. Each dissonance forms a second or inverted seventh against its neighbor. Both resolve into the third from which they came.", "supplement-087": "You may say we chose the preceding consonances and destination C arbitrarily. But those choices are good—indeed among the best. That is enough for the argument.", "supplement-088": "The last three chapters’ three cadences contain harmony’s essentials: chords, chord movement, and true modulation. Consonant chords belong to the perfect chord. Add a sound and the resulting seventh chord supplies the dissonant chords. Even the irregular cadence’s added-sixth chord reduces to a seventh. Study all three cadences closely; the rest of our teaching depends on them.", "supplement-089": "End of chapter VII.", "supplement-090": "* See chapter XIV, article I, pages 95, 96, 97, and 98.", "supplement-091": "Page 70, next-to-last paragraph: retain only its first line, “La Cadence rompuë s’évite de même que la Parfaite” (“The interrupted cadence is avoided like the perfect cadence”); delete the remainder. Third line from the bottom: replace “renversée” with “renversé” (correct the grammatical gender of “inverted”).", "supplement-093": "Page 71: replace the example with the following.", "supplement-472-p71": "Five-part example replacing page 71.", "supplement-095": "Page 72: delete the eighth paragraph, which begins with X.", "supplement-096": "Page 75: delete the example’s upper part.", "supplement-097": "Page 76: at note A in the example’s bass by supposition, write 4 over 9 instead of 4 over 2.", "supplement-098": "Page 77, fourth line from the bottom: put reference letter b after “mention” and remove it from the next line. In the Zarlino citation, put 290 before 291.", "supplement-100": "Page 78, paragraph, line 7: add a reference mark at “Onziéme” (eleventh) for this footnote: “Zarlin reports in the same chapter, folio 178, that the Pythagoreans disputed this with Ptolemy; there would be much more to reflect upon here.”", "supplement-101": "Page 80: the example’s second staff should appear as follows.", "supplement-472-p80": "Corrected second staff of page 80—third, octave; major dissonance introduced by borrowing.", "supplement-103": "Horizontal lines in this example divide text belonging to the same staff. They should not do so. Readers should correct this themselves, as we have done on pages 57 and 62.", "supplement-106": "Page 82, paragraph, last two lines: replace “Cinquiéme ou de la Sixiéme” with “Quinte ou de la Sixte” (use the interval names fifth and sixth, rather than ordinal degree names). In the second paragraph, line 2, the star beside Zarlin refers to the following example. The footnotes should read:", "supplement-107": "(A) De Brossard, Dictionnaire de Musique, pages 91 and 110.", "supplement-108": "(B) Masson, pages 74, 75, and 77.", "supplement-109": "Page 85, line 11: delete “soit.” Line 15: replace “parlerons” with “parlons” (shall speak → speak).", "supplement-110": "Page 86, last paragraph, third line from the bottom: start a new paragraph at “Si l’on fait monter la Basse,” etc. (“If the bass is made to rise,” etc.).", "supplement-111": "Page 87: the guide signs in the two parts immediately above the fundamental bass should be as follows.", "supplement-473-p87": "Corrected guide notes for page 87.", "supplement-113": "Page 88: the example’s first part should be as follows.", "supplement-473-p88": "Corrected first part of page 88.", "supplement-115": "Same page, third line after the example: replace “s’épuiser” (be exhausted) with “se puiser” (be drawn from).", "supplement-116": "Page 90: add at the end of the first paragraph: “Furthermore, two successive perfect chords over a diatonic bass progression would not follow proper modulation.”", "supplement-117": "Page 92, second paragraph, line 1: replace “qui” with “lequel” (which). Line 2: replace “dans” (in) with “audessus de” (above).", "supplement-118": "Page 92: insert the following before the last paragraph.", "supplement-119": "You may raise a minor third to an octave if a seventh is implied with that octave and the next chord reaches the consonance that should resolve that seventh.", "supplement-120": "EXAMPLE.", "supplement-473-p92": "Added page 92 example—minor third and octave through supposition.", "supplement-122": "Notes marked A must resolve the implied seventh indicated by the bass figures.", "supplement-123": "The same discussion covers the minor third and dissonances derived from it by changing the bass. This is a matter of melodic expression: the octave is allowed only by supposition. Book III explains more.", "supplement-124": "“De plus, si la Tierce mineure,” etc. (“Furthermore, if the minor third,” etc.) begins page 92’s last paragraph. Continue that paragraph to its end.", "supplement-126": "Page 95, line 4: replace “audessus” (above) with “au-dessous” (below).", "supplement-127": "Page 97, first paragraph, line 6: replace “ce qui s’éclaircira,” etc. (“which will be clarified,” etc.) with “what was explained in chapter VII of the Supplement, and must always be understood throughout the rest of this chapter.”", "supplement-128": "Page 98, line 4: replace chapter XIX with chapter XVIII.", "supplement-129": "Page 104, lines 10–11: replace “consecutive octaves” with “consecutive octaves or fifths.”", "supplement-130": "Page 113, next-to-last line: replace “ou en exclure” with “ou exclure” (or exclude; remove en).", "supplement-131": "Page 115: delete the example’s top part labeled “Partie ajoûtée” (added part). The guide sign in the part below it should be as follows.", "supplement-474-p115": "Corrected guide note for page 115.", "supplement-133": "Page 116, lines 4–6: replace the passage beginning “de plus la Partie ajoûtée,” etc., with only: “Furthermore, these two basses must not be placed above the other parts.” Second paragraph, line 6: replace “audessus” (above) with “audessous” (below).", "supplement-134": "Page 117, line 8: replace “devienne-t-elle” with “devienne telle” (becomes such, rather than an inverted question). Delete the next-to-last paragraph beginning “Ce n’est pas le tout” up to the last paragraph beginning “Au reste, nos raisons,” etc.", "supplement-135": "Page 118, line 3: replace “continuës” (continuous) with “contenuës” (contained). Line 6: replace “perfection” with “imperfection.”", "supplement-136": "Page 121, last paragraph, line 2: replace “ces Consonances” (these consonances) with “les Consonances” (the consonances).", "supplement-137": "Page 122, last paragraph, line 4: end the paragraph at “les plus naturelles” (the most natural); delete the rest.", "supplement-138": "Page 124, line 2: replace “qui” with “qu’on.”", "supplement-139": "Page 126, second paragraph, line 1: replace “tous ceux qui ne sont” with “tous ceux qui ne se sont” (restore the reflexive se).", "supplement-140": "Page 127, line 2: replace “la pratique de ceux” with “la pratique dans ceux” (practice of those → practice within those). Line 5: replace chapter XXIII with chapter XXI.", "supplement-141": "Page 128, first paragraph, line 6: replace “s’accordant” with “s’accordent” (agreeing → agree). Second paragraph, line 4: correct “prouvient” to “provient”; line 5: replace “dans un son” with “dans un seul son” (in a sound → in a single sound).", "supplement-142": "Page 130, third line from the bottom: replace “ne dépend du” with “ne dépend que du” (depends only on).", "supplement-143": "Page 134, lines 5–6: replace “chapters XXII, etc.” with “chapters XXI, XXII, and XXIII.”", "supplement-144": "Page 135, last line, and page 136, first line: replace “faire préceder” (make precede) with “faire procéder” (make proceed).", "supplement-145": "Page 136, lines 18–19: replace “Ces Sons devant être absolument extraits de l’idée dans la preuve” (“These sounds must be entirely removed from the idea in the proof”) with “Ces sons devant être absolument retranchez dans la preuve” (“These sounds must be entirely removed in the proof”). Line 25: replace “cela étant fait” (this being done) with “cela supposé” (this being assumed).", "supplement-146": "Page 139, line 27: replace chapter XXII with chapter XXI.", "supplement-147": "Page 142, ninth line from the bottom: replace “Misse” with “Ulisse” (Ulysses). Fourth and third lines from the bottom: replace “toutes les particularitez” (all the particulars) with “tous ces effets” (all these effects).", "supplement-148": "Page 143, line 6: replace “qu’ils appellent” with “qu’il appelle” (which they call → which he calls).", "supplement-149": "Page 145, second paragraph, line 3: separate the three words “par ce que.” Eighth and seventh lines from the bottom: replace “Does this perfect system therefore have nothing distinctive, etc.?” with “Does this perfect system cease to be perfect when we are to imitate it? Why, etc.?”", "supplement-150": "Page 146, thirteenth line from the bottom: replace “ainsi” (thus) with “& si” (and if).", "supplement-151": "Page 147, line 24: replace “établirent” with “établir” (they established → establish). Third line from the bottom: replace “par la Quinte & le Collateral, & où” with “par la Quinte, & le Collateral, où” (correct the comma and remove the second &).", "supplement-152": "Page 148: arrange the example as follows.", "supplement-474-p148": "Corrected page 148 example—first, second, and mediant.", "supplement-154": "Same page, ninth line from the bottom: replace “leur” with “lui” (to them → to him).", "supplement-155": "Pages 149–150: place the chapter numbered XXIV on page 157, “On the character of modes and keys,” between the chapters on pages 149 and 150.", "supplement-156": "Page 150, last paragraph, line 2: replace the spelled-out “nombres deux, trois, quatre” with “nombres 2, 3, 4.” Last line: replace spelled-out “quatre six,” etc., with “4, 6, 8, 10, 12, 15, 16, 20,” etc. Tenth line from the bottom: delete “Par une volonté contre nature” (“By a will contrary to nature”).", "supplement-157": "Page 151, first line: replace spelled-out “deux, trois & cinq” with “2, 3 & 5.”", "supplement-158": "Page 152, fourth paragraph, first line: replace “voudroit” (would wish) with “vaudroit” (would be worth). Next-to-last line before the last paragraph: replace “lourré, & aux” with “lourré aux.” Last line: replace “l’observerons” with “l’observons” (shall observe it → observe it).", "supplement-159": "Page 157, line 5: replace “& de celles” with “& des Mesures” (and of those → and of the measures).", "supplement-160": "Page 158: arrange the example as follows.", "supplement-474-p158": "Major key; minor key—corrected signatures for page 158.", "supplement-162": "Same page, fifth line below the example: replace “ne soit pas observé” with “ne sont pas observez” (correct the verb and participle to the plural).", "supplement-163": "Add the following at the end of this chapter.", "supplement-164": "First, a tune may change tempo partway through. If the note value used as one beat changes, write the new beat value in parentheses above the staff. If the beat value stays the same, no new sign is needed. See the example.", "supplement-475-mouvement": "Change of tempo: beat values in parentheses.", "supplement-167": "Second, key signatures are often incomplete. This can force singers to use “sol” where they should sing “ut,” or “ré” where they should sing “la.” These syllables move with the key; they are not fixed pitches here. We will show the correct signatures, then explain how to handle incomplete ones.", "supplement-169": "TURN THE PAGE for the continuing example. Its explanation follows.", "supplement-170": "EXPLANATION.", "supplement-171": "There is one major key without sharps or flats, so there should also be one minor key without them. French practice leaves both D minor and A minor unmarked. Singers therefore alternate between “ré” and “la” as the minor tonic’s name. This has long been recognized as wrong, but existing scores discourage reform. Frere* tried to make minor tonics use one syllable. Unfortunately he added a sharp where we would add a flat—for example, the flat marking D minor’s minor sixth. His sharp instead gives a major sixth and disrupts minor harmony. If he had chosen “la” rather than “ré” as the standard, he would have kept the natural pattern. His attempt still deserves thanks.", "supplement-172": "A better system would model every minor key on A minor’s octave. Sing every minor tonic as “la,” just as every major tonic is sung as “ut.” This changes the singing syllable, not the actual pitch of the key.", "supplement-174": "We thought of this only later. Page 158 still tells singers to call every minor tonic “ré.” We originally wanted to follow existing practice and avoid fussing over apparently minor reforms. But omitting a flat from D minor and the other flat minor signatures contradicts our rule, so we had to speak. Most musicians ignore suggestions meant simply to make teaching clearer. Those relying only on personal experience—nearly everyone—may reject explanations unlike their own. Enough of that digression.", "supplement-175": "French musicians omit a flat in minor signatures; most Italians omit a sharp in major signatures, from A major onward through the sharp keys.", "supplement-176": "The explanation continues after the example.", "supplement-177": "* Mr. Frere, Transposition de Musique, page 35.", "supplement-178": "ORDER OF SHARPS AND FLATS\nto be placed after the clef to indicate transposition of the modes.", "supplement-179": "Table of major modes or keys.", "supplement-476-majeurs": "Major keys: C, G, D, A, E, B, F♯, C♯, F, B♭, E♭, A♭.", "supplement-181": "Table of minor modes or keys.", "supplement-476-mineurs": "Minor keys: A, D, G, C, F, B♭, E♭, E, B, F♯, C♯, G♯.", "supplement-183": "With complete signatures in the order shown, sing major tonics as “ut” and minor tonics as “la.” If a major signature is missing one sharp, use “sol” for its tonic. If a minor signature is missing one flat, use “ré.” This works only if you can tell major from minor. Otherwise, sing the last sharp as “si” and the last flat as “fa.” Missing signs still cause trouble, and finding the last sign takes some effort. The correct order we prescribe makes it easier.", "supplement-185": "END OF CHAPTER XXV.", "supplement-186": "Page 163, line 1: replace “esclavage” with “asservissement” (slavery → subjection). Second paragraph, line 6: replace “trop grande repetition” with “trop frequente repetition” (too great repetition → too frequent repetition). Line 8: replace “dépendent” with “dépendant” (depend → depending). Next-to-last line before chapter XXIX: replace “suit” with “fuit” (follows → flees).", "supplement-188": "Page 165: the example should be as follows.", "supplement-477-p165": "Thirds and sixths—corrected page 165 example.", "supplement-190": "Page 167: the example should be as follows.", "supplement-477-p167": "Corrected page 167 chord—intervals 1, 2, 4, 6, 7.", "supplement-192": "END OF BOOK II.", "supplement-193": "BOOK III.", "supplement-194": "Page 271, line 9: replace the passage beginning “l’on ne doit pas moins,” etc., with “One should also practice finding descending intervals in the scale, where one will find,” etc.", "supplement-195": "Page 174, line 4: begin a new paragraph with “Comme il est absolument,” etc. (“Since it is absolutely,” etc.).", "supplement-196": "Page 176, last paragraph, line 1: replace “Composition” with “comparaison” (composition → comparison).", "supplement-197": "Page 178, second paragraph, line 9: replace “& de même que celle-cy” with “& pareillement celle-cy” (and just as this one → and likewise this one).", "supplement-198": "Page 179, below the next-to-last staff: replace “une Ronde ou deux Blanches,” etc. (“one whole note or two half notes,” etc.) with only “idem” (the same).", "supplement-199": "Page 182, line 1: replace “le Mis” with “le ♯ Mis” (restore the sharp sign before “placed”). Next-to-last paragraph, line 2: replace “se distinguant” with “se distinguent” (being distinguished → are distinguished). Last paragraph, line 1: replace “pour revenir au ♯ & aux ♯” with “pour revenir aux ♯ & aux ♭” (returning to sharps and flats).", "supplement-200": "Page 183, second paragraph, line 1: replace “lorsque le, le ♮” with “lorsque le ♯, le ♮” (restore the omitted sharp sign).", "supplement-202": "Page 185, second paragraph, line 7: replace “nous sous-entendons” (“we imply”) with “nous sous-entendrons” (“we shall imply”).", "supplement-203": "Page 186, last line before Chapter IV: replace “of the fundamental bass” with “of the tenor part”.", "supplement-204": "Page 187, third paragraph, line 3: replace “which is the bass” with “which is in the bass”.", "supplement-205": "Page 192, last paragraph, line 2: replace “être préparée & sauvée” with “être préparé & sauvé” (“be prepared and resolved”); use the masculine rather than feminine French forms.", "supplement-206": "Page 193, first staff of the example: the cue sign below letter B should be in the middle of the space, indicating C, rather than on the line.", "supplement-207": "Page 198, line 10: replace “of the third” with “of the second”.", "supplement-208": "Page 202, first paragraph after the list of chords, line 2: replace “sa Médiante se porte” (“its mediant moves”) with “sa Médiante le porte” (“its mediant bears it”).", "supplement-209": "Same page, line 13: replace “devoit” (“was to” or “should”) with “doit” (“must”).", "supplement-210": "Page 209, next-to-last paragraph, line 1: for “one cannot here make the …”, read “one cannot here distinguish a second degree from a sixth degree, nor a tonic from a dominant, because …”.", "supplement-212": "Page 214, last paragraph, lines 5 and 6: replace “the seventh being” with “the seventh of this note being”. Same page, third line from the bottom: replace “(Y) removes the tone or the second …” with “(Y) removed; the interval of a tone or second between notes (Z) and (A) is formed …”.", "supplement-214": "Page 216, line 19 of the small type: replace “remontoit” (“rose again”) with “rencontroit” (“encountered”).", "supplement-215": "Page 222: arrange the example as follows.", "supplement-478-p222": "Corrected page 222 example: sixth part, continuo bass and fundamental bass; irregular cadences A and B.", "supplement-217": "Page 227: in the second example, 3 after label G means that G is a third above the second note labelled F. In the third example, 5 after label H means that H is a fifth above the second note labelled F.", "supplement-218": "Page 229, line 9: replace “Chapter XVI” with “Chapter XIII”.", "supplement-219": "Page 231, line 2: replace “P” with “D”. In the second paragraph, line 2, letter G should begin a new paragraph. The last measure of the example’s continuo bass should read as follows.", "supplement-478-p231": "Last measure on page 231, continuo bass.", "supplement-222": "Page 232, third paragraph: replace “as N” with “as at J”.", "supplement-223": "Page 233, Chapter 19, line 8: replace “see Book II, Chapter XVI” with “see Book II, Chapter XIII”.", "supplement-225": "Page 234: the next-to-last measure of the fundamental bass should read as follows.", "supplement-479-p234": "Next-to-last measure on page 234, fundamental bass.", "supplement-227": "Page 239, fifth paragraph, line 4: replace “the bass precedes” with “the bass proceeds”.", "supplement-228": "Page 240: a dot is missing to the right of the C that begins each staff of the example.", "supplement-229": "Page 245, second paragraph, line 5, and third and fourth paragraphs; also page 247: “de cinq en cinq” (“by fives”) and “de quatre en quatre” (“by fours”) occur several times. Read “de Quinte en Quinte” (“from fifth to fifth”) and “de Quarte en Quarte” (“from fourth to fourth”), or simply “by fifths” and “by fourths”.", "supplement-230": "Page 252: remove the first G label in the example. Move the sharp below the E labelled G to the figure 6 above that same note. Line 2: replace “chiffrez” with “chiffrée”, correcting the French form of “figured”. Line 3: replace “which makes a mediant heard there” with “which is heard there requires only the perfect chord”.", "supplement-231": "The following words should begin a new paragraph: “A mediant …”.", "supplement-232": "Page 256, last line before the paragraph break: replace “of the sharp fourth” with “of the tritone”.", "supplement-233": "Page 259, last paragraph, line 8: replace “peuvent nous marquer ; le rapport” (“can indicate to us; the relation …”) with “peuvent nous marquer, a le rapport” (“can indicate to us, has the relation …”).", "supplement-234": "Page 260: add a ♭ to the E labelled F.", "supplement-235": "Page 261, last line before the example: replace “on n’en put faire ainsi” with “on n’eût pû faire ainsi”, changing the wording to “one could not have done so”.", "supplement-236": "Page 262, line 2: replace “sharp sixth” with “major sixth”. In the last paragraph, line 6, remove the “&”.", "supplement-237": "Page 266: place letter C below the first note of its measure, rather than below the second note.", "supplement-238": "Page 267: place an A below the example’s first D.", "supplement-239": "Page 268, last line before the paragraph break: replace “Chapter XX, on licenses” with “Chapter XVII of Book II”.", "supplement-240": "Page 269, second line from the bottom: replace “ne diminuent rien” (“diminish nothing”) with “ne dominent rien” (“dominate nothing”).", "supplement-241": "Page 276, line 2: replace “sharp fifths” with “augmented fifths”.", "supplement-242": "Page 277, last paragraph, lines 4 and 5: delete “although the seventh is suitable only in preparing the irregular eleventh”.", "supplement-244": "Page 278: put letter A above the first note of the next-to-last measure in the continuo-bass example.", "supplement-245": "Page 281, first example: add a ♯ to the left of the C note and another to the right of the word “Ut” (C). In the second example, remove the ♯ attached to figure 7.", "supplement-246": "Page 282, line 2: replace “Deuxiéme” with “Seconde” (both mean “second”; the latter is the interval name). On the same page replace “Cinquiéme” with “Quinte” (the interval “fifth”).", "supplement-247": "Page 284, end of the third paragraph: replace “Basse” (“bass”) with the letter B alone.", "supplement-248": "Page 287: place a ♯ instead of a ♮ beside the second note on the example’s first staff. Move the ♮ to the immediately following note at the same degree.", "supplement-249": "Page 288, line 6: replace “Chapter XXXI” with “Chapter XXIX, page 274”.", "supplement-250": "Page 290: replace the last three paragraphs with this passage. For further confirmation of this book’s rules, see the discussion of their foundations in Book II, Chapter XVIII, page 25. Chromatic motion can occur in major keys: the major third of one dominant can fall a semitone and become the seventh of another dominant. Alternatively, the fourth degree can rise a semitone to become the leading note of a new key.", "supplement-251": "Page 293: the example should read as follows.", "supplement-479-p293": "Corrected page 293 example: chords A and B.", "supplement-253": "Page 294, sixth paragraph: replace “la Cinquiéme” with “la Quinte” (the interval “fifth”). Add the following as a new paragraph immediately before Article IV:", "supplement-254": "A tritone may sometimes stand over a degree other than the fourth, and a diminished fifth over something other than the leading note. In those cases they are accompanying intervals, not the chord’s defining feature. The key’s harmonic movement requires their altered form. Some sevenths in the sequence just shown are similarly altered from their normal size. Once you know the chord and key, these alterations need not trouble you: the natural sequence of notes within that key or mode’s octave determines each chord interval’s normal or altered form.", "supplement-256": "Page 296, last line before Article VII: replace “and in Book II, the chapters …” with “and in Book II, all the chapters discussing meter”.", "supplement-257": "Page 299, Chapter XXXVI, next-to-last paragraph: replace “d’une Consonance parfaite une imparfaite” with “d’une Consonance parfaite à une imparfaite”, supplying the missing “à” (“from a perfect consonance to an imperfect one”).", "supplement-258": "Page 309: remove the figure 6 above G in the second measure of the figured bass. Move the 6 below A in the next-to-last measure of the same bass above that note. In the last paragraph, replace “the figures above” with “the figures below”.", "supplement-260": "Page 310, line 7: replace “even in the first” with “and especially in the first”.", "supplement-261": "Page 315, first paragraph, sixth line from the bottom: replace “Chapters XXV and XXVI” with “XXIV and XXV”.", "supplement-262": "Page 316, line 2: replace “Deuxiéme” with “Seconde”, the interval name for a second. In the second paragraph’s last line, replace “Ton” (“tone”) with “Temps” (“beat”).", "supplement-263": "Page 317, last line: replace “I cannot” with “I can”.", "supplement-264": "Page 336, paragraph numbered 40, line 10: replace “and we have said” with “and if we have said”.", "supplement-265": "Page 357, line 1: replace “guides us, one may” with “guides us, and one may”. Line 4: replace “parts, find” with “parts, and find”. Seventh line from the bottom: replace “Tons” (“tones”) with “Temps” (“beats”).", "supplement-266": "BOOK IV.", "supplement-267": "Page 366, paragraph 7: “distinguish thirds from sixths, majors from minors …” should read “distinguish major thirds from minor thirds, and major sixths from minor sixths …”. In the small type, fifth line from the bottom, the diminished seventh still measures 4½ tones, but replace examples C–B♭ and G–F with C♯–B♭ and G♯–F.", "supplement-268": "Page 367: place the heading “Minor thirds” above the example’s second staff.", "supplement-269": "Page 368: remove the ♯ beside D in the fourth measure of the major-sixths example.", "supplement-270": "Page 369, sixth line from the bottom: replace “sharp second and flat third” with “augmented second and minor third”.", "supplement-271": "Page 382, fourth staff counting from the bottom: in measure 5 replace figure 4 with 3. In the next-to-last measure of that staff, add F as follows.", "supplement-480-p382": "Page 382 chord with F added.", "supplement-273": "Page 383, fourth staff counting from the bottom: arrange the fifth measure’s chord as follows.", "supplement-480-p383": "Fifth measure on page 383: corrected chord.", "supplement-275": "Some figures indicating chords or fingering are missing from the examples on that page. Follow the correctly printed opening to supply them. But on page 387, the second staff’s opening 3 must become 5.", "supplement-276": "Page 393, third line from the bottom: replace “donc il doit” (“therefore it must”) with “dont celui-là doit ou du moins peut suivre l’autre, conformément …” (“of which that one must, or at least may, follow the other, in accordance …”).", "supplement-277": "Page 399: throughout the example, replace the G clef with a C clef on the first line. Arrange the first three measures as follows.", "supplement-480-p399": "Corrected first three measures of page 399, C clef on the first line.", "supplement-279": "Page 400: arrange the example’s fifth chord as follows.", "supplement-480-p400": "Corrected fifth chord on page 400.", "supplement-281": "Page 402, line 8: after “in the bass of seconds”, add “page 396”.", "supplement-282": "Page 403: the second chord of the fourth measure should read as follows.", "supplement-481-p403": "Second chord of the fourth measure, page 403.", "supplement-284": "Same page, line 3: replace “sixth; of the mediant to that …” with “sixth of the mediant; to the sixth–fourth chord of the dominant, or to the perfect chord of the tonic; one will find …”.", "supplement-285": "Page 406, Article I, line 1: replace “third” with “second”. Line 3: replace the plural French verb “se chiffrent” with singular “se chiffre” (“is figured”).", "supplement-286": "Page 407, last line: replace plural “précedent” with singular “précede” (“precedes”).", "supplement-287": "Page 408, line 2: replace “devoit” (“should” or “was to”) with “pourroit” (“could”).", "supplement-288": "Page 409, line 6: replace plural “trouvent” with singular “trouve” (“finds”).", "supplement-289": "Page 416, Chapter XVI, second paragraph, line 2: replace “Chapter XI” with “Chapter IX”.", "supplement-290": "Page 419: replace the ♯ beside F in the second chord of measure 6 with a ♮.", "supplement-291": "Here, as elsewhere, the figure does not identify the small-sixth chord distinctly. You can recognize it in the upper part, which shows every chord.", "supplement-292": "Page 423: the fifth chord of the example should read as follows.", "supplement-481-p423": "Corrected fifth chord on page 423.", "supplement-294": "Page 424: the fourth measure of the example’s chords, counting backward, should read as follows.", "supplement-481-p424": "Corrected fourth measure counting backward on page 424.", "supplement-296": "Page 425, next-to-last paragraph: replace “Chapter XIX” with “Chapter XVII”.", "supplement-297": "Page 427, end of the first paragraph: replace “contenus” (“contained”) with “continus” (“continuous”).", "supplement-298": "Page 428, end of paragraph 2: change French “naturel” (“natural”) to “nature”. In the example, the 4 for the tritone and the 6 for the small sixth should both be barred. The author was away while the book was printed. These signs were not yet usual in printing, and the printers did not think them important enough to supply. But barred 6 means the small-sixth chord, not merely a major sixth, despite some people’s claims. One figure should identify a complete chord, avoiding confusing stacks of figures. There are four kinds of sixth chord, so each should have its own sign as far as possible. This has received little attention. People have used barred 6 simply for a major sixth, assuming it comes with a third and fourth. That assumption fails: a major sixth may need a figure only because the music has moved into a transposed key whose sharps are absent from the signature. It may be a different chord altogether. The small-sixth chord may even contain a minor sixth. Custom alone defines these signs. Barred 5, or 5̸, means a diminished fifth; that contradicts the claim that the same bar on another number should mean major or augmented. Better to use the new signs to identify whole chords clearly than to change an interval to minor in one case and major in another, particularly when several accompaniments are possible for that interval.", "supplement-300": "This chapter’s advice mainly concerns future practice. Our rules can, however, help deal with the faults of older practice.", "supplement-301": "Page 430, line 11: delete “&”. In the example, combine the parts above the bass on a single staff so that they can serve as accompaniment.", "supplement-302": "Many music and harpsichord teachers find their established views hard to give up, so we do not expect unanimous approval. Anyone who cannot accept our conclusions is invited to explain their objections publicly. That will help us improve the work as fully as we hope to.", "supplement-303": "END OF THE SUPPLEMENT.", "catalogue-title": "CATALOGUE\nOther books on music theory printed in France that are available in copies.", "catalogue-001": "La Gamme du Si (The Si Scale), by Mr Nivers.", "catalogue-002": "Music for Children.", "catalogue-003": "Music Lessons, by Mr Berthet.", "catalogue-004": "The Principles of Music, taught through questions and answers.", "catalogue-005": "Mr Dupont has had a more extensive version of these principles engraved.", "catalogue-006": "Very Easy Principles for Learning to Sing Any Music at Sight, by Mr L’Affillard. 5th edition, dedicated to the Duke of Burgundy.", "catalogue-007": "— The same book, 6th edition, dedicated to nuns.", "catalogue-008": "Musical Transposition in Every Manner, by Mr Frere, intended to supplement all other teaching methods.", "catalogue-009": "A chart explaining musical principles, by Mr Fleury.", "catalogue-010": "An Easy Method, by Mr Monteclair: detailed principles and several lessons for one or two voices.", "catalogue-011": "— Music lessons in four groups, with a summary of the basic principles.", "catalogue-012": "A treatise on composition by Mr Nivers.", "catalogue-013": "A new treatise on composition by Mr Masson.", "catalogue-014": "A treatise by Mr de la Voye-Mignot. Quarto format; rare.", "catalogue-015": "A treatise by Father Parran. Quarto format; rare.", "catalogue-016": "Dictionary of Music, by Mr de Brossard. Bound folio volume.", "catalogue-017": "Harpsichord Principles, by Mr de Saint-Lambert.", "catalogue-018": "— A treatise on accompaniment for the harpsichord and all other instruments.", "catalogue-019": "Another accompaniment treatise, by Mr Boyvin.", "catalogue-020": "The accompaniment treatise by Mr Couperin.", "catalogue-021": "The accompaniment treatise by Mr Dandrieu.", "catalogue-022": "Principles for playing flutes, by Mr Hotteterre-le-Romain.", "catalogue-023": "A method for learning the theorbo, by Mr Michel-Ange.", "catalogue-024": "Another theorbo method, by Mr Fleury.", "catalogue-025": "— A chart of all musical chords, intended for accompaniment.", "catalogue-026": "A treatise on theorbo accompaniment, by Mr Campion.", "catalogue-027": "The Art of Playing Preludes, by Mr Hotteterre-le-Romain. Quarto format.", "catalogue-028": "A method for learning guitar, by Mr Desrosiers.", "catalogue-029": "A method for learning violin, by Mr Monteclair.", "catalogue-030": "Violin principles taught through questions and answers, by Mr Dupont.", "catalogue-031": "A method for learning plainchant, by Mr Nivers.", "catalogue-032": "Another method, with examples for all chant tones and detailed studies of music and plainchant.", "catalogue-033": "The chant tones used in Rome and Paris.", "catalogue-034": "The Choir Ritual, or Plainchant in Practice." }, "sourceSha256": "89d40bc079fbeaed6901dd7734992dfb505dd7dc4a75b379577888a193f82360" }