{ "schemaVersion": 1, "version": "caveman", "label": "Caveman English", "status": "Complete English reading; review draft.", "blocks": { "front-title-001": "HARMONY\nBring it back to nature’s basic rules", "front-title-002": "Four books.", "front-title-003": "BOOK I. Harmonic ratios. Harmonic proportions. How they fit together.", "front-title-004": "BOOK II. What chords are. What chords do. Everything that helps make music perfect.", "front-title-005": "BOOK III. Compose music. Basic rules.", "front-title-006": "BOOK IV. Play accompaniment. Support the music. Basic rules.", "front-title-007": "Author: Monsieur RAMEAU. Organist at Clermont Cathedral, Auvergne.", "front-title-008": "Title-page decoration.", "front-title-009": "PRINTER\nJean-Baptiste-Christophe Ballard. King’s sole music printer. Paris. Rue Saint Jean-de-Beauvais, at the Mont-Parnasse.", "front-title-010": "M. DCC. XXII. Year 1722.\nKing grants printing privilege.", "front-preface-001": "BEFORE WE START.", "front-preface-002": "Music advances. Ears notice its wonderful effects more. Yet minds seem less eager to dig into its true rules. Reason loses standing. Experience gains authority.", "front-preface-003": "Read surviving ancient writings. Reason alone helped those writers find most properties of music. Experience still supports most of their rules. Yet today we favor practice alone. We neglect what reason could give us.", "front-preface-004": "Experience shows what music does. Alone, it cannot reveal music's basic principle with the precision reason needs. Its conclusions often go wrong. Or doubt remains. Reason must clear that doubt. Example: we say our music is more perfect than ancient music. How prove it? Ancient writers claimed effects our music no longer seems able to produce. Maybe familiar things surprise us less. First we marvel. We get used to them. Marvel fades into amusement. But this proves equality at most. Not superiority. Try another path. Suppose one clear principle lets us draw sound, certain conclusions. Suppose these show our music has reached its highest possible perfection, while the ancients fell far short. See Book II, Chapter XXI. Then we know where we stand. We also better understand that point about familiarity. We know the art's limits. We pursue it more willingly. People with great musical taste and ability need not fear missing the knowledge needed for success. Experience can keep raising doubts. Reason clears them. That gives firm grounds to expect success in this art.", "front-preface-006": "Modern musicians means musicians since Zarlino.* They should copy the ancients here: explain why their practice works. Then many prejudices against them could end. Their own stubborn prejudices could end too. Experience serves them too well. It tempts them. Each day it shows new musical beauty. They rarely study that beauty's causes deeply. Their knowledge works for themselves alone. They cannot pass it on. They miss this fault. Others fail to understand; they act surprised. They rarely ask why they cannot explain themselves. Harsh charge. I admit it. I may still deserve it myself, despite all my efforts to avoid it.", "front-preface-007": "Still, I hope this criticism moves them as it moved me. I risk publishing my new findings chiefly to revive that old, noble drive to match and surpass good work. Music has natural simplicity. I try to reveal it. Mind should grasp its properties as easily as ear hears them.", "front-preface-008": "* Zarlino: famous music writer. Wrote about 150 years before this book. Later books on the same subject give only weak copies of his work.", "front-preface-010": "One person cannot finish exploring so deep a subject. Even with great care, something almost always gets missed. Still, new discoveries add to earlier work. Each opens a path. Others can go farther.", "front-preface-011": "Music is a science. It needs certain rules. Rules need one clear foundation. We can scarcely find that foundation without mathematics. I practiced music for many years. I gained experience. Still, only mathematics cleared my ideas. Before that, confusion remained. I had not even noticed it. I could not tell principle from rule. Then the principle became simple and clear. Its consequences gave me rules. Every rule had to connect back to that principle. Now I understood their meaning. Their correct use. Their connections. Their order. Start with simpler rules. Move gradually to harder ones. Even choosing terms became clear. I had not understood these things before. Someone once spoke while I praised modern music's perfection. They wished our century's musicians knew as much as the beauty of their compositions deserved. Now I had to agree. Feeling an art's effects is not enough. Same for science. Understand those effects well enough to explain them. That is my chief aim here. Four books.", "front-preface-012": "FIRST BOOK: a short account of relationships between sounds, consonances, dissonances and chords. Find harmony's foundation in one sound. Explain its chief properties. First division produces another sound: its octave. They seem like one. The original sound then uses that octave to form every chord. Chords contain only the fundamental sound and its third, fifth and seventh. The octave creates all their possible variety. Other properties appear too. Less directly useful for practice, yes. Still needed to lead us there. Demonstrations stay fairly simple.", "front-preface-013": "SECOND BOOK: theory and practice, equally. The principle becomes a musical part: the fundamental bass. Explain all its properties. Explain intervals, chords and modes too; they depend entirely on it. Also discuss how to make music perfect in performance. Use the first book's reasoning when useful. Use experience. Use the best musical writers. But criticize their mistakes. New ideas must reach different readers. Scholars: give reasons. People who trust only ears: give experience. People who trust teachers' rules too much: expose errors those rules may hold. Help readers accept the rules freely. Later books set them out in order and greater detail.", "front-preface-014": "THIRD BOOK: a special method. Learn composition very quickly. Method already tested. But people rarely believe this without trying for themselves. So I will not insist. If method is new to you, see what it produces before attacking it. Person who wants to learn cares little how teaching works, provided learning succeeds.", "front-preface-016": "No rules yet teach composition at today's full level of perfection. Skilled composers admit it: experience alone supplied almost all their knowledge. They try to teach others. Often must add this musicians' proverb: Cætera docebit usus. Practice will teach the rest. Yes, some excellence needs talent and taste. Experience can help these more than knowledge itself. Still need thorough understanding as a guide. Otherwise experience may deceive. At least, understanding connects new ideas from experience to their true foundation. It also puts talent and taste to work. Without understanding, those talents often go unused. So I sought a faster, easier path to this perfection. Until now, people reached it through practice alone. Start with a reasoned, precise, clear grasp of all harmony. Explain just three intervals. They form two main chords. They also form the whole progression of fundamental bass. That bass determines the other parts' progression too. Everything else rests on this understanding. First reading of this book can give it. Readers can readily check.", "front-preface-017": "FOURTH BOOK: accompaniment for harpsichord and organ. Hand position. Finger arrangement. Everything that helps build practical skill as quickly as possible.", "front-preface-019": "Other instruments accompany much like harpsichord. These basic rules work for them too.", "front-preface-020": "Last two books closely connected. Both help practical composers. Both help accompanists. Want nothing left unexplained? Consult second book too—assuming I forgot nothing. Others can surely improve on my work. I tried to miss nothing. My long discussions and repetitions prove the effort. This fault has two causes: I want clarity, and my ability is limited. First book is, in one sense, unnecessary for practice. Use it as you judge best. I put it first only to prove this treatise's claims about harmony.", "front-preface-021": "My job kept me from supervising printing. So I reread the work with fresh care. Found changes and necessary corrections. They appear in the supplement at the end. Two tables stand at the beginning. One lists subjects. One explains terms readers need. Together they introduce the whole work. I dedicate it to the public.", "front-preface-022": "Zarlino citations: Harmonic Institutions. Venice edition, 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,\nEssential Terms Explained.", "front-terms-002": "A", "front-terms-003": "ACCOMPANIMENT. See Book Four. page 363", "front-terms-004": "CHORD. One chord generates all others. Inversion reduces all to thirds. Chapter VII, Book I. 102. 114. 126. 127 and 128", "front-terms-005": "All chords grounded in single 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/dissonant chords easy; yield every imaginable melody, etc. Always reveal sounds completing chords. 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": "For correct conclusions, examine chord sounds against bass and 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. Must always prevail beneath other parts to subsist. 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: missing bass makes confusion; perfect cadence bass descends fifth. Yet almost all his examples forget bass. 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": "Irregular cadence: bass rises fifth, etc. Dissonance moves irregularly; always removable. See 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 progression creates chromatic genus; chiefly between minor key’s sixth/seventh in harmony. 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 suitable progression; know all interval/chord relationships. Practice everything making music perfect.", "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. Combined interval sounds greatly please ear. Third/fourth/fifth/sixth: all consonances. Consonant progression means melody moves by one of these.", "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: composition. Practitioners mean music on particular subject, usually 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 good modulation; constantly violates natural order. Fitting harmony needs rules sharing chant’s faults, chant being their object.", "front-terms-078": "Many musicians favor rules without examining principle. True-harmony listeners find them extraneous. Good modulation gives simpler, sounder rules ensuring correctness if subject follows it, as required. See Plainchant below; Book II, Chapters XVIII, XIX, 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 clash with ear. Dissonant progression: melody moves by such interval.", "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. Variable consonances, third/sixth; also cadences inverted from perfect. 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. Single part’s tune. Melodious music: each part’s melody matches harmonic beauty.", "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": "Same signs for equal/unequal beats prevent clear distinction. 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": "Pre-clef note identifies key, eases solmization regardless of sharps/flats after clef. page 158", "front-terms-146": "MODE. Determines diatonic octave-note progression and order of chords made only from those sounds.", "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": "Ears judge effects; mind needs reason to grasp properties. 125", "front-terms-153": "Experience gives many chords; reason unites all in one. Reason must govern 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": "Ordinary eleventh chord extremely harsh. Omit middle sounds; then 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. Minor dissonance preceded by same-degree consonance. Not universal. 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": "Fundamental sound/principle uses octave as second endpoint for intervals generated by its division. Shows itself their beginning/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": "Foundation/principle subsists only within own octave. Chords beyond span require foundation 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": "Fifth privileged: squares generate interval beyond octave. Resulting chord tolerable only through fifth’s harmonic division. 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": "Some harmonic sensitivity: melodic conclusion compels descending-fifth bass, etc. 50", "front-terms-235": "Harpsichord right-hand upper parts sometimes cannot avoid consecutive fifths. They connect chords; habit learned easier by tolerating small fault than strict composition rules.", "front-terms-236": "Small fault—if accompaniment fault at all. Harmonic foundation intact; Italians use without scruple.", "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. Transpose natural ordering of sounds forming 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 think supposition chords invertible, misunderstanding chord and inversion principles.", "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": "Semitone supplies all harmonic/melodic ornament; always serves major-dissonance progression. Zarlino explains well, then abandons where felt 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. Origin of all dissonances. Without seventh, major dissonance merely consonance. Squares page 38: seventh added to perfect chord generates 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": "Diminished seventh grounds all borrowed chords. Must lie below chords as lower sound of inverted 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” seem synonymous but differ greatly. Implied sounds may sound in chords currently lacking them. Implied fundamental belongs below others. Supposition: sounds stand for others absent or appearing before/after. Fundamental then immediately above supernumerary sound in supposition chord. See Suppose. Precise application to fundamental makes terms literally accurate.", "front-terms-305": "SUPPOSE. SUPPOSITION. Previously passing sounds for melodic taste, not harmonizing with chord. More precise use: added sounds altering chord perfection by exceeding octave.", "front-terms-306": "There are only two chords by supposition, from which two others derive. page 406", "front-terms-307": "Ninth chord’s extra sound cannot fit squares page 38. Immediately beneath fundamental; therefore supposes it.", "front-terms-309": "This supernumerary sound cannot be inverted. page 74", "front-terms-310": "See Cadence.", "front-terms-311": "SYNCOPATION. Dissonance clashes with nearest consonance. Term signifies this. In 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 practical meanings. First: distance between two sounds, whole tone, theoretically major/minor. 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, often replacing mode and its qualities. Sound determining modulation within octave called tonic note.", "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 chord construction, fundamental bass and thus upper progression, and key/mode changes. 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. Two modes begin C/A. Another first degree means transposed mode/key.", "front-terms-347": "Most Italians omit principal post-clef sharp in transposed major; almost all French omit principal flat in transposed minor. See 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. Augmented fourth has three whole tones; hence name. Often perfect fourth altered by modulation, not tritone as usually imagined. Likewise fifth/second/seventh/ninth altered by modulation. Understand modulation to avoid error. 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": "Glossary ends.", "I-title-001": "HARMONY\nBring it back to nature’s basic rules", "I-title-002": "Rules for composing. Rules for accompaniment.", "I-title-003": "Four books.", "I-title-004": "BOOK ONE.\nHarmonic ratios. Harmonic proportions. How they fit together.", "I01-1": "CHAPTER ONE.\nMusic and Sound.", "I01-2": "Music: science of sounds. Sound therefore music’s main subject.", "I01-3": "Usual division: harmony and melody. But melody belongs inside harmony. Know harmony, and you can fully know every property of music. Proof follows.", "I01-4": "Let physics define sound. Harmony distinguishes low pitch from high pitch. It sets aside strength and duration. All knowledge of harmony must rest on relations between high and low sounds:", "I01-5": "Low sounds: lowest pitches, such as male voices produce. High sounds: highest pitches, such as female voices produce.", "I01-6": "Interval: distance from low sound to high sound. Different distances between sounds give different intervals. Their degrees take names from arithmetic. First degree: one, unity. Two sounds on same degree: unison. Second degree: second. 3rd: third. 4th: fourth. 5th: fifth. 6th: sixth. 7th: seventh. 8th: octave. Continue likewise. Assume first degree always lowest. Form others by raising voice successively through its natural degrees.", "I02-1": "CHAPTER TWO.\nWays to Find Relations Between Sounds.", "I02-2": "To find sound relations, take string. Stretch it until it sounds. Divide string into parts with movable bridges. Compare every resulting length with the others. Finding: first five divisions contain all sounds or intervals able to agree together.", "I02-3": "Some compare numbers for string divisions. Others separate the resulting lengths, then compare numbers for those lengths. Others notice sound cannot reach ear without air; they compare numbers for vibrations of different lengths. More methods exist: different string thicknesses, different tensions made with weights, wind instruments, and so on. No need to dwell on all here. Finding: first six numbers contain all consonances.* Exception: thicknesses and weights require squares of those root numbers. Thus people attribute all harmony’s power to numbers. Remaining task: apply numbers correctly to operation chosen as foundation of system.", "I02-5": "Numbers for string divisions or vibrations follow natural progression. Arithmetic rules govern everything there. Numbers for string lengths follow reverse progression. This destroys some arithmetic rules—or rather, forces us to reverse them. Explanation comes in its place. Choice of operation should make no difference to harmony. Still, we use only operations where numbers follow natural progression. Everything there is much easier to understand.", "I02-6": "* See Table of Terms.", "I.03-001": "CHAPTER THREE.", "I.03-002": "Where Consonances Come From and How They Relate.", "I.03-003": "* Sound relates to sound as string relates to string. Every string contains all shorter strings, not longer ones. Likewise, low sound contains all high sounds. Reverse does not hold: high sound does not contain all low sounds. Therefore find higher term by dividing lower term. Divide arithmetically: equal parts, and so forth. Let A B be", "I.03-004": "A — D — C — E — B", "I.03-005": "lowest term. Want higher term forming first consonance? Divide A B into two. Two: first of all numbers. Point C shows division. A C and A B now differ by first consonance: octave, or diapason. Want consonances immediately following first? Divide A B into three equal parts. Get two higher terms, not one: A D and A E. They give two consonances of same kind: twelfth and fifth. Can also divide A B into 4, 5, or 6 parts. No further: ears’ capacity goes no farther, and so forth.", "I.03-006": "* Descartes, Compendium of Music, p. 60.", "I.03-008": "Make proposition clearer: take seven strings. Mark divisions with numbers. Assume all strings tuned to unison; require no other equality. Put numbers in natural order beside strings, as next demonstration shows. Each number gives equal-part division of its string. One exception: 7 gives no agreeable interval, as connoisseurs know. Substitute 8. First number after 7 that doubles one of first six numbers. With 1, makes triple octave. Proposed quantity of numbers does not increase: 6 and 8 give same interval as 3 and 4. Number always represents number that it doubles.", "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\nNeighboring intervals:\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": "First remember: numbers always mark divisions of unity, just as they mark divisions of whole string represented by 1.", "I.03-012": "Number order determines consonances’ origin and perfection. Octave, 1 to 2, comes first; more perfect than fifth, 2 to 3. Then fourth, 3 to 4, and so on. Always follow natural number progression. Admit sixths only last.", "I.03-013": "Note names show it: string 1, octave 2, double octave 4, triple octave 8 produce, so to speak, same sound. Arrange notes by number order and string divisions: most perfect harmony imaginable. Anyone can test it. Next, separate articles explain properties of each sound or consonance. This makes each property clearer.", "I.03-014": "ARTICLE ONE.", "I.03-015": "Harmony’s Principle: Fundamental Sound.", "I.03-016": "First assume whole string, marked 1, produces a sound. Examine sound’s properties through properties of this single string—or through unity itself, principle of all numbers.", "I.03-017": "1. Take strings equal to first. Their numbers determine divisions. Every resulting part comes from first string: every part lies within that single string. Thus divided strings’ sounds come from first sound. First sound is their principle and foundation.", "I.03-018": "2. Fundamental sound generates other sounds by division. Different distances between it and those sounds form different intervals. Fundamental sound therefore principle of intervals.", "I.03-019": "3. Join different intervals: different consonances result. Their harmony cannot be perfect unless first sound rules beneath them as base and foundation. Demonstration shows this. First sound therefore also principle of consonances and their harmony.", "I.03-020": "Next articles: sounds most closely related to this principle, and use it makes of them.", "I.03-021": "ARTICLE TWO.", "I.03-022": "Unison.", "I.03-023": "Strictly, unison is one sound. Several voices or instruments can produce it. Seven strings in previous demonstration do this before division. Thus unison is said not to be consonance. Necessary condition absent: difference between low and high sounds. Unison relates to consonances as unity relates to numbers.", "I.03-024": "ARTICLE THREE.", "I.03-025": "Octave.", "I.03-026": "Whole to half, or half to whole: relation so natural we grasp it at once. Favor octave on this ground: ratio 1 to 2. Unity is principle of numbers; 2 is first number. “Principle” and “first” closely related; names fit exactly. In practice, octave called only “replica.” Replica identified with its principle; earlier diagram’s note names show this. Less a chord than supplement to chords. Some therefore compare octave with zero. Male and female voices naturally sing octave apart while thinking they sing unison, same sound. On flutes, octave depends only on strength of breath. Take viol with strings long enough to see vibrations. Sound one string strongly. Strings octave below or above vibrate by themselves. With fifth, only higher sound vibrates, not lower. Thus octave’s principle belongs to both sounds that form it. Fifth’s principle—and therefore every other interval’s—lies only in low, fundamental sound. * Descartes erred here: false evidence from lute concerning octave.", "I.03-028": "Octave also bounds all intervals. Divide principle; compare generated sounds first with principle, then with its octave. Two comparisons give only difference caused by terms changing position: 2, 3 becomes 3, 2. Geometry calls this inverted ratio or comparison. In harmony, move low sound to high position. If 2 marks low sound when first, it marks high sound when last. Show transposition with octave’s number: 3, 4 instead of 3, 2. Number multiplied geometrically still represents, so to speak, same sound, or replica of its root sound. Earlier demonstration proves this. Begin multiplication at 2, first product of unity’s division. Unity gives 2 privilege of generating rest in its place, but loses no force. What agrees with 2 also agrees with 1. Octave, double octave, triple octave, and further octaves: fundamentally same interval. Different names only mark doubling or replica. Same for fifth and twelfth, and so on. Multiply ratio 1, 2 only to find intermediate numbers agreeing with each term. Example: 3 between 2 and 4; 5, 6, 7 between 4 and 8. Continue without limit. Ratios 2, 4 and 4, 8 remain same as 1 to 2.", "I.03-029": "Compare numbers with 1 or 2, always above both. Resulting intervals correspond. Thus same numbers compared above 1 and below 2 should give almost equal relations. More: inversion only moves sound to octave, or number to double. Relation changes only by difference of proportion. Ear scarcely notices that difference. 2 to 4 gives nearly same effect as 2 to 2. Reasoning and experience prove enough. Hence octave receives same force as its principal, fundamental sound. Zarlino says:* octave is mother, source, origin of all intervals; dividing its two terms generates all harmonious chords. True in one sense. Yet division of single fundamental sound generates every other sound, hence every interval and chord. To uphold Zarlino, add this: fundamental uses octave as second term. All intervals generated by division must answer to it. Thus fundamental more clearly their beginning and end. Octave has only properties received from fundamental that generates it. More exactly: same sound moves into octave or replica—or multiplies, if you prefer. This determines intervals in every direction for each generated sound. Properties from first comparison with fundamental remain unchanged. Perfect consonance with fundamental remains perfect with octave. Imperfect consonance or dissonance on one side remains same on other. Sound required to rise or fall on one side rises and falls on other. What agrees on one side agrees on other. Nothing changes, except this: principal-consonance chords have perfection when fundamental occupies natural lowest position. Move fundamental to octave: that perfection changes. Same consonances take different order, introducing variety. Test earlier diagram. Full arrangement gives very great satisfaction. Remove sounds 1, 2; then remove 1, 2, 3, 4. Satisfaction decreases, yet ear is not offended. Effect clearer still during a piece of music.", "I.03-030": "* Descartes, p. 59.", "I.03-032": "All these observations give conclusion: any sound always implied in its octave. * Descartes partly agrees. He says no sound is heard without upper octave also seeming to strike ears somehow. Perhaps he would add lower octave, had his lute proof not misled him, as said earlier. Or had he accepted Aristotle’s view. Desermes* reports Aristotle’s Problems 24 and 43: pluck nete, upper octave string; hypate, lower string, also sounds. High sound’s fading end becomes low sound’s beginning, like echo or image of high sound. Almost every musician says certain sound, note, or interval “is implied,” sometimes “in the bass.” Expression often comes before user understands its force. Harmonic ratios give only perfect chord. Admit derived sixth and sixth–fourth chords only by supposing perfect chord’s fundamental implied in its octave. Otherwise destroy every principle. Further evidence: third-and-fifth chord remains perfect and complete without octave. Octave generated first; therefore seems implied. Put octave above third and fifth. It now forms sixth and fourth with them. Chord remains good, though fundamental absent. Thus fundamental transposed or implied in octave. This makes latter chord less perfect than first, despite same sounds. “Principle inverted,” “identified with octave,” “transposed into octave,” “implied in octave”: same meaning. Upper octave sound is no different principle. It represents immediate generating principle and forms one whole with it. Every sound, interval, chord must begin and end there. Remember: all properties of octave, sounds, intervals, chords depend entirely on single fundamental principle, represented by 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": "Fifth and Fourth.", "I.03-039": "String divisions contain sounds forming fifth and fourth. Fundamental sound therefore generates them. But as intervals, only octave and fifth come directly from fundamental here. Fourth follows from octave: it is difference between octave and fifth. Thus original chords do not mention fourth. All their force belongs to fifth alone. Even octave goes unmentioned, though it came before fifth and fifth cannot exist without it. Apparently octave goes unmentioned because implied. Otherwise fourth could never be admitted: fourth cannot exist without octave.", "I.03-040": "Pay close attention to inverted comparison from previous article. Key to all harmony’s variety. Know it; greatest difficulties can be overcome. Needed knowledge: intervals made by comparing middle number with each octave endpoint. Take 3, arithmetic mean of 2 and 4. With 2: fifth. With 4: fourth. Difference: interval from low, fundamental octave sound must be more perfect than interval from high sound. Further proportional difference need not detain us. It comes only from octave versus unison—as if comparing 3 with 2, then again with 2. No difference there. Octave’s two sounds scarcely differ from unison; seem one. Thus 2, 4 gives nearly same effect as 2, 2. Likewise, two intervals differing only through endpoint 2 or 4 should count as almost equal. Prefer interval where fundamental keeps natural position: it comes directly from fundamental. Hence use arithmetic proportion. Simple operation: find mean of two numbers, like 3 between 2 and 4. Those following multiplication invented harmonic proportion. It merely reverses arithmetic proportion; next chapter explains. Each proportion applied to its proper object gives fifth from octave’s low sound, fourth from high sound. Apply either to other’s object: fourth on low side, fifth on high side. Deeper study reveals inversion everywhere. Examples: numbers naturally increase; harmonic progression must decrease. Arithmetic proportion works on one side; harmonic proportion gives same effect on other. First proportion requires numbers to mark divisions of unity. Second requires reversed numerical order. Natural numerical progression, with numbers marking unity’s divisions, requires dividing given string. Reversed progression requires multiplying string. Division yields higher sounds, as it should. Multiplication yields lower sounds, against natural order; harmonic proportion remedies this. Finally, octave has close relation already described. Deny it, and overthrow reason and experience. Divide octave: fifth comes first in its kind, defined against low, fundamental sound. Fourth follows as fifth’s “shadow”—Descartes’s word.* It comes from reversing the two sounds that first made fifth: transpose octave’s low sound to high sound. This last inversion is principal subject of this work.", "I.03-042": "* Descartes, p. 69.", "I.03-043": "ARTICLE FIVE.", "I.03-044": "Thirds and Sixths.", "I.03-045": "String divisions contain all sounds forming thirds and sixths. Fundamental sound generates them. Yet only octave, fifth, major third arise directly as intervals here. Minor third and sixths follow from fifth and octave. Minor third: difference between major third and fifth. Sixths: differences between two thirds and octave. Reflect on this, especially minor third.", "I.03-046": "All intervals arise from octave; all begin and end there. Minor third must belong there directly, related to fundamental or its octave—not merely indirectly between major third and fifth. Otherwise minor third could never move. Always trapped inside chord; never at outer positions. Experience contradicts this, as do properties of arithmetic and harmonic proportions. In our system, arithmetic proportion divides fifth into major third below, minor third above. Harmonic proportion reverses order: minor below, major above. New inversion of thirds’ order proves harmony’s variety rests chiefly on inversion.", "I.03-047": "Further proof: hear pleasing effect of all consonances in earlier diagram’s order. Consider each property. Octave so united with generating principle that they become inseparable. Hence no further mention needed: octave implied. Fundamental takes fifth to form all chords, then joins third to determine their construction. Fifth contains major and minor thirds. Both thirds cannot relate to principle at same time. Yet if one arises directly, other must receive same privilege. Major–minor difference changes no interval kind: both remain thirds. Fifth cannot bound intervals; only octave can. Everything between principle and fifth depends on octave, inseparable from principle as already proved. Judging interval by another requires octave’s help. Thus set fifth and major third aside to judge minor third. Imply octave of minor third’s low, fundamental sound. Give it same privileges as octave in origin of every interval. Fifth 2–3 comes directly from fundamental of octave 2–4. Invert: fourth 3–4. Same operation: transpose fundamental 2 to octave 4. Major third 4–5 comes directly from fundamental of octave 4–8. Invert: minor sixth 5–8. Minor third 5–6 comes directly from fundamental of octave 5–10. Invert: major sixth 6–10, or 3–5. No difference in direct origin of fifth and both thirds. No difference in indirect origin of fourth and both sixths. Possible objection: minor third’s principle differs, since 5 is not multiple of 2, taking 2 as unity here. Answer: ratio 5–6 only avoids fractions and follows natural number order, hence corresponding string divisions. Same ratio can be 1 to 1 1/5. Unity then its principle. Next article shows this.", "I.03-049": "1. & 1. 1/5", "I.03-050": "Conclusion: only three primary consonances—fifth and two thirds. They compose natural or perfect chord. Three secondary consonances follow—fourth and two sixths. They compose two further chords, both inversions of first. Leave octave aside: implied in each chord. “Equisonance” fits octave better than “consonance”; most best authors give it that name.", "I.03-052": "* Zarlino’s Harmonic Demonstrations: sixths are inverted thirds. His Institutions: sixths consist of fourth plus third. Latter description obscures first proposition.", "I.03-053": "* Descartes also wrong about origins of minor third and sixths. He says: minor third generated from major third as fourth from fifth; later, major sixth proceeds from major third; later again, minor sixth derives from minor third as major sixth from major third, borrowing properties and nature. But fourth comes from fifth only through octave’s force. Likewise minor sixth comes from major third, major sixth from minor third. Minor third itself does not share this same origin. Thus Descartes’s conclusions false, except about sixths’ properties. He confuses properties with origin. Shared third-and-sixth properties belong only to major or minor kind; every third and sixth belongs to one of these. Sharing major or minor properties is very different from proceeding or deriving from another interval. Yet forgive these faults. Author only touched subject. His other work shows clearly: had he devoted himself to it, he would have taken it further than another.", "I.03-054": "We gave both thirds equal force relative to fundamental. Still, positions set by fifth’s natural division suit them best, especially for deeper study. Throughout, higher position suits major third less well than 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": "Chapter Summary: Earlier Demonstration’s Properties in One String.", "I.03-059": "Part of each earlier string suffices to prove all these claims. Mark each part on one string, using number that specifies equal divisions. Take part from number to string’s right-hand end.", "I.03-060": "String points, left to right:\n1 2 3 4 5 6 8 10\nAbove:\n2–3 Fifth; 3–4 Fourth; 2–4 Octave.\n5–8 Minor sixth; 6–10 Major sixth; 5–10 Octave.\nBelow:\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 on octaves 2–4, 4–8, 5–10. Compare intermediate numbers with each endpoint. Comparison with low, fundamental endpoint gives primary interval. Comparison with high endpoint gives its inversion. Octave 2–4: fifth 2–3 is principle of fourth 3–4. Octave 4–8: major third 4–5 is principle of minor sixth 5–8. Octave 5–10: minor third 5–6 is principle of major sixth 6–10. All comes from transposing fundamentals 2, 4, 5 into octaves 4, 8, 10.", "I.03-062": "Make clearer: use same divisions, but take lengths from number to left-hand string end. Compare each length with whole string, its principle, and octave 2, its other endpoint. 3 with 1: fifth; with 2: fourth. 5 with 1: major third; with 2: minor sixth. 6 with 1: minor third; with 2: major sixth. Unity directly generates fifth and both thirds. Transpose unity to octave 2: obtain fourth and both sixths. Thus no surprise when 2, 4, 5, or any number represents unity. Sole purpose: avoid fractions.", "I.03-064": "DEMONSTRATION.", "I.03-065": "Consonance Relations in Leftward Lengths.", "I.03-066": "String points, left to right:\n2 3 4 5 6 1\nAbove:\n3–1 Fifth; 5–1 Major third; 6–1 Minor third.\nBelow:\n2–3 Fourth; 2–5 Minor sixth; 2–6 Major sixth.", "I.03-067": "Chapter XI: how to find ratios of consonances compared this way.", "I.03-068": "Most theorists treat inversion between consonances as mere difference between intervals. Distinguish two cases. Consonance versus octave is not same as consonance versus consonance. Octave represents principle. As Descartes says,* what agrees with either endpoint also agrees with other. Comparing two consonances uses only octave’s principal sound; high sound counts for nothing. Thus primary consonances and their inversions can always be taken rightward on string, the more natural side. Their difference comes only from octave’s two endpoints. Difference between successive consonances must be taken leftward, as Chapter V will show. They arose only from principal sound. Return to that origin to find their difference.", "I.03-069": "* Descartes, p. 64.", "I.03-070": "Consider ratios from octave transposition, versus ratios measuring difference between intervals without octave. To invert given interval, double smaller term or halve larger. Same result. Minor third 5–6: double 5 or halve 6; get major sixth. To find difference between two other intervals, use subtraction rule instead. Further proof of octave’s great perfection: form it from unison by dividing or multiplying either term. Unison ratio 2 to 2. Halve or double either term: octave results. Remains octave, low or high.", "I.04-001": "CHAPTER FOUR.", "I.04-002": "Properties of Harmonic and Arithmetic Proportions.", "I.04-003": "Descartes proposes equal string division to prove consonances’ origin. We have not set this account out here. Proof requires reversing natural numerical progression. Numbers then mark multiplication of resulting string lengths. Harmony’s whole order disturbed: octave naturally needs fifth below, but gets fourth below instead. Followers of reversed progression invented harmonic proportion to restore natural chord form. Know its nature, and you must admit it reproduces arithmetic proportion point for point. Reverse number order; must also reverse proportion to recover every perfection of natural order. When objects differ only by inversion, two proportions’ uniformity is obvious. No more discussion needed. Most arithmeticians and geometers unfamiliar with music merely cite harmonic proportion, without defining properties. Apparently they knew none. Reverend Father Pardie says:* discussion of this progression or proportion so far is of little use; he will not undertake extraordinary claims here. * Desermes discusses subject fully. Air movements producing consonances and dividing octave into fifth below, fourth above follow arithmetic proportion, not harmonic: numbers 2, 3, 4 show it. Later he says so-called harmonic proportion should be called arithmetic proportion or progression. Perhaps Greeks therefore ignored former. Leave that question aside. Did Zarlino have good reason to dwell on it? Focus on him: model for later authors; usual authority for practice; still oracle to some musicians. Monsieur de Brossard even calls him prince of modern musicians.", "I.04-005": "* Zarlino first admits: music subordinate to arithmetic; unity, principle of numbers, represents sounding body used to prove sound relations; unison is principle of consonances. Then demonstrations and rules forget all three. Deeper he goes, further he leaves declared principle. Whole string proposed for division still reveals sounding body. But he erases it from thought by separately comparing resulting lengths. Whole string becomes just another length, dependent on parts that previously depended on it. As if building instruments were main task, he demands measurement of lengths already fixed by numbers defining equal divisions. Those numerical relations alone give fullest desired knowledge of harmony. For proof, attach new idea to numbers. Music subordinate to arithmetic; harmonic progression decreases while arithmetic progression increases. Thus numbers multiply unity in arithmetic, but divide unity in harmony into as many equal parts as they contain units. Study number properties only: music appears simple and natural. Proof equally easy by either method. Zarlino refuses to risk this supposition. Instead, second operation wearies mind, reversing natural number order and beautiful harmonic order first revealed by string division. Test proves it. Test also shows him falling into fault he meant to avoid. Each length uses common measure. Apply measure as many times as number contains units; string grows accordingly. Numbers therefore multiply given string, sounding body represented by unity; they do not divide it. Granted: largest number can mark whole string, smaller numbers its divisions. But largest number cannot remain principle everywhere. More or fewer string divisions change its quantity. More divisions push principle further away, finally out of sight. Take 6, 5, 4, 3, 2, 1. Call 6 principle; hear all sounds from specified lengths. Error becomes clear immediately. Remove 6, call 5 principle: same. Remove 5, use 4: same, and so on. This order has as many imperfections as opposite order has perfections, under properties assigned to each. Repair second operation with third: Zarlino multiplies numbers by method explained in Chapter XI. He or others call resulting progression harmonic proportion. It only recovers what arithmetic proportion gave in first divisions. But former clarity becomes obscurity. Original root numbers and lengths disappear from consideration. Start new operations, as if previous findings useless. New operations merely recover lost path. Yet wandering too far has hidden principle; hard to recognize now. * Reverend Father Mersenne makes this clear. Harmonic number is number of air movements caused by string vibrations. It makes arithmetic division sweeter, more agreeable, easier, more familiar than harmonic division.", "I.04-006": "* 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 difficult harmonic operations would matter little if he recalled original principle. Instead, abandons it immediately. Recalls it in octave only in passing. Calls octave origin of all intervals, but forgets it also generates their inversions, discussed in Harmonic Demonstrations. Accepts interval inversion, forgets chord inversion that follows from it. Calls perfect chord principle, sole chord offered by harmonic ratios, yet no longer mentions chord’s own principle; at least his applications ignore it. Discusses bass, natural home of principle, even compares bass with earth; then rules and examples treat it otherwise. Discusses perfect cadence and bass motion, but makes no valid link with modes. Yet piece can finish only with perfect cadence in some mode. Finally, dissonance discussion has no foundation. Principle obscured throughout demonstrations, rules, examples. Book Two treats this in detail.", "I.04-012": "* 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": "Such great fruits Zarlino gathers from harmonic proportion. Give numbers the meaning we described: everything becomes simple, familiar, precise, sound, correct. Nothing simpler or more familiar than natural number sequence and arithmetic operations. These alone prove our case. Nothing more precise than all harmony's properties contained within number six. Nothing sounder or more correct than finding principle everywhere in unity. We now explain.", "I.04-016": "1. Chord shows no unity? Seek unity in its geometric multiples—or rather those of 2, which represents unity. Multiple may not head chord, but must belong to it. Halve it. This gives it proper place and reveals true chord. Chords reduced this way always supply fundamental forms for chords whose unity-multiples do not come first. Example: 5, 6, 8 or 6, 8, 10. Halve 8; halve 10 also where present. Both give 4, 5, 6: perfect chord from division of fifth. Halving 10 changes no substance of chord.", "I.04-017": "2. Number 5 or its geometric multiples can sometimes represent unity. Unity and its own multiples must then be absent. Treat multiples of 5 as we treated unity's multiples. Find origin of chord 12, 15, 20 by reducing 20 to 10, and so on.", "I.04-018": "3. Fifth and major third at bottom: unity, represented by one of its multiples, always comes first. Minor third at bottom with fifth: unity, represented through multiples of 5, always comes first. As already said,* this only avoids fractions. Fifth absent from bottom: numbers representing unity no longer come first. Thus 3 and its multiples, which generate fourth, cannot represent unity or head chords without reversing natural order. Number 3 is harmonic mean. Everywhere it must remain so. Unity represented by its multiple: 3 likewise represented by its multiple. Unity represented by multiple of 5: multiply 3 by 5 or by multiple of 5. Thus 3 and its multiples cannot occupy bottom without partly destroying foundation. If foundation could not remain implied, it would be destroyed entirely. This consequence alone proves perfection of inverted chords. Their perfection comes from truly perfect chord that produces them. Our rules on this matter will complete proof.", "I.04-019": "* Chapter III, Article V, p. 13.", "I.04-020": "See demonstrations in chapter 6.", "I.04-022": "Only very small exception: two chords with diminished fifth at bottom, shown in Chapter VII, Articles VI and VII. Unity then represented by square or cube of 5.", "I.04-023": "These most closely related operations give perfect knowledge of harmony's properties. We may then express same idea through other operations suited to intended subject. Here subject is harmony alone. Keep our first system. Yet last chapter shows close relation between numbers marking string divisions and string multiplications. Whole difference: simple inversion.", "I.05-001": "CHAPTER FIVE.", "I.05-002": "Origin and Relations of Dissonances.", "I.05-003": "Same string divisions that gave consonances can give dissonances.* Compare lengths remaining to left of each number. This also shows difference between neighboring consonances. Left-hand lengths at 3 and 4 give whole tone: fifth minus fourth. At 4 and 5, major semitone: fourth minus major third. At 5 and 6, minor semitone: major third minus minor third. These tones and semitones form successive steps of natural voice. Melody originates there. We begin to see: melody follows from harmony.", "I.05-004": "Whole tone; major semitone; minor semitone. Divided string, marks left to right: 2. 3. 4. 5. 6. 1.", "I.05-005": "* See Alphabetical Table.", "I.05-006": "Whole tone; major semitone; minor semitone. Marks: 2. 3. 4. 5. 6. 1.", "I.05-008": "Find dissonance ratios by subtraction rule. Write ratios of two neighboring consonances one above other. Seek their difference, thus:", "I.05-009": "Fifth ratio: 2. 3. Fourth ratio: 3. 4. Product: 8. 9. [Cross-multiplication.]", "I.05-010": "Cross X means multiply first number of each ratio by second number of other. 2 times 4 gives 8; 3 times 3 gives 9. Product 8, 9 gives whole-tone ratio. Same operation works for fourth and major third, and so on. Difference between fifth and major sixth: whole tone with ratio 9 to 10. Thus distinguish two tones. First called major; this one minor.", "I.05-011": "These observations establish 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": "Some harmonic dissonances could come from preceding system. But seek true origin in square of primary consonance, or addition of two primary consonances. Following demonstration proves this.", "I.05-015": "DEMONSTRATION: 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": "Other dissonances come from inversion. Seventh gives second. Diminished fifth gives tritone. Diminished seventh gives augmented second. Dissonances from augmented ones have no place in harmony: diminished second and diminished fourth, for example. Augmented dissonances allowed only by supposition. They occur only with ninth or eleventh. These exceed octave, so cannot invert. Fuller explanation: Book II, Chapters X and XI.", "I.05-018": "We said harmonic dissonances come only from primary consonances. Yet we formed some from fourth and sixths. Eleventh from sixths lacks other dissonances' privilege: inversion gives no new interval. Also, it can count as doubled fourth. Seventh from square of fourth could be omitted. Same seventh comes from minor third added to fifth. We included it to show two different ratios of same seventh. This can happen to every interval except octave and augmented seventh. Cause: difference between major and minor whole tones spread through diatonic system. Difference is comma, ratio 80 to 81. Ear cannot detect difference, especially in intervals suited to harmony and melody. Still explain it through different notes used to form any interval. Example: fourth C–F and fourth D–G have two ratios. One contains two major tones. Other contains one major and one minor tone. This alone causes 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": "Save calculation of each interval's two ratios: give catalogue.", "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 find any interval's ratio ourselves. Multiply smaller intervals to form larger. Subtract larger to form smaller. Examples:", "I.05-025": "Minor diesis: multiply ratios of two commas.", "I.05-026": "Major diesis: multiply minor diesis ratio by 15552 to 15625. Last ratio gives only very small part of 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": "Method reveals number of commas composing whole tone. Continue multiplication up to octave.", "I.05-029": "Conversely, major tone minus minor tone gives comma.", "I.05-030": "Minor semitone comes from difference between intervals distinguished as major and minor, perfect, augmented, 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 ratios used, difference between these intervals can also be medium semitone or major diesis.", "I.05-034": "Most of these semitones essential for tuning organs and similar instruments. Hence 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": "System easily shows two ratios of each interval taken on different notes. Thus see freedom to use either ratio, according to notes chosen for interval.", "I.05-039": "Explanation of each interval's formation shows exact relation between this system and preceding diatonic system.", "I.06-001": "CHAPTER SIX.", "I.06-002": "Compound Intervals, Especially the Ninth and Eleventh.", "I.06-003": "Chapter III, Article III, p. 7 already noted: practice treats compound intervals as their simple forms. Exceptions: ninth and eleventh. Harmony admits these only under their own names. Their progression and chord construction differ entirely from second and fourth, though they can be called compound forms of those intervals. Ninth and eleventh can represent second and fourth; second and fourth can represent ninth and eleventh. Octave adds no variety to harmony. Move sound freely up or down one or more octaves, provided it stays above lower sound of particular interval in question. Still, different chords need different names. Especially give chord primary in its kind the name of interval containing all its sounds. Fifth is primary object of every chord. Yet call chord seventh when seventh contains other intervals. Same custom for ninth, same reason. Names second and fourth belong only to inverted chords. Eleventh chord is primary in its kind, like seventh and ninth chords. Its compass likewise contains all its intervals. Distinguish it from inverted chord by name of interval it naturally forms. Proof comes in next chapter, Articles III and IV. Second and fourth ratios occur throughout chords formed from those intervals. Where ninth and eleventh must sound, their ratios replace former ones. Chords' origin will make judgment easier. Here reader needs preparation for names that might surprise. Fuller discussion: Book II, Chapters X and XI.", "I.07-001": "CHAPTER SEVEN.", "I.07-002": "Harmonic Division: Origin of Chords.", "I.07-003": "Harmonic division in our system is arithmetic division. Only harmonic means: fifth and two thirds. Fourth and other intervals appear only through octave. Every difference comes from rearranging sounds composing fifth and thirds. Harmony invites free mixing of sounds. Variety makes perfection of whole more strongly felt. Still, never lose sight of principle remaining throughout. Fifth and thirds divide all principal chords and also compose them: by squares or addition. Apply multiplication and subtraction to these intervals. Obtain all harmonious chords. Multiply two thirds: fifth. Subtract them: two harmonic means of 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": "20–30 divided at 25 gives major perfect chord: major third below in fifth. Same numbers divided at 24 give minor perfect chord: minor third below. Numbers 24, 25 also give minor-semitone ratio: difference between major and minor thirds.", "I.07-007": "Square major third: augmented fifth. Square minor third: diminished fifth. Subtraction in each square divides 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": "No complete chord without fifth; therefore none without two thirds united to compose it. All chords must originate in perfect chord made by their union. Fifth does not sound? Foundation then inverted, supplied by supposition, or borrowed. Otherwise chord incomplete—or worthless. Thus we did not call harmonically divided diminished and augmented fifths chords. Their resulting chord incomplete. Hence Zarlino established diminished-fifth chord without foundation. We shall see elsewhere.", "I.07-011": "Other harmonious chords must be formed from perfect chord plus one of its parts: a third. Add third to fifth: seventh interval. Subtract them: complete 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 minor-third ratio. 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": "Square fourth: seventh. But fourth cannot divide it harmonically.", "I.07-016": "Fifth reigns in every seventh chord. First two: fifths between 8–12, 10–15, 12–18. Third: fifth below, 20–30. Fourth: fifth above, 30–45. All chords fit within octave of lowest sound, their principle. Cannot be otherwise. Octave merely repeats sound; intervals beyond octave likewise repeat intervals within it, as already noted. Yet fifth has privilege: its square gives chord harmony accepts beyond octave's bounds. Name: ninth chord. Interval generated by squared fifth spans ninth, though interval alone could count as 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": "Chord divided by fifth on each side. Harmony easy to understand: divide each fifth further by major or minor third, as nature requires. Add minor third above ninth to obtain eleventh, but leave lower fifth undivided. Perfect harmony naturally admits four different sounds in chords. Can tolerate one extra for sake of fifth, its sole object. No more.", "I.07-020": "To grasp chords' compass and composition, remember: octave generated chiefly as their boundary. Chords contain only intervals within octave. Fundamental sound chose fifth to build every chord, joining either third to determine construction. Keep these principal objects of harmony. Study further natural properties and inversion already discussed. Then reason supports every new discovery experience provides. Experience shows chords beyond octave? Reason says foundation exists only within octave. Preserve foundation by placing new sound beneath it through supposition,a a fifth or third away. Count new sound as extra,b though its interval with fundamental remains one chosen by fundamental for building chords. Experience shows diminished fifth often replacing fifth? Reason points to power of thirds. Their union forms only chords more or less pleasing. Why diminished fifth accepted rather than augmented? Natural order first put major third below, minor chiefly above. Minor can always prevail above, even while fundamental adopts it too. Placement seems to mark preference for minor third when adding dissonance to perfect chord. Experience shows chords not always divided by thirds? Reason shows sole cause: inversion of intervals composing chords.c", "I.07-022": "Make matters familiar: regard thirds as sole object of all chords. Perfect chord adds one third to other. Dissonant chords add three or four thirds together. Differences come only from different positions of thirds. Reduce harmony to first elements: thirds carry all its power. Proof: add fourth proportional to each perfect chord. Two seventh chords result. Add fifth proportional to one of these sevenths. Ninth chord results, containing four preceding chords. True, method misses last two seventh chords of preceding demonstration, those containing diminished fifth. Proportion first-to-third and second-to-fourth then interrupted. But first operations showed reversal in thirds' arrangement. Could this guide new means where present means fail? Did we use arithmetic division alone for perfect chord? Fifth divided with major third below; octave immediately showed fifth could also divide with minor third below. Lose on one side, find on other. Example: first operations miss diminished-seventh chord. Seek in latter operations. Add fourth proportional to ratios of harmonically divided diminished fifth. Find exactly 125, 150, 180, 216. See Chapter VIII, Article VII.", "I.07-023": "a See “Supposer” (“To supply by supposition”), Alphabetical Table.", "I.07-024": "b See squares in next chapter, Article III. Extra sounds cannot occur there.", "I.07-025": "c See triangles and squares in next chapter, Articles I and III.", "I.07-027": "Add minor third to either perfect chord: dissonant chord far more tolerable than with added major third. Major third's resonance partly stifles sweetness of fifth, which should dominate all chords. Thus diminished chords less harsh than augmented. Three major thirds added together give no harmonious chord. Even augmented fifth, only two major thirds, tolerable only among five different sounds. Resulting chord exceeds octave. More later.", "I.08-001": "CHAPTER EIGHT.", "I.08-002": "Chord Inversion.", "I.08-003": "Only three concordant numbers, says Descartes. Likewise only three principal consonances observed: fifth and two thirds. Fourth and two sixths come from them. Now see how these consonances are distinguished in chords.", "I.08-004": "ARTICLE ONE.", "I.08-005": "The Major Perfect Chord and Its Derivatives.", "I.08-006": "Take prime numbers 2, 3, 5; use composites 4 and 6. Fifth now divides into two thirds as required. Major perfect chord: 4, 5, 6. Raise 4 an octave: 5, 6, 8. Name: sixth chord. Outer sounds form sixth. Raise 5 an octave: 6, 8, 10. Name: sixth–fourth chord. Upper sounds form sixth and fourth against lowest. All chord intervals measured against lowest sound. Raise 6 too: 8, 10, 12. Same proportion as 4, 5, 6. Go no further with lowest-sound octave transposition. Perfect chord has three different sounds; process gives only three different chords. Perfect chord is first and fundamental.", "I.08-008": "Two chords derived from perfect chord are consonant, yet called imperfect. Name distinguishes them from their principle; also their properties differ.", "I.08-009": "Notice power of 3. Fifth, origin of all chords, takes form at 3. Same number counts concordant numbers, primary consonances, consonant chords.", "I.08-010": "Put perfect chord and derivatives in three triangles, with ratios and note names. Largest triangle holds perfect chord: principle and root. Two smaller hold derived chords. Examine each corner of large triangle. Any corner chosen as base gives consonant chord. Each contains C, E, G. Difference only in placement of three sounds. Numbers agree: 8 doubles 4, still gives C. Both 5 and 10 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": "Minor perfect chord can be demonstrated like major. Same construction; inversion gives same chords. Only thirds' arrangement within fifth differs. Third major on one side, minor on other; same for resulting sixths. Substance of harmony unharmed. Indeed, this gives all its beauty: major and minor thirds equally pleasing. Arrange minor chord and derivatives more simply. Refer back to 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": "Change preceding chapter's order. Show most perfect dissonant chord first, though diminished fifth reigns above. Chord seems made to heighten consonant chords' perfection. It always precedes them—or rather, perfect chord or derivatives must always follow it. Its own derivatives share property.", "I.08-022": "Four different sounds: show chord and derivatives in four squares. Inversion gives chords in three smaller squares. Supposition beneath it gives further chords; these cannot invert. See Book II, Chapter X. Lowest sound of these latter chords lies outside 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": "Previous chord could use C, E, G, B♭ or A, C♯, E, G. Both add minor third above major perfect chord. Move added third below same perfect chord—or add it above minor perfect chord. New seventh chord results. Difference from previous chord only in thirds' arrangement.", "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 numbers for eleventh chord's ratios. Lowest sound: 20. Thus:", "I.08-032": "20. 30. 36. 45. 54.\nD, A, C, E, G.", "I.08-033": "Second chord: second ratio 18 to 20. Ninth chord: ninth ratio 8 to 18, not second ratio 8 to 9. Second and small-sixth chords: fourth ratio 15 to 20. Eleventh chord: eleventh ratio 20 to 54, not fourth ratio 20 to 27. Same observations apply to Article III's small-sixth, tritone, augmented-fifth, augmented-seventh chords. Remember: 8 to 9 and 9 to 10 both give second. 3 to 4 and 20 to 27 both give fourth. Ninth ratio: 4 to 9 or 8 to 18. Eleventh: 3 to 8 or 10 to 27. Ratios 8, 18 and 20, 54 equal 4, 9 and 10, 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": "Chord incidental; originates in modulation. Ninth almost always implied. Ninth added above sounds far less harsh than adding low sound beneath seventh chord's fundamental to form ninth. Yet lower addition is natural method, explained in Book II. Follows preceding chapter: major third added above perfect chord gives poorer effect than minor third. Still admit seventh chord among fundamentals because of modulation. Inversions bear same names as preceding article's chords.", "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 ratios: ninth's lowest sound also found at 20. Thus:", "I.08-041": "20. 24. 30. 36. 45.\nA, C, E, G, B.", "I.08-042": "Chord far less tolerable this way than with minor third added above. This latter addition goes against nature; proves seventh chord imperfect. Add ninth's upper sound: lowest sound becomes extra. Article III's squares show why. Sounds inside can invert among themselves. Lowest sound of ninth or augmented fifth cannot share inversion. Thus these notes", "I.08-044": "8. 10. 12. 15. 18.\nC, E, G, B, D,", "I.08-045": "represent preceding article's ninth chord, since", "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": "form same chord. Eleventh found here only by multiplying seventh chord's ratios by eight: second proof of imperfection. Lowest sound: 45. Thus:", "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": "Difference from Article III's chord: major third moved from bottom to top. Minor thirds dominate; chord more tolerable than previous. Derivatives get no different names, since chord also arises 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": "Add fourth proportional to harmonically divided diminished fifth: this chord forms, as preceding chapter noted. Yet cannot derive chord from another neither perfect nor complete. Seek principle elsewhere.", "I.08-057": "Fifth from first string divisions: origin of every chord. First chord made from it stays equally perfect with major or minor third below. Resulting seventh chords equally fundamental, though diminished fifth lies above in one, below in other. Division into thirds wins our favor. Added minor third gives more pleasing chord than added major third. Thus diminished fifth preserves foundation. Augmented fifth usable only through supposition. Its lowest sound counts as extra; ear tolerates it because principle remains in rest of chord. Pursue addition of minor thirds further. After perfect chord, added fourth proportional, even fifth, until further additions offended ear. Ear still tolerates three minor thirds united, though fifth—principle of all chords—no longer remains. Seek reason this imperfect chord stays tolerable.", "I.08-058": "1. Arrange sounds any way: chord still divided into thirds, except new interval from inversion—augmented second. Difference from minor third only minor diesis or lesser semitone. Exceeds diminished third by ratio 15552 to 15625. So near third that ear need not be offended.", "I.08-059": "2. Chord fits within octave; therefore can invert.", "I.08-060": "3. Take Article III's seventh chord. Raise lowest, fundamental sound one semitone. Required chord results. Only change: major third becomes minor. Example: C, E, G, B♭ becomes C♯, E, G, B♭ by sharpening C. Diminished-seventh chord. Invert: B♭, C♯, E, G, augmented-second chord. Or use notes in first seventh chord's squares: move A to B♭. Same chords result. Major-to-minor third change preserves perfect chord's perfection, though there it affects only middle sound. Could likewise justify diminished-seventh chord, except lowest-sound transposition destroys foundation. Principle survives only if original lowest, fundamental sound remains implied in replacement sound. Later rules make proof evident.", "I.08-062": "Call last chord and derivatives borrowed. Distinguishes them from source chord. They borrow perfection from absent sound.", "I.08-063": "Following demonstration has same chords as Article III's. Same names, with name of new interval added after fundamental sound's transposition. New interval spans outer sounds of diminished-seventh and augmented-second chords. These two take only those names.", "I.08-064": "Diminished-fifth, small-sixth, tritone, augmented-fifth, augmented-seventh chords share same lowest sound across demonstrations. Only difference throughout: A moved to B♭. None of latter chords fundamental. All borrow foundation 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": "Added fourth proportional makes diminished-seventh chord seem first-generated. Still relate supposition chords to augmented-second chord, as elsewhere to seventh chord. Each interval's ratio then follows order prescribed by natural division into thirds. We begin to see: seventh chord's fundamental sound lends itself to sound lowest in augmented-second chord, highest in diminished-seventh chord. Principle can remain among upper sounds only through inversion, as now understood.", "I.09-001": "CHAPTER NINE.", "I.09-002": "Observations on Preceding Chords.", "I.09-003": "Perfect chords and seventh chords differ only in placement of thirds or reversal of their order. Thus no other basic names distinguish them. Modulation requires certain sounds; sounds determine thirds' order in chords. Lower third of perfect chord—major or minor—determines modulation. Thereafter chords must follow sound order within octave of that perfect chord's fundamental. Yet Article III's seventh chord is independent, despite perfect chord's power in modulation. First of its kind. Never changes, whatever perfect chord's form. Belongs only to dominants. No perfectly felt conclusion without it. Source of all dissonances. Major third inherited from perfect chord forms all major dissonances. Minor third added to perfect chord forms all minor dissonances. Inversion and new lower sound added by supposition beneath foundation generate several chords. Yielding foundation to another sound generates same number again, without changing its required place. Other sevenths owe all perfection to this first one. Only minor dissonance belongs to them. Modulation fixes their place. Hence each derivative of first dissonant chord has exclusive name. Other seventh derivatives share common names: they determine nothing; modulation determines them.", "I.09-004": "Chapter's observations yield conclusion: harmony has only two chords—perfect and seventh. Only two dissonances—major and minor. All that follows will prove this clearly.", "I.09-005": "Nature and properties of each interval and chord: reserved for Book II.", "I.10-001": "CHAPTER TEN.", "I.10-002": "Different Ratios for Same Chord.", "I.10-003": "Chord ratios match intervals between their notes. Same interval can have two ratios. Most preceding chords can therefore share difference when taken on other notes. See chromatic system, Chapter V, p. 28. Different ratios give no new chords. Fifth 27 to 40 same as fifth 2 to 3; likewise others. Difference imperceptible to ear. Cause only different arrangement of component whole tones and semitones. Note names immaterial here; used only to clarify whole.", "I.11-001": "CHAPTER ELEVEN.", "I.11-002": "Relating Division Ratios to Vibrations and Multiplied Lengths.", "I.11-003": "Take lengths from each division of given string: number to end, extending right. Arrange to distinguish vibrations. Strings differ only in length. Vibration ratios match division ratios. Divide string further as needed for dissonance ratios. Same agreement always. See Chapter III, Article VI, p. 15.", "I.11-004": "Find length ratios: take lengths from two different divisions. Use compass to give both common measure. Lengths contain measure as often as division numbers contain units—but comparison reverses. Example: divisions 2 and 3. String 2 contains measure three times; string 3 twice. Compare 2 to 3 on one side, 3 to 2 on other. Same thing except first number must represent lower sound. Reverse any division ratio this way to get length ratio. Easy with two sounds; harder as number grows. In harmony, as in continuous quantity, middle sounds or terms relate to each extreme. Thus 4, 3, 2 differs from 2, 3, 4. Interval 2 to 3 comes first here, last there. Must invert arithmetic proportion, as stated elsewhere. Multiply each extreme by mean, then extremes together. Numbers 12, 8, 6 restore natural interval order. Most perfect harmony from united consonances: divisions 1, 2, 3, 4, 5, 6, 8. Multiplied lengths give it only through 120, 60, 30, 24, 20, 15. Needs more attention than rest.", "I.11-006": "Common measure gives interval ratios immediately for lengths taken to left of string. Or use inversion just described. Compare string 3 with string 1. One part of 3 contains 1; other two contain 2. String 1 compared with 3 must contain 3. Left-hand lengths give fifth, ratio 2 to 3. Compare string 3 with string 2. One part of 3 contains 2; other two contain 4. One part of 2 contains 3; other also contains 3. Left-hand lengths give fourth, ratio 3 to 4. Compare string 3 with string 4. One part of 3 contains 4; other two contain 8. One part of 4 contains 3; other three contain 9. Whole tone—the difference between fifth and fourth—has ratio 8, 9 by divisions, 9, 8 by multiplications. No difficulty; proof works for every kind of interval.", "I.11-007": "END OF BOOK ONE.", "II.01-001": "BOOK TWO.\nChords' Nature and Properties; Everything That Makes Music Perfect.", "II.01-002": "CHAPTER ONE.\nHarmony's Fundamental Sound and Its Progression.", "II.01-003": "Book I, Chapter III, Article I, p. 5 sufficiently explained fundamental sound and its place in harmony. Here chiefly determine its progression.", "II.01-004": "Part carrying fundamental sound called bass: sound always deepest and lowest. Zarlino* explains: earth supports other elements; bass supports, establishes, strengthens other parts. Thus base and foundation of harmony. Name bass means base and support. Earth fails, nature's beautiful order falls into ruin. Likewise bass fails, whole musical piece fills with dissonance and confusion. Compose bass with somewhat slow, separated movements, wider than other parts' movements. Then other parts can move by adjacent steps, especially soprano: this is its property. Yet compare clear, sound definition with author's rules and examples. Contradictions everywhere; doubt and uncertainty persist.", "II.01-005": "Principle supporting everything needs firmest establishment. Lose sight even briefly: destroy it. Keep stated principle; reinforce with whole string. First string divisions give consonances forming perfect harmony together. Part representing whole string can progress only by these consonant intervals. Each sound agrees with preceding sound. Each can carry chord like first divisions' chord, representing whole string as chord's principle and foundation. This explains Zarlino's separated bass intervals. Consonant intervals must be separated. His slow movement means slow relative to other parts. Those must move diatonically; upper parts can make several steps between consonances while bass makes one. For initial rules, however, all parts move equally to keep matters simple and clear. Do not confuse octave with prescribed bass progression. Fundamental may stand several octaves higher or lower, provided always beneath other parts. Fifth suits bass best. Every final cadence or melodic conclusion makes this progression primary. Anyone sensitive to harmony feels compelled to move bass this way at any melodic conclusion. Same holds for fourth, which represents fifth. Low enough voices naturally descend fifth; others ascend fourth. Clear proof of octave's power: either constituent sound represents it. Also proves relation of fourth and fifth from octave's division. Prefer fifth whenever voice permits. Substituting fourth does not destroy fifth. For pleasant suspense, bass can move by one or several thirds: fifth consists of two thirds. Thus can use representative sixths too. Reserve all cadences for fifth and representative fourth. Fundamental bass progression confined to these consonances. Dissonance sometimes forces ascent of whole tone or semitone. License comes from interrupted cadence, discussed later. Ascending tone or semitone—not descending—is inversion of seventh then sounding between its two sounds. Book III, Chapter XI shows that, except interrupted cadence, progression of third and fourth can remain implied.", "II.01-006": "* Zarlino, Istitutioni Harmoniche, third part, chapter 58, fols. 281 and 282.", "II.01-009": "Principle deserves favor if it holds everywhere. Not proposed without certainty of success.", "II.02-001": "CHAPTER TWO.\nChords for Fundamental Sounds and Their Progression.", "II.02-002": "Sounds—or rather intervals—assigned to fundamental bass progression must accompany it throughout other parts. Those parts need restraint not imposed on bass, their guide. Perfect chord: first and only chord from string division. Thus only chord proper to each fundamental-bass sound. Yet seventh chord cannot be excluded. Its added third could be removed without harming harmony's perfection. But seventh creates variety and bitterness that heightens perfect chord's sweetness. Desire it; do not reject it. Count it among fundamental chords: principle remains intact in perfect chord's lowest sound.", "II.02-003": "Other parts each carry one chord sound. Zarlino already said: their movement must be diatonic. Fundamental bass's consonant progression imposes this. Slight knowledge of interval distances makes us almost involuntarily move upper parts by steps. Pleasant chord sequence follows; no other rule needed. Nature herself guides us to her proper perfection. See Chapters XIX, XX, XXIV, XXV below; Book III, Chapters IV and VI.", "II.02-004": "Learn each part's assigned progression; then free to give one part another's movement. Still follow original disposition and fundamental-chord succession, especially for seventh. Ear accepts seventh only under these conditions: diatonic movement from preceding sound through to following sound; both surrounding sounds consonant. Perfect cadence shows this and dissonance's proper place. Two bass sounds prepare melodic conclusion. Final sound clearly principal: whole piece begins there and rests on it. Natural to distinguish preceding sound by making it less perfect. Both carry perfect chords? Soul desires nothing more after either; uncertain which sound to choose for repose. Dissonance needed: harshness makes following repose more eagerly desired. Nature's involvement shows in necessary choice of third. Only consonance compensating dissonance's harshness. Third imperfect, yet becomes sole desired object after dissonance; gives perfect chord fresh grace. Hence rule of resolving dissonances. Those failing to perceive only one minor dissonance could not imagine only one consonance resolves it. Following discussion will leave this truth beyond doubt.", "II.03-001": "CHAPTER THREE.\nOctave's Nature and Properties.", "II.03-002": "Octave contains all sounds that can combine as fundamental chords. Add it to increase perfection. Perfect chord and derivatives exist without it; with it, brighter. Natural and inverted chords sound together. Four-part pieces must use octave. In five-part pieces it agrees perfectly with fundamental seventh chord. Can always add octave to chords containing only one minor dissonance. Upper-part progression must be diatonic; easily obeys rules. Also determines modulation, as shown later.", "II.04-001": "CHAPTER FOUR.\nFifth and Fourth: Nature and Properties.", "II.04-002": "Fifth is primary object of every chord. No chord without fifth or representative fourth. Already examined both intervals' properties in bass progression. In other parts, progression much like octave's.", "II.05-001": "CHAPTER FIVE.", "II.05-002": "Perfect Cadence: Nature and Properties of All Intervals Meet.", "II.05-003": "Perfect cadence: melodic conclusion so satisfying nothing more desired. First two chapters already show bass descending fifth or ascending fourth, with perfect and seventh chords. Perfection goes further. Thirds governing chords determine all intervals' progression, except octave and fifth. These generated first; progression independent.", "II.05-005": "Fifth called primary object of all chords. Same quality belongs to its thirds. Octave divides, generates fifth, entrusts chord construction to it. Fifth divides, generates thirds, entrusts other intervals' progression to them. Other intervals follow thirds' nature and properties throughout. Major third naturally lively, cheerful: all major or augmented shares this. Minor third naturally tender, sad: all minor or diminished shares this. Zarlino* says thirds' outer sounds naturally move toward what approaches their being. Major wishes to become major: rises. Minor descends. Clear to skillful, discerning musicians, since upper part moves semitone. Semitone is salt, so to speak, ornament and cause of beautiful harmony and good modulation. Without it, modulation almost unbearable. These two progressions give all major, augmented, minor, diminished intervals' progressions. General rule: major or augmented rises; minor or diminished descends.", "II.05-006": "Zarlino seems to make semitone general progression rule. Indeed, only movement suited to major or augmented intervals. Minor and diminished may also descend whole tone, according to modulation. Extraordinary: he praises semitone, then abandons it where strongest. Perfect system places semitone between octave and sound preceding it in ascent. Octave determines repose; diatonic ascent reaches it only through semitone. Preceding sound therefore matters as much as octave: pass through one to reach other. Zarlino says major third and major sixth must rise to octave—rule from this observation. Yet forgets tritone shares rule. Mentions it only briefly; omits from perfect cadence. Other major or augmented dissonances from this major third, formed with octave's preceding sound, receive even less attention. Least discussion of what follows his semitone rule without restriction. Show blindness through perfect-cadence example: octave's preceding sound forms major third, source of all major dissonances rising semitone to octave.", "II.05-007": "* Third part, chapter 10, fol. 182; chapter 38, fols. 219 and 220.", "II.05-009": "First of two perfect-cadence bass notes: dominant. Must always precede final note; therefore dominates it.", "II.05-010": "Minor third added to dominant's perfect chord gives seventh. Seventh dissonant against dominant and its major third. Major third thus dissonant against seventh. Third originates every major dissonance; seventh every minor dissonance. No exceptions.", "II.05-011": "Perfect cadence's final note: tonic. Piece begins and ends there. All modulation determined within its octave.", "II.05-012": "Sound preceding octave forms all major dissonances: leading note. Hear major dissonance, feel tonic or its octave must immediately follow. Apt name: sound makes us anticipate object of all modulation.", "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": "Examples alike except minor dissonance: descends semitone in one, whole tone in other. Major dissonance always rises semitone, major third to octave. Remove fundamental bass. Put each other part in its place in turn. All chord inversions appear; harmony always good. Removed fundamental bass remains implied. Rearranged parts produce different dissonances, but required progressions unchanged. Major rises semitone to tonic or octave. Minor descends to tonic's major or minor third. Nothing clearer.* Zarlino's diminished-fifth and tritone examples prove it: he shows inversion unknowingly.", "II.05-017": "* Third part, chapter 61, fol. 293.", "II.05-018": "Zarlino Example; Fundamental Bass Added.", "II.05-019": "Zarlino's Example with an Added Fundamental Bass.", "II.05-020": "Take two upper parts alone: tritone (A), diminished fifth (B). Compare with Basso: tritone gives major sixth rising semitone to octave. Compare with our fundamental bass: tritone gives major third, diminished fifth gives seventh. Progression follows our rule. Different chords still represent perfect cadence: progression unchanged, foundation remains implied. Otherwise music filled with confusion and dissonance.a Zarlino believes statement, forgets execution. Saysb lowest part in perfect cadence naturally descends fifth. Example has upper part rise major third to octave (A).c Elsewhere dominant's major third rises while its fifth descends to octave (B).d As fifth descends, third above that fifth—dominant's seventh—descends to third (C). Combine three examples: complete cadence. Take Chapter VI example and add missing parts, thus:", "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": "Not harmony Zarlino implied here. Apparently intended perfect chord on second beat of whole note standing fifth above fundamental bass. Fourth struck on its first beat, he says, more dissonant than consonant. But how can final whole note's perfect chord follow other whole note's chord? Earlier note's minor third makes seventh against fundamental bass. If it descends, where do fifth and octave go? Skilled musician should always figure bass, especially two-part examples, so judgment can be sound. Otherwise deductions often false. Perhaps Zarlino omitted figures to conceal intervals he wished to ignore—and wished others to ignore.", "II.05-027": "d Chapter 6, fol. 254, measures fourteen and fifteen.", "II.05-029": "Perfect chord on each of Grave part's last two notes? Contradicts harmony's foundation, by first observations drawn from Zarlino himself. Bass cannot move diatonically beneath perfect chords. Example's fourth therefore consonant against fundamental bass: forms octave with it. If dissonant, final note no longer gives perfect cadence. Cadence then irregular.", "II.05-030": "EXAMPLE.", "II.05-031": "Zarlino's Example. Added Parts. Fundamental Bass. Irregular Cadence.", "II.05-032": "Which cadence did Zarlino intend? Apparently perfect. Whole piece revolves around C; this irregular cadence in A or D. Also never mentions irregular cadence. When it appears in examples, merely part of chord succession, not identified.", "II.05-034": "Take every perfect-cadence arrangement from first example: two, three, four, five parts. Choose parts to sound together. Freely put upper parts below another. Fundamental bass alone cannot naturally change place, though good taste permits even this, especially to avoid perfect conclusion above while bass moves diatonically. Harmony contained in two proposed chords: perfect and seventh. All rules rest on their natural progression.", "II.06-001": "CHAPTER SIX.", "II.06-002": "Interrupted Cadence.", "II.06-003": "Change progression of one sound in perfect cadence's first chord: conclusion interrupted. This interruption gives interrupted cadence its origin.", "II.06-004": "Interrupted cadence differs little from perfect. Same chords, or same fundamental bass. Same chords: bass rises diatonically instead of descending fifth. Same bass: sixth chord replaces final perfect chord. Changes only consonant sounds—fundamental, octave, fifth—not dissonant ones. Major third, object of all major dissonances, still rises semitone. Seventh, object of all minor dissonances, still descends tone or semitone. Dissonance rules preserved. Foundation altered in one principle only. Perfect chord absent? Fundamental bass unchanged. Bass changes? Perfect chord supports it. Sixth replacing fifth still gives derivative of perfect chord. Seventh already permits bass progression corresponding to its interval. Thus everything survives. Yet cadence allowed only by license: chord no longer fundamental, or bass movement not generated by consonances. Dissonance's freedom alters perfection. Alteration has no harshness; far from displeasing. Makes perfection more pleasing when it returns after 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": "Compare with perfect-cadence examples. Only difference: fifth becomes sixth in parts (A). Put part (A) below fundamental bass. Only seventh and perfect chords remain, as first proposed. Most common interrupted-cadence practice.", "II.06-011": "Invert all parts; select two, three, or four. Fundamental bass as soprano only where good taste allows. Interrupted cadence felt only through fifth-to-sixth change: sixth replaces fifth in perfect chord ending perfect cadence. All other parts match in both.", "II.06-012": "Part (A) as bass: prefer octave of third over octave of bass. Third stands for true fundamental sound; its repetition cannot displease. In perfect-harmony succession, preferring third's octave over fundamental's would be faulty. Bass octave still possible here instead of third's, but know exactly what you do. Hard to sound it without gross faults. Judgment needed. Never depart from principle before knowing it thoroughly.", "II.07-001": "CHAPTER SEVEN.", "II.07-002": "Irregular Cadence.", "II.07-003": "Perfect cadence: dominant to tonic. This cadence: tonic to dominant. Hence irregular.", "II.07-004": "Perfect chord alone belongs to fundamental-bass notes forming all cadences. Previous two cadences altered first perfect chord by adding new sound: dissonance. Same reason can apply here. Dissonance suits cadence's first note. Only chance to use it here: seek, not avoid.", "II.07-005": "Added dissonance against fundamental? Added sixth is consonant with fundamental, dissonant with its fifth. Seems to contradict claim that seventh sources all dissonances. Yet perfect chord plus sixth gives great-sixth chord: inversion of seventh. See Book I, Chapter VIII, Article IV, p. 39.", "II.07-006": "Added dissonance does not follow seventh's natural progression. Irregular describes it as well as cadence. Remember minor dissonance, formed by seventh or added sixth: seems generated to soften imperfection of third where it dies away. Same truth here. Added sixth resolves upward to third; seventh downward. Reason explained in Chapter XVIII.", "II.07-007": "Fourth note properly carries great-sixth chord; tonic carries perfect chord. Can substitute these two notes to form irregular cadence 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": "To make final note count as dominant, always give major third. Mode difference then appears only in tonic's third. Tonic must precede dominant here.", "II.07-012": "Masson does not discuss cadence as we do, yet gives inverted example, in chords whose origin he ignores. Calls (A) tritone; fundamentally only fourth altered by modulation. More precisely, only sixth against fundamental bass.", "II.07-013": "EXAMPLE", "II.07-014": "By Masson. Added fundamental bass reveals irregular cadence inverted.", "II.07-015": "Added Fundamental Bass.", "II.07-016": "Added sixth can always be removed from perfect chord: owed only to good taste. Yet creates variety, eases composition in four, five, six parts, gives pleasing melodies. Desire rather than reject it. Praise first users.", "II.07-017": "Discuss three cadences first to prove harmony consists only of perfect and seventh chords. All variety from inversion; dissonant chord also possible through supposition or borrowing. Progression always follows these cadences, especially parts dissonant together. Know dissonant chord's origin: easily know following chord, whatever bass arrangement. Consonant chord's route less restricted. Learn modulation, key-notes taking derived chords, dissonance preparation and resolution, required bass progressions. Then see necessity of three cadences: contain all dissonances' different progressions.", "II.08-001": "CHAPTER EIGHT.\nImitating Cadences through Inversion.", "II.08-002": "Imitate cadence by inversion: usually remove fundamental bass; choose another part as bass. Can also vary movement of sounds not dissonant together, such as fundamental and fifth. Book III explains. Different parts take turns as bass or soprano; yield every imaginable melody. Put another fundamental-chord sound in bass instead of fundamental itself: harmony varies. Countless melodies and chord successions appear at every step. Compose piece freely; inversion's variety continually awakens listener. Writers feeling inversion's effects did not trace origin. Rules and examples prove it. Different chord, different example, different rule. One says seventh resolves by third, fifth, octave, sixth. Another says diminished fifth resolves by third, fourth, tritone, ninth—descending, ascending, or holding still. Thus sciences made obscure: separate treatment of each part instead of simple intelligible whole. Seventh dissonance appears as diminished fifth, second, ninth, eleventh; resolves through different intervals. Cause only different bass progression. Bass passes through derived sounds of fundamental chord; comparison with these sounds gives intervals different forms. Chords remain same, rearranged. Progression unchanged. Interval seems different? Relate to foundation: always same. Fundamental basses beneath all examples prove it. Need only make things perceptible, as we hope.", "II.09-001": "CHAPTER NINE.\nAvoid Cadences while Imitating Them.", "II.09-002": "Partial imitation already avoids cadence. More precisely, avoidance means permitted alteration of cadence's chords. Endless ways; one simple principle explains.", "II.09-003": "Alter consonant chord: add third, creating seventh dissonance. Alter dissonant chord: make dominant's naturally major third minor. Thus sustain long melody and harmony without conclusion.", "II.09-004": "Terms first: tonic only for notes carrying perfect chord; dominant only for notes carrying seventh. Tonic follows only dominant with major third forming diminished fifth against seventh. Third not major, and no diminished fifth or tritone between third and seventh? Only another dominant may follow. Call dominants containing diminished fifth or tritone tonic dominants. Others simply dominants. Different seventh structures distinguish cadence from imitation, reveal whether next note tonic, thus each note's required chord. Here only fundamental chords and fundamental bass progression.", "II.09-005": "Perfect cadence gives firm principle. Descending fifth or ascending fourth—same thing: first sound may and should carry seventh chord. No diminished fifth or tritone between third and seventh? Following sound not tonic; must carry another seventh. Continue until one of those intervals appears. Leading note then requires tonic next. Descending fifth implies seventh chord on first sound; seventh chord likewise implies this progression afterward. Except imitation of interrupted cadence or later-discussed licenses. Only modulation limits number of seventh chords and bass intervals.", "II.09-007": "EXAMPLE.", "II.09-008": "Seventh Chords and an Avoided Perfect Cadence.", "II.09-009": "A, B, C each carry seventh. A–B, B–C have same progression as C–tonic. First two imitate perfect cadence, avoided through minor thirds. At C, major third creates tritone; cadence felt, tonic conclusion determined. Extend avoidance: change key, add seventh to tonic, make it dominant. No diminished fifth or tritone introduced? Simple dominant. Otherwise tonic dominant. Both allowed under good modulation. Making tonic dominant introduces chromatic genus. See Book III.", "II.09-011": "Irregular cadence cannot be avoided in first chord: dissonance cannot change minor to major or major to minor. Add sixth or seventh to second chord instead. Prepares another cadence; avoid that too, and continue.", "II.09-012": "Avoid interrupted cadence like perfect. Difference: make first note's major third minor, cannot make next note tonic dominant. Making it tonic dominant requires sound judgment however approached in cadence.", "II.09-013": "Avoid perfect or interrupted cadence even in imitation: add sixth instead of seventh to second note. Fifth must be prepared by preceding note's octave or third; fifth then represents dissonance's upper sound. Result: great-sixth chord, inverted seventh. Can produce irregular cadence; or, inverted, imitation of avoided perfect or interrupted cadence.", "II.09-014": "EXAMPLE: ALL CASES.", "II.09-015": "Complete Example: Avoided Cadences and Fundamental Bass.", "II.09-016": "A. A. A. D. E. F. S. T. Perfect cadences avoided: first chord has neither diminished fifth nor tritone between fundamental-bass note's third and seventh.", "II.09-017": "B. C. O. P. R. S. Interrupted cadences avoided: add seventh to second fundamental-bass note, C, P, S.", "II.09-018": "B. C. R. S. Perfect cadences avoided: sixth added to second continuo-bass note.", "II.09-019": "C. D. Interrupted cadence avoided: first fundamental-bass chord lacks diminished fifth and tritone; D's perfect chord gets added seventh.", "II.09-020": "D. E. S. T. Usual avoided-cadence succession in continuo bass.", "II.09-021": "F. G. Irregular cadence avoided: seventh added to G. Some licenses here; see Chapter XIII. Meanwhile, if Y becomes bass, part below must move to cue sign Z, not simultaneous ordinary note.", "II.09-022": "A. B. G. H. I. L. First note's major third becomes minor. Introduces diminished fifth in next chord; B, H, L become tonic dominants instead of intended tonics. Thus chromatic genus practiced. Explained next book. Meanwhile see upper part descending here by semitones.", "II.09-023": "E. F. Perfect cadence avoided: minor third on E, added sixth on F. Seventh more natural, especially when prepared.", "II.09-024": "N. O. P. Q. Licenses discussed elsewhere.", "II.09-025": "M. N. Two consecutive perfect chords; bass progression consonant.", "II.09-026": "L. M. T. V. Perfect cadences.", "II.09-027": "X. Sometimes transpose parts octave higher or lower to restore natural range. Must introduce neither consecutive octaves nor consecutive fifths.", "II.09-028": "Remove fundamental bass; use each other part as bass. Find different progressions from inverted fundamental chords. Figures supplied on every part.", "II.09-029": "So many consecutive dissonances make less pleasing music. Fault accepted only to fit explanation into short example. Modulation not very regular either; discussion waits.", "II.09-030": "Consonant chords easy: bass progression always consonant. Exception in certain key changes, only inverted consonant chords, only one movement between two notes. Modulation will teach details. Dissonances scarcely harder: fundamental bass immediately reveals succession. Even without bass, know minor dissonances descend, major ascend. Exceptions: chromatic genus, irregular cadence; our rules easily identify them. Next book gives short, simple examples of all practices. Master fundamental harmony rules: derive any imaginable melody, easily arrange fitting chords. In two or three parts, choose consonances or dissonances best for subject or desired beautiful melody. Always know sounds needed to complete chords. Ignorance caused false rules, often misleading supposedly skilled masters filling chords or figuring continuo basses.", "II.10-001": "CHAPTER TEN.\nChords by Supposition: Avoiding Cadences through Imitation.", "II.10-002": "Understand supposition chords: first accept chords' prescribed bounds. All chords formed from fifth and thirds—Book I, Chapters VII and VIII. Thus divide into thirds following fifth's natural division. Octave's two sounds bound all sounds forming perfect harmony. Sounds beyond merely repeat those within. Thus octave bounds every chord. Perfect chord's lowest sound holds harmony's foundation. Add third to form seventh chord and dissonance: foundation remains. Seventh stays within octave; addition preserves division. Add yet another third: foundation confused. Relation to fourth third indistinguishable from relation to corresponding sound within octave. Division into thirds interrupted too: ninth or eleventh represents second or fourth. Ignore representation; call them only ninths and elevenths. What principle then? They exceed octave, principle—or Zarlino's mother, source, origin—of every interval.", "II.10-004": "Add fifth sound to seventh chord only below, never above. Added sound stands by supposition beneath fundamental immediately above. Seek principle in fundamental's octave, not added sound's. Progression then matches earlier chords exactly. Seventh chord above added bass can invert as before. Added sound cannot change place: always lowest. Others can invert among themselves,* within harmony's bounds. Follow natural progression in represented mode. Added sound vanishes by rejoining them. Thus only extra sound: fundamental harmony exists without it; chord progression unchanged.", "II.10-005": "* See Book I, Chapter VIII, Articles III, IV, V.", "II.10-006": "EXAMPLE.", "II.10-007": "Chords by Supposition: Seven Parts and Fundamental Bass.", "II.10-008": "1. Fundamental bass carries only perfect or seventh chords. Progression follows perfect (B), interrupted (C), irregular (D) cadences.", "II.10-009": "2. Supposition chords figured 9, 5♯, 7♯, 4: fundamental bass above other bass. Put it below, must remove other bass's sounds to preserve perfect harmony without offending ear.", "II.10-010": "3. Fundamental bass forms unisons with part representing it in supposition chords. That part plus upper parts: only seventh chords, divided into thirds, following prescribed progression.", "II.10-012": "4. Eleventh chord, figured 4, extremely harsh in ordinary form. Usually remove middle sounds. Keep principal two: fundamental and seventh; sometimes minor third or fifth too. Supply new sound fifth below fundamental. Forms eleventh, not fourth, against fundamental's seventh. Call chord exceptional in construction: not divided like others. Still follows supposition-chord property: cannot invert. Sometimes filled with all its sounds.", "II.10-013": "EXAMPLE.", "II.10-014": "Eleventh Chord, Tenor, and Bass by Supposition.", "II.10-015": "Supposition bass sound (A) stands beneath fundamental-bass or tenor sound (A). Upper parts form seventh chord, following natural progression.", "II.10-016": "Compare chord (a) in other example. For diatonic movement, did not insist tenor carry fundamental-bass sound. Observe difference in treatment and reason for exceptional construction.", "II.10-017": "Examples show perfect, interrupted, irregular cadences underlying supposition chords. Thus imitate and avoid cadences. More in Book III, Chapter XXXII.", "II.11-001": "CHAPTER ELEVEN.\nFourth and Eleventh.", "II.11-002": "Distinguish fourth from eleventh. Eleventh not previously known by own name; always confused with fourth. Hence divided opinion: fourth consonant or dissonant? Ratios made consonance clear to some; practice made consonant treatment difficult to others. Disagreement only from mutual misunderstanding.", "II.11-003": "First, Zarlinoᵃ treats fourth as consonance in practice. Gives examples, cites Greeks, more strongly ratios. Says two consecutive fourths act much like two fifths: fourth is perfect consonance. We add: inverted fifth. He omits those words, but unknowingly proves them in examples; also mentions matter in Dimostrationi Harmoniche.ᵇ Says contemporary Greeks used fourth in lowest parts, no other consonance beneath as base. Shows fourth's full force. Notice he recognizes base in harmony, desires it when unheard. Base always in fifth's lowest sound. Only imply this base to prove inverted chords please ear.", "II.11-004": "a Third part, chapters 60 and 61, fols. 291, 292, 293, 294; chapter 5, fols. 177, 178.", "II.11-005": "b Ragionamento secondo, definition X, fols. 83, 84.", "II.11-007": "Zarlino also calls eleventh repeated fourth, ninth repeated second. Every interval has double, triple, quadruple repetitions, as often stated. But do not confuse different properties. Second distinguished from ninth; why not fourth from eleventh, differing far more? Second and ninth both dissonant. Fourth consonant, eleventh dissonant. Second from inverted fundamental chord. Ninth from added sound beneath fundamental chord; cannot invert; prepared and resolved differently. Thus distinguish. Fourth from inverted perfect chord; consonance, progression unrestricted. Eleventh from added sound beneath seventh chord; cannot invert; requires preparation and resolution. Ratios also prove it: Book I, Chapter VIII, Article IV, p. 39. Enough to distinguish by chords they compose, regardless of relation considered separately. Interval name identifies chord primary in its kind, containing only sounds within interval's compass. Seventh, ninth, eleventh chords so named. Last two names implied in augmented-fifth and augmented-seventh chords. Fourth only in inverted chord, represents fifth: consonant. Eleventh defines primary chord with all sounds within its compass: dissonant. Figure 4 merely follows ordinary usage.", "II.12-001": "CHAPTER TWELVE.\nBorrowed Chords: Avoid Perfect Cadences through Imitation.", "II.12-002": "Book I, Chapter VIII, Article VII, p. 41: diminished-seventh chord and derivatives borrow foundation from tonic dominant's lowest seventh-chord sound. Compare following examples. Only difference: movement of sound borrowing that foundation. Must follow progression required by dissonance it forms.", "II.12-003": "See 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 four upper parts on both sides. Same agreement remains. Only sixth note differs, borrowing foundation from dominant.", "II.12-008": "2. Ordinary note marks octave; cue marks third. Other side reverses this. Ordinary note shows first chord sound's most natural progression. Cue shows freedom to change progression. Substance of harmony unchanged. Fuller explanation in Book III.", "II.12-010": "3. Invert chords: lowest sounds stay same on both sides. Two supposition basses show it. Each plus four upper parts forms supposition chords. Only difference: sixth note borrows from dominant. Chords optional in minor keys only. Composers' good taste applies them to suitable subjects. More later.", "II.13-001": "CHAPTER THIRTEEN.", "II.13-002": "Dissonance Progression Rule from Fundamental Chords.", "II.13-003": "Dissonances have two kinds from their generating thirds. Follow thirds' properties: major rises, minor descends. Natural chord succession also shows minor dissonance preceded by consonance. Same sound becomes dissonant without moving; stays on degree where consonant. Thus specify what precedes and follows dissonance: preparation and resolution. Bass descends fifth, most perfect progression: third prepares and resolves dissonance, seventh in fundamental harmony. Bass descends third or seventh: fifth and octave prepare and resolve, though natural harmony allows only third to resolve it. Reverse direction; bass ascends same intervals. Seventh cannot be prepared. If ear accepts seventh there, preparation rule cannot be universal.", "II.13-005": "Major dissonance always accompanies minor, but do not confuse them. Resolve one upward, other downward. Minor favors preparation; major never needs it. Zarlino knows only tritone as major dissonance; mentions briefly. Later writers name others, none traces origin to major third above seventh chord's fundamental. Seventh itself originates all minor dissonances. Oversight keeps later writers from revising Zarlino's rules. Still demand preparation for every dissonance, though experience proves otherwise. De Brossard and Masson passages, supported by Zarlino examples: bass syncopates—formerly forbidden, now freely practiced—seventh naturally resolves by octave, sometimes fifth or sixth, and so on. (A)", "II.13-006": "Old prohibition absent at least in Zarlino's time.* He says earliest musicians used diminished fifth as following example shows. Syncopate bass for diminished fifth or seventh: same thing.", "II.13-007": "EXAMPLE.", "II.13-008": "Third part, chapter 30, fols. 209, 210.", "II.13-009": "Zarlino's Example: Diminished Fifth", "II.13-010": "Fifth may follow fifth if latter diminished or augmented.", "II.13-011": "Seventh also allowed, provided 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 consecutive fifths allowed: perfect, then diminished, and so on.", "II.13-017": "EXAMPLE.", "II.13-018": "Sequence like B in Zarlino: third part, chapter 61, fol. 294, third example, between Canto and Tenore.", "II.13-019": "Examples of Two Fifths", "II.13-020": "All notes C belong to same chord. Freedom to pass through chord's sounds irrelevant here. Masson claims to discuss two different chords.", "II.13-021": "Return to subject. Combine first two seventh examples A, B with fifth example B. Give sevenths natural ending, thus:", "II.13-022": "Combination of the Examples", "II.13-023": "Combination shows different progressions from one principle.", "II.13-024": "EXAMPLE.", "II.13-025": "Masson's Basses, Natural Ending, and Fundamental Bass", "II.13-026": "Parts sound well together except consecutive-octave pairs D–F, G–H. Included only to show melodies from different consonant progressions without changing underlying harmony. Any part can serve as bass. All invert; all originate in fundamental bass moving tonic–dominant–tonic. More melodies possible than shown. Yet always same point: seventh, diminished fifth, tritone, small-sixth dissonance can lack preparation only through reversal of bass's natural direction. Descending fifth becomes ascending fifth, S–T. Here reversal means direction, not octave-related inversion. Neither minor nor major dissonance prepared this way. Prepare minor by every rule: major still never prepared.", "II.13-027": "EXAMPLE.", "II.13-028": "Prepared Minor Dissonances A and B; Major Dissonance C", "II.13-029": "A, B: minor dissonances prepared. C: major dissonance cannot be prepared.", "II.13-030": "Think dissonance always needs weak-beat preparation? A disproves it. Enforce rule, destroy fine ornament: harmony suspended through several dissonances, prepared by consonances accompanying those very dissonances. Better apply rule only to first dissonance, as B. Let bass rise third or seventh, as previously fifth. Dissonance cannot be prepared there either.", "II.13-031": "EXAMPLE.", "II.13-032": "Unprepared Seventh; Ascending Third and Seventh", "II.13-033": "Seventh unprepared at J: fundamental bass rises third. At L: rises seventh or descends diatonically. Let each part serve as bass in turn; derive other dissonances' progressions.", "II.13-034": "Cue signs mark alternative part progressions. Adjust other parts accordingly, following example's harmonic order.", "II.14-001": "CHAPTER FOURTEEN.\nThirds and Sixths: Progression.", "II.14-002": "Thirds partake of consonance and dissonance. Consonant themselves; source of dissonances. Divide major third: major and minor whole tones. Add minor third to either perfect chord: seventh. Invert seventh: whole tone. Invert whole tone: seventh, source of all harmonic dissonances. No more perfect consonance follows? Thirds and representative sixths have no fixed progression; everything depends on them. Octave or fifth immediately follows? These source consonances govern movement. Octave most perfect; wants major third before it, itself more perfect than minor. Minor third precedes fifth, less perfect than octave. Major third rises to octave; minor descends to fifth. Natural properties. Zarlino rightly says nearest semitone determines movement, ornamenting harmony and melody. Major sixth follows major third; minor sixth follows minor third.", "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: perfect cadence. B: its inversion. C: irregular cadence. D: its inversion. Principal cadences contain all our rules. Thirds and sixths must rise or fall semitone. Seventh or major sixth may enter first chord. Thirds become dissonant against added sounds, forming diminished fifth or tritone, containing major and minor dissonances. Third not dissonant itself becomes dissonant against sounds completing chord. Thus fixed progression. Seventh from added minor third descends semitone; added major sixth rises semitone. Natural properties, shown by cue signs", "II.14-008": "Printed Cue Signs within the Sentence.", "II.14-009": "; hence rule: never ascend minor third or minor sixth to octave. Rules founded on fundamental harmony. Most authors misapply them to inverted harmony. Zarlino* and others wrongly say minor third should descend to unison or octave. Occurs only in inversion of harmony where fifth or diminished fifth descends to 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's error: rules based on only two parts at once. Happens almost everywhere. Same passage says major third usually rises to fifth. Again inverted harmony, where third may rise to seventh. Even that progression not most natural harmony.", "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": "Could give perfect or seventh chord to note whose fifth follows major third. Only by license. Natural harmony requires consonant fundamental-bass progression; absent here.", "II.14-017": "Major-mode irregular cadence: major third must descend to fifth despite usual direction. No dissonance with possible added sixth. Movement governed only by nearest consonance: fifth.", "II.14-018": "EXAMPLE.", "II.14-122b": "Major Third Descending in an Irregular Cadence.", "II.14-020": "Read rule correctly. Does not forbid minor third rising or major descending. Says only major third's nature is ascent to octave, and so forth.", "II.14-021": "Fundamental-harmony rules remain in derived chords. Rule names interval against original chord, not derivative. Third, fifth, octave may become sixth, fourth, and so on through inversion. Regard new sixth or fourth as representing original interval governed by rule. Once rule established, follow modulation. It reveals source chord sequence. Inverted intervals must follow prescribed progression of originals. Otherwise could reject following sequence because minor sixth rises to octave.", "II.14-023": "EXAMPLE.", "II.14-123a": "Minor Sixth Ascending to the Octave.", "II.14-025": "Fundamental harmony: not sixth, but octave rising to fifth.", "II.14-026": "EXAMPLE.", "II.14-123b": "Fundamental bass of an irregular cadence A–B and a perfect cadence B–C.", "II.14-028": "Might also reject minor third rising to octave this way.", "II.14-123c": "Minor Third Ascending to the Octave.", "II.14-030": "Fundamental harmony: fifth rises to third, not third to octave.", "II.14-031": "EXAMPLE.", "II.14-124a": "Fundamental bass of a perfect cadence.", "II.14-033": "Follow modulation as well as interval's fixed place in fundamental chord. Ascend minor third to octave in A or D, thus:", "II.14-124b": "Minor Third and Octave in A or D.", "II.14-035": "Bad: each bass note actually carries perfect chord, rule's basis. Allowed in F or B♭: each bass note carries sixth chord, inverted perfect. Perfect chord implied; rising interval really fifth, not minor third. Still doubtful? Examine first example: minor sixth rises to octave in F or C, freely practiced by skilled musicians. Bad in G. Same reasons.", "II.14-036": "Double minor third or minor sixth in chord: one copy may move against nature, provided other follows rule:", "II.14-037": "EXAMPLE.", "II.14-125": "Doubled Thirds and Sixths, Examples A and B.", "II.14-039": "A: minor third descends correctly. B: minor sixth stays on same degree to form following seventh, then descends correctly. Doubled copies must rise; otherwise hard to avoid consecutive octaves. Natural progression gives full satisfaction; copy seems extra sound escaping attention. Yet dissonance never doubled. Thirds representing dissonance follow same law, especially major third. Minor third excepted only in more than three parts, or when subject absolutely requires it for beautiful melody, fugue, or imitation contributing musical beauty.", "II.15-001": "CHAPTER FIFTEEN.", "II.15-002": "When Ninth Chord Must Lose Seventh.", "II.15-003": "Chapter X suggests seventh always belongs in ninth chord. Yet unsuitable when ninth chord on tonic. Reason follows.", "II.15-004": "Ninth on tonic requires preceding leading note, in bass or chords. Leading note in bass cannot be doubled: progression fixed. Duplicate also rises, making consecutive octaves even if later than bass. Dissonance once heard demands particular following sound. Must move there. Hold duplicate before same move: offensive suspension destroys satisfaction from consonance first following dissonance. Let duplicate descend as seventh, while leading note rises? Supposed tonic no longer tonic; key changes. Possible only in major keys. Minor key: note's minor third forms augmented fifth with such seventh. Augmented fifth's lower sound must stand beneath all others. Here minor third forming that lower sound stands above. Inversion also gives diminished fourth, wholly excluded from harmony. Supposition interval like augmented fifth cannot invert: chord exceeds octave, lowest sound cannot change place.", "II.15-006": "Leading note in chords or soprano may stay on degree, becoming seventh above following bass tonic. But seventh always augmented. Then chord is eleventh, not ninth; third cannot enter. Replace eleventh with third: ninth chord implied. Seventh no longer augmented; can retain that status only in eleventh chord. Now ordinary seventh, must descend. Key always changes: tonic ceases to be tonic when carrying ninth or seventh chord. Only perfect or augmented-seventh chord belongs to tonic.", "II.15-007": "Ninth chord above tonic: always omit seventh. Would have to be augmented; incompatible with rest.", "II.15-008": "EXAMPLE.", "II.15-009": "Examples A and B: Seventh Removed from the Ninth Chord.", "II.15-010": "A good. B bad where leading note doubled at C, both rise to D. C–F forms augmented fifth. Put C above F: diminished fourth. In major key, add ♯ to note F and tolerate it—but key changes. Supposed tonic becomes fourth note, as experience proves. Leading note then ordinary seventh, must descend instead of rising to D as augmented seventh.", "II.16-001": "CHAPTER SIXTEEN.", "II.16-002": "Dissonant Consonances: Fourth Misunderstood through Irrelevant Rules.", "II.16-003": "Every dissonant chord unites consonances. Compare two consonances within chord: dissonance appears. Seventh chord unites two fifths and three thirds. Outer sounds neither fifth nor third apart; form seventh, or inverted second. Thus dissonant together.", "II.16-005": "Most musicians err here. Compare other sounds only with bass; ignore intervals among all sounds. Thus call dissonant sound consonant. Small-sixth chord: third, fourth, sixth consonant with bass. Third and fourth dissonant together. Great-sixth chord: third, fifth, sixth consonant with bass. Fifth and sixth dissonant together. Which sound forms dissonance? Refer chord to foundation. Small-sixth: third. Great-sixth: fifth. Both are seventh above original seventh chord's fundamental.", "II.16-006": "EXAMPLE.", "II.16-007": "Seventh, Great Sixth, and Small Sixth Related to the Fundamental Sound.", "II.16-008": "G always seventh above fundamental A. Invert original seventh chord: same sounds remain. Refer to foundation: G always dissonance. Arrange as small-sixth or great-sixth chord; dissonant sound always prepared and resolved like original seventh. No underlying harmony changes. Clear proof.", "II.16-010": "Exception: great-sixth chord from added sixth on irregular cadence's first perfect chord. Consider perfect chord only; seventh chord absent from this cadence. Added sixth then forms dissonance. Clearer later: Chapter XVII, Article III; Chapter XVIII.", "II.16-011": "Small- and great-sixth chords only recently used; some musicians still reject them. Abandon experience for false rules. Rules call fourth dissonant without distinction, yet allow bass syncopation beneath fourth as beneath any dissonance. Countless errors follow. Oppose nearly universal opinions: must return everything to principle. Exact inquiry shows apparent novelty in our rules follows from rules we seek to destroy. Old rules based on different dissonance properties, each with different source, each needing separate rule. Divide into articles for clarity.", "II.16-012": "ARTICLE ONE", "II.16-013": "PRINCIPLE OF DISSONANCE;", "II.16-014": "Which Sound Dissonant; Which Sound Preparation and Resolution Rule Governs.", "II.16-015": "Same principle generates consonance and dissonance: first fundamental sound. Everything refers to it. Division generates intervals; their identity depends on relation to it. Third, fifth, seventh comprise all intervals, as Book I showed and Chapter XIX further explains. All originate in first sound. Thus principle of dissonance. Seventh compares generated sound with fundamental. Every other minor dissonance—only kind considered here—comes from seventh or inverted second. Ninth and eleventh, called fourth, do not overturn rule. Remove extra sound from their chords: only seventh or second dissonance remains.", "II.16-017": "Conclusion: dissonance has one principle. Seventh chord's third and fifth cannot supply another. Compare them with seventh: no new minor dissonance, only same third and fifth. Useful later.", "II.16-018": "Principle perfect itself; source of consonance and dissonance. Cannot be dissonant. Dissonance resides only in sound compared with it. Proof: preparation by syncopation, resolution by descent govern seventh's upper sound, not lower principle. Invert seventh into second chord. Principle above; governed sound below. Lower sound now syncopates and descends. Rule governs dissonance alone, not principle. Required bass syncopation applies only here. Elsewhere another principle explains it and must be stated first. Third or fifth syncopating with seventh follows consonances' natural progression, not dissonance rule. Any chosen consonance may syncopate for taste; only dissonance obliged by rule. Bass syncopating beneath second is itself dissonant. Its principle solely second's upper sound, naturally seventh's lower sound—not other accompanying sounds. Likewise seventh's principle solely lower sound. Accompanying sounds may syncopate by choice or progression relative to bass. Second's lower sound syncopates against second's upper principle, not fourth or sixth. Otherwise each comparison creates another principle. Call upper sounds of second and fourth dissonant instead? Rule loses solidity. Dissonant sound no longer required to syncopate; uncertainty permits any sound at will. Seventh ceases to govern all dissonance; principle confused.", "II.16-020": "EXAMPLE.", "II.16-021": "Syncopations of Consonances and Dissonances: A, B, C, D, E.", "II.16-022": "A: fifth syncopates from natural consonant succession and composer's choice, not dissonance rule. B: bass syncopation beneath fourth merely inverts that fifth. C: fifth syncopates for same reasons; accompanying seventh because rule demands. D: seventh syncopates by rule; consonant third does not. F: bass represents seventh's upper sound governed by rule, so syncopates. Fourth does not: consonant, represents D's third in fundamental harmony. D's seventh syncopates against principle in bass. F's second-bass syncopates against principle now above, second's upper sound. Not against accompanying fourth. Likewise C's seventh not syncopated against fifth, nor D's against third.", "II.16-024": "Every minor dissonance: seventh or inverted second. Always true in complete chords. Not between part and bass? Then between two upper parts. Rule governs seventh's upper sound, becoming second's lower through inversion.", "II.16-025": "ARTICLE TWO.", "II.16-026": "Source of All Dissonant Chords: Number of Sounds and Dissonances; Bounds.", "II.16-027": "Seventh originates all dissonances; seventh chord all dissonant chords.", "II.16-028": "Four different sounds; one minor dissonance, seventh. All within octave.", "II.16-029": "Seventh chord: perfect chord plus seventh. Perfect chord always remains. Fundamental may carry major or minor third. Major third often forms new dissonance against seventh; originates all major dissonances. Minor dissonance, still seventh, keeps prescribed progression. New major dissonance need not detain us. Complete chord always contains seventh or second; governed sound now known. Third inseparable from perfect chord; does not obstruct dissonance's natural course. Major third can form new dissonance with seventh, but not ultimate principle. Principle chiefly in lowest fundamental of both third and seventh.", "II.16-031": "Test origin in seventh chord. Do inversions have same number of sounds and dissonances, same bounds, unchanged modulation? Exact agreement proves origin in seventh, first dissonant chord given by harmonic ratios. Musicians all accept second, diminished-fifth, tritone chords with these properties. Why reject small- and great-sixth chords sharing them? Each inversion simply chooses seventh-chord sound as bass. Third or seventh allowed below, giving diminished-fifth, great-sixth, second, tritone. Why forbid fifth below, giving major or minor small-sixth chord? Great-sixth grouped with diminished-fifth: same bass relative to source fundamental chord, differing major/minor, like second and tritone. Minor dissonance everywhere in seventh or second. Seventh's upper sound, second's lower sound forms it. Always follows fixed rule.", "II.16-033": "Reject small- and great-sixth chords because Zarlino omitted them, or small-sixth contains fourth? Zarlino also omitted seventh chord with major third dissonant against seventh, yet discussed its diminished-fifth and tritone derivatives. Musicians still used seventh chord, and other chords discovered gradually. Such appeal to authority contradicts itself. Fourth in small-sixth consonant for same reason as fourth in second chord, explained earlier. Dissonance lies in seventh's upper or second's lower sound. Fourth joined to third forms either interval according to arrangement. Third dissonant, not fourth. Second chord: bass dissonant. Great-sixth: fifth against sixth. Eleventh chord, called fourth: fourth against fifth. Exact examination corrects old false idea of fourth.", "II.16-034": "All these chords reduce to seventh chord divided into thirds, except eleventh. Hence name eleventh. Reduction into thirds requires removing bass. In natural arrangement, upper sound forms eleventh with that bass, not fourth. Fourth in second and small-sixth chords lies within octave. All chord sounds within octave freely invert. Lowest sound of ninth or eleventh cannot: must never change place.", "II.16-036": "Second chord inverts seventh chord; second inverts seventh. Then fourth inverts fifth too. For certainty, consult fundamental chord for derivative's properties. Judge intervals by originals they represent: third, fifth, seventh. These compose fundamental perfect and seventh chords. Progression determined only by lowest sound of these chords.", "II.16-037": "EXAMPLE.", "II.16-038": "Same chords serve each bass.", "II.16-039": "Shared Chords for Inverted-Chord Basses, the Fundamental Bass, and Basses by Supposition.", "II.16-040": "Fundamental bass's perfect and seventh chords form all others. Same dissonance, same progression everywhere. Same number of sounds within octave, except extra supposition-bass sounds: ninth one side, eleventh other. Modulation unchanged whatever bass or chords chosen. Remove octave of each tested bass from dissonant chords as needed to avoid consecutive octaves.", "II.16-042": "Curved link ⌢: dissonance prepared by syncopation. Following line ╲: downward resolution. Small-sixth chord's third, great-sixth chord's fifth, second chord's bass all form same dissonance: fundamental bass's seventh. Remove extra bass from supposition chord: same seventh dissonance remains.", "II.16-043": "Semicircle: ⌢; short descending line: ╲.", "II.16-044": "ARTICLE THREE.", "II.16-045": "Fourth Dissonant over Syncopated Bass? Destroys Music's Finest General Rule.", "II.16-046": "Rule: prepare every dissonance with consonance. No exceptions. Call fourth dissonant when bass syncopates, rule fails. Bass naturally descends step after syncopation; fourth then prepares diminished fifth or great-sixth chord's dissonant fifth.", "II.16-047": "EXAMPLE.", "II.16-048": "Natural Harmonic Succession: Syncopated Bass and Fundamental Bass.", "II.16-049": "Most natural harmonic succession. Only objection: first syncopation not begun on weak beat. Requirement applies only if second belongs to or is implied in sixth–fourth chord. Second then dissonance; syncopation starts weak, ends strong—unless immediately preceding dissonance already syncopated by rule. Every dissonance prepared by consonance means only every dissonance capable of preparation.", "II.16-050": "ARTICLE FOUR.", "II.16-051": "Authors' Faults in Harmony Rules: Different Principles, Spreading Errors.", "II.16-052": "All harmony-rule writers abandon principle. First sound, first chord get no privilege; all equal. Rank consonances only to choose chord filling. Explain thirds' and sixths' movement only by comparisons. Dissonances confused: second, seventh, ninth. Demand preparation, then contrary rules. Demand consonant preparation and resolution, then contradict elsewhere. No explanation why some rise, others descend. Hide principle; each reports limited experience. Experience alone convinces, yet music differs from sciences giving sensory certainty. Sight less deceptive than hearing. One approves chord another dislikes. Musicians stubbornly defend imagination or little experience. Authority usually defeats reason and experience. What supports authority? Who reasons from solid principle? Who guarantees perfect senses of self-proclaimed expert? Neither reason nor experience guided rule-makers. From Zarlino onward, each interval studied separately. Principle resides in first fundamental sound, then its chord. Must define fundamental and complete accompanying chord before interval's properties. Without complete chord, harmony imperfect. Otherwise reason weak, experience misleading. Away from principle, reason loses force. Isolated interval tells no fixed properties. Examine every containing chord: sound descends here, rises there; step here, leap there; dissonant here, consonant there; syncopates here, cannot there. Source of obscure rules. Example: every dissonance prepared through syncopation; also bass may syncopate beneath dissonance. Contradiction. Either dissonance need not syncopate, or syncopated bass is dissonance. Soundest conclusion from opposed rules; perhaps never considered. Explain now.", "II.16-055": "1. For melodic taste, introduce one or more dissonances while bass or other part syncopates. Not our subject here.", "II.16-056": "2. Perfect chord's natural major third remains when added seventh syncopates. Seventh syncopates against major third and fundamental. Major third then represents all major and augmented dissonances. Invert chord; minor dissonance, seventh, goes below. Must syncopate if prepared. Thus bass syncopates against major dissonance—or more precisely, fundamental remaining in complete chord. Explain apparent exception to remove doubt. Also supposition chord: added bass sound far more dissonant than others, must syncopate when upper major dissonance forms augmented seventh.* De Brossard overlooked this. Berardi table in his Dictionary shows seventh above syncopated bass is augmented. Only this seventh naturally resolves to octave here, exactly as marked. Berardi also errs about fourth over syncopated bass: fourth not dissonant here.", "II.16-057": "3. Dissonance cannot be prepared, as Chapter XIII explains. Bass often syncopates, only in inverted harmony, receiving dissonance after consonance. Masson example, p. 77.", "II.16-058": "Example by Masson, p. 77.", "II.16-059": "4. Bass syncopates freely when all sounds above belong to chord of first syncopated note. See Zarlino example.", "II.16-060": "* 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": "Different principles explain bass-syncopation rule. Without explanation, confusion: consonance or dissonance must syncopate? Where should note go next? Simple principles give two certain rules. First: consonance prepares every preparable dissonance. Second: unpreparable dissonance follows consonance by ascent or descent. Both from fundamental bass beneath fundamental chords. Rest depends on taste. Any chord sound may serve as bass. Sound shared by consonant chord and following dissonant chord, whose dissonance cannot prepare, must syncopate or stay on degree—nearly same thing. Still clearer if chord unchanged and its sounds pass successively above held or syncopated bass. Separate rule unnecessary: free choice. Yet rule arose from these varied properties glimpsed through experience. Writers preserve demand that every dissonance syncopate, then nearly destroy it by allowing bass syncopation under fourth, seventh, and so on. First rule makes syncopated bass dissonant; fourth and seventh then not dissonant. Writers deny yet imply this. Why separate bass rule? Beneath second, tritone, augmented seventh, bass obeys first rule: minor dissonance syncopates. Elsewhere outside rule: choice or natural consonant progression relative to fundamental bass. Like syncopating fifth or any consonance. Slavery to syncopation carries consequences too far.", "II.16-066": "Another rule defect: vague part movement. Sixth follows fifth; seventh resolves by third, fifth, sixth. But one part stays? Both move? Which rises or descends? Remove doubts with precise, intelligible modulation rules guiding all. Then: every minor dissonance descends diatonically; every major rises semitone, whatever bass does. Origin makes dissonances easy to recognize. Explained elsewhere; no more now.", "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": "Always derive conclusions from same principle: known fundamental-bass progression. Suppose it consonant here. Unrestricted with consonant chords; not so with dissonant chords, though new dissonant interval expands its resources. Added dissonance depends on perfect chord, cannot exist without it. Perfect chord depends on lowest sound, foundation of both chord and dissonance. In most natural harmony, bass moves toward that low sound when sounding and resolving dissonance, seeking support against harshness. If dissonance obscures principle, bass searches more attentively: descends third or fifth. Even then, only fifth gives pleasant resolution. Fifth first harmonic interval; octave merely repetition. Bass descending seventh or rising second begins license, even if consonance prepares and resolves dissonance. This supports claim: descending seventh still approaches principle. But seventh owes origin more to taste than nature; unlike perfect-chord intervals, it is absent from harmonic body’s most natural operations. License comes from it alone. Those crediting taste more excusable than those rejecting licenses beyond their understanding without reason or experience. Descending seventh/rising second forms interrupted cadence. Ear expects desired perfect conclusion, then meets interruption and surprise, somewhat offended. Surprise means departure from natural course; departure means license. If descending third, fifth, even seventh naturally sound prepared/resolved dissonance, their inversions allowing unprepared dissonance also count as license. So does any departure through supposition, borrowing fundamental sound, or alteration of either fundamental chord. Yet restricting harmony to most natural alone gives it too narrow bounds. Refusing its full properties denies its rights. Refusing what its principle offers abandons senses and reason. Principle lies solely in thirds, fifths, sevenths forming fundamental chords and bass progression. Every proposed license comes from this source.", "II.17-008": "Musicians long ceased trying to satisfy reason in music. Great masters aim to please, disregard scrupulous critics enslaved to one author. Such critics confine reason and experience to following him. Accept interrupted cadence, reject several successions from its inversion. Inversion unknown to them here, though recognized in sixth, second, tritone, diminished-fifth chords. Zarlin accepts ninth but forgets augmented fifth, without which ninth and even seventh cannot occur on minor-key mediant. Accepts tritone/diminished fifth, forgets foundation: cannot otherwise imagine seventh chord containing them. Discusses another seventh, loses small/great-sixth inversions, though second/tritone/diminished fifth equally invert seventh. Great sixth differs from diminished fifth only through major/minor third above seventh chord’s lowest sound. Judge their foundation and critics’ worth. Ask reasons: cite rules’ authority. Ask listening to apparently rule-breaking music, to reveal mistaken interpretation or exceptions: become deaf. Such faction opposes century’s accomplished musicians. However charming music seems, they call it worthless.", "II.17-009": "Fortunate to face only such scholars when defending good taste. Reason true means of convincing them. Not enough to say best masters used all licenses proposed later, therefore experience authorizes practice. Add proof from indisputable principle, whose simplicity makes evidence clearer. No need repeat chapters VI/VII on interrupted/irregular cadences, XIII on freedom from dissonance preparation, X/XII on supposition/borrowing.", "II.17-011": "SECOND ARTICLE.", "II.17-012": "Licenses drawn from the interrupted cadence.", "II.17-013": "Interrupted-cadence inversions yield licenses. Sixth chain credited only to taste; Zarlin* forbids, since fourths invert to fifths with supposedly similar effect. Our explanation: interrupted cadence plus chapter XIII freedom from preparation when fundamental bass rises third/fifth/seventh.", "II.17-014": "EXAMPLE.", "II.17-015": "Succession of sixths—interrupted cadences", "II.17-016": "Every measure interrupted cadence except penultimate. There perfect cadence avoided by added sixth A. Sixth prepares irregular cadence, avoided by added seventh B. B prepares final perfect cadence.", "II.17-017": "* Terza parte, chapter 61, folios 291 and 292.", "II.17-019": "Invert upper parts: fourths become fifths. But inversion greatly reduces fifths’ dullness. Fourth not bound by fifth/octave restriction.", "II.17-020": "THIRD ARTICLE.", "II.17-021": "How one dissonance may resolve through another.", "II.17-022": "Dissonance likes consonant preparation/resolution; can sound unprepared. Can resolution break general rule too? Fundamental chords/bass use third/fifth/seventh; fundamental intervals therefore. Use upward/downward/inverted. Examine bass movements admitting seventh chord; test dissonance resolving through dissonance.", "II.17-023": "Rule comes from principle, never principle from rule, still less from famous author’s opinion. Reputation can overawe. Scientific obscurity comes from inadequate penetration and judgment. Best authors propose third/fifth as principles, always forget seventh, first of its kind. Fifth from harmonic division of octave; third from harmonic division of fifth; with inversion, seventh also from harmonic division of major third. Moreover, seventh naturally equals two fourths or third added to fifth. Source of all dissonance: either fundamental, or exclude every dissonance from harmony. Neglect of inversion’s precision and power hides sole route to harmonic secrets. Examine its exactness in numbers, divisions, multiplications; string lengths taken right or left; resulting intervals and progressions; chords formed from those intervals and their progressions. Cannot then deny inversion as key to harmony’s immense, infinite variety.", "II.17-025": "Most musicians take license to mean fault; Brossard therefore omits it from dictionary. Do not be misled. Music, above other sciences put into practice, can make everything clear. Elsewhere ornamental licenses resist precise rules. Here same principle explains all; license evident inversion of first-known things. Perfect and seventh first among consonant/dissonant chords. Third, fifth, seventh or second first among fundamental-bass progressions, because first-known intervals. If reason finds nothing beyond these two chords and three intervals except derivatives, agree that everything rests upon them.", "II.17-026": "Return to subject after digression aimed at prejudiced minds. Dissonance resolves not to sweetest consonance but imperfect third. Seventh naturally third added to fifth; naturally descends diatonically. Only fundamental chords perfect/seventh; fundamental bass moves through their thirds/fifths/sevenths. Therefore accept two successive fundamentals meeting all these conditions except seventh resolving through another seventh. To prevent surprise, recall seventh already resolves imperfect consonance and derives from it in every way: second from major-third division is inverted seventh. Ear can tolerate this small defect in favor of principle remaining intact elsewhere. Experience proves it.", "II.17-028": "Ascending third/fifth more perfect than seventh licensing this move, but cannot provide resolution: dissonance cannot follow natural path in those fundamental progressions.", "II.17-029": "Example of a seventh resolved by another seventh.", "II.17-030": "A seventh resolved by another seventh", "II.17-031": "Any part may serve bass. Never continuo above fundamental: supposition low sound must stay lower. Added part cannot sound with two basses; basses cannot sit above other parts.", "II.17-032": "C/D each seventh over fundamental A/B descending step or rising seventh. Dissonance resolves through dissonance.", "II.17-033": "Best sequences: ninth→seventh, C D against F G; seventh→diminished fifth, C D against H I; second→tritone, H I against C D placed above.", "II.17-034": "Brossard dictionary* and Masson show seventh→diminished fifth. Masson also tritone→fifth of same note. Add fundamental A B under his D etc.: similar harmony. His major dissonance first seventh chord, ours second. Other differences unanticipated because no fundamental-bass approach.", "II.17-035": "Fundamental bass used? Move N to guide pitch.", "II.17-036": "L–M fundamental irregular cadence avoided by added seventh M. Reflections follow.", "II.17-037": "1. Irregular cadence original when both fundamental notes take perfect chords. Added sixth extra sound tolerated by taste. Result not fundamental; lacks full perfect/seventh privileges despite inverting seventh. Original chords freely invert. Added sounds cannot freely change place, though originals retain force. Added sixth clashes with fifth, not bass. Never invert clash onto bass; only small-sixth inversion allowed, dissonance between upper parts. Reduce to seventh? Changes principle from perfect alone; impossible here, since seventh cannot resolve over ascending fifth. Cadence means melodic conclusion; requires consonant bass movement under fundamental chords. Added sixth only tasteful license. Distinguish fundamental/derived properties.", "II.17-038": "* De Brossard, page 131, article 5, note A. Masson, page 115. [Page 98.]", "II.17-040": "2. Added dissonance interrupts closing perfect chord: no cadence remains. Fundamental chords/progressions then provide true principle. Previous example shows this. Freely invert its fundamentals; supposition allowed too.", "II.17-041": "Added part’s second resolves against natural rule, seems worse. Yet accept rest, must accept this: fundamental bass governs. Same sort of license as irregular cadence’s upward third resolution. Do not confuse true principle with that cadential license.", "II.17-042": "Experience stronger than our reasons. Best masters’ works give further testimony.", "II.17-044": "Continuous licenses harsh. Use very rarely, with expert judgment. Great difficulty accompanying correctly even proves their perfection. Composers benefit from accompaniment instructions specifying natural chords.", "II.17-045": "FOURTH ARTICLE.", "II.17-046": "The seventh may also resolve to the octave.", "II.17-047": "Seventh first dissonance, prepared/resolved by all consonances except fourth. Fourth resolves second only in inversion of seventh resolving fifth.", "II.17-048": "Third/fifth/octave prepare seventh; natural fundamental resolution only third. Interrupted cadence adds pleasing fifth resolution. Bass descends fifth/seventh respectively. Descending third more perfect than seventh: seek resolution there. Octave works, despite apparent hidden octaves. Prove resolution first, refute false objection afterward.", "II.17-049": "All allow ninth→third over bass descending third. Seventh within ninth chord then must resolve octave.", "II.17-051": "Ninth, seventh, and octave—small example", "II.17-052": "Return to foundation: ninth really seventh, seventh really fifth. Same progression. Ninth chord comes from added bass sound supposing fundamental immediately above.", "II.17-053": "EXAMPLE.", "II.17-054": "Fundamental bass of two avoided perfect cadences", "II.17-055": "Guide marks extra ninth-chord sound; ordinary note above is fundamental.", "II.17-056": "Whole ninth chord considered: forbid ninth→third or permit seventh→octave; inseparable. Fundamental origin makes both most natural. Accept seventh→octave or reject ninth chord.", "II.17-057": "Seventh→octave also in inverted harmony.", "II.17-058": "EXAMPLE.", "II.17-059": "Inverted bass and fundamental bass", "II.17-060": "Hidden-octave/fifth rule founded on fundamental harmony. Poor explanation left doubts; clarify.", "II.17-062": "Hidden octaves/fifths forbidden only to prevent extravagant voice movement, especially with dissonance. In consonant writing, contrary motion easily avoids fault. Yet perfect and irregular cadences constantly require such passages: hidden octaves in one, hidden fifths in other. Fill bass leap with diatonic steps and pairs become actual. Rule false there; useful only for inversions of those cadences, where former bass would move unsuitably in top part while bass took former top line. But upper parts already should move diatonically whenever possible, especially where fourth occurs, as in this inversion:", "II.17-063": "Hidden octaves and fifths—diatonic progressions", "II.17-064": "Inversion of parts—the fourth", "II.17-065": "Separate rule unnecessary here too.", "II.17-066": "Dissonance follows natural movement; accompanying consonances move as desired, retaining key and resolution-chord substance. Seventh→octave not hidden octaves. Existing/implied octave holds or moves elsewhere. Second octave must derive from its own movement, not another interval. Example.", "II.17-067": "Seventh resolving to octave—movement of consonances", "II.17-068": "Countless other resolutions follow; Book III discusses.", "II.17-069": "Foundation implied in every chord always guides: natural major/minor third and sixth movement, and avoidance of consecutive fifths/octaves. Eye often seems to find what ear does not hear. Masson* and others permit shown sixth-to-fifth movement. Intervening diatonic degree from F to D seems to create two fifths. Fundamental bass must instead be D–G, avoided perfect cadence; imaginary fifths disappear. Skilled composer reasons: hidden fifths here, but sounding note supposes another; with that note, fifths vanish, so passage good. Such supposition should occur only between principal beats. Music permits frequent, even successful abuse of infinite freedom to vary. But when reason agrees with ear, all possible variety preserves highest perfection. Written fifths/octaves need not sound as such if foundation remains fully regular.", "II.17-070": "Sixth to fifth—in four parts", "II.17-071": "Fundamental bass D, G", "II.17-072": "Longer explanation needed: correct readers clinging to words without their force.", "II.17-073": "Seventh may resolve through all these consonances, but natural fundamental resolution only third. Interrupted cadence gives fifth; inverted bass progression gives another seventh. License comes from seventh added to perfect chord, new bass route. Octave resolution only through supposition/inversion; underneath, still third, as examples show.", "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": "Sixth with seventh makes harsh chord. Bearable only passing: clashing sounds held, present in chords before/after. Bass 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": "Name: pedal point.", "II.17-083": "Held sound escapes attention as upper notes move naturally. Here, previous article’s added part, and musette and hurdy-gurdy music in France and elsewhere. Source calls these “coliers” [word uncertain]. Examples in Book III chromatic rules, Book IV pedal-point rules.", "II.17-084": "Chromatic, melodic/supposition dissonance, false relations could follow here. Next book’s rules simple and clear; leave until then.", "II.17-085": "SIXTH ARTICLE.", "II.17-086": "Occasions when dissonance seems to be prepared by another dissonance.", "II.17-087": "Article listed among licenses, yet content agrees with natural harmony. Our claim there: dissonance must be prepared by consonance, absolutely, without exception. Experience seems contrary; most musicians draw false conclusions. Place article according to their expectation so they find explanation where they suppose it belongs.", "II.17-088": "Brossard says on page 131: after syncopated dissonance, diminished fifth often follows; after it, syncopated fourth often follows, with diminished fifth serving as preparation. Satisfies only readers already knowing as much as he. Misleads uninformed readers. Does not remove prejudice of strict readers who take rule literally: every dissonance must be prepared AND resolved by consonance. They hear apparent contrary cases and call them faults. Explain apparent opposition to general rules, or do not propose it. Had author stayed within title’s scope without practical-rule detail, criticism here would be unfair. But elsewhere he gives rules opposing this teaching. Must state our view to clear doubts he creates.", "II.17-089": "Article III treated dissonance resolved by diminished fifth. Syncopated fourth apparently prepared by diminished fifth is different matter: both contained in same fundamental chord. Second dissonance is same as first. Dissonant note stays while bass part moves among chord sounds. Only interval between held dissonance and other part changes, not underlying harmony. Dissonance against fundamental bass remains identical. Add fundamental bass to Brossard example to prove it.", "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": "A–B: seventh preceded by same seventh. Moreover M seventh prepared by consonance L; later appears diminished fifth and eleventh against continuo. Always same seventh and chord against fundamental bass. Extra eleventh/fourth sound must lie below fundamental; remove it for analytical proof. No need repeat further. Do not imagine dissonance prepared by another dissonance: fundamentally one dissonance throughout succession; whenever prepared, consonance prepares it. Freedom to move bass among one chord’s sounds has no bearing on rule concerning two distinct chords.", "II.17-098": "Earlier commentators failed to reconcile reason with experience, confusing principle and derivatives. Principle here equally strong throughout. Natural harmony and license need only perfect/seventh chords and constituent intervals to form fundamental bass. Its initial descending thirds, fifths, and optional sevenths guide natural harmony. Inversions of these progressions, together with supposition and borrowing, guide all practicable licenses.", "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": "Judge music by hearing. Reason authoritative only with ear. Agreement strongest proof: ear satisfies naturally, reason satisfies mind. Judge through both.", "II.18-004": "Experience offers infinite chord variety; no principle, get lost. Everyone trusts supposedly infallible ear. Reason offers one chord, properties found with little experiential help. Experience not contradicting? Reason leads. Simple principle makes decisions convincing. Experience strengthens proof.", "II.18-005": "Earliest musicians—in short, all confined to speculation—accept perfect chord as sole principle. Zarlin joins practice to theory and discusses sixth/sixth–fourth, already known derivatives of same principle. Can dissonances also refer there? Easily proved: all generated by new sound added to original chord, which remains in full perfection. Reason alone can therefore authorize and determine practice. Addition follows naturally by rule of three or fresh multiplication of original chord’s numbers, Book I, chapter VII, page 29. Musical rules concern usable consonances/dissonances. All consonances contained in perfect chord; dissonances in same chord plus added seventh. Thus rules chiefly founded on original perfect chord and resulting seventh chord. Our conclusions from simple natural principle match, point by point, finest musicians’ statements and practice, always conforming to experience’s approval. Who can doubt this is rules’ true foundation?", "II.18-006": "Examine Zarlin on fundamental bass, its movement, upper movement it determines, thirds, consonances generally, dissonances. Omits major dissonances; interrupted cadence poorly defined; irregular cadence and inversion unmentioned despite teaching sixth/second inversions. Ninth cited without distinction of supposition. Modes ill-founded, as chapter XXIII will show; his music misses our refinements, examples mismatch discourse. Are reasons real reasons or words? Examine sources, explanations, comparisons, limits. Sound conclusions: all harmony/melody revolves around two chords, more precisely their lowest sound, same in both, and its progression. Then hear and examine finest masters. Add fundamental bass by chapter-end method. Find only perfect/seventh, tonic/dominant—provided modulation understood enough to identify all key changes. Also note sixth often replaces dominant only in minor keys.", "II.18-008": "Principle more precisely lowest sound of perfect/seventh: harmonic center. All sounds relate there. Divided string chosen because low-sounding whole generates divisions, as unit generates numbers.", "II.18-009": "Chords/properties from perfect/seventh; those depend on center and movement. Intervals defined relative to center; center moves by same, determines chord order. Basics third/fifth/seventh. Inversions sixth/fourth/second; compounds ninth/eleventh; alterations tritone/diminished fifth. Octave repetition omitted. Inverted intervals→inverted chords; compounds→supposition; alterations→borrowing. All from three fundamentals, all refer center.", "II.18-011": "Ear approves fundamentals and all following their root progression, nothing else. Root implied/inverted/supposed/borrowed: reason and ear agree without exception.", "II.18-012": "Wonderful simplicity! Many chords, fine melodies, infinite variety, exact expression, feelings—all from two/three intervals in thirds, one sound as principle:", "II.18-013": "Fundamental sound. Third. Fifth. Seventh.\n 1. 3. 5. 7.", "II.18-014": "Earlier remarks persuade; following rules complete proof.", "II.18-015": "1. Consonances all in perfect chord. Fundamental bass consonant movement, chapters I/II and Book III IV. Upper diatonic path gives almost all rules; dissonance freedoms only exception. Main rules, especially ancients’ supposedly sole rules, remain.", "II.18-016": "Natural progressions never consecutive octaves/fifths. Prescribed parts show perfect→imperfect and reverse, plus permissible perfect successions. Third succession unrestricted; thirds/sixths free. Fourth might inherit fifth’s ban; experience permits consecutive diatonic fourths, outweighs inference.", "II.18-018": "Plainchant only diatonic/consonant, even major sixth forbidden. Principle holds. Complete music not bound thus: dissonance wonderful. Modulation alone judges. Modern practice overcomes former difficulty singing expressive dissonances.", "II.18-019": "2. Descending fifth first/most perfect bass progression. Only its final cadence fully satisfies. Fifth returns to source octave note; ascending fourth equivalent. Study cadence’s properties. This first principle-movement alone completes rules, as follows.", "II.18-020": "Major third rising octave, minor third never rising there: rule solely from proposed progression, only place third moves diatonically to octave. Avoid misapplication. One third relative to principle, which lives only in perfect/seventh chord. Do not measure it indiscriminately from any note inversion permits as bass. Only fundamental third meant. Sixth rule confirms: sixth in inverted chord follows third’s property only when representing it. Reduce to one original chord and see. Proper interpretation needs no separate sixth rule: fundamental-third statement covers every representative. Dissonances will prove it further.", "II.18-022": "3. Add naturally minor third above perfect chord’s fifth. Creates dissonance, also clashes with root’s major third. Two sources: added minor third→minor dissonance; original major third→major dissonance. New distinction fixes all motion: major up, minor down, no exceptions. Also proves only perfect/seventh fundamentals if major dissonance reduces to major third, minor to seventh. No difficulty there.", "II.18-023": "Minor-third movement’s origin not yet examined. Earlier evidence assures truth; fuller account later.", "II.18-024": "Chromatic and irregular-cadence license might seem exceptions. But irregular added sixth supernumerary: omit it, harmony loses no perfection; taste alone governs use. Other dissonances omitted, harmony becomes dull. Chromatic major dissonance may fall semitone instead of rising, yet rule intact. 1. Expected rising destination implied unless sounded in another part; it is fundamental, naturally belonging in bass. 2. Major dissonance not dissonant by itself; minor is. Remove minor, no major dissonance remains, as experience shows. 3. Generating major third natural to perfect chord; saying it must rise does not absolutely forbid holding same degree. 4. Major dissonance only tonic dominant’s major third; incidental relative to immediately following key. 5. Regarded as holding degree to prepare following minor dissonance. Interval kind unchanged: hold underlying bass, third remains third, seventh remains seventh. Only major→minor or augmented→just. Written note likewise same; flat or natural added changes it.", "II.18-026": "Skilled readers feel proof without tedious expansion. Chromatic new harmonic kind has special properties; apparently divergent, still principle-dependent. Small clarification enough.", "II.18-027": "4. Upper movement naturally diatonic; minor third cannot rise octave. Thus hold third through perfect/final cadence, allowing later diatonic descent in similar cadence, obvious to knowledgeable musicians. This may have introduced dissonance and its rules. Held minor third becomes seventh, descends to another third; hence apparent origin of consonant preparation/resolution rule. Derive rule from perfect cadence preferably, also matching general ideas. Universal demand for preparation/resolution considers only first descending fundamental movements: third, fifth, seventh. Only these allow both; fifth primary. Chapter II also suggests dissonance originates in perfect cadence. All rules same source. Seventh, source of all minor dissonances, naturally resolves only third in fundamental harmony: chapter XVII, article IV.", "II.18-029": "First rule-maker may have deep knowledge of all harmonic properties while guided only by our principle; quite plausible. Zarlin repeatedly says earliest musicians knew only perfect chord, though himself ignorant of some now-used chords. Starting with him, each writer fixes on one interval’s properties, gives vague principle. Inverted-chord knowledge evidently grew over time through experience alone. Derivatives mistaken for originals, principle lost. Endless detours/exceptions/equivocations confuse terms, intervals, chords, progressions, properties, especially modes. Seems deliberate obscuring of simplest, most natural science. Compare ancient/modern rules with our reduction; good sense sees it. Geometer proposed principle vainly: lacked experience to explain as we do, called ignorant by ignorant readers lost in derived chords. Easy correction now. Accept chord reduction into thirds within octave,* compelled by experience. Only perfect/seventh originals. Sixth contains perfect; second contains seventh; all inversions imply fundamental. Ninth/augmented second likewise contain seventh; supposition/borrowing supposes or borrows root. All chord kinds thus derived from fundamentals, themselves generated by lowest sound using first-generated octave. All usable consonance/dissonance follows. Cannot repeat truth too often: theorists half-admitted it, most practitioners always contested.", "II.18-031": "5. Main rules drawn from bass descents, demanding prepared dissonance. Opposite progressions give exceptions. See XIII.", "II.18-032": "6. Major dissonance from natural major third; only precaution rise semitone. No preparation needed. Minor shares privilege in prescribed fundamental progressions.", "II.18-033": "7. Melodic dissonance/syncopation rules omitted: taste-based, still same principle.", "II.18-034": "8. Modulation binds rules, confirms principle. Connection missed by Zarlin/others needs length; reserved XXII/XXIII/XXIV.", "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 supposition/irregular-cadence sounds and borrowed foundation seem to need separate rules. Only voluntary additions, principle untouched; other books explain. Test through fundamental bass added as follows.", "II.18-038": "SECOND ARTICLE.\nHow to compose a fundamental bass beneath every kind of music.", "II.18-039": "1. Harmony at beat’s first instant, or each equal half-beat’s beginning. All parts/fundamental must agree then. Watch melodic additions: may occur within beat or even at first instant without belonging to harmonic body.", "II.18-040": "2. Fundamental always below others. Whole forms perfect/seventh chord; omit extra/borrowed sounds when needed.", "II.18-041": "3. Ninth/augmented fifth: fundamental third above written bass. Eleventh/fourth or augmented seventh: fifth above. Other parts make seventh chord. Octave of extra eleventh bass also extra, though full arrangement sounds good.", "II.18-043": "4. Borrowed chord: substitute dominant for sixth in fundamental bass. Sixth makes augmented second/inverted diminished seventh against dominant’s major third. Remaining chord becomes seventh. More in VIII.", "II.18-044": "5. Irregular cadence: omit supposed seventh-root sound; remaining perfect chord alone. More VIII/IX/X.", "II.18-045": "6. Seventh+sixth, XVII article V: disregard; fundamental holds previous degree.", "II.18-046": "7. Analytical bass only. Ignore faults created solely with it, such as consecutive octaves absent from original parts.", "II.18-047": "8. Modulation knowledge reveals key, scale position, chord, implied/supposed/borrowed root. Borrowing only minor: sixth borrows tonic dominant’s foundation. Dominant stays fundamental even with supposition. Irregular cadence tonic→dominant or fourth→tonic; fundamentals perfect, lower dissonant sound mentally removed.", "II.18-048": "9. Prefer consonant fundamental-bass progressions wherever possible. Exceptions only when seventh resolves fifth or another seventh, or octave prepares seventh. Other parts form only third/fifth/octave/seventh against bass. Chords sometimes incomplete; analyst must notice. Underlying chord persists even when melodic taste doubles one sound instead of supplying missing member. Exclude extra supposition sound, always below fundamental; irregular cadence’s added sound; sound borrowing tonic dominant’s foundation. For proof, mentally remove all as absent. Minor key’s second-note fifth often naturally diminished. Regard as just/perfect here, altered incidentally, provided it belongs to perfect/seventh chord relative to fundamental. Then check:", "II.18-050": "10. Minor dissonance always fundamental seventh: prepared/resolved properly in fixed movements? Ascending fourth equals descending fifth; same for equivalent pairs. Sometimes imply unwritten dissonance to give fundamental bass consonant movement or permitted chords only. Do not blame composer for faulty movement of that implied dissonance if absent without analytical bass. Same for other faults created only with bass, which composer need not intend to sound. Fault present without it means composer erred. None destroys harmonic substance, always within two proposed chords.", "II.18-051": "Second’s upper or seventh’s lower rises while other holds: irregular cadence. Rising sound extra, never bass. Major dissonance leading note/tonic-dominant major third, dissonant only with minor present; check semitone ascent resolution.", "II.18-052": "11. Resolution qualifications. 1. Dissonance holds same degree, then resolves correctly: valid while same fundamental chord persists. 2. Minor third between ordinary and fundamental bass need not detain us. 3. Same fundamental chord persists: dissonance may move to any chord sound, but ordinarily next goes to originally required destination. If major or minor dissonance sounds last, it may preserve own proper resolution privilege. 4. Major may resolve to consonance naturally following minor, and minor to consonance naturally following major. Must remain natural harmony; rise where ascent required, descend where descent required. Zarlin’s example shows this.*", "II.18-169": "Minor dissonance.\nMajor dissonance.", "II.18-054": "5. Chromatic major dissonance falls semitone instead of rising; counted same degree, as explained.", "II.18-055": "Music admitting this bass under all stated conditions always good. At most faults in particular consonance order, melody, modulation, equality of preparation/dissonance/resolution note values, or beats where preparation and dissonance occur. No fault against harmonic foundation, chief concern. Remaining rules easy to observe; taste dictates most, sometimes even requires departing from them.", "II.18-056": "* Terza Parte, chapter 30, folio 210.", "II.18-058": "Fundamental bass beautiful in chorus. If sounding, strict rules between all parts. Continuo may repeat unisons/octaves with it, especially sixth chords, supposition, borrowing; no concern then about fundamental sound.", "II.18-059": "Earlier teachers omitted principle. Extended account needed to make evidence overcome doubts/disputes.", "II.19-001": "CHAPTER NINETEEN.", "II.19-002": "Previous chapter continued: melody comes from harmony.", "II.19-003": "At first, harmony seems born from melody: each voice makes melody; voices unite into harmony. But each voice first needs assigned path, so voices agree. Any melodic order in separate parts scarcely makes good harmony—perhaps cannot—unless harmony's rules dictate order. Yet teaching starts with making melody, to clarify harmonic whole. Student progresses; then adds another part, and ideas vanish. Melody no longer under control. Seeking one part's path relative to another, we lose original plan or must change it. Keep first part unchanged, and its constraints may deny other parts their best melodies. Harmony guides us, not melody. Skilled musician can plan beautiful melody suited to harmony. Whence ability? Nature may help, certainly. If nature denies gift, only rules bring success. Where do rules come from? Must examine.", "II.19-005": "First string division gives two sounds fit for melody? No. Singing octave after octave makes no very beautiful melody. Second and third divisions generate all harmony, but their sounds no better suited to melody alone. Only thirds, fourths, fifths, sixths, octaves still make imperfect melody. Harmony generated first. Melody's rules must come from it. Take harmonic intervals separately; form fundamental progression—not yet melody. Put intervals together above one constituent sound. They naturally follow diatonic path fixed by their progression while serving each other as foundations. Consonant and diatonic progressions yield all needed melody. Harmonic intervals had to be known before melodic ones. Beginner's teaching consists of these consonant intervals, if such thing counts as melody. Chapter XXII shows ancients also derived modulation only from melody, though modulation comes from harmony.", "II.19-006": "Know consonant progression: adding three sounds above bass no harder than adding one. Two instructions: 'Put third, fifth, OR octave above bass'; 'Put third, fifth, AND octave above bass.' Both require same interval knowledge. Known intervals no harder together than separately. Part making third must next make fifth when bass descends third; this is our explanation. Bass moves differently; third here, octave there, fifth elsewhere. Must know what follows each under each bass movement. Thus teach four-part composition unknowingly while explaining only two parts. Each consonance appears in turn; must know each one's succession. Using all together no harder than individually. Cannot distinguish all at once? Attend to each separately. Move from one to next; construct perfect four-part harmony. Draw all further knowledge needed for perfection from it. Added explanation prevents error, if we trust experience of several people: knowing only note values, they read rules twice and composed harmony as perfect as desired. Composer hearing own work* also trains ear gradually. Become sensitive to perfect harmony taught by these beginnings; success assured. Success depends entirely on first principles.", "II.19-008": "Four parts familiar? Can certainly reduce to three or two. But what knowledge does two-part composition give, even perfectly mastered? Such mastery almost impossible: no foundation guides it. Teaching stays barren. Memory insufficient; method scarcely encompasses everything. Teacher finally says: Cætera docebit usus—practice teaches rest. Move to three or four parts? Explanations so scant, need great masters' own genius and developed taste to understand them. Zarlin* says four parts scarcely teachable on paper. Leaves composers to discretion, trained by earlier two- and three-part rules. Our view opposite. Teach harmony in four parts: all its distinctive features occur in only two chords, as shown throughout. Easy then to reduce to three or two. Zarlin fully defines neither two nor three; admits inability to define four. Yet concedes perfect harmony consists of four parts, likened to four elements. (Chapter 58, folio 281. Conclusion: earlier harmonic rules failed to yield perfect knowledge. Our principle offers sure goal for reaching knowledge that misses nothing.", "II.19-009": "* Partly for this reason, we give accompaniment rules.", "II.19-010": "* Terza Parte, chapter 65, folio 320.", "II.20-001": "CHAPTER TWENTY.", "II.20-002": "Character of chords.", "II.20-003": "Harmony stirs different passions according to chords used. Chords can be sad, languishing, tender, pleasing, cheerful, startling. Certain chord sequences express same passions. Subject far beyond my powers; I give what explanation experience permits.", "II.20-004": "Consonant chords occur everywhere. Use them often as possible for gladness and magnificence. Dissonant chords cannot be entirely avoided. Let dissonances arise naturally; prepare them when possible. Most prominent parts—top and bass—always consonant with each other.", "II.20-005": "Prepared minor dissonances sometimes express gentleness and tenderness well.", "II.20-006": "Tender laments sometimes need dissonance by borrowing and supposition. Prefer minor to major. Major dissonances that occur should dominate middle parts, not outer parts.", "II.20-007": "Languor and suffering: dissonance by borrowing works very well; chromatic especially. Next book discusses chromatic.", "II.20-008": "Despair, passions leading to fury, astonishing things: use unprepared dissonances of every kind. Major dissonances especially in top part. Sometimes beautiful to pass between keys through unprepared major dissonance. But excessive distance between keys must not hurt ear. Great judgment needed, here as everywhere. Heap dissonance wherever possible? Far greater fault than consonance alone. Use dissonance discreetly. Harshness unsuitable to expression? Skillfully omit dissonance even from chords ordinarily inseparable from it. Distribute remaining consonances among all parts. Remember: seventh produces all dissonances; seventh merely sound added to perfect chord. Does not destroy chord's foundation. May always remove it when judged appropriate.", "II.20-010": "Melody has as much expressive power as harmony. Almost impossible to give certain rules: good taste matters most. Leave gifted minds pleasure of excelling here; almost all force of feeling depends on this. Skilled people hear nothing new from us. Hope they do not resent secrets revealed—secrets they might wish to keep alone. Our limited understanding cannot rival their final degree of perfection. Without it, finest harmony sometimes dull. Through it, they can always surpass others. Still, proper chord sequence can yield melody suited to subject; later discussion shows how. Taste always first impulse.", "II.20-011": "Ancients seem superior here, if their stories deserve belief. One melody made Misse weep. Another made Alexander take arms. Another made furious youth gentle, humane. Astonishing musical effects reported everywhere. Zarlin gives sensible judgment: harmony often meant mere melody for ancients. Effects came chiefly from forceful speech, strengthened by sung delivery, not melody alone. Their melody lacked variety supplied today by perfect harmony, unknown to them. Their harmony, he also says,* was perfect chord beneath airs of every kind, sung indiscriminately—like our musettes or hurdy-gurdies. Name for this: Sinfonia.", "II.20-013": "Good musician enters every character portrayed. Like skilled actor, takes speaker's place. Imagines being where events happen. Shares concern of people most deeply involved. Good declaimer, at least inwardly. Feels when voice rises or falls, and how far. Fits melody, harmony, modulation, tempo to this.", "II.20-014": "* Terza Parte, chapter 79, folio 356.", "II.21-001": "CHAPTER TWENTY-ONE.", "II.21-002": "On modes.", "II.21-003": "Modern authors teach only two modes, yet enslaved to borrowed rules. Miss discovery’s benefits. Call chords arbitrary; leave judgment to us where mode alone should guide.", "II.21-004": "Mode lies within one sound’s octave; contains notes for melody and chords. Ancients saw melody alone. Error: melody depends wholly on mode’s fixed chords.", "II.21-005": "Two modes named from principal sound’s third. Third major or minor; mode major or minor. Names imply third accompanying fundamental sound.", "II.21-006": "First known mode from perfect diatonic system. C octave contains six other notes; alter intervals against C, change mode. Principal notes from C’s perfect chord: third mediant, fifth dominant. Sixth chord found better on mediant than fifth chord; unexplained reason: inversion of tonic’s perfect chord, thus mediant represents tonic. Dominant likewise takes perfect chord with major third. Seventh containing diminished fifth assigned only to dominant immediately before tonic. These two make perfect cadence. But authors omitted that diminished-fifth/tritone chords derive from seventh chord. Seventh precedes tonic perfect chord; derivatives must precede same or its derivatives. Experience knows; rules silent. Principle would clarify: such seventh or derivative demands tonic perfect chord or derivative next. Two chords contain every mode note except sixth, easily found by third’s nature. Also give chords before tonic/mediant. Need chords before dominant. Perfect chord preceded by seventh a fifth above; dominant normally perfect, added seventh leaves foundation intact. Thus dominant too preceded by seventh a fifth above. New chord’s third must be minor to preserve mode—same note as tonic dominant’s seventh or tonic’s fourth. New seventh chord contains mode’s sixth. Thus know octave intervals and their chords, derived by inversion from fundamentals. Minor differs only in minor third/sixth, with sixth qualifications in next book.", "II.21-009": "With this principle, no need for Masson’s* “bass rises semitone: minor sixth then fifth, or two major sixths,” etc. Different notes in different modes; rule fixes nothing without mode. His melodic/supposition dissonances often already belong to chord of surrounding consonances. Same chord includes consonance and dissonance; dissonance already implied, supposes nothing. Other similar mistakes omitted.", "II.21-010": "Rule writers copy others too deferentially. Borrowed material sometimes contradicts own good statements.", "II.21-011": "Ancients well described modal effects and control over harmony/melody, but never understood nature. Credited melody alone, confined to seven diatonic notes. Each note made principal supposedly gave different effect. Forgot model. Perfect system not worth imitation? They flattened B for fourth above F, copying consonances, yet ignored tonic approaches. C–D tone; C–B semitone. E tonic retained E–F semitone and D–E tone instead of sharpening F/D to match model, as B had been flattened. “These differences distinguish modes”? Experience proves error. Zarlin’s reflections contradict rules. Bass, he says,* foundation of all parts;* natural perfect cadence falls fifth. Examples include rising semitone to final; others also descending tone. Gather approaching notes: rising one dominant’s major third, falling one dominant’s fifth. Perfect ending: dominant then tonic. Dominant perfect chord contains major third/fifth. Thus tone from fifth to tonic, semitone from major third to tonic. Every mode needs these. Bass falling fifth cannot give perfect cadence unless upper parts rise semitone and fall tone. Piece must end perfect cadence on principal note, or soul unsatisfied. Absurd to propose modes incapable of this. Zarlin’s ban on minor third/sixth rising to octave follows same principle. Dominant needs major third, semitone below tonic octave, like B–C. Ancient D/E/G/A modes lack semitone. Melody alone guided them; harmony would prevent gross errors. Zarlin abler, but too deferential to Church plainchant, long established, hard to reform through custom/cost. Only keys matching perfect system suit harmony. Tasteless people steeped in misunderstood ancient rules vainly seek pleasing harmony on such chants. Yet this should occupy study and labor: music made only to praise God. Believer distressed, unable to unfold genius on great subject. Can pile correct chords to end; faultless music differs greatly from perfect music. Ancients enslaved to discoveries made melodies first, then harmonic rules from them. Should start with harmony—string division proves priority—then derive melody. Would give easier, more flowing church chant. Authentic/principal versus plagal/collateral distinction reveals 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": "Harmonic/arithmetic proportions fascinated them. Applied to octave what belonged only to fifth. Distinction proper to harmony used almost solely for melody.", "II.21-018": "Zarlin divides octave by fourth for new mode: merely relocates sounds of octave divided by fifth. Inversion. Principal and collateral same mode: same tonic, mediant, dominant. Difference only melodic.", "II.21-020": "His example:* principal first, collateral second. C means traditional “C sol ut,” tonic in both. E labeled b remains mediant; G labeled a remains dominant. Principal melody C-to-C; collateral G-to-G. Useless distinction: only voices limit melodic range; natural experience immediately teaches limits.", "II.21-021": "Zarlin’s example: principal mode and its collateral.", "II.21-022": "Fifth divided by lower note’s major/minor third gives genuinely different modes, not corresponding as previous pair. Mediants differ, thus sixths. Whole modulation difference there—not second/fourth/fifth/augmented seventh rising to octave, all unchanged. Still less in melodic range; intervals outside octave same as within. Plato says,* as Zarlin reports, melody born from harmony. Follow that and harmony gives modulation’s foundation, sure paths to claimed perfection. True modulation and all good harmony/beautiful melody come from tonic perfect chord, dominant chord with optional seventh, second-note seventh chord. Previous rules follow principle, equally strong 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 movement between modes or keys is possible.", "II.22-003": "Fundamental bass moves by consonant intervals. Only perfect chords sound above it. Each different bass sound offers different key: perfect chord belongs specifically to tonic, so each note establishes key. Consonances from first string divisions thus supply all chords, all melody, movement within one key, and movement between keys. Book III explains last point. No separate worry whether new key should be major or minor: key being left governs choice. Here mode is included under word key when major/minor difference is not heard on same tonic. But mode can change major to minor, or minor to major, with tonic unchanged. Example: cheerful subject becomes sad, or sad becomes cheerful. Most chaconnes and passacaglias do this; often two successive airs of same kind do too. Then mode changes, key does not. C remains tonic in major and minor alike. To avoid confused terms, say major key or minor key. Regarding melodic and harmonic movement, key changes only major to minor or minor to major. Regarding tonic, key can start on twenty-four different notes of chromatic system—but not freely anywhere within piece. Any chosen note may begin and end piece. Leaving it requires another note related to it or to notes of its chord. Chain of such connections must bring us back when piece concludes.", "II.23-001": "CHAPTER TWENTY-THREE.", "II.23-002": "On meter.", "II.23-003": "Meter alone can stir passions attributed to other musical elements. Without it, expression languid, fruitless. Natural to everyone; draws us to follow almost unwillingly. Only extraordinary accident removes this sensitivity. Descartes, page 58: animals could dance in time if trained or long accustomed; needs only natural effort and movement. Wrong to call people earless because unfamiliar with movement, or because dancing, singing, playing demands attention otherwise available for meter.", "II.23-004": "Meter derives from harmony’s principle: numbers 2, 3, 4 divide octave arithmetically and harmonically. Meter means equal movement; reduce to two beats. Interval between first two movements naturally repeats evenly. Walking, hand tapping, head movement prove it. Later movements match first two unless deliberately altered against nature. One note per beat, as plainchant, would make meter easy. Equal notes within beat also easy: equality natural. Larger counts give no new proportions, like chord ratios: 4, 6, 8, 10, 12, 15, 16, 20, etc. built from 2, 3, 5. Dots, syncopations, similar passages need long practice.", "II.23-006": "Ear training: pupil chooses even, somewhat slow pace. Sing or play one note per beat. Habit secure? Use 2, 4, 8, 16 notes per beat, pace unchanged. Stay at each step until effortless. Then 3 and 6 likewise. Dots and syncopations last. Afterward repeat faster or slower; feel first and last beats; mark with hand or foot. Teacher and pupil need patience.", "II.23-007": "Some may find advice misplaced; others welcome it. Many lose taste for music, blaming nature for lack that only habit remedies.", "II.23-008": "Understand opening numerals and note/rest values to read meter. De Brossard, Loullier, l’Affillard, others explain thoroughly. Almost any musician can teach them. No basic examples here; composition and accompaniment students assumed prepared. Yet many find numeral arrangements confusing. Use only 2, 3, 4 to distinguish every meter.", "II.23-009": "Only two-, three-, four-beat meters: only those numerals needed. Note values best show speed. Whole-note tempo slower than half; half slower than quarter; quarter slower than eighth; eighth slower than sixteenth. Therefore whole-note beat slower than half-note beat, and so onward. Immediately understandable.", "II.23-011": "Whole-note beat slowest: Adagio or Largo.", "II.23-012": "Half-note beat less slow; tender, graceful music. Andante or Gratioso.", "II.23-013": "Quarter-note beat lively, cheerful: Vivace or Allegro.", "II.23-014": "Eighth-note beat fastest: Presto. Three-beat meter may use sixteenth-note beat for Prestissimo. Two-beat meter expresses that speed with eighth-note beats. Values distinguish slow, less slow, lively, cheerful, very fast. Add only fitting expressive terms: tenderly, gracefully, detached, connected, louré.", "II.23-015": "Opening numeral gives beat count. Put beat-value note immediately before clef. Saves performers adding up notes within beat. Their total must equal beat value. Also place marker at staff position of key, as following examples show.", "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": "Slowly, lively, etc. unnecessary: opening note’s natural speed already tells. But sad/mournful belong to slow movement; tender/graceful to slow and cheerful; furious to very fast. Add expressive words when needed.", "II.23-034": "First four-beat measure: eight quarters + two halves + one whole = four wholes. Whole-note marker avoids calculation. Same for half-, quarter-, other note beats.", "II.23-035": "Beat ordinarily divides at most into four. Whole-note beat may hold four quarters; rarely eight eighths, though some suit melodic taste. Only occasional passages divide beat into eight; division mentally conceived. All notes totaling beat value must pass inside beat in proportion to values.", "II.23-036": "Faster movement, fewer subdivisions.", "II.23-037": "Three equal notes per beat? Put dotted note before clef equal to their combined value.", "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": "Also two, four, six unequal beats. Split each preceding beat in two; first always twice second. Show first two beat lengths with equivalent note signs.", "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": "Same numerals used for unequal beats and three equal notes per beat: confusion, wrong movement for air. Unequal beats require slight emphasis on second, fourth, sixth; brings special grace to first, third, fifth. Effect unlike equal-beat conducting. Four unequal beats share layout of two beats with three equal notes each. Six unequal share layout of three such beats. Two unequal share ordinary triple meter. Opening note signs distinguish them.", "II.23-073": "Six unequal beats little used: difficult to conduct, though suitable for particular expressions. Strike first. Lower hand second through wrist; lower farther third through arm. Raise arm for remaining beats as in four-beat meter.", "II.24-001": "CHAPTER TWENTY-FOUR.", "II.24-002": "Character of modes and keys.", "II.24-003": "Only two modes, as already said: major and minor. Each can start on every note of chromatic system. Thus twenty-four keys. Name key belongs to note serving as mode's principal note.", "II.24-004": "Major mode follows major third's nature. Minor mode follows minor third's nature. Semitones occupy different places within octave of each possible principal note, or tonic. These placements give different character to melodic and harmonic movement within each octave. Their character needs explanation.", "II.24-005": "Major mode on C, D, A: gladness, rejoicing. On F, B♭: storms, furies, similar subjects. On G, E: tender songs and cheerful songs alike. On D, A, E: grandeur and magnificence also.", "II.24-006": "Minor mode on D, G, B, E: gentleness, tenderness. On C, F: tenderness, laments. On F, B♭: mournful songs. Other keys little used. Experience gives surest knowledge of their character.", "II.25-001": "CHAPTER TWENTY-FIVE.", "II.25-002": "Use of new meter signs.", "II.25-003": "Skilled musicians may find new method unnecessary for themselves. Cannot deny great use for beginners. Numeral at piece's start gives beats per measure. Note before clef gives each beat's value. Explain this; beginners understand all meters and their differences at once. Many meters no longer bewilder: signs familiar, few, fixed in position. Want key of air? This note's pitch position declares it. Key may be major or minor. Put sharp above or below note for major; flat for minor.", "II.25-004": "Thus.\nMajor key.\nMinor key.", "II.25-005": "Sign saves counting sharps or flats after clefs to find notes sung as “si” or “fa.” Call sharp-marked note “ut”; flat-marked note “ré.” Movable singing syllables here, not fixed pitches. Then sol-fa all music without error, even where order and number of sharps or flats are not exactly observed. No more worry about number of ♯ or ♭ signs. No counting to find “si” or “fa.” Sharp versus flat gives needed knowledge.", "II.25-006": "Simple numerals give beat count; notes give beat values. Music master can confidently hand direction of piece to another. Need not fear performance fails for this reason. Such failure fairly common. New method avoids it more easily than Mr. Loullier's chronometer, neglected because difficult. Chronometer nevertheless ingenious: determines intended degrees of tempo with very precise accuracy.", "II.26-001": "CHAPTER TWENTY-SIX.", "II.26-002": "Measure count and particular movement for each air.", "II.26-003": "Numbers giving beats per measure also give measure counts for dance airs. Especially two and four, chief numbers. Cadence always felt at fourth measure, often second, rarely third.", "II.26-004": "These airs usually have two sections. Best section lengths: four, eight, twelve, sixteen measures. Five or six rare; three rarer. Four multiplied by any number works best here. 7, 9, 11, 13, 14, 15, 17, etc. produce no good effect.", "II.26-005": "Natural movements for each air listed next.", "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 use gavotte’s movement marking. French gigue often uses loure’s marking too, as in Prologue of opera Roland. Apply observations less to existing music, more to music yet unwritten.", "II.26-023": "Very slow airs: half-note beats in four-beat measures; whole-note beats in two- or three-beat measures.", "II.26-024": "Every character, every passion has particular movement. Taste governs more than rules.", "II.27-001": "CHAPTER TWENTY-SEVEN.", "II.27-002": "Setting words to music.", "II.27-003": "Beginners: prefer verse to prose, as customary. Verse has cadence. Melody must follow it. Cadence shows suitable movement and places of repose.", "II.27-004": "Rhythmically measured airs need lines with equal syllable or foot counts. Meaning should be somewhat complete at each line's end. Last syllable sounds at first instant of measure's first beat. Two qualifications: feminine rhyme may place penultimate syllable there instead. Avoid final cadence on closing syllables when line does not fully finish sentence's meaning.", "II.27-005": "EXAMPLE.", "II.27-006": "Chantez (“Sing”). Masculine rhyme.\nJe chante (“I sing”). Feminine rhyme.", "II.27-007": "Line-ending cadences help beginners. Cannot avoid perfect-cadence likeness before meaning ends? Disguise through bass. Use stepwise bass made from sounds in chords accompanying perfect cadence's fundamental bass. Or use irregular- or interrupted-cadence bass movement.", "II.27-008": "Recitative needs more caution than airs. Narrating stories or events: melody imitates speech, seems spoken rather than sung. Perfect cadence only where meaning finishes. Needs all good musician's abilities already described. Long syllables take suitable note lengths; short syllables shorter notes. Verbal rhythm should emerge as clearly as skilled spoken delivery. Equal-length notes may carry several long and short syllables, provided long syllables start beats, especially first beat.", "II.27-009": "Operas and many good musical works prove these points. Repeated seeing and hearing often forms taste more than rules.", "II.28-001": "CHAPTER TWENTY-EIGHT.", "II.28-002": "Design, imitation, fugue: their properties.", "II.28-003": "Words always carry expression—sad or cheerful. Melody, harmony, movement must convey it. No words? Composer imagines subject imposing similar constraint. Whole design rests on melody, harmony, movement. First choose key, mode, movement, melody suited to expression. Then fit harmony to melody written for subject. Movement stays unless words' meaning demands change. Key or mode changes introduce variety into melody and harmony. Thus overall design rests chiefly on melody's continuation and development.", "II.28-005": "Melody planned? Examine later words. Similar feelings needing similar expression? Same words repeated? Repetition desirable? These occasions suit imitation and fugue, both parts of design.", "II.28-006": "Similar feelings in several passages call for similar melody. Name: imitation. Only limits: no boredom through length or excessive repetition. Imitate part or whole melody, using sound judgment. Taste chooses pitches. Intended melodic likeness must remain recognizable.", "II.28-007": "Same words recur, or can recur? Good to give same melody each time. Produces more restricted imitation called fugue. Rules in Book III.", "II.28-008": "Imitation may stay in one part, usually called subject. Fugue must alternate through every part. Starting part seems to follow part that follows it. Chain continues from part to part.", "II.29-001": "CHAPTER TWENTY-NINE.", "II.29-002": "Intervals distinguished as major and minor; just or perfect; augmented and diminished.", "II.29-003": "Octave: source of all intervals. No alteration allowed in harmony.", "II.29-004": "Fifth and fourth come from octave division. Alterable, but lose original perfection. Names then show span only. Two minor thirds make diminished/false fifth; two major thirds make augmented fifth. Invert diminished fifth: augmented fourth, tritone. Invert augmented fifth: diminished fourth, unusable in harmony for reasons given elsewhere. Altered intervals no longer original selves; represent intervals causing imperfection.", "II.29-006": "Fifth division gives two thirds: major, minor. Both still thirds. Fifth/fourth alterations depart from origin; major/minor labels unsuitable. Use just/perfect, augmented, diminished. Original source makes fifth/fourth independent and perfect. Alteration terms refer to major/minor thirds forming all altered intervals.", "II.29-007": "Major third divides into major and minor tones. Difference inaudible. In practice one tone, one second, one seventh: tone makes second; inversion makes seventh. Custom nevertheless calls second/seventh major and minor.", "II.29-008": "Major tone divides into major/minor semitones. Relation unlike major/minor thirds: tone’s origin differs from semitones’, while both thirds arise from one fifth. Minor semitone separates major/minor thirds. Other interval altered by same semitone? Power comes from thirds, born with that difference. Fifth, fourth, tone lacked difference originally. So-called major/minor sevenths differ by this semitone; same with fifth/diminished fifth. Yet nobody calls diminished fifth minor fifth, augmented fifth major fifth. Major/minor properly belongs to thirds and direct dependents: inverted sixths, modes governed by thirds. Altered fifth/fourth called augmented/diminished, signaling improper proportion. They did not originate from thirds; thirds originated from them.", "II.29-010": "Within octave under proper modulation, fifth/fourth/seventh/second fixed; third/sixth movable. Only latter deserve major/minor. Seventh/second should use fifth/fourth terminology. Seventh changes in minor keys only descending; sixth changes ascending. Changes adapt movement toward tonic or dominant. Second never changes. Second and seventh invert each other; property of one must belong to other.", "II.29-011": "Intervals called major/minor can also be augmented/diminished.", "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": "Example: four kinds of third and sixth. No other interval has four.", "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": "Ordinary seventh called minor, augmented seventh called major? No augmented form left as for third/sixth. Diminished second called minor? No diminished form left. Seventh/second have three kinds like fifth/fourth; use same names. Major/minor wrongly borrows third/sixth qualities. Brossard justifies major for true augmented seventh by inventing another augmented seventh, B♭–A♯. Thus:*", "II.29-020": "Thus.*", "II.29-021": "He admits interval unused, often confused with octave. Examine only to expose error. Says diminished second is C–C♯.* No relation to proposed B♭–A♯ augmented seventh. Inversions must use same notes: see previous example, Book I chapter V table. Alter notes only through sharp/flat? Basic interval name stays; add fitting major/minor/augmented/diminished. C–C♯ thus augmented unison. B♭–A♯ larger than diminished octave—indeed octave, since same keyboard key on organ and most instruments. Possible objections omitted for brevity; easily solved.", "II.29-022": "* See Settima in his dictionary.", "II.29-023": "* See Seconda.", "II.29-025": "His seventh-chord explanation and resolution no better. Does not specify augmented seventh,* but gives this usage.", "II.29-026": "7, 6, 4, 2, 1.", "II.29-027": "Certainly did not consult ear: chord worthless. Flat added to 6, or minor-key restriction, would excuse somewhat. Rule without exceptions must be general. Fifth instead of sixth needed to make this one even somewhat general.", "II.29-028": "Some still want major/minor sevenths and seconds, allowed in practice. But dissonance classification follows thirds: major from major third, minor from minor third; each follows source’s properties. How call interval major when following minor third? Seventh always descends unless augmented. So-called major seventh equals our augmented interval: choose. Both ratio 8:15. Augmented rises like major third forming it—tonic dominant’s major third in fundamental harmony. So-called major descends like minor third. Ninth almost always implied with latter seventh; seventh then represents only fifth fundamentally. Why not call basic seventh just/perfect dissonance, words confined to dissonance, then diminished or augmented? No other proper distinction.", "II.29-029": "* See Settima.", "II.29-031": "Fifth/fourth confirm problem. Seventh chord on second note of minor key naturally has diminished fifth. Does lower sound rise semitone, as usual diminished fifth from major third? Instead stays, or rather falls fifth, while upper falls. Seventh governs chord, not diminished fifth. Tritone in small-sixth on minor key’s sixth note: must rise? No, stays. Book I explained: these intervals replace naturally expected ones, tolerated for modulation. Still never called minor fifth or major fourth. Such adjectives forbidden for inherently just/perfect intervals. Cannot grant them to seventh made major only through modulation, unless granted to all intervals.", "II.29-032": "Thirds govern modulation. Fifth/fourth/seventh may become major/minor in explained sense, but merely follow modulation, determine nothing. Major/minor mode labels should belong only to intervals governing order and progression.", "II.29-033": "Same applies to second and ninth. Second inverts seventh; ninth repeats second, or fundamentally represents seventh.", "II.29-034": "Eleventh called fourth never changes 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": "Seven diatonic sounds,* seven successive natural voice steps: C D E F G A B. Called scale. More notes? Repeat first after last, same order. Repeated forms of same notes called octaves.", "III.01-007": "Add first note’s octave at end: C D E F G A B C. Learn descent equally: C B A G F E D C.", "III.01-008": "Practice other starting/ending notes, though contrary to diatonic order. Add further octave copies. G ascent: G A B C D E F G. Descent: G F E D C B A G. Same for others.", "III.01-009": "Intervals.", "III.01-010": "Know scale upward/downward from any start. Also count distances between notes. For now upward only.", "III.01-011": "* See the glossary.", "III.01-012": "Distances make all musical intervals. Arithmetic numbers give names:", "III.01-013": "2 Second; 3 Third; 4 Fourth; 5 Fifth; 6 Sixth; 7 Seventh; 8 Octave.", "III.01-014": "Numbers above names become shorthand. Remember 2 second, 3 third, 4 fourth, through 8 octave.", "III.01-015": "Choose first note, degree 1. Count through destination; note count names interval. From C: D second, E third, F fourth, G fifth. From D: E second, B sixth, C seventh. Practice every starting note until instant: E fifth of A; B fifth of E; D fifth of G. Use following scale.", "III.01-016": "Circular scale—interval distances", "III.01-017": "C=1; follow circle to D=2, E=3, onward to octave C=8. Octave repeats name. D=1 instead: E=2, F=3, etc. Numbers show intervals from chosen 1; connecting lines form circle 1 through 8.", "III.01-019": "Unqualified third/fourth/etc. always counted upward from proposed first degree, assumed lowest note.", "III.01-020": "Practice downward equally. Fourth below C is G; fourth above G is C. Simple, useful.", "III.01-021": "Inversion of intervals.", "III.01-022": "Octave endpoints essentially same note; bound all scale intervals. Other note compared with both Cs seems unable to yield different intervals. Yet lower C below it, upper C above it. Difference needs explanation.", "III.01-023": "Interval inversion—scale and numbers", "III.01-024": "D second above lower C; upper C seventh above D. E third above lower C; upper C sixth above E. F fourth above lower C; upper C fifth above F. G fifth from lower C, fourth from upper C. One interval generates another. Any note at both scale ends gives same results: second becomes seventh to octave, etc.", "III.01-026": "First degree and octave inseparable in thought. Compare note with first degree, then octave. First interval fundamental/principal; second inverted. C–E then E–C reverses comparison. Numbers: 1 and 8 same note; 1–3 then 3–8.", "III.01-027": "Only three fundamental intervals to remember: 3, 5, 7. Chart first notes = 1; thirds, fifths, sevenths numbered accordingly. Know these from any of seven starting notes. Add that starting note’s octave: third → sixth, fifth → fourth, seventh → second. Last three invert first 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": "Do not rush. Own experience confirming truth makes rest easier.", "III.01-030": "The staff: the lines on which notes are placed.", "III.01-031": "Note signs show duration. Positions on/between five horizontal lines show degrees.", "III.01-032": "STAFF—five numbered lines", "III.01-033": "Five lines together: staff. Each line: line/rule. Gaps: spaces. Bottom first, top fifth.", "III.01-034": "Clefs.", "III.01-035": "Three clefs. Signs and named notes follow.", "III.01-036": "F clef: two alternative signs. C clef. G clef.", "III.01-037": "Clef lies on crossing line, gives line name. One clef at staff start. May replace anywhere, always on line. Latest clef names its line.", "III.01-038": "F clef lowest. Usually line 4 or 3.", "III.01-039": "C clef’s C fifth above F clef’s F. Any line except 5.", "III.01-040": "G clef’s G fifth above C clef’s C. Usually line 1 or 2.", "III.01-041": "Note on clef line takes clef name. Until note-shape explanation, use O heads on lines/spaces. Count scale from clef. First-to-fifth line ascends; fifth-to-first descends. Spaces named too. No mistake if followed. See example.", "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": "First note may lie on any line/space. Count from clef. Need instant naming to avoid distraction while composing. Choose suitable clef position; memorize lines/spaces. F clef line 4: line 3 D, line 2 B, line 1 G, line 5 A. Space above F is G, below E; others likewise.", "III.01-047": "EXAMPLE.", "III.01-048": "Lines and spaces—note names", "III.01-049": "Names mastered? Move clef to another position, repeat observations. Do same with other clefs.", "III.01-050": "Add lines above/below five ordinary lines; same note order.", "III.01-051": "Parts.", "III.01-052": "Harmony unites agreeing different sounds. Each producing voice/instrument called part. Parts also have particular names, sometimes unstated; clef kind/position reveals them.", "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": "First two parts only female voices. Higher sing first upper part; lower sing 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": "Six vocal parts have limits marked by notes. Use intervals between endpoints. Guides permit rare extensions. Keep voices near middle; extremes nearly always force them.", "III.01-077": "Each instrument different range. Violin limited octave below clef, virtually unlimited above. Without personal experience, do not exceed printed note/guide. Ordinary bass ranges marked; only bass viol reaches lowest sound. Other instrument ranges omitted. Violin can play all music generally, so others dispensable; their players can tell composers needed facts.", "III.01-078": "Unison.", "III.01-079": "UNISONS—eight clefs, one sound", "III.01-080": "Unisons: two notes same degree, one note repeated. To locate parts while keeping higher above lower, put same sounding note in every part. All unison.", "III.01-081": "Parts distinguished by different sounds, not quantity. All unison parts represent one. Hence unison forbidden in composition. Beginners may substitute for octave until more capable.", "III.01-082": "Meter.", "III.01-083": "Simplest composition of meter: natural repeated movements, always equal, as walking shows when nature unaltered.", "III.01-084": "Each walking step=beat. Walk faster/slower; meter likewise.", "III.01-085": "Perpendicular barlines divide measures. Each contains 2,3,4 beats. Hand/foot marks: first strike/down, last up, middle right/left.", "III.01-086": "Barlines separating measures", "III.01-087": "First beat good/principal; others bad. In four beats, first and third equally good.", "III.01-088": "Use numbers 2,3,4 for beat count. Apparently rejected for simplicity, replaced with ambiguous signs.", "III.01-089": "C marks four-beat meter.", "III.01-090": "A slashed C marks two-beat meter, etc.", "III.01-091": "Art abstract enough; no added obscurity needed. Existing music full of ambiguous signs: learn properties to judge it, not as teaching basis. Other authors abundant; omit here. See Book II chapter XXIII. Master two beats, other movements easily learned through aptitude/taste.", "III.01-092": "Meter sign immediately after clef, except key sharps/flats come first. Mid-air movement change: new sign at beginning of affected measure.", "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 may beam like eighths; value then halves.", "III.01-099": "Shapes named above. Values below: whole=two halves; half=two quarters; quarter=two eighths; onward. Reverse: thirty-second half of sixteenth, sixteenth half of eighth. Whole replaced by 2 halves,4 quarters,8 eighths,16 sixteenths,32 thirty-seconds. Whole likewise replaces any equal total. Mix any values if every beat complete.", "III.01-100": "Signs below notes: rests. Silence part or delay start by eighth/quarter beat, half/full measure, any desired beats/measures. Use rests instead of notes.", "III.01-101": "Bars separate measures; sign gives beat count. Fill with notes/rests. Whole usually measure, half half-measure, but either may equal one beat. Others proportional. Whole always 2 halves,4 quarters,8 eighths. Rests normally match note duration. Whole-measure rests independent: two/three/four beats, any beat notes except whole. Two-beat measure may hold two wholes/halves/quarters/eighths if each is beat. Beat may contain 2,3,4,6,8 equal notes or mixed values totaling beat. More notes, smaller values. Whole cannot be less than one beat; others proportional.", "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": "Quarter/eighth can replace half; triple meter also sixteenth. Choices indicate slowness/speed. Book II chapter XXIII.", "III.01-109": "Numbers above mark beats 1,2,3,4. Replace beat note with any notes/rests equaling it. May begin/continue with other values if beat total retained.", "III.01-110": "The dot and the tie.", "III.01-111": "Dot right of note adds half value. Equals same-pitch note plus half-length note. Separate second note means new attack; dot avoids it. Or tie notes with semicircle endpoints touching each.", "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": "Second divides into tone/semitone. E–F and B–C semitones; other adjacent scale pairs whole tones.", "III.01-120": "Semitone smallest practical interval. Not naturally between every pair, but signs raising/lowering semitone can create it. Same signs can make whole tone E–F or B–C.", "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": "Sharp raises semitone; flat lowers. Natural sometimes serves sharp’s purpose; also cancels prior sharp/flat, restoring natural note.", "III.01-124": "Signs do not change note names. Singing learners call sharpened notes “si,” flattened “fa”: movable syllables, not fixed pitches. Diatonic movement matches scale’s “si” and “fa.” Composer needs understanding more than vocal practice. Attend to intervals and semitone alterations by ♯ ♮ ♭.", "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♯ A raises F: E–F♯ equals D–E, both tones. F♯–G semitone. D E F♯ G matches G A B C, B labeled D. B♭ C lowers B: descending C–B♭ tone, B♭–A semitone. C B♭ A G matches G F E D. Naturals at second F B and second B D restore natural order.", "III.01-130": "Same-named intervals differing semitone: major/minor or augmented/diminished. C–E third major, semitone larger than minor D–F. E–C sixth minor, semitone smaller than F–D. Others likewise. More explanation later.", "III.01-131": "Sharps/flats usually show distinctions. Sharp on lower note F: usually minor interval; upper G: major. Flat lower H: major; upper J: minor. Augmented relates major; diminished minor.", "III.01-132": "EXAMPLE.", "III.01-133": "Major, minor, diminished, and augmented intervals", "III.01-134": "Compare top note with opposite bass note for labeled major/minor interval.", "III.01-135": "♯ ♮ ♭ above/below bass never alter bass itself. Indicate major/minor intervals, explained later.", "III.01-136": "Compound intervals.", "III.01-137": "Octave repeats first degree; higher notes repeat octave’s contents. Names suffice; doubled/tripled intervals need no full count. Low C below F clef to high G above G clef:19 degrees, still fifth by name. G above C enough. Wider spacing matters only to keep parts above bass and in natural ranges already shown.", "III.01-139": "EXAMPLE.", "III.01-140": "Simple and compound octaves, fifths, and thirds", "III.01-141": "Other parts compared with lowest. Here simple/double/triple/quadruple octaves, fifths, thirds; could name fifteenths, twenty-seconds, etc. Enough now: octave C, fifth G, third E. Rest unnecessary.", "III.02-001": "CHAPTER TWO", "III.02-002": "Fundamental bass.", "III.02-003": "Main knot in composition—harmony or melody, especially now—is fundamental bass. Here bass moves by consonant intervals: third, fourth, fifth, sixth. Each note rises or falls only by these. Prefer smaller moves. Want rise by sixth? Better fall by third. Want fall by sixth? Better rise by third. Rising third equals falling sixth; rising sixth equals falling third; rising fifth equals falling fourth; rising fourth equals falling fifth. Remember each interval in one direction only; other direction gives equivalent result.", "III.02-004": "EXAMPLE.", "III.02-005": "Bass progressions—up or down", "III.02-006": "Note name alone determines intended interval, as already said. Third of C is E. In this bass progression, E above or below C makes no difference. Same for other intervals. Remember: 'rise third, fourth, fifth, sixth' also means 'fall sixth, fifth, fourth, third.' 'Fall third' also means 'rise sixth,' and so on. Applies only to bass progression.", "III.02-007": "Octave excluded from consonant bass-movement list. Octave merely repeats 1. Staying on 1 equals rising or falling octave. Sometimes bass must fall octave to free other parts, especially to keep them above bass, as required.", "III.03-001": "CHAPTER THREE.", "III.03-002": "Perfect chord begins four-part composition.", "III.03-003": "Chord: several sounds arranged together. Each sound marked by note in one intended part.", "III.03-004": "Only perfect chord needed now. Bass takes one note. Other parts take its third, fifth, octave.", "III.03-005": "Use chapter I scale to find intervals from any chosen bass note. Bass represented by 1. Thus:", "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": "Write 1 or 8: octave has same note name as chosen bass. Count rightward, following numbers around scale circles.", "III.03-008": "Third, fifth, octave may go in any part. Third above fifth or octave allowed; fifth above octave allowed. All must remain above bass. Lower bass as far as desired to free other parts. With growing skill, keep each part in natural range: tenor above bass; haute-contre above fundamental; top part above haute-contre.", "III.04-001": "CHAPTER FOUR.", "III.04-002": "On the succession of chords.", "III.04-003": "Bass moves by consonant intervals; upper parts by diatonic steps. C goes only to neighboring D or B, or stays still, often. Same for other notes. Procedure follows.", "III.04-005": "1. Choose tonic: bass begins and ends there. Governs notes in octave. Tonic C: all parts use C D E F G A B, no sharps or flats.", "III.04-006": "Bass C; perfect chord above. Note which part has octave, fifth, third.", "III.04-007": "2. Bass rises third A or fourth B: former octave part, here tenor, takes new fifth.", "III.04-008": "Haute-contre had C’s third; takes new bass note’s octave.", "III.04-009": "Top part had C’s fifth; takes new bass note’s third.", "III.04-010": "3. Bass rises fifth C or sixth D: tenor octave→third; haute-contre third→fifth; top fifth→octave.", "III.04-011": "4. Avoid memorizing every route: upper part can stay, rise step, fall step. If staying gives third, fifth, or octave above new bass, must stay. Otherwise one diatonic step up or down finds chord interval, whatever bass route.", "III.04-012": "Two parts meet, chord interval missing? One had both upward and downward choice. Reverse its movement. Bass rises fourth: former fifth can fall to octave or rise to third; here rise. Bass rises fifth: former octave must fall to third above 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 changes: 8–5, 8–3 at E F; 3–8, 3–5 at G H; 5–3, 5–8 at J L. Bass rises third A/fourth B: 8→5 E, 5→3 J, 3→8 G. Bass rises fifth C/sixth D: 8→3 F, 3→5 H, 5→8 L. Present interval plus bass route determines next interval. Continue to end. Cannot handle all parts together? Work each separately.", "III.04-019": "Three upper parts always contain third, fifth, octave. First chord: assign freely. Later: obey each interval’s prescribed movement. Rule applies within measures and across barlines. Same bass progression, same upper relationships. A in first measure and final pair requires same treatment; likewise B C D above/below bass. Do not seek pattern in one fixed voice: chord succession changes its role. Whichever part holds third, fifth, octave follows rule for that interval.", "III.04-020": "First bass pair arranged? Continue second-to-third, third-to-fourth, fourth-to-fifth, through end. Each bass move uses prescribed consonant interval. Each interval determines upper movement.", "III.04-021": "1 above/below every bass note shows each chord contains only 1 3 5 8.", "III.04-023": "Compose bass freely, beginning and ending C. Any consonant movements allowed. C D E F G A B unchanged by sharps/flats. Avoid B only in bass, as examples do. Arrange first perfect chord; each upper part follows bass-determined route for third, fifth, octave.", "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": "Beginners always use two-beat meter. Half or quarter may fill each beat; examples use whole.", "III.04-027": "Rise sixth equals fall third; rise fourth equals fall fifth.", "III.04-028": "Bass shape depends on imagination and taste. First follow this bass, compare upper parts with ours. Then invent freely. Final bass note preceded by fourth below or fifth above: G before final C.", "III.05-001": "CHAPTER FIVE.", "III.05-002": "Rules to observe.", "III.05-003": "1. Never two octaves or two fifths in succession. Figures reveal fault: no 8 8 or 5 5 in same part. Present method avoids fault without special attention. Exception: four-part piece may use both successions when involved parts move oppositely. One rises, other falls.", "III.05-004": "Examples: two octaves and two fifths in contrary motion.", "III.05-005": "8. 8. 5. 5. 8. 8. 5. 5.", "III.05-006": "2. Avoid part rising from minor third to octave. Earlier examples could not show this: major and minor not yet discussed. Coming discussion of dissonance makes us follow rule without separate attention.", "III.06-001": "CHAPTER SIX.", "III.06-002": "On the seventh chord.", "III.06-003": "FIRST ARTICLE.", "III.06-004": "Consonant chord intervals and bass movements understood? Examine interval relations. Ignore octave: repetition of bass 1. Perfect chord has three sounds, 1 3 5. Third from 1 to 3; third from 3 to 5. Add same distance again: 1 3 5 7. Third from 5 to 7. Seventh chord differs only by added seventh.", "III.06-005": "Added interval dissonant; whole chord called dissonant. May add octave for five parts or easier diatonic upper movement. Octave often replaces fifth; either acceptable. Let parts follow natural stepwise course. Third scarcely removable.", "III.06-006": "For now, seventh chord only on bass notes approached and left by ascending fourth or descending fifth.", "III.06-007": "Seventh needs consonant preparation and resolution. Its part makes third before and after. Preparing third remains same pitch or staff line as seventh. Resolving third reached by descending diatonic step.", "III.06-008": "First seventh on first beat; prepare on preceding second beat. First means not immediately preceded by another seventh. After entering seventh chord by rising fourth or falling fifth, bass keeps these movements until tonic C. Seventh chords on every note except C and F. C as tonic needs perfect chord. F seventh would force move to forbidden bass B. E also excluded: would need B before it. Thus only A, D, G carry sevenths now.", "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": "Upper parts: seventh always between thirds, 3 7 3. First seventh prepared on second beat or second measure-note, at C.", "III.06-012": "3 7 3", "III.06-013": "Seventh must fall to third. This disturbs part normally rising fifth to third when bass rises fourth. That part can instead fall to octave; must do so when seventh present. Seventh’s movement fixed; change fifth at A. Earlier rule: octave sometimes replaces fifth to keep upper parts diatonic. Chapter IV: if two parts meet on same note, change part able to reach another chord interval up or down.", "III.06-014": "Part making fifth may make another fifth if moving opposite bass, as preceding chapter allowed. Makes fuller chords, restores natural ranges, or improves melody. Guide B shows avoided octave already in other part at L. Choice depends on composer’s taste when melody leads rather than harmony.", "III.06-015": "SECOND ARTICLE.", "III.06-016": "Seventh first dissonance, source of all others. Every consonance may prepare and resolve it. Other resolutions derive from preceding one; discussion waits. Fifth preparation: bass descends third. Octave preparation: bass rises diatonic step. With bass rising, all upper parts descend except seventh-bearing part. It stays for preparation, then descends to third.", "III.06-017": "Sixth also prepares seventh, but not discussed yet. Only fundamental harmony now: bass, third, fifth, seventh—1 3 5 7.", "III.06-018": "Article I bass progression changes only at first seventh. Only first may have fifth or octave preparation. Later sevenths always between two thirds. Every preparation still resolves to 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": "Now seventh chords on E, A, D, G. Bass may fall third for fifth preparation, rise second for octave preparation. At C two parts rise octave together to restore ranges. Allowed only without consecutive fifths or octaves between them. Bass-versus-part rules also apply to any pair. Earlier arrangement made explicit warning unnecessary.", "III.06-025": "Two parts may rise octave; single part certainly may. Bass J rises instead of staying. Upper part preparing dissonance cannot: must hold same pitch.", "III.06-026": "Ignore F sharp for now. Beginners need no sharps or flats until better instructed.", "III.06-027": "Bass exceeds range; tenor above haute-contre. Reason: preserve diatonic upper-part order, chief obligation here.", "III.06-028": "All remaining teaching depends on first principles. Greater mastery, easier understanding.", "III.07-001": "CHAPTER SEVEN.", "III.07-002": "Dissonance remarks.", "III.07-003": "Dissonance eases composition, does not obstruct it. Bass rises second, fourth, or sixth: some upper note, consonant with first bass, can stay unchanged and become seventh over second bass. Use whenever possible. Often avoids rise from minor third to octave; by inversion, minor sixth to octave, discussed elsewhere. But next bass note must provide third that resolves seventh. Otherwise use perfect chord.", "III.07-004": "EXAMPLE.", "III.07-005": "A. B. C. D.", "III.07-006": "No seventh over B when next bass is C. Fifth over A prepares it, but C's third cannot resolve it. Replace C with D: seventh over B now resolves naturally to D's third. Same elsewhere. Remember: tonic acting as tonic cannot bear seventh chord. Only fundamental harmony discussed here.", "III.08-001": "CHAPTER EIGHT.", "III.08-002": "Key and mode.", "III.08-003": "Tonic: bass's beginning and ending note. Determines progression of other notes in its octave. Choose C tonic: no sharp or flat may alter C D E F G A B without destroying premise. Scale shows these within C's octave. Word ton normally names interval, such as third. Here chiefly names key based on chosen note. Note names key; therefore called tonic. Determines all diatonic intervals—tones and semitones—between consecutive notes up to octave. Such proceeding called modulation. Now distinguish mode from key.", "III.08-004": "Mode lies in tonic's third. Third only major or minor; mode likewise only two kinds. Usually include mode within word key: major key, minor key.", "III.08-005": "C with major third: say C major, not key C, mode major. C with minor third: C minor. All modulation has these two kinds, determined solely by tonic's third. C octave represents all usable major keys. Major/minor difference small; learn major fully before examining difference.", "III.08-006": "C knowledge must serve every key. Hence use names for scale positions, not only pitches. Tonic can be C, D, E, F, G, etc. Choose tonic; other notes defined relative to it. Tonic always first. Second, third, fourth, fifth only mean positions compared with that tonic. In C: D second, E third, F fourth, etc.", "III.08-008": "Names in every key, shown 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": "Besides tonic, three special names: mediant, dominant, leading note. First two complete tonic's perfect chord. Also have properties distinguishing them from others.", "III.08-011": "Mediant divides tonic-to-dominant into two thirds; lies in middle. Also decides mode. Major third: major mode. Minor third: minor mode. This third already given that property.", "III.08-012": "Tonic dominant always immediately precedes tonic at endings. Earlier examples: G, dominant of C, preceded C wherever heard, especially at end.", "III.08-013": "Leading note never heard in any part without tonic immediately following. Makes key perceptible. In C: E mediant, G dominant, B leading note. Every key gives same intervals from tonic as E G B from C. Sole exception: minor-key mediant forms minor third, not major third shown here.", "III.09-001": "CHAPTER NINE.", "III.09-002": "How to proceed harmonically when the bass moves diatonically.", "III.09-003": "C octave is model. Major/minor intervals: thirds, sixths. E makes C’s major third. See Book IV chapter II list.", "III.09-004": "Perfect-chord notes may count as tonics; seventh-chord notes as dominants. Tonic dominant always major third; ordinary dominants often minor third. In C only C tonic; only C may take perfect chord.", "III.09-005": "Only G tonic dominant in C; only G takes seventh with major third.", "III.09-006": "Essentially only perfect and seventh chords; all others made from them. Present bass progression fits these forms. Change bass progression: same sounds, altered arrangement by octave displacement. New names distinguish derivatives.", "III.09-007": "List of consonant chords derived from the perfect chord.", "III.09-008": "1=bass. Other numbers give distance. 8 10 12 repeat 1 3 5. Octave repetition explains all.", "III.09-009": "Reduce numbers, preserve distances: 4 5 6→1 2 3; 6 8 10 12→1 3 5 7. First number reduced to unity. Unity represents fundamental perfect/seventh-chord bass, source of all consonant/dissonant chords.", "III.09-010": "Octave omitted: repeats bass 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": "Tonic lends perfect chord only to mediant/dominant: sixth over mediant, sixth–fourth over dominant. Know these notes, know chords. Dominant prefers perfect to sixth–fourth; seventh especially before tonic. Seventh merely added sound; may remove, leaving perfect chord. But know what removed and why. Seventh chord generates all dissonant chords. Know construction and following chord; both govern derivatives.", "III.09-020": "Dominant seventh before tonic also means before tonic-chord derivatives on mediant or dominant. Dominant may change seventh to sixth–fourth if duration permits, composer chooses. Tonic derivatives share tonic’s preparation; dominant derivatives must immediately precede tonic or derivatives. Study construction, progression, arrangement. Bass notes moved above, upper notes below: new names reveal bass position. Mediant/dominant represent tonic through inverted perfect chord. Likewise dominant-seventh notes before tonic harmony must carry its seventh-chord derivatives. In C: G B D F before C or E, other three accompany chosen bass. G omitted as destination here because G B D F is starting object.", "III.09-021": "Dominant takes perfect or seventh; seventh contains perfect. Both approached same. Every seventh-bearing note gets dominant, fifth above/fourth below. G’s dominant D. Dominant means preceding note fourth above/fifth below; takes seventh. D’s chord D F A C follows G B D F pattern. Any D F A C before G must carry that set. Any G B D F before C likewise. Dissonances form chain of dominants. Foundation easy; relation to varied bass notes difficult, demanding all attention. Restrict to octave: know consonant approach, since dissonant approach same. Use scale intervals, not pitch names, to cover every key. Once only tonic identification remains, difficulties overcome.", "III.09-023": "Tonic always perfect; mediant sixth; dominant perfect unless immediately before tonic. Then add F seventh to G B D.", "III.09-024": "Second note between tonic/mediant in diatonic bass: only small-sixth D F G B.", "III.09-025": "Leading note rises tonic: diminished-fifth B D F G. Descends to note outside tonic chord: treat as dominant’s mediant, third of dominant. Takes sixth B D G, inversion of G B D.", "III.09-027": "Fourth rises dominant: analogous chord to leading note rising tonic. Both destinations approached alike. G dominates C; D dominates G. F in C takes great-sixth F A C D, inversion of D F A C.", "III.09-028": "Great-sixth differs from diminished-fifth chord only by perfect versus diminished fifth. Underlying third G–B major, D–F minor. Otherwise same arrangement; both on third of fundamental seventh-chord bass. Later explain naming distinction in derivatives, not fundamentals.", "III.09-029": "Fourth descends mediant: tritone F G B D.", "III.09-030": "Sixth before dominant/mediant: small-sixth A C D F, inversion of D seventh; D dominates G. Same principle as second’s small-sixth before tonic/mediant.", "III.09-031": "Compare rules with chord list. Dominant may count as tonic: both approached with same chords. In diatonic bass, identify derivatives of tonic/dominant chords and following notes. Same bass note may belong to two fundamental chords; next note decides choice. Keep full three/four-note perfect/seventh set accompanying bass above.", "III.10-001": "CHAPTER TEN.", "III.10-002": "Continuo bass.", "III.10-003": "Do not confuse present diatonic bass movement with consonant movement in earlier perfect- and seventh-chord examples. Those two chords are fundamental. Later examples gain fundamental bass below them: only perfect or seventh chords on its notes. Ordinary bass, called continuo, carries every chord kind. Whole together forms perfect harmony. Fundamental bass checks all our works. Different chords arise only from movement opposed to fundamental bass, as just explained. Compared with either bass, chords remain same in substance. Difference comes from freedom to place any fundamental-chord note in bass. Complete set of notes unchanged; progression assigned within fundamental chords also unchanged.", "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": "Consonant bass notes—tonic, mediant, dominant—move freely within key. Here only C D E F G A B; no error from foreign notes.", "III.11-004": "Dissonant bass movement restricted: dominant seventh and derivatives, anything outside perfect chord and derivatives. Dissonant note governs another. Chord not seventh? Derived from seventh. Find foundation; following chord certain whatever bass note.", "III.11-006": "Dissonant chord has adjacent pair: 3 4 [F G], 5 6 [C D]. Seventh with bass octave raised: 7 8 [F G]. Second: 1 2 [C D]. Higher note/number becomes fundamental bass; lower becomes its seventh. Reduces to 1 3 5 7, page 202. Fundamental G demands C next; actual bass may use C-chord member, perfect or seventh in another key. Fundamental D demands G or derivatives. Seventh-chord fundamental always descends fifth.", "III.11-007": "Bass violating succession must change. Check scale-note chords and movements, or fundamental bass proof. Only perfect/seventh fundamentals; seventh root falls fifth. Same rule for checking and composing. Exceptions—interrupted/irregular cadences—wait.", "III.11-008": "Chord leading to perfect harmony relates to following chord, not preceding. Usually tonic↔dominant; treat dominant as tonic. Know diatonic approach to one, know other. General rules follow.", "III.11-010": "1. Bass rises tone/semitone to perfect chord: 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 bass differs; upper sounds same for tone or semitone rise. Composer may choose either, even foreign semitone. Dominant treated as tonic accepts tonic approaches. Sharp on fourth creates leading note. Normal distinction: whole tone rises to dominant, semitone to tonic. Semitone may give dominant tonic attributes; original key can still continue afterward. Perfect chord permits free onward movement.", "III.11-015": "2. Bass descends to perfect chord: small-sixth chord.", "III.11-016": "EXAMPLE.", "III.11-017": "Small-sixth chord; mediant guide notes.", "III.11-018": "Guides: bass may go to each destination’s mediant; harmony unchanged. Mediants then take sixth chords.", "III.11-019": "Here second note cannot be distinguished, nor tonic from sixth note or dominant. Same perfect-chord approaches obscure tonic/dominant in major. Minor differs: sixth only semitone above dominant; second whole tone above tonic. Dominant major third, minor tonic minor third. Uncertain major dominant? Treat as tonic, adapt preceding chords. Following notes reveal true role.", "III.11-020": "EXAMPLE.", "III.11-021": "Bass progressions, references A, B, C, D, F, G.", "III.11-022": "Opening→A leaves tonic/dominant uncertain; chords same either way. A→B reveals tonic, so A dominant. B→C uncertain until D reveals C dominant. F similarly reveals G dominant. Note below tonic semitone away; below dominant whole tone away.", "III.11-024": "Minor descent toward dominant, or at least sixth, may put whole tone below tonic. Tonic’s minor third identifies it; dominant always major third.", "III.11-025": "3. Bass note third above/below tonic or dominant, leading there: sixth chord.", "III.11-026": "EXAMPLE.", "III.11-027": "Sixth chords leading to tonic or dominant.", "III.11-028": "Perfect-chord destinations B D G L require sixth chords on A C F J.", "III.11-029": "4. Mediant sixth represents tonic perfect chord. Fourth descending mediant takes tritone. Great-sixth also possible; explained elsewhere.", "III.11-030": "EXAMPLE.", "III.11-031": "Tritone on the fourth note descending to the mediant.", "III.11-032": "Five examples show rearranged fundamental sounds. Fourth→dominant: great sixth. Fourth→mediant representing tonic: tritone. Leading note→tonic: diminished fifth. Second/sixth→tonic/dominant: small sixth. All derive from seventh roots governing next note. Fundamental bass under octave example clarifies. Leading note only such when rising tonic; descending, dominant’s mediant. Treat dominant as tonic to avoid error.", "III.11-033": "General example of the octave, ascending and descending.", "III.11-034": "General octave example—five parts.", "III.11-035": "Fundamental bass only proves perfect/seventh harmony and natural root progression. Do not enforce strict voice-leading between it and parts. Check only figured chords. Actual sound succession relates to continuo bass; diatonic bass now subject.", "III.11-036": "1. J–L, B–M ascending and N–K, O–U descending all relate to dominant/tonic, only natural perfect-chord notes. Notes third above act as mediants when descending; tonic mediant always retains role. Perfect chord preceded by governing dissonance. Small/great sixth, diminished fifth, tritone all inverted fundamental sevenths. Second’s small sixth, leading note’s diminished fifth, fourth’s tritone derive from dominant seventh D, then tonic. Fourth’s great sixth and sixth’s small sixth derive from second-note seventh A/C, then tonic dominant. Plain sixth on mediant/sixth/leading note because third above/below next tonic/dominant.", "III.11-038": "2. Sixth-note B seems to need small sixth matching fundamental B seventh. Omit one dissonant sound: either acceptable; next bass leading note forms major dissonance, resists doubling; small-sixth third would descend onto same dissonance. Also sixth-chord rule still applies before perfect chord a third away.", "III.11-039": "3. Replace continuo fourth R with second A/C or sixth T before dominant L/K: sharpen fourth in harmony, as S. Perfect-chord note likes leading-note approach. Minor exception: sixth falls semitone to dominant; dominant’s own leading note cannot sound, whatever preceding bass. Otherwise dominant becomes tonic, true key known only afterward. Example likewise reveals dominant through following note. Tritone derives from same dominant’s seventh, fundamental D below.", "III.11-041": "4. Diatonic continuo disturbs upper movement at F G H. Needed to avoid consecutive octaves/fifths, restore range above bass, or include all chord sounds.", "III.11-042": "Upper diatonic rule applies only over consonant bass movement. Bass changes method; others may too. Breaking steps often varies melody well. Upper order/progression could change without error; not yet our concern.", "III.11-043": "5. Several unprepared sevenths contradict first rule. Explanation later. Now follow octave’s prescribed chords. Later: consonant chord permits free movement within modulation rules.", "III.11-044": "6. Previous-book point: fundamental rise tone/semitone implies third and fourth. Added Y between Z/A shows this. Z fifth prepares seventh; third prepares A seventh. Chord substance unchanged. Remove Y: tone/second Z–A uses same notes as seventh A–X.", "III.12-001": "CHAPTER TWELVE.", "III.12-002": "Further rules from previous example.", "III.12-003": "Bass takes seventh chord: may omit seventh unless previous consonance prepared it. But consonance major—third or sixth? Better raise it semitone. Chord derived from seventh chord? May omit either sound forming dissonance. Easy to recognize: two sounds always adjoining, as chapter XI explained.", "III.12-004": "Repeat same bass note as often as good taste allows. Same chord or different chords, as later instruction permits.", "III.12-005": "May move to another note whose chord differs only in name. From seventh chord: third above original bass takes diminished-fifth chord; fifth takes small-sixth chord; seventh takes tritone chord. All essentially same chord. Same principle in similar cases. See example.", "III.12-006": "Equivalent chords by inversion; same harmony.", "III.12-007": "Bass note lies third above next note; next takes perfect or seventh chord. First should usually take derivative of following chord. A: sixth chord derives from following perfect chord. B: great-sixth or diminished-fifth chord derives from following seventh chord.", "III.12-008": "Bass changes position, chord substance unchanged: consonant upper parts may stay. Dissonant chord must retain all four different sounds. Add octave of departing note D if absent from preceding chord on same fundamental-bass note. Or remove octave of present note J, replace with octave of departing note C.", "III.13-001": "CHAPTER THIRTEEN.", "III.13-002": "Perfect cadence.", "III.13-003": "Melodic conclusion on tonic after dominant: perfect cadence. Tonic must sound on first beat so conclusion is felt. Preceding dominant takes seventh chord, or at least perfect chord; seventh may remain implied. See example.", "III.13-004": "Perfect cadence—arrangements and fundamental bass.", "III.13-005": "Perfect cadence identifies bass notes needing perfect chords. Melody rests? Perfect chord must sound there. Rest felt not only in cadence's natural progression but in progressions drawn from accompanying sounds, shown beside text. Each part figured for chord it would carry as bass. Perfect chord may follow great-sixth or diminished-fifth chord. Stay in key: melody rests only on tonic or dominant. Clear target. Whatever continuo-bass progression, hear and know resting notes and preceding chords required by its movement. Each part's figures show this. Choose any part as bass; others still accompany it.", "III.13-006": "For clearer understanding, examine leading note's force here: distinguishes dissonances, imposes chord order.", "III.14-001": "CHAPTER FOURTEEN.", "III.14-002": "Leading note; resolution of all dissonances.", "III.14-003": "Leading note enters dissonant chord: conclusion determined. Tonic's perfect chord must follow, on tonic or in derived forms. No leading note? No fixed conclusion. Another dissonant chord follows; chain continues until leading note appears. Then conclusion, or imitation of conclusion—for example mediant instead of tonic. Earlier seventh-chord examples prove it: seventh follows seventh until tonic dominant brings leading note.", "III.14-004": "Exception: dominant's perfect chord may follow great-sixth chord on fourth note. That chord lacks leading note but remains dissonant.", "III.14-005": "To identify leading note here, dissonant chord must contain diminished fifth or tritone, between upper parts or between part and bass. Those notes must be major third and seventh of fundamental seventh chord. Root must be tonic dominant; otherwise rule false. In C: B and F form diminished fifth or tritone according to order. B gives G's major third; F gives G's seventh. G is tonic dominant.", "III.14-006": "EXAMPLE.", "III.14-007": "Tritone, diminished fifth, leading notes, resolution guides.", "III.14-008": "Perfect-cadence example shows same. Any part may become bass; others form chord. Diminished fifth or tritone always remains. Difference only in positions of same two notes.", "III.14-009": "Guide signs after intervals show natural movement, also shown by notes in perfect-cadence example. From this comes firm rule for all dissonance movement: resolution.", "III.14-010": "Thirds divided major/minor; all dissonances divided same way.", "III.14-011": "Major dissonances formed by leading note. Leading note naturally rises semitone to tonic, as examples show. All major dissonances do likewise.", "III.14-012": "Know key? Note semitone below tonic, when in dissonant chord, is major dissonance. Key unknown? Refer chord to foundation. Major dissonance always major third of tonic dominant bearing seventh chord. Thus that third counts as major dissonance. So do leading note beneath diminished-fifth chord, major sixth above key's second note, tritone above fourth note.", "III.14-013": "Minor dissonances formed by note making seventh against fundamental bass. Resolve downward by diatonic step. Seventh and diminished fifth belong here.", "III.14-015": "No major dissonance in dissonant chord? Minor alone present. Major present? Minor always accompanies it. Prescribed movements unchanged.", "III.14-016": "All resolution methods learned at once. Difference lies in bass movement, not dissonant notes' required movement. Bass may go to any note of naturally following chord. Refer every chord to foundation to understand.", "III.15-001": "CHAPTER FIFTEEN.", "III.15-002": "Eleventh called fourth.", "III.15-003": "Perfect cadence usually preceded by dissonant chord called fourth,* better called eleventh. Here only difference from perfect chord: fourth replaces third. Occurs only on bass notes naturally taking perfect or seventh chord. One of those follows on same bass note. Fourth resolves by descending diatonic step to displaced third. Thus minor dissonance; like others, formed from seventh above fundamental sound. Explanation waits for dissonance by supposition. Present example shows every preparation and resolution.", "III.15-004": "* See Book II, chapter XI.", "III.15-005": "EXAMPLE.", "III.15-006": "Eleventh/fourth prepared by 3, 4, 5, diminished fifth, 6, 7, 8.", "III.15-007": "Eleventh still figured 4 by custom. Every consonance prepares it; diminished fifth and seventh can too. See note pairs joined by semicircle ⌢. Always prepared on last beat, heard on following first beat.", "III.15-008": "Learn preparations carefully in C. Differences come only from bass progression; same in every key. Not quite proper place for this dissonance. But almost every perfect cadence has it immediately before; some authors do not separate them. We follow those authors here.", "III.16-001": "CHAPTER SIXTEEN.", "III.16-002": "On the irregular cadence.", "III.16-003": "Irregular cadence* usually tonic to dominant. Perfect cadence: dominant to tonic. Perfect falls fifth; irregular rises fifth. Irregular also fourth note to tonic: falling fourth equals rising fifth. Both closing notes naturally take perfect chords. Add sixth to first: clearer conclusion, pleasing harmony and melody.", "III.16-004": "Added sixth makes great-sixth chord. Fourth note naturally takes it before tonic dominant. Give fourth note same chord but move to tonic’s natural chord: irregular cadence. Also irregular: tonic to dominant, sixth added to tonic’s perfect 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": "Added sixth dissonates against fifth. Cannot descend onto fifth; must rise to third. Previous example marks path with ╱ from first note’s sixth to next note’s third.", "III.16-011": "Invert added-sixth chord: easy four- or five-part setting of successive bass notes. One part moves continually in sixths with bass. No broken rules; fundamental bass proves it.", "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": "Six parts could sound together except at J: fundamental bass rises second to seventh-bearing note. One part makes consecutive fifths with bass; must change it there. Notice two parts always moving in sixths, up and down. Added sixth lets three more parts join easily. Whole progression uses only three different chords.", "III.16-017": "C: tonic’s perfect chord becomes sixth chord on mediant. D: same becomes sixth–fourth on dominant. F: tonic dominant’s seventh becomes small-sixth on second note. G: same becomes tritone on fourth note.", "III.16-018": "H: fourth note’s perfect chord plus sixth becomes small-sixth on sixth note L. Not always irregular cadence. Otherwise same chord comes from seventh chord on second note J, following natural progression there.", "III.16-019": "Before small- and great-sixth chords understood, scarcely possible to add two parts correctly to these sixths. Now three added easily; fundamental bass may join too. Observe inversion: put any required fundamental-chord note in bass, others above. Fit harmony to either cadence just discussed or natural fundamental progression from opening examples. After consonant chord, bass movement unrestricted, but chosen movement restricts next chord. Cannot easily find foundation? Check note positions in present key—only C for now. Know required chord for each note and movement; give correct chord, avoid error. Practice builds judgment between two possible chords on same note. Fourth note may take tritone or great-sixth; may take both successively, great-sixth first. Applies when fourth falls to mediant or tonic. Semicircles mark these measures above/below parts: H C; G C; H G.", "III.16-021": "H C; G C; H G.", "III.16-022": "Bass follows fundamental progression? Give each note fundamental chord. Exception: sixth note to mediant. Inverted irregular cadence fits wonderfully.", "III.16-023": "EXAMPLE.", "III.16-024": "Figured bass A–N; cadence H–J and its fundamental bass.", "III.16-025": "Second note A takes seventh chord: A-to-B progression fundamental.", "III.16-026": "B takes seventh: minor third over A prepares it. Hold minor third; do not raise to octave—strictly forbidden. Exception: doubled in more than three parts; one copy may rise while other holds and obeys rule. Leading note at B must rise to tonic; tonic’s perfect chord must sound. Bass has no tonic here, only dominant. Thus dominant at C takes sixth–fourth, representing tonic’s perfect chord.", "III.16-028": "Fourth note D descends to mediant. Either great-sixth or tritone chord possible.", "III.16-029": "Mediant F must take sixth chord; only it resolves preceding dissonance. F-to-sixth-note-G movement fundamental, but mandatory dissonance resolution takes priority.", "III.16-030": "Inverted irregular cadence between H and J. See the fundamental bass below.", "III.16-031": "L takes great-sixth: same harmony as M’s seventh chord a third below. See chapter XII.", "III.16-032": "M takes seventh chord for same reason as A.", "III.16-033": "M, N prepare eleventh; eleventh prepares following perfect cadence.", "III.17-001": "CHAPTER SEVENTEEN.", "III.17-002": "Related bass progressions; upper harmony unchanged.", "III.17-003": "Tonic, mediant, dominant can carry same chord sounds. Natural bass goes to tonic? May substitute mediant or dominant. Goes to mediant? May substitute tonic. Dominant takes seventh chord? May substitute its third, fifth, seventh. Takes only perfect chord? Substitute third or fifth.", "III.17-004": "See the following example.", "III.17-005": "EXAMPLE.", "III.17-006": "Arrivals on the tonic, mediant, and dominant.", "III.17-007": "Last four arrivals and next four unsuitable for dominant: would make it pass for 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": "Examples begin on tonic. Could equally begin mediant or dominant. See guides.", "III.17-011": "Guide notes for starting notes: silent alternatives.", "III.17-012": "Not speaking of piece’s beginning: tonic must head it. Fugues and similar cases may break rule; not reached yet.", "III.17-013": "Second note immediately before tonic dominant acts as its dominant; takes seventh chord. Third and fifth may replace it. Seventh rarely: seventh is tonic, which for present purposes, acting as tonic, takes only 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": "Exchange these notes freely only if harmonic succession unchanged. Refer to foundation to know succession.", "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": "Second note dominates tonic dominant here; fundamental bass for others.\nSecond note A replaces tonic dominant.\nFourth note B replaces second note; second note C replaces tonic dominant.\nFourth note D replaces second note; at F replaces tonic dominant.", "III.17-022": "Substitutions through leading note G and sixth note H.", "III.17-023": "Leading note G replaces tonic dominant after fourth note.\nSame with different progression.\nSixth note H replaces second note when second dominates tonic dominant. Tonic dominant again represented by its 3♯, leading note G.", "III.17-024": "Diatonic progression: sixth–fourth often better than perfect chord on dominant, especially on weak beat.", "III.17-025": "With all teaching since book’s start, these few words cover every bass progression in most natural harmony. Other dissonances not yet discussed have tightly restricted movement. Master present teaching; their use becomes easy.", "III.18-001": "CHAPTER 18.", "III.18-002": "How to prepare dissonances.", "III.18-003": "We explained preparation and resolution of seventh. We meant all dissonances too: seventh is their source. We divided dissonances into major and minor. Only minor ones follow seventh in every respect. Major ones come from leading note, though leading note also belongs to seventh chord. Leading note needs no preparation. Therefore major dissonances need none either: Book Two, Chapter XIII. Seventh must be prepared by a consonance. All minor dissonances must too. Stay in key being treated: a note consonant in previous chord may now form dissonance. Same possible between keys, once their connection can be made pleasing. Remember: one note can serve successive dissonances when their chords are fundamentally the same chord. Also, seventh or diminished fifth can prepare eleventh, though both are dissonances. Thus a note already dissonant can form another dissonance in a chord that seems different in some respect. Condition: no change of key in that case.", "III.18-004": "We said: seventh prepared only by third, fifth, octave. This concerns fundamental bass progression. Most natural bass movements: down third, fifth, seventh. Up second equals down seventh; other related intervals work likewise. Usually choose smaller related interval for bass. Prefer up second to down seventh; same principle elsewhere. Now consider inversion. Any note of fundamental chord can occupy bass. Chord name changes with intervals its sounds form above that bass note. Here, sixth or fourth prepares seventh instead of third or fifth. Elsewhere, third, fourth, fifth, sixth, even octave prepares diminished fifth. Diminished-fifth chord represents seventh chord, as does every other dissonant chord. Any consonance can therefore prepare dissonance without error, unless we deliberately avoid natural movement. Example: replace bass tonic with its mediant or dominant, each carrying chord derived from tonic's perfect chord. Want seventh prepared by tonic's octave, fifth, or third? Octave becomes sixth above mediant, fourth above dominant. Fifth and third change correspondingly. Thus first rule for sevenths applies to all minor dissonances. Likewise, after tonic's perfect chord—bass tonic, mediant, or dominant—we may sound diminished fifth, tritone, great-sixth or small-sixth chord, and so on, instead of seventh that a consonance of perfect chord must prepare. Reason: another note of seventh chord now replaces its fundamental note in bass.", "III.18-006": "EXAMPLE.", "III.18-007": "Dissonance preparation — first series", "III.18-008": "Previous example continued.", "III.18-009": "Dissonance preparation — continued", "III.18-010": "1. A: octave prepares seventh in fundamental harmony. D: mediant in bass; fundamental bass octave becomes sixth. F: dominant in bass; that octave becomes fourth.", "III.18-011": "Thus octave, sixth, fourth prepare seventh. G: fifth in great-sixth chord represents seventh; octave prepares it. Cue signs on mediant and dominant show that sixth and fourth above those notes can prepare this fifth too. Same meaning at other cue signs.", "III.18-012": "H: third of small-sixth chord represents seventh. Prepared by octave, sixth, fourth.", "III.18-013": "J: second prepared in bass; third precedes it in upper part.", "III.18-014": "2. B: fifth prepares seventh in fundamental harmony.", "III.18-015": "L: fifth of great-sixth chord represents seventh. Prepared by fifth, third, octave.", "III.18-016": "M: third of small-sixth chord represents seventh. Prepared by fifth, third, octave.", "III.18-017": "N: octave prepares second, or fourth shown by cue sign.", "III.18-018": "3. C: third prepares seventh in fundamental harmony.", "III.18-019": "O: fifth of great-sixth chord prepared by third above fundamental note to which seventh is added.", "III.18-020": "P: same fifth prepared by fourth above note forming seventh of fundamental bass. That note must carry second chord.", "III.18-021": "Q: second prepared as at J.", "III.18-022": "R: same fifth prepared by sixth above dominant of fundamental bass note. Any note that dominates another can always represent it. It carries inversion of perfect or seventh chord belonging to that other note. Resulting inversion: sixth–fourth or small-sixth chord.", "III.18-023": "S: same fifth prepared by octave of note forming third, or mediant, of fundamental bass note.", "III.18-024": "T: third of small-sixth chord prepared by third, sixth, or octave. Preceding seventh resolves to sixth above same note over which seventh sounded.", "III.18-025": "Second not yet discussed. Before more explanation, note: it prefers preparation only in preceding manner.", "III.18-026": "All preparations of dissonance come from preparation of seventh. Difficulty: recognize in bass the notes belonging to chord of fundamental note. Give this full attention. Otherwise everything doubtful; no firm guide. First dissonant chord must always follow consonant chord. That consonant chord: perfect chord of tonic, its dominant, or its fourth note. Sixth chord on mediant of each such note can represent its perfect chord. Sixth–fourth can also represent it, but only on tonic's dominant.", "III.18-027": "With only two or three parts, often only consonances sound from a chord containing dissonance. Ignore bass progression or fail to know key: all our rules become useless. Understand these rules thoroughly. We restrict them to key of C. Knowledge of C suffices for other keys; afterward only need distinguish those keys.", "III.18-028": "Piece must start with consonant chord. Dissonant chord therefore follows consonant one. But dissonant chord often follows another dissonant chord. As said earlier, consonant chord cannot follow dissonant one unless leading note is distinguishable in that dissonant chord. Otherwise dissonant chords keep succeeding one another: see rules of seventh. Hard to recognize in two- or three-part pieces. Dissonant chords always contain at least two consonances: third and fifth, or inverted sixth and fourth. Octave may occur too. Thus we often pass between dissonant chords unknowingly. Want to know what we do? Do not neglect first principles. Greatest satisfaction should come from complete understanding.", "III.19-001": "CHAPTER 19.", "III.19-002": "When dissonances cannot be prepared.", "III.19-003": "Make fundamental bass rise by third, fifth, seventh instead of descend by them: seventh can no longer be prepared. Yet these progressions almost compel us to sound it. Evidence: diatonic octave progression, Chapter XI, tonic to dominant and immediately back to tonic. See Book Two, Chapter XIII. All masters agree; ear not offended.", "III.19-004": "Bass rises third, immediately falls fifth: seventh over risen note cannot be prepared either.", "III.19-005": "EXAMPLE.", "III.19-006": "Rise by fifth or third — seventh unprepared", "III.19-007": "Example A represents rising fifth: it starts on mediant, representing tonic. Example B proves seventh cannot be prepared when fundamental bass rises third. Note forming seventh with second bass note cannot form consonance with first.", "III.19-009": "Give second note of Example B a major third: key changes. Very common practice, especially in inverted harmony, as shown here.", "III.19-010": "EXAMPLE.", "III.19-011": "Inverted harmony — parts exchange roles", "III.19-012": "Each part can serve as upper part or bass. Example shows diminished fifth, tritone, seventh without preparation.", "III.19-013": "Rising seventh or falling second leaves seventh unprepared. See Book Two, Chapter XIII.", "III.19-014": "Unprepared dissonance allowed only after consonant chord. After dissonant chord, preparation absolutely required by preceding rules.", "III.19-015": "Do not count leading note among these prepared or unprepared dissonances. Here we discuss minor dissonances only. Major dissonance from leading note lies outside these latest rules. Minor dissonance often sounds unprepared for sake of that major one. Example: fundamental bass rises third or fifth, then falls fifth. Final fall forms perfect cadence. Cadence impossible unless leading note has sounded in chord on note from which bass falls fifth. Valuable consequences follow. Discuss them after explaining movement between keys.", "III.20-001": "CHAPTER 20.", "III.20-002": "Exact list of bass progressions for each kind of dissonance.", "III.20-003": "Derive dissonance rules from fundamental bass and fundamental seventh chord. Seventh chord alone governs all dissonant chords we use. Bass moves differently through sounds of that chord. Upper parts then form different intervals above bass. Chord names must match those intervals.", "III.20-004": "Extend first seventh rule: give every note of key a seventh chord while bass rises by fifths or falls by fourths.", "III.20-005": "First seventh: prepare with any consonance, or leave unprepared, as preceding chapters allow. Afterwards obey rule: third must always prepare and resolve seventh.", "III.20-006": "See following example.", "III.20-007": "EXAMPLE.", "III.20-008": "Sevenths in four parts", "III.20-009": "All parts keep descending. Seventh accompanied alternately by third and fifth, then third and octave: 1. 3. 5. 7., or 1. 3. 7. 8.", "III.20-010": "More complete harmony needs five parts, as we shall see.", "III.20-011": "Some sevenths lack natural proportion: those on C and F, expressly forbidden in first rules. No need for trouble in this chain of dissonances. Modulation produces them; no note may receive added sharp or flat. Later, other false intervals arise from these. Circumstances make them false; write them as though correct. Cannot avoid them while staying in starting key. Ear not offended at all: already occupied with sounds belonging to modulation.", "III.20-012": "Take tenor part A as bass. Note aligned with first seventh carries small-sixth chord; next note carries seventh chord. Result: new bass progression, apparently new chords. Next example shows it; same part marked A.", "III.20-013": "Next use haute-contre part B as bass. Note aligned with first seventh carries second chord; following note, great-sixth chord. Another progression results. Next example marks same part B. Second and tritone chords contain same intervals except fourth: perfect in one, augmented in other. Augmented fourth contains three whole tones; hence name tritone. Cause distinguishing great-sixth from diminished-fifth chord also distinguishes second from tritone chord.", "III.20-015": "Major and minor small-sixth chords share same distinction, though no two separate names distinguish them. All come from seventh chord: bass has major third in one case, minor third in other. No different names for this difference. But chord whose major third forms diminished fifth or tritone with seventh belongs only to tonic dominant. Other dominants take chord with minor third; no diminished fifth or tritone between third and seventh. Those dominants must succeed one another until tonic dominant appears. Same rule for their derived chords and dominants themselves.", "III.20-016": "Next example shows chords from different bass progressions. Each part can serve as upper part or bass. Exceptions: fundamental part and part below it can serve only as basses.", "III.20-017": "Turn page for example.", "III.20-018": "EXAMPLE.", "III.20-019": "Six interchangeable basses; fundamental bass; supposition", "III.20-020": "1. First four basses: most natural progression relative to fundamental bass. Fifth and sixth borrow progressions from first four.", "III.20-021": "Fifth bass takes progression from first and fourth. All three marked ∞.", "III.20-022": "Sixth bass borrows progression from second and third, marked †. Each measure of fifth and sixth basses takes one note from each of its two source basses. Thus borrowing can be recognized. Same degrees in different basses have same chord figures. Not every seventh-chord note in fifth and sixth basses bears figure 7. Purpose: perfect chord alone may be used there; possible seventh may be omitted. Then avoid octave in chord on preceding notes: that octave prepares seventh.", "III.20-023": "2. First four basses: first and second lie in thirds; third and fourth likewise. Last two descend while first two hold same degree. They alternate to end. Minor dissonance naturally descends; at least parts forming it must descend. In this harmonic succession, consonance a third below follows same movement. Remember: sixth above equals third below, as here:", "III.20-024": "Third below or sixth above", "III.20-025": "Consonance's movement restricted here only relative to fundamental bass. Consonance may stay on same degree and become dissonance if bass moves first:", "III.20-026": "Thus:", "III.20-027": "A, B: bass falls third instead of fifth. Consonance C, third below dissonance F, stays on same degree and becomes dissonance D.", "III.20-028": "Held consonance becomes dissonance", "III.20-029": "3. Hear parts together: omit fifth and sixth basses. Want to hear those two? Omit four upper parts, or at least first and third. Even then, unisons or octaves occur constantly and sound unpleasing.", "III.20-030": "4. Take first four basses alone. Upper three contain every sound of chords figured on fourth. Choose another as bass: transpose it down octave beneath others, or transpose others up octave. Other parts still contain chords figured on selected bass. Choose fifth bass: sound only second, third, fourth above it. First resembles fifth too closely. Choose sixth bass: sound only first, second, fourth above it. Change one note causing two consecutive octaves in first measure.", "III.20-031": "One example teaches construction of all dissonant chords, movement of dissonances, and chord differences caused by different bass progressions. Everything consists simply in inversion.", "III.20-032": "5. Fifth and sixth basses sound pleasing taken separately. Can even syncopate them:", "III.20-033": "Thus:", "III.20-034": "Fifth and sixth basses, syncopated", "III.20-035": "Or invert parts.", "III.20-036": "Invert two syncopated basses", "III.20-037": "Adding two more parts is difficult. Inversion introduces a kind of supposition requiring deep knowledge of harmony. For now, practise only as written: two parts alone.", "III.20-038": "Part serving as bass must begin and end on tonic. At ending, dominant must precede tonic. Other parts need only very small change. Match it to their progression when heard above fundamental bass.", "III.21-001": "CHAPTER 21.", "III.21-002": "Second chord.", "III.21-003": "Second interval inverts seventh. Second chord likewise inverts seventh chord.", "III.21-004": "EXAMPLE.", "III.21-005": "Second, seventh, and their chords", "III.21-006": "Inversion also reverses preparation and resolution of these dissonances.", "III.21-007": "Minor dissonances prepared and resolved in upper part. Second reverses this: minor dissonance lies in bass. Prepare and resolve it in bass, with movement required for minor dissonance. Sound bass note on second beat; form second above it on first beat of next measure. Bass note then descends. Continue same bass pattern: give notes chords like following example. Continue until major dissonance appears; consonant chord follows.", "III.21-008": "Important qualification. In progression like example, major dissonance may appear without demanding attention. Bass continues through same degrees, reaches mediant without closing, reserves close for tonic one or more measures later—tonic itself or its derivatives. Next example shows this. Major dissonance then avoids natural movement and is treated as minor. Allowed only for modulation that delays close. Still, after leading note, better always to rest on tonic's perfect chord or mediant's sixth chord.", "III.21-010": "Seventh prepared and resolved in upper part.", "III.21-011": "Seventh prepared and resolved in upper part", "III.21-012": "Second prepared and resolved in bass.", "III.21-013": "Second prepared and resolved in bass", "III.21-014": "A, B: second prepared and resolved in bass as seventh is in upper part. Fundamental bass shows same chord sounds in both examples.", "III.21-015": "Both basses descend diatonically, sounding each note twice at same degree. Progressions nearly alike. Choose chords by position of barline: one example puts both notes in same measure; other separates them with barline. Bass matches either pattern? Use its corresponding chords. Follow this rule and never go wrong.", "III.21-017": "Some basses in previous chapter seem inconsistent with these chord progressions. They represent upper parts only. Otherwise follow our rule to proceed correctly.", "III.21-018": "Second absolutely requires preparation by third, though upper part may prepare it by any consonance. Bass must always syncopate here.", "III.21-019": "Different bass progressions let any consonance prepare or resolve dissonance. Avoid error: always add fundamental bass beneath composition. Minor dissonance always forms seventh against it. There, preparation only by octave, fifth, third; resolution only by third. Otherwise composition neither correct nor regular.", "III.21-020": "Repeat: first dissonance after consonant chord may be prepared by fundamental note's octave, fifth, or third. Immediately following dissonances must use third, not another consonance: most natural harmonic succession. Variety sometimes calls for seventh prepared by fifth or octave of fundamental note, even among or after several sevenths. Purpose only to vary melody or harmony. Use rarely, or at least with judgment. Same principle applies to every minor dissonance referred to its foundation; seventh always governs there.", "III.21-021": "Seventh should resolve only to third of fundamental note. Yet fifth, even octave, can also resolve it. These are licences. Use only after fully mastering everything else. No discussion of them yet.", "III.22-001": "CHAPTER 22.", "III.22-002": "Keys and modes in general.", "III.22-003": "Master keys and modes from Chapter VIII. Then learn what follows.", "III.22-004": "ARTICLE 1.", "III.22-005": "Major keys.", "III.22-006": "Any note may be tonic of major key. Make its octave progression match C's. Sharps and flats raise or lower intervals by semitone where needed for this match. Know number of signs, normally placed after clef. All notes on their marked degrees rise or fall a semitone. Example: choose D. F gives D a minor third; C's third is major. Add sharp to F: D's third becomes major, like E above C. Likewise, fourth above F is B♭. Key of F needs flat on B to match C's pattern.", "III.22-007": "All transposed major keys: octave modulation follows C's octave pattern.", "III.22-008": "Major keys: sharps", "III.22-009": "Major keys: flats", "III.22-010": "Eleven major keys here; add C, total twelve. Entire octave system has only twelve chromatic notes. See Book One, Chapter V.", "III.22-011": "Order of sharps: F, C, G, D, A, E, B, and so on. One sharp: F only. Two: F and C. Three: F, C, G. Count upward by fives, from first sharp F to last.", "III.22-012": "Major key's leading note determines number of sharps: last sharp always on leading note. D major needs two before clef. Leading note C♯; cannot sharpen C line without first sharpening F line. First sharp always F. E major needs four: leading note D♯. Same for others. Or count by fives from one-sharp major key, G: G, D, A, E, B = 1, 2, 3, 4, 5 sharps.", "III.22-013": "Order of flats: count upward by fours from B. B, E, A, D, G, and so on. Major key's fourth note determines number. F's fourth is B♭; place flat on B line for F major. Same for others. Flat major-key series starts with F. Count by fours, as by fives for sharps, to find answer.", "III.22-014": "ARTICLE 2.", "III.22-015": "Minor keys.", "III.22-016": "Usual model for all minor keys: D's octave.", "III.22-017": "See 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": "Ascending minor differs from major only in third: minor versus major. Descending: restore B's flat; remove sharp from leading note C.", "III.22-021": "EXAMPLE.", "III.22-022": "D-minor octave progression", "III.22-023": "Use these progressions in all minor keys; never go wrong.", "III.22-024": "All transposed minor keys: octave modulation matches preceding D octave.", "III.22-025": "A minor", "III.22-026": "Minor keys: sharps", "III.22-027": "These two keys are the same.", "III.22-028": "Minor keys: flats", "III.22-029": "Twelve minor keys here too, including D. D and A written without sharp or flat.", "III.22-030": "First minor key with sharp before clef: E. Count keys by fives from E: E, B, F♯, C♯ = 1, 2, 3, 4 sharps. B minor is second: needs two. Same for others. Second note of key also determines number: it carries last sharp.", "III.22-031": "First minor key with flat before clef: G. Count by fours: G, C, F, B♭, E♭ = 1, 2, 3, 4, 5 flats. Thus find each key's number. Minor third carries last flat; it too determines number.", "III.22-032": "Keep every major and minor key's number of sharps and flats in mind. Need this before clefs, and beside individual notes when key changes: add or remove signs appropriately. Not only for choosing a composition's key. Also for recognizing keys entered and making them clear to performers.", "III.22-033": "Name every major tonic ‘ut’ in transposition: octave follows C model. Name every minor tonic ‘ré’: octave follows D model, ascending and descending. Relative tonic names, not fixed C or D pitches in every key. Intervals and chords never change among major keys; same among minor keys. Remember required change in any part when ascending or descending.", "III.22-034": "Book Four, Chapter VI: octaves of all keys, ascending and descending, with sharps and flats.", "III.23-001": "CHAPTER 23.", "III.23-002": "Moving between keys, also called modulating.", "III.23-003": "1. Note carrying perfect chord counts as tonic. Thus first perfect-chord examples show as many keys as notes. Use those examples as models here. Natural movement between tonics requires consonant interval. After starting in one key, move to another a third, fourth, fifth, or sixth above or below. First tonic becomes new key's mediant, dominant, fourth, or sixth note. Link key to key this way.", "III.23-004": "2. Beyond preceding possibilities, major-key tonic may sometimes become seventh, even second degree. Never leading note. Minor-key tonic has only second-degree option here.", "III.23-005": "This seventh lies whole tone below octave. Not leading note a semitone below octave; leading note naturally belongs to every key.", "III.23-006": "3. Make major key's dominant a new tonic during piece: its key naturally major. Sometimes minor allowed, with judgment. Minor key's dominant can become only minor key.", "III.23-007": "May break rules when able to judge own work. Still beware going astray. Even most skilful not exempt from this concern.", "III.23-008": "4. Whatever starting key, modulate within it at least three or four measures. Stay longer as invention and good taste dictate.", "III.23-009": "5. Prefer dominant key of starting key over another destination. First tonic becomes fourth degree. Irregular cadence can make this change.", "III.23-010": "6. Change key: identify new tonic at once. Think of tonic as ‘ut’ or ‘ré,’ relative names from major and minor models. This fixes progression of notes in its octave and chords to use. Sharps and flats make intervals match C and D models. C to G major: sharpen every F in every part. F♯ becomes G's leading note, as B is C's. Choose G minor instead: sharpen F only when ascending; flatten E when descending. E is G's sixth degree, matching D's sixth, flattened in descent. Flatten B too, making G's third minor like D's. Same principle for others.", "III.23-011": "7. Ear dislikes hearing same key too often. Starting key alone may return from time to time. Do not immediately revisit another key just left. Example: start in C, visit another key, return to C—allowed. But do not then revisit that other key after leaving it for C or a third key. Prefer new key. Move judiciously between keys; gradually return through keys closest to starting key. Finish there as though never away. After several key changes, spend a little longer modulating within principal key at end than at beginning.", "III.23-012": "8. Major key: prefer sixth-degree key over mediant key. Minor key: prefer mediant key over sixth-degree key. Less good option still allowed. Mediant and sixth degree reckoned major in major key, minor in minor key.", "III.23-013": "9. New key major or minor? Its tonic, third, fifth must use notes in octave of key just left. Further rule: unless long piece requires some departure, perfect chords of all tonics used should come from starting key's octave, with no new sharps or flats altering those notes. Example, start C: E, F, G, A, sometimes D, plus their thirds and fifths, use notes belonging to C's modulation. Thus major may lead to minor, minor to major. Thirds must fit diatonic order of starting key, or at least key being left. C major to A: A must be minor, since C is its minor third. Same elsewhere. For minor keys, use descending octave pattern only; leading note loses sharp, becomes natural. This permits corresponding change in major keys by flattening leading note. Earlier statement that tonic can become second requires whole tone between tonic and its second. This modulation already mentioned in second article.", "III.23-015": "10. Move between keys almost imperceptibly. Ear should scarcely notice. Follow prescribed order to achieve this.", "III.23-016": "11. Last note of key being left must carry consonant chord. Choices: tonic, mediant, dominant; sometimes sixth degree with sixth chord. At first, practise only tonic to dominant. Dominant becomes new tonic. Then follow routes in next example, modulating a few measures in key of each note reached by bass.", "III.23-017": "EXAMPLE.", "III.23-018": "Modulation routes — first or second measure", "III.23-019": "Bass may start with first or second measure. Stay less time in next note's key than in starting note's key; still less in others. Sometimes use only one, two, three, or four notes of later key before moving onward. Taste matters more than rules here.", "III.24-001": "CHAPTER TWENTY-FOUR.", "III.24-002": "Previous Chapter’s Rules Continued.", "III.24-003": "First learn key changes through cadences. Cadence creates rest within piece. Then enter desired key; sound another cadence there. Continue chain this way. After perfect chord ending each cadence, any chord may follow.", "III.24-004": "Sometimes repeat tonic where cadence ended. Give repeated note chord suited to next key.", "III.24-005": "Repeated note with seventh or sixth–fourth chord becomes dominant, A.", "III.24-006": "Tritone or great-sixth chord makes it fourth note, B.", "III.24-007": "Sixth chord makes it mediant, C; or sixth note rising to leading note, D.", "III.24-008": "Small-sixth chord makes it sixth note descending to tonic dominant, F; sometimes second note, G.", "III.24-009": "Instead of repeating tonic, raise it semitone. Give raised note diminished-fifth chord. Note becomes leading note, H.", "III.24-010": "Tonic bearing major third can become dominant unchanged, J.", "III.24-011": "Turn page for 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": "Notes marked (6/5), with B above, may simply receive perfect chord. Irregular cadence sounding mediant can become sixth note; sixth note can likewise become mediant. Previous example at T showed part of this.", "III.24-018": "EXAMPLE.", "III.24-019": "A as sixth note or mediant — S and T", "III.24-020": "A, sixth of C, becomes mediant of F, S.", "III.24-021": "A, mediant of F, becomes sixth of C, T. Chord stays unchanged in either case. Note serving as mediant or sixth always lies between keys fifth apart. It divides fifth into two thirds. Example: F to C, with A between.", "III.24-022": "Key change also possible through 7, 7 and 6, 2, 4♯, 6/5, barred 5. Move one or more bass notes beneath these chords. Introduce tritone or diminished fifth to determine desired new key. Interval must consist of major third and seventh of tonic dominant.", "III.24-023": "EXAMPLE.", "III.24-024": "Modulation through dissonant chords — three systems", "III.24-025": "Dissonance entering new key must always be prepared by consonance in last chord of old key.", "III.24-026": "Use this to compose bass fitting desired chords. Now take another approach: compose bass freely. Its progression tells which chords it must bear.", "III.25-001": "CHAPTER TWENTY-FIVE.", "III.25-002": "Finding Chords for Bass Notes in Any Progression.", "III.25-003": "ARTICLE ONE.", "III.25-004": "First attend to cadences and melodic conclusions. Beginners can scarcely avoid frequent conclusions in bass, especially at key changes. Conclusions always fall on measure’s first beat. Even slightly trained taste hears them at once. First-beat notes where melody rests must always bear perfect chord. Therefore treat them as tonics.", "III.25-005": "2. After tonic, bass moving by consonant intervals may bear perfect chords up to note followed by diatonic interval. Exception: note third above or below another bearing perfect chord may take sixth chord; this is even preferable. Conversely, first note requiring perfect chord makes next note third above or below take sixth chord—unless another consonant progression follows that second note. Consonant progression naturally requires perfect or seventh chord on each note. More explanation follows.", "III.25-006": "In this case, note eligible for sixth chord is always mediant or sixth note. If unsure, simply give each note 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, note third above C and below following dominant must bear sixth chord, A.", "III.25-011": "B. Note third above dominant, equivalently sixth below, could bear sixth chord. Diminished-fifth chord fits better: note is leading note of C. Key of C continues through C. Add diminished fifth to sixth chord: diminished-fifth chord. Add seventh to perfect chord: seventh chord. Could have added seventh to dominant immediately preceding diminished-fifth chord. See Chapter XI.", "III.25-012": "Four notes rise in successive thirds from tonic. Mediant bears sixth chord; dominant bears sixth–fourth at C, not perfect chord. Flat on B determines new key. Bass reveals it through diminished fifth between B-flat and following E. E, lower sound, becomes leading note. B-flat chord must fit key prepared by that leading note. B-flat lies outside C, key being left. C’s dominant also adapts chord to following harmony. Still within C, it bears sixth–fourth making up B-flat’s tritone chord. Perfect chord on this dominant would require minor third to avoid false relation. False relation: successive notes in different parts share name, but added sharp or flat changes one. Example: B sounding as G’s major third in one part forbids B-sharp or B-flat next in another. More later. Sixth–fourth at C therefore brings harmony closer to next chord. Perfect chord with minor third also possible. Small-sixth chord possible too, with diminished-fifth chord on immediately preceding note: E and following B-flat form diminished fifth. Such bass interval determines key absolutely. Its lower sound always leading note, as stated. Tritone likewise determines key; upper sound is leading note. Exception: after interval, bass rising fourth or falling fifth may remove this leading-note role. Each note can act as dominant seeking tonic dominant. Tonic dominant immediately follows notes forming diminished fifth or tritone: G, H, J. This applies only between second and sixth notes of minor keys, forming diminished fifth or sharp fourth.", "III.25-014": "Earlier rule calls for sixth chord at D. Sixth could only be minor, matching key of preceding and following notes. But B loses flat immediately afterward. Favor following harmony over preceding harmony. Give D perfect chord: avoid ensuing false relation and obey consonant bass-progression rule.", "III.25-015": "Note at F bears diminished-fifth chord: diminished fifth connects it with preceding note. At key change, fit harmony to coming key rather than departing key. Especially do this when note allows two otherwise equally suitable chords.", "III.25-017": "ARTICLE TWO.", "III.25-018": "Imperfect Cadences.", "III.25-019": "Besides natural bass progression of perfect cadence, related progressions exist: imperfect cadences. See Book II, Chapter VIII.", "III.25-020": "Imperfect cadences relate to perfect cadence through harmony, not bass motion. Arrange all sounds of perfect cadence together. Take each part’s progression separately; make it bass. Chords differ only in disposition.", "III.25-021": "EXAMPLE.", "III.25-022": "Minor dissonance. C. Major dissonance. A. Fundamental bass.", "III.25-023": "To hear combined parts, omit A and C. They resemble highest part too closely. Note resolving minor dissonance there dislikes octave doubling in this case. Or omit highest part and hear A and C. Printed combination merely distinguishes their movements. Dissonant parts have fixed progression; others may rise or fall. Fundamental-bass note appears in lowest three parts. It may stay, fall third, or naturally fall fifth. When falling third at A, usually omit chord’s seventh: effect resembles consecutive octaves. Strictly speaking, effect tolerable, especially in four parts.", "III.25-024": "Octave example, Chapter XI, specifies these progressions with same chords. Check by making any chosen part bass. Avoid putting lowest two parts above others. Remaining parts sound well in any arrangement. Figures in one part describe chords contained in others.", "III.25-025": "Most preceding examples contain such imperfect cadences. Ending notes need not fall on first beat: cadences occur within diatonic progression, which cannot determine perfect conclusion.", "III.25-026": "ARTICLE THREE.", "III.25-027": "Finding Key of Imperfect-Cadence Progressions.", "III.25-028": "Diatonic progression can lead to several keys. To distinguish destination, observe several things.", "III.25-029": "1. Leading note determines choice first. Here is how to identify it in bass.", "III.25-030": "Opening key reveals its leading note. Key moves only among certain notes within its octave, following C-major or D-minor pattern. Sharp or flat altering one of these notes certainly changes key.", "III.25-031": "First new sharp marks leading note. With two or three successive sharps, last sharp identifies leading note. F-sharp makes F leading note, indicates G key. Add G-sharp: F-sharp loses leading role; G-sharp becomes leading note, indicates A key. Count in sharp order F, C, G, D, A, etc.; no mistake possible. Ignore flats mixed among sharps. Without sharps, flat marks new key. Leading note is note that would take next added flat. Example: B-flat, no sharp; next flat would be E-flat, so E is leading note. With E-flat, A is leading note. Follow flat order B, E, A, D, etc. Next unflattened note after flattened note is leading note. Recall Article One: bass diminished fifth or tritone also reveals leading note. Note eligible for next flat lies tritone above or diminished fifth below last flattened note. Never use natural sign here; avoid confusion.", "III.25-033": "2. Bass need not reach leading note. Key can change without this clue. Bass often forms diminished fifth or tritone between minor key’s second and sixth notes—rather, sixth to second. This applies without sharp; sharp always decides. First check suggested key’s proper relation to departing key. Then check note after repose partly established by diatonic progression: does it favor one key? Especially inspect consonant motion after last diatonic note. Such motion often reaches final cadences determining 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": "First leading note easily recognized. From A, diatonic progression runs to interruption at B; apply sevenths rule there. Interruption leads to C cadence. Fit diatonic notes from A’s dominant onward to C key. Nothing after dominant maintains A. Give repeated dominant sixth–fourth chord, fitting following harmony more closely. G becomes natural at B: no longer leading note. No sharp or flat before C cadence. Thus C key declared from A onward. Favor coming key over present key, especially when chords readily fit it and no sharp, flat, consonant progression, or repose demands different route.", "III.25-038": "G-sharp gone; following C-sharp indicates new key. Repose at C precedes consonant interval requiring seventh on note at C. Return to A determined: rising-fourth progression ends on A.", "III.25-039": "F-sharp indicates new key; no other sharp follows.", "III.25-040": "Flat at F requires minor third on previous note for closer harmonic agreement. B-flat and E-flat imply A leading note. E then loses flat and becomes leading note: B-flat remains, no sharp appears.", "III.25-041": "Diminished fifth between notes at D may reveal leading note. Candidate rises semitone at J: natural leading-note motion. But consonant intervals from L, where F key ends, require perfect or seventh chords on following notes according to bass intervals. They also favor key established by next leading note. Rules for thirds would nevertheless allow this:", "III.25-042": "Proceed thus. D. L. J.", "III.25-043": "Then F key continues to D, followed by leading note. Choice free under good taste. Taste delights in variety; leave overlong key whenever possible.", "III.25-044": "Diminished fifth above D’s leading note does not resolve in next chord. It also forms sixth above note at G; chord foundation unchanged. Immediately afterward, it resolves downward to neighboring note’s sharp sixth. Diatonic progression requires harmony fitting key prescribed by next leading note.", "III.25-046": "Augmented-second chord at G not yet discussed. Disregard for now.", "III.25-047": "H becomes leading note for two reasons: semitone motion to following note in next measure; and its diminished-fifth chord matches seventh chord required on immediate next note, which rises fourth. No sharps remain; B-flat remains. Therefore E leading note. Then all flats and sharps vanish. Only B remains leading note; C key established. Give C’s notes prescribed chords through conclusion. Exception at M: rising fourth requires seventh chord on C, perfect chord on F, since consonant interval follows F. Perfect chord always makes its bass tonic; thus F becomes tonic again. But F’s required B-flat disappears instantly. No sharp or flat remains; B becomes leading note again. C interrupted briefly for variety, consonant bass progression permitting it.", "III.25-048": "Concluding rule: consonant progressions decide absolutely. Fit diatonic passages to following consonant motion rather than preceding motion. Leading note unclear? Keep chord sequence prescribed in Chapter XI’s octave, starting from last consonant chord borne by last note in consonant progression. Bass rising semitone may suggest first note is leading note. Check for following sharps or notes losing flats: stronger evidence. Rising semitone also occurs from mediant to fourth in major, second to mediant in minor, or dominant to sixth in minor. In last case, sixth immediately descends. Consonant progression, sharp, flat, or particular chord sequence must decide.", "III.25-050": "Consonant motion after diatonic motion: shared ending/starting note must bear perfect or sixth chord. Perfect-chord note approached from leading note by rising semitone; alternatively, dominant approached by rising whole tone. Mediant approached by rising semitone in minor, whole tone in major. Downward approach: whole tone to tonic always; semitone to dominant in minor, whole tone in major. Such differences must provide clues. You already know required relation of new key to old. Major/minor distinction comes from third and fifth, formed from old key’s notes. Leading note almost certainly appears before or after; following consonant progression almost certainly reaches determining conclusion. Fourth/fifth progressions determine conclusions, except when followed by two or three diatonic notes rising or falling. Melody then rests on last note before fresh consonant or disjunct progression.", "III.25-051": "EXAMPLE.", "III.25-052": "A. B. C. D. F. G. H.", "III.25-053": "Bass falls fifth at A, yet no seventh on first note. Second note must bear neither perfect nor seventh chord. Following diatonic progression and its melodic repose decide.", "III.25-055": "Melody rests on third note after B. Fit B to its key. Preceding note takes chord required by key, not by consonant progression: B must bear neither perfect nor seventh chord.", "III.25-056": "Fit second note at C to key of following melodic resting note. Give C seventh chord before its proper small-sixth chord. Seventh prepared in previous chord; resolves agreeably onto sixth over same note. More next chapter.", "III.25-057": "At D and F, follow thirds rule. Further guide: first-beat notes preferably bear perfect chord; last-beat notes then bear sixth chord. Perfect chord on every note also allowed, as at G.", "III.25-058": "Final consonant interval suggests conclusion. Fit all preceding diatonic chords from H onward to that key.", "III.25-059": "ARTICLE FOUR.", "III.25-060": "Finding Whether Diatonic Melody Rests on Tonic or Dominant.", "III.25-061": "To find resting note, remember: tonic to dominant means bass rising fifth or falling fourth. Dominant to tonic means rising fourth or falling fifth. Diatonic progression exceeding this range either includes leading note in bass or does not. Leading note present: tonic declared. Absent: melody certainly rests on 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, rising whole tone reveals dominant. At B, rising semitone reveals tonic.", "III.25-065": "Diatonic passage may start on any key note. Clues reveal its place in present or replacement key: consonant interval from preceding note; immediate following repose; whole tones and semitones within passage; consonant or disjunct motion interrupting it. Preceding consonant interval less decisive than following one: see previous article’s last example. Yet whole-tone/semitone pattern alone suffices. Learn semitone positions in each mode, ascending and descending. Diatonic movement normally stops after tonic, mediant, or dominant. Sometimes another note ends it. Then following consonant progression still decides; existing rules prevent error. Know requirements of rising/falling thirds, fourths, fifths. Know same chord often represented over two notes in successive thirds or otherwise, according to following progression. Attend to all this. Put modulation first. Compare chords with bass movement; check whole against fundamental bass; watch leading note, helpful wherever present. Error then difficult. Once chord on one note known, follow octave order until diatonic movement stops. See Chapter XI. Further harmonic variety taught later.", "III.26-001": "CHAPTER TWENTY-SIX.", "III.26-002": "Using Sevenths on All Key Notes in Diatonic Motion.", "III.26-003": "Only tonic must always bear perfect chord. Other notes may bear seventh chord. Distinction: rising fourth onto perfect or seventh chord makes all notes dominants; seventh chords allowed. Diatonic motion requires seventh-bearing note divided into two beats or sounded twice—much same thing. Second beat takes sixth chord suited to following note. Always prepare seventh, except first may remain unprepared according to bass progression.", "III.26-004": "EXAMPLE.", "III.26-005": "A. B. C.", "III.26-006": "A, B. Could fit diatonic chords to key declared by following conclusion. Or continue preceding key. Its tonic at B takes chord suited to coming key on second beat.", "III.26-007": "C naturally bears great-sixth chord, possible after seventh chord given here. Instead of resolving seventh onto same note’s sixth, resolve onto next note’s fifth. Next note’s small-sixth chord and C’s great-sixth chord have same foundation. Once dissonance sounds, retain it until resolution possible. Natural resolving bass note may be absent. Check whether following bass note can bear same sounds as intended resolving chord. Explanation follows.", "III.27-001": "CHAPTER TWENTY-SEVEN.", "III.27-002": "Same Dissonance in Successive Chords on Different Notes; Resolution on Seemingly Foreign Notes.", "III.27-003": "Seventh chord contains four different notes, each able to precede same note. Arrange them successively in bass. Each bears apparently different chord, same foundation: Chapter XII. Dissonance unable to resolve in next chord? See whether it can serve that chord instead. Continue until resolution possible.", "III.27-004": "EXAMPLE.", "III.27-005": "Examples A, B.", "III.27-006": "A includes major dissonance; B has minor dissonance alone. Small-sixth chord at A belongs naturally to second note. Third and fourth clash; third must descend to resolve. Next bass note cannot support resolution. Same sounds instead form its tritone chord. Dissonance still unresolved; continue until C, where it descends onto C’s third. G with seventh chord grounds all four chords. Always trace dissonant chord to foundation, then find resolving bass note. Bass containing only notes of dissonant chord cannot resolve dissonance. Bass must contain note of resolving chord: minor dissonance descends, major ascends. Find target by reasoning: fundamental note dominates note fourth above. Seek that note in bass, or note of its perfect chord; if melody does not rest there, note of its seventh chord also possible. Only target’s dominant available? This is current dissonant chord’s foundation. Unless repeated, divide it into at least two beats. Second beat bears chord derived from target note. Few small exceptions: Chapter [number obscured], on licenses.", "III.27-008": "Seventh placed on note naturally requiring different chord by following note or octave order? If duration too short for proper chord afterward, next note must support same underlying chord. Its chord must contain sounds belonging to first note’s natural chord.", "III.27-009": "See next example.", "III.27-010": "EXAMPLE.", "III.27-011": "Continuo bass. Fundamental bass. A. B. C. D.", "III.27-012": "Second key note at A and D naturally bears small-sixth chord. Same sounds occur in tritone chord after A, seventh chord after D.", "III.27-013": "Descending sixth note at B naturally bears small-sixth chord. Same sounds occur in next note’s great-sixth chord.", "III.27-014": "Seventh above dominant resolves onto sixth when dominant repeats at C. Thus different consonances can resolve dissonance. Minor dissonance resolves correctly downward onto consonance above same bass note or next note. Major dissonance resolves upward onto consonance.", "III.27-015": "One more point: natural sequence seems to require chord derived from next note’s chord. Could first note instead bear chord dominating next? Prefer dominant chord over same underlying chord repeated. Especially preferable when preceding consonance prepares its dissonance.", "III.27-016": "Harmony is chain of tonics and dominants. Know their derivatives well; make each chord dominate next. Perfect chord and derivatives dominate nothing. Any chord may follow, subject to modulation rules. Any dissonant chord dominates next: examples 7, 7 and 6, 2, 4♯, 5, barred 5. Need full judgment to recognize derivatives and arrange suitable sequence. Existing rules for each chord and bass progression suffice to overcome difficulties.", "III.27-018": "Example: Prefer Chord Suited to Following Chord.", "III.27-019": "A. B.", "III.27-020": "Second note at A naturally bears small-sixth chord derived from immediately following tonic dominant’s seventh chord. For variety, use second note’s role as dominant of dominant. Give chord prescribed for that role instead. Dominant does not immediately follow B; intervening note can bear only derivative of B’s seventh chord. Thus B takes seventh chord, especially because previous consonance prepares seventh.", "III.27-021": "Rules so far concern harmony alone. They restrict each part’s melody except bass supporting harmony. Master harmony before considering melody. Melody follows discussion of licenses, which adorn harmony through added variety.", "III.28-001": "CHAPTER TWENTY-EIGHT.", "III.28-002": "Licenses: First, Interrupted Cadence.", "III.28-003": "Interrupted cadence interrupts perfect cadence’s conclusion. Sound seventh chord on tonic dominant. Instead of natural move to tonic, raise bass only whole tone or semitone. Seventh resolves onto fifth of raised note. Bass rises whole tone in major, semitone in minor. See Book II, Chapter VI.", "III.28-005": "EXAMPLE.", "III.28-006": "Interrupted cadence in the major key. In the minor key.", "III.28-007": "Final perfect chord doubles third rather than bass at octave: contrary to natural order. Cause lies more in false bass progression than other parts. Minor dissonance still resolves downward; major upward. Doubled third represents expected fundamental sound. Major key allows descent to bass octave instead of ascent to third, as cue sign shows. Minor key must follow example strictly.", "III.28-008": "Now invert interrupted-cadence chords; see advantages they offer.", "III.28-009": "EXAMPLE.", "III.28-010": "Major key. Minor key. Fundamental bass.", "III.28-011": "Put each bass below others in turn. Hear different figured chords. Derive pleasing harmony and melody over diatonic bass, ascending or descending.", "III.28-012": "See next example.", "III.28-013": "EXAMPLE.", "III.28-014": "D. F. G. H. J. Continuo bass. Fundamental bass. A. B. C.", "III.28-015": "This part as bass: omit D, change F’s final two notes. F as bass: likewise change this part.", "III.28-016": "This part cannot serve as bass.", "III.28-017": "This part as bass: diatonic motion to end, preferably ascending.", "III.28-018": "This part as bass: omit D. D forms irregular cadence against fundamental-bass notes B, C. Cannot invert it with seventh or second chord on first of its two notes.", "III.28-019": "Added sixth on B’s perfect chord evades perfect cadence A–B. Prepares irregular cadence; added seventh at C evades that. Perfect cadence then sounds at end.", "III.28-020": "See Book II, Chapters IX and X.", "III.28-021": "Omit fifth from B chord: A–B gives interrupted cadence, like H–J in part G.", "III.28-022": "Continuo bass limits upper parts’ motion. Each becoming bass may receive desired progression. Meaning: replace consonant motion with diatonic motion, keeping harmonic foundation unchanged. Fit remaining upper parts’ motion accordingly.", "III.28-024": "Interrupted cadence’s second note may bear sixth after whole-tone or semitone rise. Then forbid seventh chord on first note: seventh could not resolve.", "III.28-025": "Add dissonance to final note to interrupt any cadence. Prepare and resolve according to fundamental bass; always follow it to avoid error. At C dissonance cannot be prepared, yet remains good: fundamental bass falls fourth, equivalently rises fifth.", "III.28-026": "Count irregular cadence and unprepared dissonances among licenses: fundamental bass rising third, fifth, seventh, and all results of inverting such progressions. Yet these licenses belong inseparably to good harmony. Therefore discussion followed order judged best for beginners.", "III.29-001": "CHAPTER TWENTY-NINE.", "III.29-002": "Augmented-Fifth Chord.", "III.29-003": "Some chords introduced by license remain. First: augmented-fifth chord. Occurs only on minor key’s mediant.", "III.29-004": "Tonic dominant’s seventh chord, with fifth sound added third below: that is this chord.", "III.29-005": "EXAMPLE.", "III.29-006": "Seventh chord; augmented-fifth chord. Tonic dominant. Added sound.", "III.29-007": "Foundation lies in tonic-dominant chord, not added sound. Original rules stand. Seventh chord on tonic dominant follows usual motion: major dissonance rises, minor falls, all resolving onto tonic perfect chord. Added sound becomes part of that perfect chord or descends to tonic.", "III.29-009": "EXAMPLE.", "III.29-010": "Preparation and resolution of the augmented fifth.", "III.29-011": "Prepare with seventh chord on dominant of tonic dominant. Second note, here dominant, rises only semitone instead of fourth onto tonic dominant. Other parts sound tonic dominant’s seventh chord alone. It then resolves as always prescribed.", "III.29-012": "Chord sometimes interrupts cadence: tonic dominant rises semitone onto added sound. Sixth note becomes mediant. New leading note forming augmented fifth changes key.", "III.29-013": "EXAMPLE.", "III.29-014": "Interrupted cadence, change of key, and cue signs.", "III.29-015": "Only four parts? Put cue-sign notes in upper part instead of one corresponding note in other parts.", "III.29-016": "Original chord from which this derives can also prepare it.", "III.29-017": "EXAMPLE.", "III.29-018": "Preparation through the derived chord; four alternatives.", "III.29-019": "Others prepare with fifth of same note, minor sixth of note semitone below, or derivatives of seventh chord on note semitone below. Somewhat bold.", "III.30-001": "CHAPTER THIRTY.", "III.30-002": "Ninth Chord.", "III.30-003": "Previous chord’s augmented fifth becomes perfect here. More precisely, fundamental sound’s third changes from major to minor. Take dominant seventh chord with minor third; add note third below dominant. Result: 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 derives from dominant’s seventh chord: ninth, augmented fifth, eleventh, augmented seventh. Last two discussed in following chapters. Reason for emphasizing this: preparation and resolution become clear at once. Fundamental bass shows all follow sevenths rules.", "III.30-008": "See next example.", "III.30-009": "EXAMPLE.", "III.30-010": "Ninths and augmented fifths; continuo bass and fundamental bass.", "III.30-011": "Fundamental bass sounding below? Omit continuo notes bearing ninths or augmented fifths. Otherwise fundamental notes must lie above notes marked 9 or 5♯. Fundamental sound displaced by supposition can sound only above added sound beneath it.", "III.30-012": "Notes marked 9 and 5♯ may stay or descend third, as cue signs show. Ninth resolves onto octave when bass stays, onto third when bass falls third. Seventh then resolves onto octave; more elsewhere.", "III.30-014": "Some allow ninth to resolve onto fifth as bass rises fourth. Resulting harmony unsuitable. Leave choice to good taste.", "III.30-015": "Example: Ninth Resolves onto Fifth.", "III.30-016": "Ninth resolving to the fifth; alternative resolution through cue signs.", "III.30-017": "Prefer resolution onto sixth with bass rising third. Harmonic foundation stays unchanged. See other example’s cue signs.", "III.30-018": "Minor dissonance by supposition must be prepared. Ninth prepared by preceding consonance, bass rising second or fourth? Use it. Resolve as example prescribes; keep good modulation.", "III.30-019": "Seventh may always accompany ninth, but never add unless preceding consonance prepares it. See qualification in Book II, Chapter XVII.", "III.30-020": "Minor dissonances by supposition—ninth and next chapter’s eleventh—may be prepared by ordinary dissonance: seventh or diminished fifth. Seventh suits only heteroclite eleventh’s preparation. These dissonances belong to same fundamental chord. Chapter XII: same note can form successive dissonances derived from same fundamental chord.", "III.30-021": "Turn page for next example.", "III.30-022": "EXAMPLE.", "III.30-023": "Successive dissonances; continuo bass and fundamental bass.", "III.30-024": "Continuo notes A bear derivatives of chords figured on fundamental bass; likewise B. Supposition dissonance may follow dissonance. Yet consonance must precede and follow dissonance. To preserve rule, successive dissonances on same degree cannot truly be separate. All derive from initial seventh. Its fundamental chord stays until apparent dissonances end on consonance. Example shows this; so it is.", "III.30-025": "See Chapter XV: heteroclite eleventh also prepared by diminished fifth, etc.", "III.31-001": "CHAPTER THIRTY-ONE.", "III.31-002": "Eleventh Chord, Called Fourth.", "III.31-003": "Eleventh chord has five sounds: [D, A, C, E, G: 1. 5. 7. 9. 11.]. Added sound lies fifth below seventh chord’s foundation:", "III.31-004": "A, C, E, G.\n 5. 7. 9. 11.\n 1. 3. 5. 7.", "III.31-005": "Chord rarely used: extremely harsh, with three minor dissonances, 7, 9, 11. Yet easy to use: preceding chord’s three consonances stay to prepare them. Do not resolve all three together. Minor dissonances must descend; simultaneous descent creates unavoidable consecutive fifths. Resolve harshest first—eleventh and ninth—then seventh.", "III.31-007": "EXAMPLE.", "III.31-008": "Eleventh chord and successive resolution; cue signs.", "III.31-009": "Continuo progression prepares ninth and eleventh as in ninth chord. Best resolve eleventh with bass stationary, then sound seventh chord. Bass may instead rise third, as cue sign shows. Then hear great-sixth chord derived from stationary note’s seventh chord.", "III.31-010": "Upper cue signs show fifth sounds sometimes omitted from eleventh chord, especially with four parts. Substitute fifth sound for another if consonant; if dissonant, at least prepare it.", "III.31-011": "Here discussing true eleventh chord, fully constructed. Great harshness requires removing most sounds, as in Chapter XV’s chord—therefore called heteroclite. Alteration makes chord more tolerable. Full form rarely used, though apt use sometimes gives pleasing harmonic and melodic suspensions.", "III.31-012": "EXAMPLE.", "III.31-013": "Heteroclite eleventh; suspensions A and resolutions B.", "III.31-014": "Customary figures: heteroclite form, 4 alone; complete form, add 9: [4/9] or [9/4]. Heteroclite form sometimes includes seventh: [7/4] or [4/7].", "III.31-015": "Supposition chords only delay naturally expected sounds. A’s sounds suspend expected B sounds. Same wherever these chords occur. Compare with continuo bass, not fundamental bass, which always represents perfect harmony.", "III.32-001": "CHAPTER THIRTY-TWO.", "III.32-002": "Augmented-Seventh Chord.", "III.32-003": "Augmented-seventh chord differs from eleventh only in fundamental sound’s third: major here, previously 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 Supplement.]", "III.32-008": "Chord occurs only on tonic. Same tonic’s perfect chord must precede and follow.", "III.32-009": "EXAMPLE.", "III.32-010": "Augmented seventh; suspensions A and resolutions B.", "III.32-011": "A sounds suspend B sounds. Marks [diagonal lines] show A’s natural progression.", "III.32-012": "Bass falling whole tone or semitone: often omit sound forming augmented seventh.", "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": "Figure 2: preparation same as second chord. Fifth and fourth coexist; fourth therefore dissonance by supposition. Chord represents eleventh or augmented seventh with one sound omitted—the sound entering bass next at D. That sound dislikes octave doubling.", "III.33-001": "CHAPTER THIRTY-THREE.", "III.33-002": "Augmented-Second Chord and Derivatives.", "III.33-003": "Augmented-second chord and derivatives are chords by borrowing. Tonic dominant yields foundation to sixth note, in minor keys only. Augmented-second chord and derivatives arise 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": "Borrowing origin justified: sixth note occupies tonic dominant’s place. Seventh chord’s other sounds remain unchanged; major and minor dissonances keep natural progression. In middle of piece, choose either bass note freely beneath these sounds. But following harmony no longer free: must follow seventh chord’s required course. Tonic perfect chord follows either chord.", "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": "Borrowed chords contain two major, two minor dissonances. Foreign ones arise from replacing tonic dominant with sixth note. Minor dissonances always descend. Foreign major dissonance need not rise, unlike leading note. Cue sign H allows its ascent; ascent required when minor dissonance C or A lies in bass.", "III.33-015": "Only difference between examples: sixth note replaces tonic dominant A. Dissonance succession same in both; modulation unchanged.", "III.33-016": "Dominant replaced by sixth creates augmented-second chord; corresponding change affects all derivatives of tonic dominant’s seventh chord.", "III.33-017": "Leading note normally bears diminished-fifth chord. Same substitution yields diminished-seventh chord: 7♭ replaces 6, B.", "III.33-018": "Fourth note’s tritone chord: minor third replaces second, C.", "III.33-019": "Second note’s small-sixth chord: diminished fifth replaces fourth, D.", "III.33-020": "Mediant’s augmented-fifth chord: fourth replaces third, F.", "III.33-021": "Tonic’s augmented-seventh chord: minor sixth replaces fifth, G.", "III.33-022": "To understand difference, take four upper bass lines alone. Each serves as bass in turn; others serve as upper parts.", "III.33-023": "Lower two basses bear supposition chords; cannot serve as upper parts. Hear each separately with upper four. Lower basses sound poorly together.", "III.33-024": "New minor dissonance may descend alone. Tonic dominant’s seventh chord then remains naturally constructed.", "III.33-025": "EXAMPLE.", "III.33-026": "Descent of the new minor dissonance; six chords.", "III.33-027": "Leading note may rise alone only in invertible chords, not final two supposition chords. After ascent, return it to place in tonic dominant’s seventh chord.", "III.33-028": "EXAMPLE.", "III.33-029": "Ascent and return of the leading note; four chords.", "III.33-030": "Borrowed chords and augmented-fifth chord work only in minor keys, as stated. Each has fixed particular bass note. More in Chapter XXXV. Further licenses: Book II, Chapters XIII and XVIII.", "III.34-001": "CHAPTER THIRTY-FOUR.", "III.34-002": "Chromatic Movement.", "III.34-003": "Chromatic melody moves by semitones, up or down. Wonderful harmonic effect: most semitones fall outside diatonic order, continually creating dissonances that suspend or interrupt conclusions. They also help fill chords with all sounds without disturbing upper parts’ diatonic order.", "III.34-004": "Chromatic used only in minor keys. Descending parts harder to understand than ascending.", "III.34-005": "ARTICLE ONE.", "III.34-006": "Descending Chromatic Movement.", "III.34-007": "Begin chromatic descent in any part. Continue in same key, dominant’s key, especially fourth note’s key. Original tonic then becomes dominant. Chain continues: each tonic becomes next key’s dominant. Stay near opening key; return at first opportunity.", "III.34-008": "First understand chromatic through successive tonics becoming dominants.", "III.34-009": "Go tonic to dominant; return to tonic, now made dominant. Follow sevenths rule, Chapter XXI. Upper parts descend by as many semitones as possible. Each note forms third, seventh, sometimes diminished fifth above fundamental bass, which still bears seventh chord. Only difference from ordinary rules: leading note may descend semitone instead of required ascent. Expected upper sound remains understood in chord. Chromatic alone permits liberty.", "III.34-010": "EXAMPLE.", "III.34-011": "Descending chromatic movement; fundamental bass of sevenths.", "III.34-012": "[Handwritten note: see Supplement.]", "III.34-013": "Naturals ♮ beside 7s make previously major intervals minor. See parts.", "III.34-014": "Each part becomes bass in turn; omit fundamental bass. First find 7–6 succession like derivative of fundamental sevenths, with chromatic difference. Then tritones and diminished fifths replace 2 and [6/5]. Chromatic lets these intervals resolve one another. Leading note descends everywhere except ending, instead of ascending.", "III.34-015": "Another chromatic method: tonic held or stationary in bass.", "III.34-016": "EXAMPLE.", "III.34-017": "Pedal point; chromatic movement over a held tonic.", "III.34-018": "Call this pedal point.", "III.34-019": "Leading note almost always present in chromatic. Use all chords containing major dissonance, as above; also augmented second and derivatives, especially augmented fifth to interrupt cadence. See Chapter XXX example: leading note descends semitone. Construction of augmented/diminished chords by borrowing or supposition now known. Use wherever leading note fits. Still use perfect and seventh chords and derivatives when encountered. Preserve upper parts’ diatonic order 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 can ascend. Lacks descending kind’s sadness. Resulting harmony fits 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. Fundamental note cannot sound while C borrows its foundation.", "III.34-027": "A. Interrupted cadence.", "III.34-028": "EXAMPLE", "III.34-029": "Two Parts Ascend and Descend Simultaneously by Semitones.", "III.34-030": "Turn page for example.", "III.34-031": "Three Upper Parts Interchange; Each May Serve as Bass.", "III.34-032": "Contrary chromatic movements; continuo bass and fundamental bass.", "III.34-033": "All chromatic semitones concern current key’s sixth and seventh alone. Minor key: lower leading note semitone to descend; raise sixth semitone to ascend. Notes can pass through both forms, ascending or descending.", "III.34-034": "To confirm rules’ truth fully, compare details with recap, Book II, Chapter XVIII. All chords, different successions, and usable melodies appear there.", "III.34-035": "Also see observations on establishing rules; very useful.", "III.34-036": "Chapter XLIV: chromatic example with supposition and borrowed chords, producing very good effect.", "III.35-001": "CHAPTER THIRTY-FIVE.", "III.35-002": "Practicing Everything So Far.", "III.35-003": "ARTICLE ONE.", "III.35-004": "Bass Progression.", "III.35-005": "Compose bass with most beautiful melody imaginable. Use familiar key leading to other familiar keys: Chapter XXIV. Include perfect cadences often. Natural bass progression favors consonant over diatonic intervals. Admit interrupted/irregular cadences only when understood and felt appropriate. Interrupted cadence avoids too many perfect cadences in same key: pleasing variety. Irregular cadence gives repose on tonic dominant or tonic: pleasing suspense. Also include progressions supporting harmony derived from different cadences, as examples show. Remember 7, 7 and 6, 2 and 6, barred 5, 4♯, 2♯, 9, 11, 5♯, 7♯ progressions.", "III.35-006": "Each bass note and chord represents beat. Whole note may divide into four quarters, making four beats, assuming four-beat meter.", "III.35-007": "Doubt ability to compose good bass? Lack natural taste inventing varied, pleasing melodies? Move bass freely among key’s notes. Prefer small intervals: rise third rather than fall sixth. Leading note must lead to tonic, except chromatic. Sound final cadence before changing key. Proceed similarly in new key, then next: Chapters XIII, XIV, XV, XVI, XXIV, XXV. Perfect, interrupted, irregular cadences end on first beat. Compose accordingly. First cadence misplaced but melody wanted unchanged? Shift starting beat: first to second/third, or second/third to first, etc. Problem midpiece? Add or remove one or two notes as needed. Cadences should be felt every two or four measures. Break last rule when taste dictates or words require; follow words then.", "III.35-009": "ARTICLE TWO.", "III.35-010": "Using Consonant and Dissonant Chords.", "III.35-011": "Perfect chord begins, ends, and serves all internal cadences. It and derivatives—sixth, sixth–fourth—also suit diatonic bass. Consonant/dissonant chords intertwine there. See octave, Chapter XI; sixths, Chapter XVI. Prepare and resolve dissonances by rules. Master chord succession; little attention then needed. Unprepared dissonances allowed only after tonic perfect chord, on tonic or derivatives, key unchanged. Exception: key may change when bass rises third then falls fifth.", "III.35-012": "EXAMPLE.", "III.35-013": "Rising third, then falling fifth; key changes A and B.", "III.35-014": "[Handwritten note: see Supplement.]", "III.35-015": "Bass rises third then falls fifth, changing key: major becomes minor at A; minor becomes major at B. Lines running between notes,", "III.35-016": "thus, [lines converge from the two notes on the left toward the one on the right],", "III.35-017": "show right-hand note’s dissonance unprepared, and required upper-part progression.", "III.35-018": "Use inversions of these fundamental progressions freely.", "III.35-019": "Keep upper parts diatonic for now. Exceptions: complete chord, restore part above bass, return it to natural range. Avoid consecutive octaves/fifths, unless inverted.", "III.35-020": "Parts moving up or down together: use thirds/sixths, fewest possible fourths, never octaves/fifths. Two parts forming third/sixth may repeat interval in next chord, and onward.", "III.35-021": "One part moves diatonically up/down while another moves consonant interval: always good, pending more exact explanation.", "III.35-022": "Chord succession same in every key. Identify key; give each note chord suited to rank. Second, mediant, dominant, etc. keep same ranks and chords in every key.", "III.35-023": "ARTICLE THREE.", "III.35-024": "Leading-Note Major Dissonances and Their Bass Notes.", "III.35-025": "1. Tritone only on fourth note, then descending to mediant or tonic.", "III.35-026": "2. Diminished fifth only on leading note, then rising to tonic or sometimes mediant.", "III.35-027": "3. Major small-sixth chord only on second key note. Minor sixth version usually on sixth note.", "III.35-028": "4. Major third and seventh forming tritone/diminished fifth coexist only on tonic dominant. These four dissonances most used.", "III.35-029": "5. Augmented seventh only on tonic, stationary for preparation and resolution.", "III.35-030": "6. Augmented fifth only on minor-key mediant, as stated elsewhere.", "III.35-031": "7. Augmented second only on minor key’s sixth; note then descends.", "III.35-032": "8. Diminished seventh only on leading note; note then ascends.", "III.35-033": "9. Other derivatives of last two use same notes as corresponding chords differing only by dominant-to-sixth substitution. Minor keys only.", "III.35-034": "ARTICLE FOUR.", "III.35-035": "Minor Dissonances.", "III.35-036": "1. Heteroclite eleventh, called fourth, allowed on notes requiring perfect/seventh chords, provided proper chord follows immediately. Exclude first/last note of piece. Preparation assured with two observations.", "III.35-037": "First: perfect chord after own derivative is same chord. Eleventh forbidden there.", "III.35-038": "Second: note rising third onto intended eleventh-bearing note always takes sixth.", "III.35-039": "2. Seventh without major dissonance prefers preparation by octave, fifth, sixth, third, or sixth; even fourth allowed as consonance from tonic dominant’s sixth–fourth chord. Choice follows bass progression.", "III.35-040": "3. Ninth always prepared by third/fifth according to bass motion; diminished fifth also allowed.", "III.35-041": "4. Eleventh prepared by fifth, sometimes seventh but rarely. Heteroclite form: any consonance, seventh, or diminished fifth may prepare.", "III.35-042": "5. Second prepared in bass: any upper consonance may precede while bass holds. Resolve all dissonances as stated.", "III.35-043": "Any dissonant chord: omit one sound of dissonant pair; leave perfect chord or derivative.", "III.35-044": "ARTICLE FIVE.", "III.35-045": "Preferred Consonances for Doubling.", "III.35-046": "Preference order: octave, fifth, fourth, third, sixth. Prefer octave to fifth, and so on. Octave already duplicates. Consonant sixth chord: octave doubling of third/sixth as good as bass doubling.", "III.35-047": "ARTICLE SIX.", "III.35-048": "Meter and Beat.", "III.35-049": "Music without movement loses grace; beautiful melody impossible without it. Do more than make chords. Parts need movement revealing caesura, section, cadence, long versus short syllable, proper dissonance beats. All felt at first instant of measure’s first beat. See Chapter I; Book II, Chapters XXVI, XXVII, XXVIII, XXIX.", "III.35-051": "ARTICLE SEVEN.", "III.35-052": "Syncopation.", "III.35-053": "Natural meter: note begins and ends within beat. Note starting at strong beat’s first instant may stay same pitch as long as taste allows, sustained or not. Note beginning elsewhere, half its value sounding in next strong beat, strikes against ear: syncopation. Four forms follow.", "III.35-054": "First: barline divides note into equal halves. Thus:", "III.35-055": "First form of syncopation; meters in 2, 4, and 3.", "III.35-056": "Second: equal successive same-pitch notes joined by semicircle [upper arc] or [lower arc]. Sound remains continuous.", "III.35-057": "EXAMPLE.", "III.35-058": "Second form of syncopation; tied notes.", "III.35-059": "Third: note or rest worth half first beat precedes note extending into following 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, J: syncopated notes.", "III.35-063": "Fourth: repeat equal same-pitch notes instead of tying. First strikes weak beat, second strong. Fits words or makes air livelier, more cheerful.", "III.35-064": "EXAMPLE.", "III.35-065": "Fourth form of syncopation; repeated notes.", "III.35-066": "Syncopated note starts weak beat or second half of first beat. Value must divide equally between first beat and next. Replace single note with two half-value notes if desired. Repeat them or tie with semicircle for sustained sound. Tied pair performed as one note of combined value.", "III.35-067": "Let composer choose syncopation form freely: most skilled masters agree. Forms serve harmony and melody alike. Harmony: prepared dissonances. Melody: greater expression without changing interval species across two notes or single syncopated note.", "III.35-068": "EXAMPLE.", "III.35-069": "Syncopation in harmony and melody.", "III.35-070": "Consonance-only figures, 3, 6, etc.: syncopation serves melodic taste. Dissonance after consonance: syncopation serves harmony.", "III.35-071": "Melodic syncopation allowed in bass and upper part, together or separately. Harmonic bass syncopation only in 2, 4♯, augmented-seventh chords.", "III.35-072": "Strict harmonic syncopation: preparing consonance, dissonance, resolving consonance equal in duration as far as possible. Exception only triple meter, with two weak beats. Preparing/resolving consonance may then last twice or half dissonance’s value.", "III.35-073": "Successive dissonances: only first can follow weak-beat preparation, strong-beat sounding rule.", "III.35-074": "Unprepared dissonance: syncopation no longer involved. Prefer diatonic motion from preceding consonance through dissonance to resolving consonance, with equal note values. Equality less necessary than in syncopation. Diatonic approach to unprepared dissonance not universal rule, especially for seventh, diminished fifth, all major dissonances.", "III.36-001": "CHAPTER THIRTY-SIX.", "III.36-002": "Two-Part Composition.", "III.36-003": "Fewer parts, stricter rules. Licenses allowed in four parts may become faults with fewer.", "III.36-004": "1. Distinguish perfect/imperfect consonances.", "III.36-005": "Perfect consonances: octave, fifth. No consecutive octaves/fifths here, even inverted.", "III.36-006": "Fourth also perfect consonance, poorly suited to two parts. Merely prescribe its use.", "III.36-007": "Imperfect consonances: third, sixth. Repeat and mix freely, preserving good modulation.", "III.36-008": "Third to sixth or sixth to third, parts moving by consonant intervals: use contrary/inverted motion. One rises, other falls.", "III.36-009": "Prefer alternating perfect and imperfect consonances.", "III.36-010": "Perfect-to-perfect, perfect-to-imperfect, imperfect-to-perfect: scarcely possible unless one part moves diatonically, other by consonant interval. Contrary motion advisable even then.", "III.36-011": "EXAMPLE. Perfect-Consonance Succession.", "III.36-012": "Succession of perfect consonances", "III.36-013": "Any other succession of two perfect consonances is bad.", "III.36-014": "A measures alike; B measures likewise.", "III.36-015": "2. One part stays; other may move through any number of consonant intervals. Parts must always agree.", "III.36-016": "3. Good transitions: octave→third; fifth→third/sixth; sixth→third; third→sixth.", "III.36-017": "4. Octave→fifth good with contrary motion. Bass descending diatonically: bad.", "III.36-018": "5. Octave→sixth good; both parts moving consonant intervals require contrary motion. Bass falling third: all good.", "III.36-019": "6. Sixth→octave good except bass rising diatonically, upper part falling diatonically, or both moving consonant intervals.", "III.36-020": "7. Sixth→fifth good except upper part rising diatonically, bass falling diatonically, or both moving consonant intervals.", "III.36-021": "8. Fifth→octave good except bass rising diatonically or both moving consonant intervals.", "III.36-022": "9. Third→octave good except bass descending diatonically. Bass rising fifth requires contrary motion.", "III.36-023": "10. Third→fifth also good. Bass rising second/third/fourth requires contrary motion. Rise fourth rather than fall fifth; otherwise progression bad.", "III.36-024": "11. Fourth: example shows all consonances allowed before and after.", "III.36-025": "Consonances that may precede and follow the fourth", "III.36-026": "Cue signs show consonances and dissonances following fourth. Figures between parts likewise. Figures below bass show required chords.", "III.36-027": "A/B cue signs offer tritone or great-sixth chord. One excludes other.", "III.36-028": "Other progressions bad. Rules favor smaller intervals naturally. Rise sixth equals fall third; prefer fall third. Likewise other equivalent motions. Taste may demand opposite only where rules’ foundation stays intact.", "III.36-029": "Rules valid in all keys, thirds/sixths major or minor.", "III.36-030": "Other four-part rules apply everywhere: natural major/minor-third motion and dissonance motion alike.", "III.36-031": "Know good modulation; almost all rules follow without much attention.", "III.37-001": "CHAPTER THIRTY-SEVEN.", "III.37-002": "False Relations.", "III.37-003": "Single part: avoid false relations through diatonic/consonant motion. Diminished fifth, seventh, fourth also allowed downward, not upward. With good modulation, any known interval within octave allowed, but unnamed intervals need more care. Italians add descending diminished third, E-flat→C-sharp. Composer decides.", "III.37-004": "Master modulation; false relations between two parts become impossible.", "III.37-005": "EXAMPLE.", "III.37-006": "False relations — major and minor modes", "III.37-007": "A shows major mode; B minor. Cannot modulate in half-major, half-minor key. Same tonic cannot switch major/minor either way before perfect cadence in opening key. Even then, great caution needed. Master modulation; these rules almost unnecessary. No more needed here.", "III.38-001": "CHAPTER THIRTY-EIGHT.", "III.38-002": "Making Melody Above Bass.", "III.38-003": "First compose bass in one key with familiar modulation. Know consonance/dissonance succession and preparation/resolution. Faultless melody above bass then easy.", "III.38-004": "For greater invention, know each bass note’s chord; choose one chord sound for melody. Perfect chord: third, fifth, octave. Seventh chord: seventh also, if wanted and permitted. Seventh needs preparation except bass rising third/fifth with upper part descending diatonically, or ascending then descending diatonically. See Chapter XIX. Seventh cannot descend diatonically to next consonance? Omit seventh or change bass. Exception: following bass notes belong to same seventh chord, then later note permits consonant resolution. Hold seventh until then, unless bass doubles it at octave. Then lower seventh third; raise new note onto expected resolving consonance. Or descend to leading note if within same chord. Downward-third destination forms sixth above bass doubling seventh; leading note forms tritone.", "III.38-005": "EXAMPLE.", "III.38-006": "Seventh unprepared or prepared by the third", "III.38-007": "A. Begin fifth; octave/third possible. Fifth preferable for following unprepared seventh, as explained.", "III.38-008": "B. Hold seventh until bass octave at C. Descend third, then rise to expected resolving consonance. Could instead descend to cue sign.", "III.38-009": "D. Third prepares seventh. Hold to F, where bass gives octave. Then descend to leading note F within same chord.", "III.38-010": "Held seventh over moving bass: bass notes form third, fifth, diminished fifth, octave of seventh; or seventh forms third, fifth, diminished fifth of bass note. Same for other dissonances referred to foundation. Otherwise known limits of consonance/dissonance progression prevent error.", "III.38-011": "Upper note may stay while bass moves through same chord. Conversely bass may stay while upper part traverses all its chord intervals.", "III.38-012": "Same bass note, multiple chords: shared third/fifth/sixth/etc. usable in either. Interval absent from chord cannot sound there.", "III.38-013": "Taste undeveloped but bass chords known? Figure chords; choose notes for upper melody within rules. Rules often favor certain notes because of preceding/following notes.", "III.38-014": "Two parts: upper part always ends octave, rarely third, never fifth.", "III.38-015": "GENERAL EXAMPLE.", "III.38-016": "General example — upper part, continuo bass, and fundamental proof", "III.38-017": "Upper part written against continuo alone has many faults against fundamental bass. Faults concern part progression, not harmonic foundation. Fundamental bass only proves perfect harmony supplying desired melodic sounds.", "III.38-019": "A. Pass freely through all chord sounds.", "III.38-020": "Fifth moves to sixth at B. Could keep preceding pitch as fourth, part of B’s small-sixth chord. Third also possible.", "III.38-021": "B, C, D, E: four successive sixths, all chord members. Other chord intervals also possible.", "III.38-022": "F, G: leading note moves to mediant, not tonic. Consonance-progression rules intact. Mediant represents tonic and belongs to tonic chord.", "III.38-023": "H: fourth belongs to second chord. Then sixth at J; second at K belongs to tritone chord.", "III.38-024": "L sixth prepares M seventh; resolves downward to N sixth. This leading note rises properly to O tonic. Then tonic’s third at P, preparing second at Q.", "III.38-025": "P, Q, R, S, T: seconds prepared/resolved in bass; upper preparation third at P, sixth at R. Octave/fifth/fourth also possible. Any chord consonance may precede/follow second. T gives following fourth from small-sixth chord. Prescribed bass motion unchanged.", "III.38-026": "Third best prepares/resolves second; use often. Substitute fourth at T would clash with third. Fourth must fall to third’s expected descending destination, as at V. General rule: substitute for upper resolving note forms seventh/second with absent note. Send substitute to note that should follow absent note, which would form minor dissonance with substitute. Applies third/fourth in small-sixth chord; fifth/sixth in great-sixth and diminished-fifth chords. Third/fifth meant to resolve then descend diatonically? Replacing fourth/sixth must reach that expected destination.", "III.38-028": "Rest continues same rules. Key changes at M: leading note becomes tonic’s seventh instead of rising to tonic octave. Tonic becomes fourth through great-sixth/tritone chords at N/O. Return C key at J: consonant bass progression ending U reveals C tonic. Prepare by removing F sharp at D. Then B-flat announces F key. Sharp restoring natural B declares C again.", "III.38-029": "Clarify by comparing upper part, then continuo, against fundamental bass. Each fundamental perfect/seventh chord supplies third, fifth, octave, seventh for continuo and upper parts. Fit their motion to earlier rules. At G, H, J, K, L, etc., diatonic continuo often accompanies upper motion like fundamental bass. Thus consonant motion in one part often demands diatonic motion in other; converse also true.", "III.39-001": "CHAPTER THIRTY-NINE.", "III.39-002": "Figured Melody, or Supposition.", "III.39-003": "Previously called supposition; we call it figured melody. Rules follow.", "III.39-004": "Harmonic perfection must appear each beat. Beat felt at arrival, hand down or up. Between one beat’s instant and next, pass as many notes as invention and taste permit.", "III.39-005": "ARTICLE ONE.", "III.39-006": "Figured Melody Through Consonant Intervals.", "III.39-007": "Consonant intervals between beats: only current chord’s notes allowed. Land on next beat’s chord note. Continue to end.", "III.39-008": "EXAMPLE: Figured Upper Part.", "III.39-009": "Figured melody through consonant intervals — upper part", "III.39-010": "Upper notes use only sounds fitting figured bass chords.", "III.39-012": "Composer may divide two-beat measure into four. A’s two chords divide note into two beats. Slow/fast tempo permits multiple chords per beat, or one chord across one/several measures.", "III.39-013": "EXAMPLE: Figured Bass.", "III.39-014": "Figured bass and fundamental bass — conditional cue signs C, D", "III.39-015": "Figures below figured bass: intervals with fundamental bass. Figures above: chords borne by notes.", "III.39-016": "First write fundamental bass, then figured bass above, much like figured upper part. Difference: do not avoid shared notes. Use fundamental root sounds in figured bass whenever possible, even at beat’s first instant.", "III.39-017": "Fit upper part to sounding companion. Both basses sounding? Rules must hold against both. At C/D upper part forms two fifths with fundamental; replace notes with cue signs.", "III.39-018": "Or compose figured bass first. Mark beats; add fundamental bass obeying its progression/chord rules completely. Then write upper part with more or less figuration than figured bass.", "III.39-019": "Figured-bass notes often fit two chords. Following beat decides uncertain choice. Fundamental bass also guides.", "III.39-020": "Seek variety; avoid overrepeating passages.", "III.39-021": "Figure all beats or not. Sometimes figure only half beat, in bass, upper part, or both. Always follow rules.", "III.39-022": "EXAMPLE.", "III.39-023": "Two figured parts — variety of beats", "III.39-024": "One part starts; other enters two/three beats or one/two measures later, as taste dictates. Same for further parts.", "III.39-026": "Start anywhere, even beat’s last quarter. Part may stop temporarily. Bass can stop only one/two measures maximum. Continuo always implied, even with single sounding part.", "III.39-027": "Mark silences with quarter rests and other signs from Chapter I.", "III.39-028": "Dot continues preceding note. Usually forms chord with other parts, nearly always on strong beat. Value half preceding note. If only half beat or less, following note admitted solely for melodic taste.", "III.39-029": "ARTICLE TWO.", "III.39-030": "Figured Melody Through Diatonic Intervals.", "III.39-031": "Any number of notes between beats. Diatonic motion: first must belong to chord; others need not. Last note moving consonant interval to next beat must also belong to current chord.", "III.39-032": "Beat slow enough for two equal beats? Divide passing notes equally too. First note of each division belongs to current chord.", "III.39-033": "Taste sometimes breaks rules. Diatonic beat’s first note may be outside chord. It serves as coulée, sliding approach, leading immediately to chord note before beat ends.", "III.39-034": "EXAMPLE.", "III.39-035": "Figured melody through diatonic intervals", "III.39-036": "Two-beat meter divided into four almost everywhere. First of two eighths always chord member.", "III.39-037": "At A, first of final two eighths outside chord: melody proceeds diatonically between beats. First two eighths, outside that progression, belong to chord.", "III.39-038": "B: each note bears chord; divide beat four ways. Tonic following leading note requires natural chord immediately. Tonic at next measure’s start with melodic repose would leave B undivided. But melody rests on dominant; irregular cadence felt from B’s final eighth to next note.", "III.39-040": "C’s first/third eighths outside chord: coulées into second/fourth chord notes. Fourth must belong, since next-beat motion consonant. Similar coulées at F/D.", "III.39-041": "D dot represents preceding note. Figured tritone chord lasts through dot. Resolution only on following beat.", "III.39-042": "Thus we explain what previously appeared only through abstract rules.", "III.39-043": "Figured melody’s flexibility and chord inversion produce music’s incomprehensible variety.", "III.40-001": "CHAPTER FORTY.", "III.40-002": "Making Fundamental Bass Under Upper Part.", "III.40-003": "Fundamental bass most reliable for fitting bass to existing upper part when taste cannot yet sense both together. Every melody has natural bass, best fit, anticipating thought. Slight sensitivity to perfect harmony makes us sing cadence bass on hearing upper part. Key becomes known. Successive perfect/irregular cadences reveal key changes; interrupted cadence’s upper part same as perfect. Fundamental bass allows only perfect/seventh chords, deciding faster.", "III.40-004": "EXAMPLES. Upper-Part Cadence Progressions.", "III.40-005": "Perfect or irregular cadences in major and minor keys", "III.40-006": "All cadences established in C alone, though related to other keys.", "III.40-007": "Perfect cadence A: leading note rises to tonic in major/minor. Could instead rise second→mediant in minor, as F.", "III.40-008": "Perfect cadence B: second descends to tonic in major/minor. Minor also allows fourth→mediant, as G. First two cadences closely connect C major/A minor. Generally shared by major and minor keys minor third apart: C major/A minor, F major/D minor, G major/E minor, etc.", "III.40-009": "C/D/F/G may be perfect or irregular. Bass choice decides: up fourth to tonic gives perfect; down fourth to tonic or dominant gives irregular. Dominant option means keys beyond C. C/D irregular in D; D also irregular in F. F/G perfect in E-flat; G also irregular in A-flat. True irregular cadences on C’s dominant: H/J/L/M. Yet H perfect or irregular in B-flat; J irregular in A minor; L perfect in D; M irregular in B-flat major, G minor, E-flat major or minor. Uses of these ambiguous upper cadences follow.", "III.40-011": "1. Write C major or D minor if other keys less familiar. Start only octave/third/fifth. Check first cadence, usually measure two/four. Opening C/E/G belongs to C chord; first cadence on D does not make D key. D key would require opening D/F/A. Melodic semitones requiring sharps/flats immediately determine key: Chapters XXIV/XXV. Opening C can be A’s minor third, F’s fifth, C’s octave. Sharps/flats/cadences distinguish key. Naturally tasteful air: final note should be tonic, enough to identify key.", "III.40-012": "2. Key certain: assign all fitting cadences to it. Compare foreign ones with preceding example; observe following rules.", "III.40-013": "1. Upper part always third/fifth/octave/seventh against fundamental bass.", "III.40-014": "2. Prefer descending fifth, then fourth, then third, then seventh. Rising second equals falling seventh, etc. Descending fifth cannot fit upper part? Seek fourth/third/seventh, most perfect first.", "III.40-016": "3. Practice fundamental bass with unfigured upper part. Figuration confuses beginners. Each upper note lasts at least beat.", "III.40-017": "4. Begin characteristic airs: gavottes, sarabandes, etc. Cadences felt almost every two measures; quicker decisions. Book II, Chapters XXV–XXVIII: tempo, measure count, suitable verse, word-setting rules.", "III.40-018": "5. Foreign cadence: does it end melody? Words clarify. If yes, key changes, usually to dominant/mediant/fourth/sixth of departing key. Compare preceding example. Cadence ending thus:", "III.40-019": "Thus — cadences in F, G, D, E, and A", "III.40-020": "represents perfect cadence in one of these keys, just as this", "III.40-021": "Perfect cadence in C", "III.40-022": "represents one in C. Same for other proportionally related cadences. Melody not fully ended? Bass follows natural course; prefer most perfect progressions where possible.", "III.40-023": "6. Upper part third/fifth/octave of existing bass? Bass may stay. Change if natural progression intact; variety, chief harmonic beauty, then demands change.", "III.40-025": "7. First beat principal. Bass note intended elsewhere also fits neighboring first beat? Advance/delay it there. First case: note after first beat fits first; bring forward. Second: weak-beat note same as next first-beat note, no intervening notes possible. Keep previous first-beat bass if possible, or choose different note before next first beat.", "III.40-026": "EXAMPLE.", "III.40-027": "First beat preferred — examples H and J", "III.40-028": "H better: second measure’s second-beat note fits first beat; prefer it there.", "III.40-029": "ANOTHER EXAMPLE.", "III.40-030": "Another example — held or varied bass", "III.40-031": "A: cannot hold same bass through first measure, though may change as B. Another note fits between first measure’s second beat and next first beat. C/F: avoid first measure’s second bass note, needed immediately on next first beat. D: keep prior first-beat note; still fits second beat. G: choose another; first no longer fits.", "III.40-033": "8. Often split upper note into equal halves for two compatible bass notes. Preserves consonant bass motion; most perfect progression joins second bass note to next.", "III.40-034": "EXAMPLE.", "III.40-035": "Dividing an upper note and progressing the bass", "III.40-036": "Division also puts key’s best fundamental notes on principal beats. Preference: tonic, dominant, fourth, sixth, sometimes second. Mediant rare; seventh never on any beat. Unavoidable seventh means key changed, revealed by sharps/flats/foreign cadences.", "III.40-037": "9. First prepared dissonance sounds principal beat. Successive dissonances: regard only first. Unprepared dissonance requires upper three-degree diatonic descent, or ascent then immediate descent, while bass rises third/fifth then falls fifth. Middle degree dissonant.", "III.40-039": "EXAMPLE.", "III.40-040": "Unprepared seventh and cadence cue signs", "III.40-041": "Rise bass fourth instead of fifth here: no dissonance. Converts perfect↔irregular cadence. A–B perfect; move A to cue sign, irregular with B.", "III.40-042": "Cue signs above first bass note show further progressions. Move first note to either cue.", "III.40-043": "Against fundamental bass, only seventh dissonant. Others arise by inversion: bass taken from another note of its seventh chord. Follow Chapters XVII, XVIII, XX, XXI, XXII, XXVI.", "III.40-044": "Unprepared seventh sometimes good despite upper leap. Keep preceding fundamental bass note stationary. Upper part must immediately descend diatonically; bass can then rise fourth to form third after seventh.", "III.40-045": "Turn page for example.", "III.40-046": "EXAMPLE.", "III.40-047": "Upper-part leaps — examples A, B, J and C, D, F", "III.40-048": "Upper leap A→B would make seventh over held first bass. But upper does not descend after B; held bass rising fourth cannot form third with J. Change bass as shown, choosing most perfect progression. C/D/F gives conditions absent in A/B/J. Former name: supposition, or dissonance for melodic taste. Dissonant harmony already present at first upper note; bass stays to receive later dissonance. Hear full seventh chord on first bass under C to verify. After seventh, upper may visit other same-chord notes, then return to third—or at least octave—of bass rising fourth at G.", "III.40-049": "EXAMPLE.", "III.40-050": "Dissonance for melodic taste — examples G and H", "III.40-051": "Bass may rise degree instead of fourth: interrupted cadence. Only borrowed/inverted bass permits this. Composer’s taste decides inside piece only; no consecutive fifths with upper part.", "III.40-053": "10. Repeated same-key cadences: seek internal nonfinal cadence fitting another key. Use foreign cadence for variety. Constant same cadences make air languid. Taste forbids upper change? Vary bass inside air, especially nonfinal cadences.", "III.40-054": "Major key: related foreign cadences only from minor third-below minor key. Minor key: only from minor third-above major key. Difference in bass alone possible; upper unchanged.", "III.40-055": "EXAMPLE.", "III.40-056": "Same upper part — cadences in C and A", "III.40-057": "Upper perfect cadences A/B and irregular C/D fit C major or A minor naturally. In either key, use same cadence for other. Likewise D minor/F major, G major/E minor, other equivalent pairs.", "III.40-059": "Transferring cadence between keys also useful for definite key change.", "III.40-060": "Interrupted cadence usable in either case.", "III.40-061": "11. Irregular cadences excellent midair. Often end first of two sections, but avoid habit. Prefer measures 2/6/10; perfect cadences suit 4/8/12. Perfect cadence in 6/10 may become interrupted.", "III.40-062": "12. Cadence transferred between keys sometimes favors less perfect fundamental progression. Use judgment and discretion.", "III.40-063": "13. Free melody writing may ignore figuration, ties, continuous steps. Figuration: beginners may confuse harmonic notes with melodic-only notes. Leaps: fear consecutive fifths/octaves against fundamental bass. But melody then follows fundamental bass’s natural course. Need different bass fitting existing part. Fundamental bass reveals chords; choose chord notes for new bass agreeing harmonically and melodically. Consecutive fifths/octaves do not destroy harmonic foundation; forbidden to avoid dry, tedious monotony. Original rules based on natural bass/upper motion. Upper part borrowing bass motion makes natural bass course impossible. Need new reciprocal-motion rules, fitting second-composed part to first. New rules still grounded in old: natural part order avoids consecutive fifths/octaves; dissonances resolve correctly, prepared or not according to most perfect bass progression.", "III.40-065": "Often abandon natural bass motion to avoid frequent conclusions from most perfect progression. Put another cadential chord note in bass instead of natural note. Maintains melodic/harmonic suspense required by subject. Absolute conclusion only for completed meaning. Next chapter clarifies.", "III.41-001": "CHAPTER FORTY-ONE.", "III.41-002": "Composing Continuo Bass Under Upper Part.", "III.41-003": "True continuo should be fundamental bass. Custom names bass chosen by taste to fit other parts “continuo.” We keep term to distinguish from fundamental.", "III.41-004": "Cultivated taste naturally senses best bass for any air: previous chapter. Natural gift needs knowledge to avoid error; knowledge needs taste for perfection. Free chord-note choice does not identify best notes. Only rule for taste: compositional variety. Pursue it with following observations.", "III.41-005": "1. Now avoid consecutive octaves/fifths. Follow consonance/dissonance rules exactly: Chapters XIV, XVIII, XX, XXI, XXX.", "III.41-006": "2. Fundamental bass written: inspect upper design, expression, tempo, distinctive features. Reproduce expression in new bass. Avoid unwanted final cadences by choosing fundamental-chord notes fitting upper part and consonance/dissonance rules. Prepare dissonances when required; resolve each seventh-chord sound as prescribed. Vary intervals between parts. Fixed upper part allows different bass chord notes. Sixth then consonance/dissonance here; elsewhere choose different route: tritone→sixth, diminished fifth→third, seventh→sixth/third/fifth, according to bass motion. Or use seventh chord’s consonances only: octave/fifth/third, inverted sixth/fourth. Supposition/borrowed chords allowed when diatonic bass leads there. Diatonic progression most singable; use often, especially without conclusion. Minor supposition dissonances require syncopated upper preparation, bass ascending; descending bass must leap. Major-dissonance chords require precautions from octave and Chapters XI, XXII, XXXI, XXXIV, XXXV: augmented fifth/seventh, tritone, augmented second. Second requires syncopated bass preparation. At melodic ending, follow fundamental bass. Result: artful, tasteful bass.", "III.41-008": "EXAMPLE.", "III.41-009": "Continuo bass beneath an upper part — eight measures", "III.41-010": "Measure four: C perfect cadence could become A irregular cadence, as continuo cue signs show. Variety even demands it here.", "III.41-011": "Fundamental measures one/two show equal progressions A/B. Save more cadential one for measure two, usual cadence location. Cadence here irregular; measure four perfect. Measure one continuo moves diatonically, fitting upper part. Continue in measure two: second-beat note forms seventh against fundamental, resolves through its third, still fits upper. Continue diatonically to perfect cadence; there follow fundamental. Seek diatonic motion afterward. Final measure-four note stays: third against fundamental, octave against upper. Measure five: sixth against upper, seventh against fundamental. Measure six: ninth. Follow fundamental motion again only at final conclusion. Continuo/fundamental intervals reveal chords. Correct fundamental carries perfect/seventh chords alone. Its thirds/fifths/sevenths imply corresponding derived chords. Upper part could likewise be figured as bass. Measure-six first note lies third below or sixth above fundamental: admitted only by supposition. Fundamental seventh chord therefore requires continuo ninth chord, though upper part lacks ninth. Upper fifth belongs to ninth chord; implied ninth prepared/resolved by all rules.", "III.41-013": "Reason through every continuo variation: endless task. Make needed observations on treatise examples; apply questions to each. Also consult skilled masters’ works. Soon overcome all difficulties.", "III.42-001": "CHAPTER FORTY-TWO.", "III.42-002": "Useful Notes on Previous Chapter.", "III.42-003": "1. Bass beneath another part possible without fundamental bass. Know precisely defined consonance succession. Alternate perfect/imperfect where possible. Avoid successive perfect consonances when avoidable. Imperfect may repeat, but excess harms variety. Prefer diatonic bass; consonant motion needed occasionally, absolutely at principal cadences.", "III.42-004": "2. Compose bass from prescribed chord sequences: octave, 7 and 6, 2 and 6/5, 9, others. Each chord leads to required next chord. See Chapters XI, XXI, XXII, XXVII, XXVIII, XXIX.", "III.42-005": "3. Seek variety in Chapter XVII’s alternative basses under same upper part. Four example parts offer matching successive note pairs for your melody; choose pair here, pair there. Check same mode/key relation carefully. Compare scale rank, not note names. Examples in C; mediant→dominant, sixth→fourth, etc. allow same chords in any key.", "III.42-007": "Then Chapters XIV/XVIII: preparation/resolution. Never use dissonance without knowledge.", "III.42-008": "Also Chapters XXIV/XXVI, Articles I–III: change keys, distinguish them, find chords for any bass progression. Combined knowledge removes endless recurring doubts.", "III.42-009": "Once secure, study licenses for proper use. Figure upper melody, bass too if wanted. Track principal beats and harmonic note each beat for accurate bass figures. Doubt chord foundation? Add fundamental bass under two parts. Reveals faults and continuo chords. Note third/fifth/seventh of fundamental permits corresponding chord only. Continuo third/fifth below fundamental means supposition; verify rules.", "III.42-010": "Correct bass figures make adding two/three parts easy, unless overelaborate upper/bass melody prevents regular arrangement. More parts require closer agreement with fundamental bass motion. Yet examples show stepwise octave bass, ascending/descending, in four/five parts: ordinary chords, sixths, 7 and 6, 2 and 6/5, 9, etc. Next: rules for multiple parts.", "III.43-001": "CHAPTER FORTY-THREE.", "III.43-002": "Rules for Two, Three, Four Parts.", "III.43-003": "Perfect two/three-part writing requires composing parts together. Each needs flowing, graceful melody. Skilled composer senses companions’ effect while writing any part.", "III.43-004": "1. Usually one part holds imagined beautiful melody: subject. Other parts lacking proportionate melody diminish subject’s beauty. Only recitative allows bass/others merely to supply harmonic foundation. Otherwise two/three parts need near-equal melody. Singing bass rightly promises beautiful music.", "III.43-005": "Fewer parts require greater chord variety. Rule strictest in two parts.", "III.43-006": "2. Three parts: chords as complete as possible. Always third/sixth between at least two parts. Octave rare unless design,* fugue, beautiful melody demands; especially perfect cadences, each part usually ending tonic.", "III.43-007": "* Design/fugue: last chapter.", "III.43-008": "EXAMPLE.", "III.43-009": "Three-part composition", "III.43-010": "Four-plus parts form choruses, quartets, quintets, etc. Final chapter gives quintet/canon. Chorus: any number of voices per part. Quartet/quintet: usually one. Beautiful natural melody in all simultaneous parts difficult. At least bass/top must have it, especially chorus. May give melody to any part or pass between parts. Prefer highest voice, or instrument without voices: penetrating sounds attract attention. Bass separate from this comparison; takes precedence, always guides such pieces.", "III.43-011": "Still strive for beautiful melody in every quartet/quintet part. Perhaps fugue invented chiefly for them. Little charm without it. Fugue returning in successive parts pleasantly surprises listener, diverts attention from temporarily unmelodic parts to returning subject. Skillfully fix attention on strongest object. Fugue melody, companion melodies, rests where melody lacks grace: all depend on taste. Choose well for success; next chapter explains. Only choruses please without fugues, leading parts’ beauty sufficiently occupying attention. Same for duets/trios.", "III.43-012": "More than five parts possible, but only great masters: double consonances aptly, give contrary progressions, vary whole with more/less figured melodies.", "III.44-001": "CHAPTER FORTY-FOUR.", "III.44-002": "Design, Imitation, Fugue.", "III.44-003": "Design generally means intended subject. Skilled composer first chooses tempo, key/mode, melody, harmony fitting subject: Book II, Chapter XXX. Here more precisely recurring melody throughout piece, fitting words or chosen by taste/fancy. Design becomes imitation or fugue.", "III.44-004": "Imitation: repeat chosen melodic passage freely in any part. No further regularity requiring attention.", "III.44-005": "Fugue likewise repeats chosen melody in any part, but with greater care under following rules.", "III.44-006": "Imitation repeats one/several measures or whole air, in one/all parts, any pitches. Fugue requires alternation between principal upper part and bass; another chosen part may replace upper. Several parts: better if fugue visits each alternately. Pitches not freely chosen. Rules follow.", "III.44-007": "1. Not yet confident? Prefer tonic/dominant for fugue’s first/last notes. Melody confined to key octave; notes outside count like octave equivalents inside.", "III.44-008": "2. One part begins/ends tonic; other dominant. Corresponding octave notes follow same rule. Second immediately above tonic answers sixth immediately above dominant. Likewise third/fourth/fifth above/below tonic corresponds to same distance above/below dominant, melody rising/falling. Entire fugue melody follows opening/ending correspondence.", "III.44-010": "3. Diatonic tonic↔dominant routes differ by one note. Especially inside subject, either adjacent note of longer route may answer required note of shorter. Descending tonic→dominant uses sixth/seventh only between; dominant→tonic offers fourth/third/second. Choose latter notes nearest final tonic for closest melodic match. Longer route first? Fit shorter to it. Prefer conformity toward end over beginning. See example.", "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": "Example one: sixth/seventh answers mediant A.", "III.44-015": "Example two: sixth answers mediant C.", "III.44-016": "Example three: seventh answers mediant D.", "III.44-017": "Example four: dominant B or fourth F answers tonic B/F.", "III.44-018": "Example five: mediant answers seventh G or sixth H.", "III.44-019": "Example six: mediant↔seventh L/sixth N; second↔sixth J/dominant P; dominant↔second M/tonic Q; tonic↔fourth R.", "III.44-021": "Free choice among five tonic→dominant notes must match melody within four dominant→tonic notes. Many precautions needed. Rising/falling subject still has five versus four. Sometimes borrow second/fourth to make five dominant-up-to-tonic or tonic-down-to-dominant notes. Fugue writers neglected this; give lessons from experience.", "III.44-022": "1. First/last notes: tonic answers dominant, dominant tonic. Internal exception: fourth substitutes dominant, second tonic for closer melodic match. Second-up-to-dominant/fourth-down-to-tonic gives four degrees, matching dominant-up-to-tonic/tonic-down-to-dominant. Same borrowing yields five second-down-to-dominant/fourth-up-to-tonic, matching dominant-down-to-tonic/tonic-up-to-dominant. Approximate, not exact: mode’s diatonic steps fixed; no new sharps/flats. Minor exception: flat on descending sixth, sharp on ascending leading note. Sometimes sharpen minor mediant or any key’s fourth answering leading note, as sixth example T, provided major third/sixth with bass.", "III.44-024": "Invent fugue melody with bass and answer together. Answer supplies variety. Then begin either invented melody or answer.", "III.44-025": "3. Bass found: seek two/three other accompanying parts. Bass/others follow roughly same progression under melody and answer. Well-imitated bass bears same chords both times. These parts enable simultaneous fugues or canon, discussed later.", "III.44-026": "4. Fugue melody admits several basses; may itself suit bass best. Inversion supplies different basses, or makes upper-type melody bass. Alternate these accompaniments for pleasure, especially fugue: variety lies in accompanying parts. Earlier same-bass/same-chords statement only clarifies melodic imitation. Chord correspondence alone proves it.", "III.44-027": "5. Choose notes between tonic and dominant using these endpoints as guides. Still match answer intervals, especially inside: third/fourth/fifth/sixth/seventh answers same. Yield exact match to diatonic motion or principal scale notes. Favor following over preceding context, tonic/dominant opening/ending over interval identity. Fourth often answers fifth, vice versa. Consonant leap followed by steps toward tonic: imitate from leap’s last note toward dominant. Motion toward dominant answered toward tonic, especially cadence. Final fugue cadence always tonic/dominant; internal cadence may substitute fourth for dominant, sometimes second for tonic.", "III.44-029": "Fugues usually begin/end tonic, dominant, mediant. Mediant answered sixth/seventh: fifth example. Favor following context and matching bass chords under subject/answer; errors unlikely.", "III.44-030": "EXAMPLE.", "III.44-031": "First melody. Answer. First melody. Answer. FUNDAMENTAL BASS. CONTINUO BASS.", "III.44-032": "Continuo shows any imagined bass may preserve correspondence through same chords. Fundamental still better here.", "III.44-033": "6. Fugue melody at least half measure. More than four? Answer must begin in fourth. Tempo somewhat lively, else long melody without harmony cannot please.", "III.44-034": "7. Begin any beat; naturally end first, or third of four-beat measure. Other ending usually from feminine rhyme: actual words, imagined text, or fancy. Novelty sometimes breaks taste-based rules. Unexpected endings please with judgment/discretion; may end beyond tonic/dominant.", "III.44-036": "EXAMPLES.", "III.44-037": "First melody. Answer.", "III.44-038": "First melody. Answer.", "III.44-039": "8. Imitate melody fully where possible. Same count of whole/half/etc. notes in corresponding beats at every entry.", "III.44-040": "9. Entries at unison/octave allowed; fifth/fourth more pleasing. Any part may start/repeat fugue. Change key by matching each note’s scale rank. Preserve tonic relation, note kinds/counts, opening/ending beats.", "III.44-041": "10. Wait for whole subject before next entry, or enter midway where design allows. Very good effect, other features unchanged. See sixth example.", "III.44-042": "11. Inversion, source of harmonic variety, adorns fugue. Rising intervals descend; falling ascend. Nothing else changes: Article IX.", "III.44-043": "EXAMPLE. First melody. INVERTED FUGUE. or. Inverted answer. Same.", "III.44-044": "12. Multiple fugues simultaneous or successive. Avoid same entry beat/measure, especially first appearance. Opposite progressions, distinct characters: one wholes, another halves/quarters/etc., composer’s choice. Whole subjects cannot combine? Combine portions. Example clarifies.", "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": "Example has four fugues; rarely more simultaneously. Often one/two enough. Inversion adds much perfection.", "III.44-061": "“Raucæ factæ sunt” answer to dominant mostly ends second note. Tonic ending more perfect, as bass entry shows. Second replacing tonic tolerable, especially other simultaneous fugues fit only second. Chord sequence or taste sometimes interrupts true subject. Often skillful variety, allowed only after sufficient entries heard.", "III.44-062": "Remember free passing notes between beats for melodic taste. Fundamental bass identifies them: no harmony with those notes.", "III.44-063": "Fundamental bass only proves entire piece uses perfect/seventh chords and derived rules. Compare chord foundations, not its voice-leading against others. Progression rules observed among five upper parts and continuo. Fundamental supplies chord foundations, almost all rule-generating progressions. Other parts form its octave/fifth/third/seventh, except irregular cadences, supposition/borrowed chords: Book II.", "III.44-064": "Fugues as numerous as melodies; impossible to exhaust. Taste chooses; preserve opening/ending/answer rules. Simultaneous fugues need one guide, freely chosen. Pleasing subject: add three/four parts, find new fugues there. Same starts/ends and note counts/values make fugues insipid, mere accompaniments. Avoid by rules preceding last example. Unequal prose naturally supplies desired variety. Equal verse needs staggered starts/ends and suitable runs. No confusion: each entry distinct, none obscuring other. Rest entering part beforehand when apt, only on consonance. First fugue appearance must not directly continue earlier melody. Later possible after subject heard once in every part.", "III.44-066": "Present all first-subject entries, then second/third, mixing old with new. Or present independently, combine later. Simultaneous new subjects risk confusion: one design hides other, yet both must remain present. Distinct designs, opposite motion, different measure “tones” for entries make each clear. One part may sing two subjects initially seeming one, later separating: pleasing effect. Next part enters at division point, though several beats or over one measure earlier/later allowed.", "III.44-068": "Successive entries keep same quarter-rest/measure delay. First answer waits one measure? Each later part waits same after immediate predecessor. Exception, especially after every part heard: third entry may advance/delay one measure, not quarter/half or more than one. Second waits two; third may wait one/three. Likewise later entries at third’s unison/octave. Tonic↔dominant, second↔sixth means fit after one/two measures on one side may fail on other. Fixed initial limits overconstrain invention. Thousands of designs may resist restriction.*", "III.44-069": "All parts stop to reveal new fugue? Melody must not seem absolutely finished. Keep listener wanting next event. Silence only at interrupted/irregular cadence; perfect cadence at least in foreign key. Examples observe this.", "III.44-070": "Fugue ornament rests on taste alone. General rules insufficient for perfection. Different feelings/events generate unruleable novelties. Harmony mastery reveals paths; taste chooses. Taste needs experience from repeated study/listening to greatest masters of genre.", "III.44-071": "* See preceding example’s “Raucæ factæ sunt” and “Defecerunt oculi mei” fugues.", "III.44-073": "Perpetual fugue, or canon: whole air repeated strictly by all parts.", "III.44-074": "Common canons: unison/octave, suited to ranges. Compose melody, add desired parts. Join all into one air, each melody following next pleasantly. First starts air; second enters when first completes original melody. Others follow successively. First reaches end, restarts; others follow as before, entries correctly timed. See example.", "III.44-075": "1. 2. 3. 4. 5.", "III.44-076": "Invent one of five melodies; add others easily. Join into most flowing air taste dictates. Entire canon difficulty lies here. Air follows.", "III.44-077": "CANON. Da capo (from the beginning). Awake, endless sleeper, Relindindin, Relididin, Relididin, A-", "III.44-078": "Five part melodies easily recognized, with few small notes added for melodic taste. Each enters when preceding part reaches marked note/beat: [repeat sign].", "III.44-080": "Repeat sign: marks each part’s entry.", "III.44-081": "Continue indefinitely. First restarts at end; others follow.", "III.44-082": "Perpetual fugue also at fifth/fourth; every part same melody. Conceive whole air; add sharps/flats where natural degrees block exact repetition. Regard melody alone, not modulation. Much harder: each entry new key fifth/fourth away accordingly. Previous canon unlimited parts; here probably no more than four. Even four-part example not 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": "Cannot sing octave at A? Take preceding note’s unison.", "III.44-086": "“At fifth” means above. Fifth up equals fourth down. Allow, especially for vocal ranges.", "III.44-087": "Four parts written together for judgment. Could merely instruct each to enter fifth above predecessor after two full measures. Restart cue [cue sign] may not match line at return mark [repeat sign]. Continue at cue’s pitch. Imagine new clef, better new key—as actually changes—while returned melody’s modulation stays same. Continue indefinitely.", "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": "Last two canon kinds require perfect inversion knowledge. Avoid fifth/fourth/eleventh where possible.", "III.44-092": "Some cultivated taste plus mastery of modulation/fundamental harmony gives perfect, quick compositional success. These alone ground all variety through inversion; fundamental harmony’s modulation never changes.", "III.44-093": "End of Book Three.", "IV.01-001": "BOOK FOUR.", "IV.01-002": "Accompaniment Principles.", "IV.01-003": "CHAPTER ONE.", "IV.01-004": "Recognize Intervals by Keyboard Layout.", "IV.01-005": "Previous book's first chapter essential up to clefs and vocal ranges. Those topics unnecessary for accompaniment.", "IV.01-006": "Harpsichord or organ contains all sounds used in composition. Play keys successively. Left to right: pitches rise. Right to left: descend.", "IV.01-007": "Each key gives different sound. Greater key distance, greater interval; smaller distance, smaller interval. Smallest: semitone. No playable step divides it, as E–F with no key between. F–G: whole tone, sharp key between. All adjacent keys, white and black, semitone apart.", "IV.01-008": "Turn page for 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": "Tones and semitones have different kinds. Pure practice need not distinguish.", "IV.01-012": "Take D or chosen note as first degree, as we took C. Count semitones between neighboring keys. Find tones or semitones from starting note to any compared note.", "IV.01-013": "Accompaniment requires thorough keyboard and music knowledge. Assume readers have it. Then intervals easy to distinguish on keys: same numbered operation as on scale. See Book III, Chapter I.", "IV.01-014": "C, D, E, F, G, A, B used far more than others. Treated as only notes entering composition. Base rules on these seven natural keys. Attend to intervening sharps and flats only when needed for intended interval.", "IV.01-015": "Seek second, third, fourth, fifth? Starting natural key = 1. Next natural key above = second; third key = third; fourth = fourth; and so on. Learn closely: accompaniment chiefly depends on intervals. Always above starting note or foundation, never below.", "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 within octave. Larger ones repeat them. Note names prove it: seventeenth, tenth, third share name; likewise others. Know C's fifth is G: any G above that C works. Compare from every key as from C. Make intervals familiar from any first degree.", "IV.02-001": "CHAPTER TWO.", "IV.02-002": "Distinguish Major, Minor, Perfect, Augmented, Diminished Intervals.", "IV.02-003": "Thirds, sixths: major or minor.", "IV.02-004": "Fifths, sevenths: perfect, augmented, diminished.", "IV.02-005": "Fifths, sevenths: perfect, augmented, diminished.", "IV.02-006": "Seconds, fourths: perfect or augmented.", "IV.02-007": "Diminished fourth and diminished second excluded from accompaniment and harmony.", "IV.02-008": "Some writers call second, seventh, ninth major or minor. Improperly. Prescribed interval size sometimes differs by semitone; ignore for now.", "IV.02-009": "First distinguish thirds, sixths, major, minor. Sharps and flats identify augmented or diminished intervals. Know which key forms third, fourth, fifth, sixth above another? Count intervening tones or semitones to find major, minor, perfect, augmented, diminished.", "IV.02-010": "Tones and Semitones Composing 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": "Different intervals here share tone count. Theory distinguishes otherwise; unnecessary in practice. Later see only practical distinction involving ♯ 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": "Interval nature and kinds explained. Accompaniment student must find all intervals, all forms, from every key. Make knowledge immediate: imagine any note, name and play minor or major third, sixth, tritone, perfect/diminished/augmented fifth, seventh, and so on.", "IV.02-030": "1. First learn thirds and fifths from every key. Fourths, diminished fifths between third and fifth. Augmented fifths, sixths just above fifth. Sevenths below octave. Seconds, ninths above starting note or octave.", "IV.02-031": "2. Keys counted as fourth, fifth, seventh may lack required size. Correct note name enough to start; substitute sharp or flat. B's fifth: F, but wrong tone count. Use F♯. F's fourth: B, but use B♭, as tone count shows. Same for other intervals.", "IV.02-033": "3. Two immutable consonances besides octave: fifth, fourth. Starting key sharp or flat, fifth and fourth likewise. F counted flat: musical naming calls all flats “fa.” B counted sharp: all sharps called “si.”", "IV.02-034": "Three immutable dissonances: seventh, second, ninth. Seventh naturally tone below octave; second tone above. Certain exceptions discussed later.", "IV.02-035": "4. Required interval note name never changes. F's major third A; minor third A♭, not G♯. Same key usually called G♯ now A♭. G cannot form third with F.", "IV.02-036": "Each note has sharp and flat. B's major third D♯, not E♭, though same key. G♯'s major third B♯, not C; major sixth E♯, not F. Key takes name required by interval's numerical order. Augmented second and minor third share keys. Likewise 7♭/6♯, 5♯/6♭, diminished fifth/tritone. D's tritone G♯; diminished fifth A♭. Same key, different names. Remember fourth spans fourth by name, D–G; fifth spans fifth, D–A. Same for rest.", "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": "Find diminished interval easily: start sharp rather than flat. For augmented, reverse choice.", "IV.02-042": "In practice diminished fifth and tritone halve octave equally. Example follows.", "IV.02-043": "Diminished Fifth. Tritone.", "IV.02-044": "Find one, find other: take either key of interval as first degree.", "IV.02-045": "Same relation: major third and minor sixth.", "IV.02-046": "Also minor third and major sixth.\nFourth and fifth.\nSecond and seventh.\nAugmented 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": "Find any interval. Raise starting key an octave: find related interval. Master everything here before proceeding.", "IV.03-001": "CHAPTER III.", "IV.03-002": "Place hand. Arrange fingers.", "IV.03-003": "First degree, or fundamental sound: in practice, call it bass. Left hand plays bass. Right hand plays intervals measured against bass. Usually three or four together. From now on, call that group a chord. Later instructions say “chord”: right hand plays it.", "IV.03-004": "1°. Left hand: one note at a time. Let fingers follow each other. Avoid same finger on successive different notes. Follow printed fingering numbers.", "IV.03-005": "2°. Do not use right thumb, except in special cases explained later. Small hand may force thumb use. That greatly slows building good habit. Practice needs habit as much as knowledge.", "IV.03-006": "3°. Right hand: at least three notes together. Second finger plays lowest. Little finger plays highest. Third or fourth finger plays middle note. Follow exact positions shown beside notes. Thumb = 1. Next finger = 2. Continue counting. Little finger = 5.", "IV.03-007": "4°. Fingers strike chord. Whole hand does not. Fingers move independently, from joints where fingers meet hand.", "IV.03-008": "5°. First finger strikes with bass. Other fingers follow quickly. Whole chord seems simultaneous. Still, it is slightly arpeggiated: like three or four thirty-second notes played very fast, one after another.", "IV.03-010": "6°. Never lift all fingers together, unless change is too fast for anything better. First finger moves alone. Better: it glides from key to key, starting with bass. Others follow immediately, as already explained. Fingers must not hang in air. Leave one key only to touch next at same moment. Release and strike form one action. No audible or noticeable time gap.", "IV.03-011": "7°. Let fingers move naturally. Never force. Good habit brings speed. Force does not.", "IV.03-012": "These points are essential. Chords closely related. Their sequences are almost always alike. Fingers learn when to come together and spread apart. Accompaniment becomes more graceful. Mastery comes sooner. Lift hand for every chord: often must look away from score to search. Keep fingers on keyboard: they could find chord themselves.", "IV.03-013": "Hand-position rules mainly concern harpsichord. Organ has these exceptions only. Strike all chord notes together. Key used in current and next chord: do not release it. Connect sounds as much as possible.", "IV.04-001": "CHAPTER FOUR.", "IV.04-002": "Find Chords on Keyboard.", "IV.04-003": "Start with chord table. Figures mark intervals and recall chord composition. One accompaniment figure usually means three, four, five sounds. Keep accompanying intervals ready in mind; see figure, know whole chord. Seventh accompanied by what? Immediately answer third and fifth. Same for all following chords.", "IV.04-005": "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 mark principal intervals. Accompanying ones rarely written; remember them.", "IV.04-008": "♯ alone: major third. ♭ alone: minor third. Alone above or below note, signs indicate perfect chord with specified third.", "IV.04-009": "♯ with figure enlarges interval semitone; ♭ reduces semitone.", "IV.04-010": "Stacked figures: one chord. Successive figures: successive different chords.", "IV.04-011": "Turn page for example.", "IV.04-012": "Perfect Chord and Finger Arrangement.", "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": "Second and fifth fingers always outer notes; mark only middle fingers. Same throughout except thumb replacing second finger. First three chord arrangements apply to rest. 1 = thumb; 2, 3, 4, 5 continue to little finger.", "IV.04-021": "Before proceeding, move each perfect chord up and down whole keyboard, as shown on C octave. Arpeggiate evenly end to end, all notes equal. Finger starting new chord neither faster nor slower than finger ending previous.", "IV.04-023": "Ascending chords start finger 2; descending finger 5. Accompaniment always starts finger 2, or thumb when required.", "IV.04-024": "Sixth Chord: Third and Octave Accompany.", "IV.04-025": "Right Hand: Chords. Left Hand: Bass. Sixth Chord; Two Possible Bass Positions.", "IV.04-026": "Play any perfect chord. Keep chord; move bass third up or sixth down, same thing. Original perfect chord becomes sixth chord above changed bass, as example shows.", "IV.04-027": "Sixth–Fourth Chord: Octave Accompanies.", "IV.04-028": "Right Hand: Chords. Left Hand: Bass. Sixth–Fourth Chord; Two Possible Bass Positions.", "IV.04-029": "Same method: bass fifth up or fourth down.", "IV.04-030": "Seventh Chord: Third and Fifth Accompany.", "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": "Find as before: bass third down or sixth up. Or add seventh to perfect chord, nothing else changed. Same accompanying intervals except octave unspecified, freely added or removed. Add octave: use four fingers without thumb.", "IV.04-034": "Tritone Chord: Second, Sixth. Second Chord: Fourth, Sixth.", "IV.04-035": "Right Hand: Chords. Left Hand: Bass. Tritone and Second.", "IV.04-036": "Lower bass whole tone. Perfect chord's third major for tritone chord; minor for second chord.", "IV.04-037": "Fourth Chord: Fifth and Octave Accompany.", "IV.04-038": "Right Hand: Chords. Left Hand: Bass. Fourth and Fingering 4.", "IV.04-039": "Take perfect chord; move third to fourth. Octave in middle always played finger 4.", "IV.04-040": "Later chords shown in one keyboard place only. Practice from every note across whole keyboard, as perfect chord. Finger arrangement unchanged everywhere.", "IV.05-001": "CHAPTER FIVE.", "IV.05-002": "Useful Observations on All Chords.", "IV.05-003": "Accompaniment and all harmony: only two chords. Consonant = perfect chord. Dissonant = seventh chord.", "IV.05-004": "Play perfect chord: source of all consonant chords. Only three different sounds: bass, third, fifth, e.g. C, E, G. Octave C not different sound; repeats first C.", "IV.05-005": "C, E, G with C bass: perfect chord. E bass, C and G right hand: sixth chord. G bass, C and E right hand: sixth–fourth chord. All consonant chords. Add bass octave in right hand to complete. Quick demonstration: hold any perfect chord right hand; left plays each chord note octave lower in turn. Three consonant chords result.", "IV.05-006": "EXAMPLE.", "IV.05-007": "Right Hand: Chords. Left Hand: First Bass, Second Bass, Third Bass.", "IV.05-008": "Same chord: perfect over first bass, sixth over second, sixth–fourth over third. Three basses contain chord's same three notes.", "IV.05-009": "Seventh chord has four different sounds. Each in turn as bass gives all harmonic dissonant chords, with exceptions discussed later.", "IV.05-011": "EXAMPLE.", "IV.05-012": "Right Hand: Chords. Six Alternative Left-Hand Basses.", "IV.05-013": "This bass: seventh chords.", "IV.05-014": "Great-sixth or diminished-fifth chords. Difference from first bass's third: minor here, major there.", "IV.05-015": "Small-sixth chords: major or minor according to first bass's thirds.", "IV.05-016": "Second or tritone chords; difference again from first bass's thirds.", "IV.05-017": "Ninth or augmented-fifth chords; difference still from first bass's thirds.", "IV.05-018": "Eleventh chords, called fourths, or augmented sevenths. Difference, and so on.", "IV.05-019": "Do not dwell on first chord; merely incidental.", "IV.05-020": "Ignore last two basses' chords for now.", "IV.05-021": "Take any perfect or seventh chord. Add bass octave to seventh. Hold chord; put each chord note in bass. Same chords as examples. Perfect chord: third below gives sixth chord; fifth below gives sixth–fourth. Seventh chord: third below gives great-sixth or diminished-fifth; fifth below small-sixth; seventh below second or tritone. Reverse process for any dissonant inversion. Add bass octave. Fingers now arranged in thirds? Lowest finger's note, placed in bass, supports original seventh chord. Otherwise two fingers adjacent; higher note of pair goes in bass to reveal seventh chord. See Book III, Chapter XI. Consonant chords easy to recognize. Arrange right-hand fingers in thirds. Note under second finger, put in bass, supports perfect chord.", "IV.05-022": "Study chord relations closely. Greatly ease knowledge and practice. Know instantly new chord from bass third, fifth, seventh higher. Seventh up = second down. Third up = sixth down. Fifth up = fourth down. Third down = sixth up. And so on.", "IV.06-001": "CHAPTER SIX.", "IV.06-002": "Keys and Modes.", "IV.06-003": "Good accompaniment needs certain knowledge of keys and modes. Read Book III, Chapters VIII and XII. Practice following octaves until easy. Chords shown in different keyboard positions, fingerings both hands. Added fundamental bass below first two examples proves only perfect and seventh chords occur. Chords over stepwise rising/falling bass derive from figured perfect and seventh chords beneath. Note names clarify: derived-chord bass stands third, fifth, or seventh above original perfect- or seventh-chord bass. Notes carrying such chords usually occupy same degree in every key.", "IV.06-004": "Fundamental bass for proof only, unnecessary in practice. Chords arranged by rules against continuo bass, not fundamental. Left hand plays continuo bass.", "IV.06-005": "Explanation unclear? Practice chords now; later material resolves difficulty.", "IV.06-006": "Keys and Modes: All Chords for Each Note, Bass Ascending and Descending Octave by Steps.", "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": "First degree, second degree, etc., or tonic note, second note, etc.: same meaning. Terms synonymous.", "IV.06-010": "Master one key before next. Study each in three positions with given fingering. No surprise wherever hand lies; no need to lift it.", "IV.06-011": "Notice chord link: one note almost always shared with next chord. Great aid to practice.", "IV.06-012": "Add missing continuo-bass octave to chords. Reveals relation to fundamental-bass chords.", "IV.06-013": "Major and minor examples give fingering and each note's key-name. Serve all keys. Difference only keyboard layout. Know first two in theory, know all: major compared with major, minor with minor.", "IV.06-014": "Sixth chord follows perfect by step: sometimes double third or sixth instead of bass octave. Easier hand position; avoids consecutive octaves. Thumb then needed.", "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": "Last two keys use same keyboard keys, different names. Other keys likewise have two names. C may be B♯; C♯ may be D♭. All octave notes change names together. Rare practice, so brief idea enough. Free to learn keyboard's double naming. Essential for greatest difficulties.", "IV.06-040": "Look at book while accompanying; fingers only when unavoidable. Practice trains ear to detect errors better than eye. Octave exercises build finger habits, naturally finding chord keys. Never neglect hand position or fingering. More important than imagined.", "IV.06-041": "Master all octaves. Then name every chord inwardly, without book or hand in sight. If possible add: derives from perfect or seventh chord on this note; normally next this chord, derived from that. Cannot use too many approaches for quick, thorough knowledge. Know chord sequence through every key's octave: nearly all difficulties passed. Same sequence in every key.", "IV.06-043": "Tired of all keys? Proceed after first sixteen or eighteen. Return to others when seeking complete certainty.", "IV.07-001": "CHAPTER VII.", "IV.07-002": "Chords within each key’s octave. Order to follow.", "IV.07-003": "Treat each note bearing perfect chord as tonic. In each key, only tonic and dominant have this privilege. Even dominant with seventh chord can count as tonic here. This quickly reveals chords needed before tonic or dominant. Nearly always same chords.", "IV.07-004": "1°. Bass rises fourth or falls fifth to tonic: seventh chord comes first. Both movements equivalent. Same progression to dominant: same rule.", "IV.07-005": "EXAMPLE.", "IV.07-006": "Bass rises fourth to tonic. Bass rises fourth to dominant.", "IV.07-007": "2°. Step down to tonic: small-sixth chord first. Step up to tonic: diminished-fifth chord first. Corresponding rule applies to same approach to dominant.", "IV.07-008": "EXAMPLE.", "IV.07-009": "Step down or up to tonic. Step up or down to dominant.", "IV.07-010": "Dominant bears perfect chord: add ♯ to preceding sixth. Resulting small-sixth chord matches chord before tonic in same progression. Only what follows then distinguishes dominant from tonic. But seventh on dominant identifies it immediately.", "IV.07-011": "Upward stepwise approaches differ. Diminished-fifth chord before tonic; great-sixth chord before dominant. Difference lies only in bass. Semitone up to tonic. Whole tone up to dominant. Other chord notes arranged alike. Example proves it. Distinguish leading note from fourth degree; tonic from dominant.", "IV.07-012": "EXAMPLE.", "IV.07-013": "Leading note: semitone up to tonic. Fourth degree: tone up to dominant.", "IV.07-014": "Seventh, small-sixth, great-sixth, diminished-fifth chords preceded tonic and dominant. Different bass movements. Chords differ only in appearance. All derive from seventh chord. Bass rises fourth or falls fifth to next note: first note needs seventh chord. Bass moves by step: first note needs derivative of seventh chord. Condition: arrival note bears perfect chord or seventh chord. Figures tell you. Beginners must never accompany without figures.", "IV.07-015": "EXAMPLE.", "IV.07-016": "Bass up fourth or down fifth. Bass steps down. Bass steps up.", "IV.07-017": "Same chords serve each bass. Diminished-fifth, small-sixth, great-sixth: same notes as seventh chord whose bass rose fourth. Different bass progressions give different names. All derive from one chord.", "IV.07-018": "Major–minor differences in chords, such as diminished fifth versus great sixth: recognize through bass movement or modulation. Given key requires certain notes or keyboard keys. Key changes: sharps or flats beside figures signal change.", "IV.07-020": "Note lends perfect or seventh chord only to its third, fifth or seventh. Sixth and sixth–fourth chords derive from perfect chord. Therefore need same preceding chord as that perfect chord. Earlier octaves show it. Mediant demands same preceding chord as perfect chord.", "IV.07-021": "EXAMPLE.", "IV.07-022": "Chords before mediant.", "IV.07-023": "Consonant chord to another consonant or dissonant chord: not hard to play. Needs less attention. Dissonant chord to another dissonant chord: more important. Most often uses seventh-chord progression in next-to-last example. Following example gives derived chord sequences.", "IV.07-024": "See next example.", "IV.07-025": "EXAMPLE.", "IV.07-026": "Seventh-chord bass. Five basses with derived chords.", "IV.07-027": "These chords serve every bass. May keep all four notes. Exception: leading note labelled A. Remove when also in bass. Or remove from each chord octave of note played in chosen one of five lower basses. Fuller rule comes later.", "IV.07-028": "First note’s perfect or seventh chord must precede second note’s chord. Therefore second must follow first. Knowing one relationship teaches other. Keep progressions in mind both ways. Applies to original chords and derivatives.", "IV.07-029": "Check earlier octaves. Upward mediant to dominant: same chords as sixth degree to tonic. Downward seventh degree to dominant: same chords as mediant to tonic. Mediant everywhere approached like tonic. Details follow.", "IV.08-001": "CHAPTER VIII.", "IV.08-002": "General rules.", "IV.08-003": "Consider one key now. Perfect chord belongs only to tonic and dominant. Do not worry yet about seventh added to dominant’s perfect chord.", "IV.08-004": "Note rises tone to perfect chord: great-sixth chord. Rises semitone: diminished-fifth chord. Seventh chord also possible on rising note, but figure must explicitly require it.", "IV.08-005": "Step down to perfect chord, or step up to mediant: small-sixth chord first.", "IV.08-006": "Step down to mediant: tritone chord first. Sometimes great-sixth chord instead.", "IV.08-007": "Sixth chord first when: step up to great-sixth or tritone chord; step down to small-sixth chord; third up or down to next note bearing perfect chord.", "IV.08-008": "Notes moving by consonant intervals may take perfect chord. Leap of third: first note sometimes suits perfect chord as well as sixth chord. Figure decides.", "IV.08-009": "Bass rises fourth or falls fifth: may add seventh to first perfect chord. Bass rises fifth or falls fourth: may add sixth to first perfect chord. Arrival note must bear perfect chord or seventh chord. These last two rules underlie all preceding rules.", "IV.08-010": "More conclusions follow from these rules.", "IV.08-011": "After great-sixth or tritone chord, may step down to mediant. Therefore may also fall fourth to tonic, or step up to dominant bearing sixth–fourth chord. Tonic’s perfect chord supplies mediant’s sixth chord and dominant’s sixth–fourth chord. But upward move to dominant after tritone chord is rare. More explanation follows. Chord must precede another: therefore must, or at least may, be followed by it. Follow specified bass movement. Nearly all these rules come from Chapter VI octaves.", "IV.08-012": "Example. Seventh chords and inverted derivatives.", "IV.08-013": "Minor keys. Seventh chords. Three upper positions. Two alternative basses.", "IV.08-014": "Same chords over two basses. First rises fourth or falls fifth. Seventh chord throughout. Other descends by step. Each repeated bass degree bears seventh chord and small-sixth chord. Matches earlier rules.", "IV.08-015": "Notes (A): three different sixth chords. Any may precede first seventh chord only, with bass progression shown.", "IV.08-016": "Example serves all minor keys. Remove flats after clefs: serves all major keys too. Copy pattern into other keys, minor and major. One extra flat added beyond customary signature. Marks minor sixth found in every minor key. Should have done this throughout. Custom prevailed instead.", "IV.08-018": "Practice sequence in every key. Use all three keyboard positions shown. Same rule for every later example. Previous example: two fingers descend, other stays. Then that finger descends, first two stay. Alternate to end.", "IV.08-019": "Other sequences derive from these. New example in major. Add preceding example’s flats after clef to use in minor. Final leading note stays same in both keys.", "IV.08-020": "Add one note to each chord. Two fingers stay, two descend. Then those two stay, first two descend. Continue to end. No thumb.", "IV.08-021": "Turn page. See example.", "IV.08-022": "EXAMPLE.", "IV.08-023": "Four-note chords. Three positions. Five alternative basses.", "IV.08-024": "Both ways necessary. Four parts: three in right hand. Or five parts. First serves inverted chords. Second serves seventh chords not mixed with other chords—except great-sixth chords or chords by supposition, discussed later. To make last example four parts, remove chord note forming octave with each bass note. Do not remove it for bass rising fourth or falling fifth. Habit of that version equally useful, as just stated.", "IV.08-025": "Chords connect closely here. Sequence binds most natural harmony. Habit often comes before understanding. Fingers anticipate mind—provided fingers follow positions and arrangement already explained.", "IV.08-026": "Easy to make own examples in three keyboard positions and all required keys. Therefore only one example given.", "IV.08-027": "Small-sixth, great-sixth, diminished-fifth, tritone, seventh chords shown. Progressions follow earlier rules. No more needed here. Seventh chords approached like perfect chords. More remains about seventh chords and chords of second. Next chapters explain.", "IV.09-001": "CHAPTER IX.", "IV.09-002": "Seventh chord. Bass stays same. Which chord follows?", "IV.09-003": "ARTICLE ONE.", "IV.09-004": "Note bore seventh chord. Next chord on same note must contain sixth. Several chords contain sixth. Need explanation.", "IV.09-006": "After seventh chord on same degree, possible chords: small-sixth, great-sixth, diminished-fifth, sixth, sixth–fourth, tritone, second. All contain sixth. Choice depends on bass note after repeated notes. Same if one long note supports two chords. Method follows for missing or wrong figures. Very common problem.", "IV.09-007": "Composer may give same chord to repeated bass notes. But two repeated notes, first starting measure: first usually bears seventh chord. Second then needs one of listed chords. Must understand modulation to choose well. Easy within one key. Tonic and dominant naturally bear perfect chords. Set aside optional seventh on dominant. Second degree: small-sixth chord. Sixth degree descending: same. Mediant: sixth chord. Sixth degree ascending and seventh descending: same. Fourth degree descending: tritone chord. Ascending: great-sixth chord. Leading note, or seventh degree, ascending: diminished-fifth chord. Bass must use one of these notes. Thus know chord after seventh on same degree. Step up or down to next note also reveals natural preceding chord. Cannot go wrong with these rules. Repeated dominant: only sixth-containing chord is sixth–fourth. Then need recognize key changes through piece. Not hardest part.", "IV.09-008": "EXAMPLE.", "IV.09-009": "Seventh then sixth. Same bass note. Second degree, mediant, fourth, sixth, dominant, leading note. A.", "IV.09-010": "Find chord containing sixth after seventh. Use current note’s degree, next note’s degree, and next note’s required chord.", "IV.09-011": "Bass steps up: rule unfailing. Bass steps down, each note long enough for two chords—or figures show two: use previous chapter’s rule. Small-sixth chord always precedes step down to seventh chord.", "IV.09-012": "At (A), bass steps up after perfect chord to seventh chord. Accompany seventh with octave, not fifth. Finger on former bass’s octave stays. Now forms seventh. Other two fingers step down.", "IV.09-013": "After seventh chord, bass moves by step. Only exception to last rules: bass immediately leaves for nearest note. No time for chord naturally following seventh on original note. Upward move then leads only to perfect chord or another seventh chord, as previous chapter says. Downward move leads only to another seventh chord. Often next bass note carries same chord notes expected over original bass after seventh. Rule still holds: fingers follow usual progression. See Book III, Chapters XXVI and XXVII.", "IV.09-015": "ARTICLE TWO.", "IV.09-016": "Note becomes sharp or flat, or altered note becomes natural: treat as same note for chord rules. C to C♯, C♯ to C, B to B♭, B♭ to B, etc. Decide as for two Cs or two Bs. Follow earlier rules. Fit chords to modulation.", "IV.09-017": "After seventh chord, leaping bass never rises fifth or falls fourth. Falls third, rises sixth, rises third or falls sixth: choose arrival chord from note after arrival.", "IV.09-018": "EXAMPLE.", "IV.09-019": "Altered and natural notes. Thirds. A, B, C.", "IV.09-020": "Sharp notes descend to naturals. Naturals rise to sharps. Natural chord succession still works. For quicker choice: descending sharp does not belong naturally, so treat note as without sharp. Ascending sharp belongs naturally, so treat note as sharpened. Exception: composer may give perfect chord to note rising semitone, as (A). Could instead give great-sixth chord. Then same upper chord as diminished-fifth chord on sharpened (A).", "IV.09-021": "At (B), bass falls third after seventh chord. Next note alone determines B’s chord. Next note needs perfect chord. B steps down to it: small-sixth chord. If stepping up instead: great-sixth or diminished-fifth chord. Same reasoning elsewhere.", "IV.09-022": "Bass rises third after seventh chord: arrival usually bears derivative of preceding chord. At (C), diminished-fifth chord is preceding seventh chord rearranged.", "IV.09-023": "Third up equals sixth down. Remember same relationship for other intervals.", "IV.09-024": "Fifth down after seventh chord: covered in previous chapter. Not repeated here.", "IV.10-001": "CHAPTER X.", "IV.10-002": "Chord of the second.", "IV.10-003": "Earlier rule: first of two notes at same degree may take seventh chord. This applies only if first note is not bar's last beat. Put seventh there anyway: chord of the second must follow immediately, on same note at next bar's first beat. Chord of the second now governs. Seventh does not. Seventh may happen to come before it. Perfect chord or any sixth chord may also come before it. But second repeated note on first beat must carry chord of the second. Natural preparation: great-sixth chord on first repeated note, at previous bar's last beat. See bass of seconds. Also Book III, Chapters VIII and XXI.", "IV.10-005": "Same degree across two bars like this: notes are syncopated. See Book III, Chapter XXXV, Article VII. In bass, this syncopation occurs only with chords of the second or augmented-fourth chords, 4♯.", "IV.10-006": "First syncopation: chord of the second may follow perfect chord, seventh chord or any sixth chord. Several syncopations in row: naturally put great-sixth chord before and after chords of the second. Tritone chord, 4♯, can sometimes replace chord of the second. Especially at last syncopation. After final chord of the second, choose next chord by the chord beyond it. Always look ahead for guidance, rather than behind.", "IV.10-007": "Chords of the second can mix with small-sixth chords too. Very rare.", "IV.10-008": "Four-beat bar: divide it into two two-beat bars here. Always. Avoid mistakes.", "IV.10-009": "Accompanist needs practice even more than knowledge of rules. Practice earlier examples often. Transpose to different keys. Get used to all three keyboard positions. This helps with figured bass and unfigured bass alike.", "IV.11-001": "CHAPTER XI. Sixth chords.", "IV.11-002": "Bass often moves by scale steps. Sixth chords only. Follow next example. Practice becomes easy.", "IV.11-003": "EXAMPLE.", "IV.11-p403": "Sixth-chord sequence. “Or” marks choices.", "IV.11-005": "Remember Chapter VIII. Great-sixth chord can lead to sixth chord on mediant. Or sixth–fourth chord on dominant. Or perfect chord on tonic. Nothing new here. [List uses author's corrected punctuation from supplement.] Still practice this sequence. It occurs often. Observe added flat: example works in all minor keys. Remove flats: works in all major keys.", "IV.11-006": "Fourth note (A) descends to mediant (B), or even tonic (C). It can carry great-sixth chord, tritone chord, or both in sequence. Both used: great sixth must come first.", "IV.11-007": "Last rule comes from irregular cadence. Could discuss perfect, imperfect and interrupted cadences here too. But other rules already include them. Example: seventh chord, then sixth–fourth chord on tonic dominant. This represents imperfect cadence. Perfect cadence must go dominant to tonic; see all octave examples, Chapter VI. Sixth–fourth chord on dominant stands for perfect chord that tonic should naturally have carried after dominant seventh. Dominant can also move to mediant. Basic harmony of those two chords stays unchanged. Chapter VIII gives another rule: rise by step after seventh chord, to perfect chord or another seventh chord. This comes from interrupted cadence. Still read Book III, Chapters XIII, XVI, XXV and XXVIII. Their cadence discussion gives much insight. Into inversion. Into recognizing keys. Into notes that can or must carry certain chords. Into bass movements that reveal these things.", "IV.12-001": "CHAPTER XII. Augmented-second chord. Chords derived from it.", "IV.12-002": "Augmented-second chord: figure 2♯. Add tritone and major sixth. Use only on sixth note of minor keys.", "IV.12-003": "Start with seventh chord on key's dominant. Raise bass a semitone to sixth note. Example: dominant E. Right hand plays its major third, fifth and seventh. Left hand plays F instead of E. Same method for other tonic dominants.", "IV.12-004": "EXAMPLE.", "IV.12-p404": "A minor. D minor. G minor. Dominant, then sixth note.", "IV.12-006": "Move dominant to sixth note. Same kind of change affects every chord derived from its seventh chord. See next example.", "IV.12-007": "Chords from 2♯.", "IV.12-p405": "One upper part. Six bass choices. Not all at once.", "IV.12-009": "Chord notes always divided by thirds. Same anywhere on keyboard.", "IV.12-010": "Sixth note descending to dominant: usually small-sixth chord. Compared with augmented-second chord, only one difference. Third replaces augmented second.", "IV.12-011": "Fourth note: usually tritone chord. Here minor third replaces second.", "IV.12-012": "Second note: usually small-sixth chord. Here diminished fifth replaces fourth.", "IV.12-013": "Leading note: usually diminished-fifth chord. Here diminished seventh replaces sixth.", "IV.12-014": "Mediant: sometimes augmented-fifth chord. Here fourth replaces third.", "IV.12-015": "Tonic note: sometimes augmented-seventh chord. Here minor sixth replaces fifth.", "IV.12-016": "See Book III, Chapter XXXIII.", "IV.12-017": "Small-sixth, diminished-fifth, tritone, augmented-fifth and augmented-seventh chords come from tonic dominant's seventh chord. Moving dominant to sixth note can change them all, as shown. Practice each chord in every minor key. Alternate its two possible accompaniments. Notice which notes of each key can take it. Gain a more accurate idea of these chords.", "IV.12-018": "Last two basses show other chords. Read next chapter before studying them. It explains them.", "IV.12-019": "Play last example's chords: remove bass octave from every chord.", "IV.13-001": "CHAPTER XIII. Supposition chords.", "IV.13-002": "Two supposition chords only: ninth and eleventh. From these come augmented-fifth and augmented-seventh chords. Difference lies only in third of underlying seventh chord. Minor in one case. Major in other.", "IV.13-003": "Each chord contains five different notes.", "IV.13-004": "ARTICLE I.\nNinth chord.", "IV.13-005": "Printed text says ninth interval equals third. Supplement corrects “third” to “second.” Chord differs. Add third, fifth and seventh. Notes: 1. 3. 5. 7. 9. Figure: just 9.", "IV.13-006": "Find chord easily. Hold previous chord. Add third above bass note marked 9. Or previous chord has note a fourth above new bass: slide that finger to third. Change nothing else. Chord may lack some of its notes. That need not matter. Bass rises by step from seventh chord to ninth chord: fingers follow Chapter VIII's seventh-chord pattern. See F to B.", "IV.13-007": "EXAMPLE.", "IV.13-p406": "Ninth chords. Marks A, B, C, D, E, F.", "IV.13-009": "(A) Third added to previous chord. (B) Two fingers descend from (A), following seventh-chord rule. After this ninth chord, right hand normally follows that rule's route.", "IV.13-010": "(C) Finger on fourth slides to third. Others stay.", "IV.13-011": "(D) Same.", "IV.13-012": "ARTICLE II.\nAugmented-fifth chord.", "IV.13-013": "Build like ninth chord, but fifth is augmented. Figure 5♯. Only on mediant of minor keys. Often used to interrupt cadence.", "IV.13-014": "ARTICLE III.\nAugmented-seventh chord.", "IV.13-015": "Accompany with fifth, ninth and eleventh. Notes 1. 5. 7. 9. 11. Figure 7♯. Tonic note only.", "IV.13-016": "ARTICLE IV.\nEleventh chord. Also called fourth chord.", "IV.13-017": "Construct like 7♯, but seventh is unaugmented. Usual figures:4, ⁴₉, ⁹₄. Plain 4: same chord used in octave examples' final cadences. Add 9: chord now has five notes. For hand's convenience, right hand often holds only three. Bass makes four total.", "IV.13-018": "Easy to find. Same notes, same keyboard keys as previous chord.", "IV.13-019": "Turn page. See example.", "IV.13-020": "EXAMPLE.", "IV.13-p408a": "Eleventh chord. Cue A shows note to add.", "IV.13-022": "Cue (A): add this note to ⁹₄ chord.", "IV.13-023": "Sometimes add fifth and second when bass next descends by step. Under fingers, same shape as diminished-fifth or great-sixth chord that must follow on lower bass note.", "IV.13-025": "EXAMPLE.", "IV.13-p408b": "Fourth–second chord. Then great-sixth or diminished-fifth chord.", "IV.13-027": "Should be figured²₄. Usually figured⁵₂.", "IV.13-028": "These chords: see Book III, Chapters XXIX, XXX, XXXI and XXXII.", "IV.14-001": "CHAPTER XIV. How earlier chords connect.", "IV.14-002": "Right hand holds perfect chord: also holds consonant sixth and sixth–fourth chords. Holds seventh chord: also holds all dissonant types. Small sixth. Great sixth. Diminished fifth. Tritone. Second. Ninth. Eleventh or fourth. Augmented fifth. Augmented seventh. Some special details need attention.", "IV.14-003": "Dissonant chords: major or minor. Depends on third above root of underlying seventh chord.", "IV.14-004": "Chord sequence almost always follows same pattern. Minor dissonant chord usually leads to another. Continue until major dissonant chord appears. Consonant chord usually follows it. Chapter VIII's seventh rule trains successive dissonant chords. Octave and sixth rules, Chapters VI and XI, train mixing consonant and dissonant chords. Patterns agree closely. They also work for supposition chords. Use four fingers there: follow seventh-chord route until major dissonant chord determines ending.", "IV.14-006": "Make progressions easy: know which fingers move. Normally four right-hand fingers. Two descend. Two stay. All notes stacked in thirds: highest two descend. Otherwise find adjoining pair. Lower finger of pair descends with finger below it. No finger below that pair: highest and lowest descend together. Moving notes: fifth and seventh in seventh chord; seventh and ninth in ninth chord; ninth and eleventh in eleventh chord. Only three fingers used: those same two intervals still descend. Other finger stays.", "IV.14-007": "Rule has exceptions. Interrupted cadence, or matching sequence H: three fingers may descend. Upper finger of adjoining pair stays. If none adjoin, lowest finger stays. Another case: lower finger of adjoining pair descends alone. Other three stay. If none adjoin, highest finger descends alone instead. This matches bass descending by thirds, every note carrying seventh chord.", "IV.14-008": "See next example.", "IV.14-009": "EXAMPLE.", "IV.14-p410": "H and J progressions. One upper part. Three bass choices.", "IV.14-011": "Can add seventh to perfect chord. Note may seem to allow perfect chord only. It can sometimes carry seventh chord instead. Composer's taste and knowledge decide.", "IV.14-012": "Know this sequence with its different basses. Much less common than others. Still, leave nothing unknown if you want no surprises. Rarely add bass octave to major dissonant chords. It can fit only seventh, small-sixth and great-sixth chords. Learn to play these in four parts: three right-hand notes plus bass. Supposition chords contain five parts without bass octave. Never add bass octave there.", "IV.14-013": "Why forbid bass octave in dissonant chords? To make accompaniment more regular. Otherwise consecutive octaves or fifths become unavoidable. Composition strictly forbids them. So in sixth chords we often double third or sixth instead of bass octave. Still, missing this regularity does not automatically make accompaniment bad. Accompaniment's purpose: sound all chord notes, with no further requirement. Yet perfection is better when possible. Our arrangements train chord sequences that avoid almost all faults without special attention.", "IV.14-015": "Chord relationships: see examples in Chapters V, VIII, XI and XII. Also Books II and III. Still to explain: how preparation and resolution of dissonances connect chord sequences.", "IV.15-001": "CHAPTER XV. Prepare and resolve dissonances. Find key. Find each note’s chord.", "IV.15-002": "Dissonant chords called major or minor because of particular interval inside. Now speak of dissonance itself, rather than chord.", "IV.15-003": "Earlier rules make preparing dissonances easy. Enough for accompanists. More in Books II and III. Rules make resolving almost as easy. Following explanation gives fuller understanding.", "IV.15-004": "Dissonances: major or minor. Play seventh chord on tonic dominant. Its major third forms all major dissonances. Its seventh forms all minor dissonances.", "IV.15-p411": "Seventh chord. Minor and major dissonance.", "IV.15-007": "ARTICLE ONE.\nMajor dissonance.", "IV.15-008": "Major dissonance never without minor. Major present: no need to focus on minor. Dissonant chord with no major dissonance: minor becomes whole focus.", "IV.15-009": "Major dissonance always formed by current key’s leading note. Leading note is major third of tonic dominant. Dissonant chord containing it always derives from that dominant’s seventh chord. Chord or leading note reveals key. Know key: immediately know dissonant chord and note forming dissonance. Leading note always semitone below tonic, or tonic’s octave, double octave, triple octave, etc.", "IV.15-010": "Starting key gives leading note. Key changes later: sharp alone as figure, beside figure, or on bass note marks new leading note. Opposite signal: flat added to old leading note, or its sharp removed. May occur in bass or chords. Old note no longer leading note. Find new one. This determines key, major-dissonant chord, and every chord in key by Chapter VI rule of octave. Note sometimes bears different chord from normal one, as seventh rules show. Immediately resumes normal chord, or same chord appears over following note. Bass takes different route; chords do not change for that reason. New sharp changes, another appears: use order of sharps. Last sharp gives leading note. Fuller account: Book III, Chapter XXV, Article III. Accompanist must master this.", "IV.15-011": "Resolve major dissonance: finger slides semitone up. Never fails. Chord resolves to tonic’s perfect chord. Only exception: sometimes add seventh to that perfect chord.", "IV.15-012": "EXAMPLE.", "IV.15-p413": "Major dissonances. Upper part. Nine alternative basses. Specified bass changes.", "IV.15-014": "Two chords serve different basses below. All major-dissonant chords contained here. Leading note forms major dissonance and major third of tonic dominant. Always rises semitone to tonic.", "IV.15-015": "Dominant seventh chord resolves naturally to tonic’s perfect chord. Other basses’ chord sequences derive from this.", "IV.15-016": "Dominant moves to mediant. Chords unchanged.", "IV.15-017": "Dominant stays. Same chord sequence.", "IV.15-018": "Fourth degree bears tritone chord. Moves to mediant or tonic. Same chord sequence.", "IV.15-019": "Mediant bears augmented-fifth chord. Stays or moves to tonic. Chords unchanged.", "IV.15-020": "Second degree bears small-sixth chord. Moves to mediant or tonic. Same chords.", "IV.15-021": "Tonic bears augmented-seventh chord. Stays to regain perfect chord.", "IV.15-022": "Leading note always bears diminished-fifth chord. Moves to tonic or mediant. Same chord sequence.", "IV.15-023": "Sixth degree replaces dominant here. Remove dominant from first chord. Sixth degree moves to dominant or mediant. Same chord sequence. To find other bass progressions from inversions of this augmented-second chord, replace dominant in first chord with sixth degree. Dominant cannot remain in bass while sixth degree takes its place.", "IV.15-025": "Augmented-second chord and derivatives: raise major dissonance alone, others stay. Or lower minor dissonance alone. Example: Book III, Chapter XXXIII.", "IV.15-026": "Any key: degree names for preceding example’s chords stay same. 5♯ only on mediant. And so on.", "IV.15-027": "Minor-key example serves keys generally. Exception: major keys exclude 5♯ and 2♯ chords and derivatives of 2♯.", "IV.15-028": "Could discuss minor dissonance with major. Both present. Line to next note shows minor always descends. Take diminished fifth or tritone to see it.", "IV.15-029": "EXAMPLE.", "IV.15-p414": "Diminished fifth. Tritone. Major and minor dissonance movement.", "IV.15-031": "These intervals invert each other. Resolve to inverted intervals too: third at (A), sixth at (B). Major dissonance always up. Minor always down. F and B resolve to E and C. All keys: leading note forms major dissonance, rises to tonic. With major present, fourth degree forms minor dissonance, falls to mediant. Verify in every key.", "IV.15-033": "ARTICLE TWO.\nMinor dissonance.", "IV.15-034": "Every minor dissonance comes from seventh. Without major beside it, cannot fix degree forming or resolving it. Any note in key may bear seventh chord. To find key, fingers follow habitual dissonant-chord sequence until major dissonance appears. Then key declared. Exception: consonant chord after great-sixth chord may itself declare key. Such consonant chord normally belongs to particular degree. See Chapters VI, VII, VIII, IX. But sometimes great-sixth chord rises to perfect chord without declaring key. Chapter on sevenths shows bass rising thus to perfect chord, falling third, rising similarly again. Final progression settles key absolutely. Such basses always end on dominant or tonic; tonic then preceded by diminished-fifth chord.", "IV.15-036": "No new example needed. Previous example explains minor-dissonance resolution. Chords by supposition contain at least two minor dissonances, always descending. Full eleventh chord, called fourth, contains three. Otherwise only one. Of three, usually descend only harsher two: ninth and eleventh. Seventh stays. Some music requires opposite. Less common.", "IV.15-037": "Major dissonances listed in example. Minor: second, diminished fifth, seventh, ninth, eleventh called fourth. Also third of small-sixth chord; fifth of great-sixth chord.", "IV.15-038": "Second differs from other minor dissonances. Dissonance lies in bass. Bass must descend to resolve second.", "IV.15-039": "Two fingers together in dissonant chord: lower forms minor dissonance. Chord of second: only bass can lie next to second. Other chords with no fingers together: top finger plays minor dissonance. Must descend.", "IV.15-040": "Exception: irregular cadence. Great-sixth chord’s sixth forms dissonance, not fifth. Sixth steps up. Fifth stays.", "IV.16-001": "CHAPTER XVI. Chromatic motion.", "IV.16-002": "Chromatic motion: minor keys only. Sixth and seventh notes move by semitones. Up or down. In bass or in chords.", "IV.16-003": "See earlier outline, Chapter XI, Article II. Here major dissonance does opposite of usual rule. Normally rises one semitone. Here falls one semitone. Goes to flattened form of same note, or its natural keyboard key. Add that lowered note to consonant chords normally following major dissonance. Added note lies just below the note that should have become tonic after the leading note. Same principle as preceding chapter: add seventh to perfect chord where major dissonance resolves.", "IV.16-004": "Borrowing chords and supposition chords often appear here too. Unfigured bass becomes hard to play without mistakes.", "IV.16-005": "EXAMPLE.", "IV.16-p417": "Chromatic example. Two connected systems. Marks A, B, C, D, F, G, H, J.", "IV.16-007": "Whole chord sequence follows our rules.", "IV.16-008": "Leading note descends in one part. Elsewhere, A–B–C follows seventh progression. F–G gives its inversion. C–D comes from interrupted cadence.", "IV.16-009": "H to J: ninth delays following octave.", "IV.16-010": "Rest of example roughly follows octave patterns, Chapter VI. Difference: thirds change minor to major or major to minor. In supposition and borrowing chords, notice replacement notes: they occupy places of naturally expected notes. Train fingers in these different sequences. Often fingers then act before deliberate thought. Watch intervals closely. Descending: major changes to minor. Ascending: minor changes to major.", "IV.16-011": "Avoid mistaking keys here. Sharps identify each different leading note. Leading notes reveal the keys.", "IV.16-012": "Natural sign on figure or note restores natural note. Cancels earlier ♯ or ♭. Some writers use sharp or flat as cancellation instead. Less regular. 7♭ usually means diminished seventh. 7♯ means augmented seventh.", "IV.17-001": "CHAPTER XVII. Review chord sequences.", "IV.17-002": "Master harmonic movement in every key. Recognize current key from each chord played.", "IV.17-003": "Consonant chords alone often leave key uncertain. First dissonant chord still unclear: major dissonance absent. Other clues compensate. Bass movement gives next chord. Minor dissonance always wants down. Uncertainty chiefly in Chapter VIII seventh-chord progression or derivatives. Major dissonance almost always ends it, immediately revealing key. Know and practice sequences thoroughly to avoid mistakes. Review follows.", "IV.17-004": "Study following review carefully.", "IV.17-005": "Fundamental bass up third. Dissonance A cannot be prepared. | Down fourth, as Chapter VIII. | Fundamental bass down third. Third prepares dissonance; octave resolves. | Down fifth. | Up second. Octave prepares dissonance; fifth resolves. | Down fifth with chromatic motion. | Sixth added to perfect chord C. Prepares irregular cadence. Rises to third to resolve. | Final cadence.", "IV.17-p419": "Review. Upper part. Nine alternative basses. A–R.", "IV.17-007": "Curves ⌒: preceding consonance prepares dissonance. Horizontal lines —: same in chromatic motion. Preparing consonance nevertheless forms major dissonance there. Sloping lines ╲ or ╱: consonance resolving dissonance.", "IV.17-008": "Same chords serve each bass. Fundamental-bass movement determines chord sequences in others. Most other bass movements are extravagant for these chords. Rare in well-composed music, especially D, F, G, H, J, K, L, M, N. If encountered, proceed as follows.", "IV.17-009": "1°. If unconcerned about consecutive octaves or fifths: add octave to first dissonant chord. Fingers follow natural course shown.", "IV.17-010": "2°. Avoid faults: usual accompaniment, three right-hand fingers. Omit bass’s octave from dissonant chord. If chord awkward, omit dissonant sound instead of octave. Dissonant chord becomes consonant. After dissonant chord, following seventh may become perfect chord. Following small-sixth or great-sixth may become simple sixth chord. Small-sixth may also become sixth–fourth. Great-sixth may become perfect. Use natural finger motion, almost always stepwise. Also use rules linking next chord to bass movement. Major small-sixth chord with bass stepping down requires perfect chord next. Seventh or great-sixth there: reduce to perfect, as M. Diminished-fifth or great-sixth chord with bass stepping up likewise requires perfect chord. Following great-sixth or seventh: reduce to perfect, again as M.", "IV.17-012": "Sixth–fourth may follow small-sixth with bass stepping down, or great-sixth with bass stepping up. Following small-sixth in those movements may become sixth–fourth. Condition: first small-sixth has no leading note. If it does, following small-sixth must become simple sixth chord.", "IV.17-013": "Tritone chord then step down: sixth chord naturally follows. Major small-sixth then step up: same. Following small-sixth or great-sixth in those movements may become simple sixth chord. See N, F, G, H, R. F, G, H in seventh bass do not follow specified movement. Still, finger habit finds chords. Same for small-sixth after seventh with step down, at D in sixth bass.", "IV.17-014": "3°. Bass moves by step. Two successive chords same kind, or against natural rule. If not reducing chords, use contrary motion. Bass up: chords down. Bass down: chords up. Apply at P–Q or P–M–Q unless M in third bass reduced to perfect chord. Reducing one chord removes need to reduce next, especially with stepwise bass. Contrary motion must not move lowest or highest finger if its key serves next chord. Exceptions with ascending stepwise bass: diminished-fifth or great-sixth after seventh; seventh after ninth. Example follows.", "IV.17-015": "EXAMPLE.", "IV.17-p422": "Contrary motion. Seventh, diminished-fifth, great-sixth, ninth chords.", "IV.17-017": "Dissonance merely adds sound to consonant chord. Consonant chord alone holds harmony’s foundation. Dissonance awkward under fingers: omit. Play expected consonant chord that fingers naturally reach. Must contain only sounds properly accompanying dissonance. Must also have mastered all examples. Overcomes many difficulties caused by bass figures listing composer’s intervals without concern for rest.", "IV.17-018": "Reduction unsuitable for chords of second, supposition chords, borrowing chords. Hardly suitable for seventh chords either.", "IV.17-019": "4°. B–B: consecutive fifths between parts. Hard to avoid with finger arrangement. Same when bass rises from perfect chord to sixth chord.", "IV.17-020": "5°. Eighth and ninth basses: supposition chords. Fill with as many constituent sounds as possible. Add bass octave to immediately preceding chord. Follow other given rules. Will not fail.", "IV.17-021": "6°. Several dissonant chords in row. All sevenths or mixed kinds. No consonant chord between. Right-hand fingers always descend until leading note appears. Then rise—at least finger playing leading note.", "IV.17-023": "EXAMPLE.", "IV.17-p423": "Dissonant-chord sequence. Two continuous systems.", "IV.17-025": "Figured ninth chords contain seventh. Sixth must follow seventh, even unfigured. Octave figure after ninth may seem to mean perfect chord. Still need sixth to resolve seventh, as octave resolves ninth. Fingers find this without thought: slide down neighboring keys. Natural motion after minor dissonances.", "IV.17-026": "Same when only 5 figures note that could take seventh or ninth chord before bass steps up. See Chapter IX first example. Same note marked 5 then 6, then step up: may confuse accompanist. Seventh or ninth under fingers sounds very well with perfect chord indicated by 5. Choose 6 chord from current chord, more certainly from bass note’s degree in key. Chapter IX example shows it. May add ninth to chords marked only 7 when finger from preceding chord already holds that ninth.", "IV.17-028": "7°. Same dissonance often forms another before resolving. See Book III, Chapters XII, XV, XXVII. One note often bears several different chords in row. Most examples show it. Next: pedal point.", "IV.17-029": "EXAMPLE.", "IV.17-p424": "Pedal point. Two systems. Pedal bass and fundamental bass.", "IV.17-031": "Pedal point lasts while bass note unchanged. Ends at A. Starts again immediately after.", "IV.17-032": "Fundamental bass proves pedal harmony follows rules. Borrowing chords: sixth degree replaces dominant. Supposition chords: fundamental bass must lie above other bass.", "IV.17-033": "Notes B: double supposition. First naturally needs augmented fifth. Second must take irregular eleventh chord. Sustained bass slips from attention. Attention follows chord sounds. Chords progress regularly, so sustained bass counts only as point, like zero among figures. Hence freedom to sound sixth with seventh here.", "IV.17-034": "EXAMPLE.", "IV.17-p425": "Pedal point. Sixth with seventh. Fundamental-bass proof.", "IV.17-036": "Remove pedal bass. Consider chords with fundamental bass. Regular harmony. Only proper way to judge.", "IV.17-037": "Another sixth-with-seventh method: Book II, Chapter XIX.", "IV.17-038": "Hurdy-gurdy and musette airs in some sense arise from pedal point. Thus understand their different bass types.", "IV.17-040": "Master knowledge and practice of chord inversion—or rather altered bass progression—in every example. Fundamental basses prove chord differences come from bass-movement differences. Countless relationships between sequences train fingers with little practice. Fingers help when memory fails. Natural path: minor dissonance down to neighboring key; major dissonance up. No need to name interval consciously. Seventh, ninth, eleventh, diminished fifth, third of small-sixth chord, often fifth of great-sixth chord: descend. Finger finds destination itself. Tritone and augmented second: ascend. Two fingers together: lower always descends. Exception: irregular cadence.", "IV.18-001": "CHAPTER XVIII. Accompany well. Essential rules.", "IV.18-002": "1°. Before hands touch keyboard: find key, mode, meter and tempo. Check whether mode, meter or clef changes later. Watch figures on notes. Watch attached ♯ and ♭ signs. Follow bass motion to supply missing figures. Apply all earlier rules.", "IV.18-003": "2°. Match accompaniment to voices and music. Enter spirit of words. No words: follow melody's expression. Match singers' or instruments' strength. Too loud: drown them. Too soft: fail to support them. Depending on situation, double right-hand chords with left hand. Do not double dissonances under this rule. Or remove octaves from chords. Sometimes remove particular dissonances too.", "IV.18-005": "3°. Harpsichord or theorbo sound fades: repeat chord if needed. Prefer first beat of bar. Align with word's last syllable. Repeat in middle of word or phrase: meaning may become hard to hear. Organ does not need this. Sounds stay “contained”. [Printed error. Supplement says “continuous”.]", "IV.18-006": "4°. Keep chords in keyboard's middle, as far as bass allows. Need another register: shift on same chord if possible. Otherwise shift after consonant chord. Never after dissonant chord. Cannot always control this: composer may send bass two octaves up or down unexpectedly. To shift, find a key shared by current and next chord. Look or feel for it. Moving up: put lowest finger on that key. Moving down: put highest finger there. Do not lift whole hand. One finger takes another's place and makes the shift. Eyes can stay on score. Remember earlier rule for arpeggiating chords.", "IV.18-007": "Accompany without figures: add composition rules to all our other rules. Still difficult unless ear, taste and fingers act before conscious knowledge catches up. Best preparation: practice earlier principles often. Train ear in good, true harmony.", "IV.19-001": "CHAPTER XIX. Add bass figures. Know each figure’s chord.", "IV.19-002": "Perfect chord: any of its three intervals can name its figure. Usually no figure. To distinguish third: ♯ for major, ♭ for minor.", "IV.19-003": "♯ alone: major third. ♭ alone: minor third. Attach to number: alter that interval by one semitone from its natural form.", "IV.19-004": "Use chord’s naming number as figure. Examples:", "IV.19-006": "Interval already naturally major or minor in current key: do not add ♯ or ♭ to its figure. If sign needed, prefer ♮. Customarily, only tritone figure takes ♯.", "IV.19-007": "Change chord’s natural construction: add figure for change to figure naming chord.", "IV.19-008": "EXAMPLE.", "IV.19-010": "Chord can contain major dissonance: identify it with figure also naming that dissonance’s interval.", "IV.19-012": "Many continuo basses ignore this consistency. Figures alone can mislead. Follow our rules: see why they are needed here.", "IV.19-013": "Some writers add many figures. One would suffice. Much confusion follows.", "IV.19-014": "Figure beside note: play that chord. Figure placed later, note can take perfect chord: start with perfect chord. Change to figured chord on second, third or fourth beat. Figure’s distance after note shows when.", "IV.19-015": "Note lasts several beats. Can change chord every beat. Sometimes hold same chord for two beats. Figures’ spacing unclear: ear decides.", "IV.19-016": "Dot continues preceding note. Figure above or below dot: play chord during dot’s added time.", "IV.19-p429": "Figure 6 on note’s dot.", "IV.20-001": "CHAPTER XX. Which bass notes need chords.", "IV.20-002": "Play chord at start of each beat. Same note may keep same chord for several beats or bars.", "IV.20-003": "One-beat note can divide into two time-units. Two different chords can fit. More divisions possible. But chord changes then rush too much.", "IV.20-004": "Figurated bass often puts several notes in one beat. Chord goes on first note of each beat. Right hand strikes chord each beat. In effect, keeps time.", "IV.20-005": "Tempo fairly fast. Same chord fits several beats. Do not repeat until instrument’s sound dies completely. Same chord repeated too often becomes tiresome.", "IV.20-007": "Moving bass can be hard to figure. Its notes do not always belong to chord that must sound. Our rules help. Use chords that naturally follow each other. Example: bass moves by step. Several dissonant chords in row, such as 7s or 2s. Required sixth chords are missing between them. Even if dissonant chords begin on each beat, split each beat into two equal halves. On note starting second half, play chord that should follow and precede those dissonant chords. Earlier principles build finger habits. Trained fingers often find this before thought. Bass note beneath unfigured or unusually figured chord may not be the naturally expected note. Trust fingers’ natural chord sequence rather than bass note that could mislead.", "IV.20-008": "EXAMPLE.", "IV.20-p430": "Moving bass. Three upper parts. Continuous example begins.", "IV.20-p431": "Same moving bass and three upper parts. Two systems continue example.", "IV.20-011": "Bass descends by step: small-sixth chord must precede seventh chord. Two bass notes at same degree: great-sixth or diminished-fifth chord must precede chord of second. Still follow rules when needed bass note is not at beat’s first instant. Still follow when chord has no figure, as A and D. Or confusing figures, as B and C. Put small- or great-sixth chords between seventh or second chords as rules require. After minor dissonance, one or two fingers descend. Others stay. Same applies to other progressions with these difficulties.", "IV.20-013": "Sharp or flat served one chord and can serve next: keep it. Drop only when new figure explicitly cancels it. Alteration may belong naturally to current key. It can create diminished or augmented fifth. Here prefer that to perfect fifth. Same for other intervals. Composer must mark contrary choice when subject needs it. Otherwise only ear can decide.", "IV.20-014": "END.", "IV.20-015": "King grants sole music-printer’s office.", "IV.20-016": "Royal letters patent. Fontainebleau, 5 October 1695. Signed LOUIS. On fold: “By the King, Phelypeaux.” Great seal, yellow wax. Confirmation letters called “Suranation”: Marly, 28 May 1715. Signed same way. All verified and registered in Parlement, 7 June 1715. Permission goes to J B-Christophe Ballard. King’s sole music printer. Music copyist to royal chapel. May print music, have it printed, sell it and distribute it. Vocal or instrumental. Any author or authors. Others need Ballard’s leave and permission. Applies to printers, booksellers, engravers, type-founders and every other person. Must not engrave, cast or counterfeit his notes, type, decorative initials or other inventions. Must not undertake or commission that music printing anywhere in kingdom or lands and lordships under King’s authority. Contrary letters do not override this. Penalty: confiscate books or copies, musical type and other printing equipment. Fine: six thousand livres. Full letters give fuller terms. King orders this extract placed at book’s beginning or end to carry same authority as 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": "Perfect cadence dominant→tonic. Here tonic→dominant, or fourth→tonic. Thus irregular.", "supplement-042": "New dissonance, already used successfully by skilled musicians. Charming harmonic variety, graceful melody, great help in 4+ parts. First users deserve praise.", "supplement-044": "Sixth consonant against bass, dissonant against fifth. Must resolve upward; proof follows.", "supplement-045": "Added sixth makes great-sixth chord. Normally derived from seventh.* Here original; elsewhere follows source chord’s properties.", "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": "Final note always major third: becomes dominant. First note tonic; its major/minor third alone shows mode.", "supplement-052": "Masson gives inverted example without our explanation or knowledge of origin. Calls A tritone; actually fourth altered by modulation, fundamentally 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 silent; Masson/Brossard call cadence imperfect. Brossard’s irregular means ending outside essential modal notes:b tonic, third, fifth. Describes usage, not cadence kind. Leaves choice unclear, treats types alike. Really calls modulation irregular when cadence leaves first mode’s essentials.", "supplement-058": "a Masson, Nouveau Traité de Musique, page 99.", "supplement-059": "b Mr. de Brossard’s dictionary, under irregolare.", "supplement-061": "Brossard overlooks ancient/modern modulation difference. Ancients restricted, called foreign cadences and range irregular, though range depends on voice. Zarlin suggests all music stayed/ended in initial mode. Outside cadence irregular, perhaps faulty. Modern skillful mode changes are perfection and variety. Ancient rules hid defects, now unnecessary. Brossard should recall own old/new-mode discussion and qualify definition.", "supplement-062": "Only naming dispute? Follow usage? Usage unsettled. Performers confuse terms, sometimes to confound opponents; writers follow whim. Tradition means Zarlin first. Calls inverted perfect cadences Cadenze fuggite.* Better French name imperfect, not interrupted: inversions do not interrupt, modern interrupted cadence does. His irregular labels regular things. Our cadence reverses perfect: root up fifth not down, sixth up not seventh down. Imperfect merely removes/transposes/inverts fundamental bass. Near-synonyms, but imperfect nearer perfect here.", "supplement-064": "Enough naming. Substance next.", "supplement-065": "All masters use dissonance; pleasing as perfect cadence’s, useful melodically/harmonically. Writers silent. Add reasons to experience.", "supplement-066": "Many names ease practice. One fundamental dissonance, others derivatives. Seventh most clearly heard as inverted second. Ratios give consonances first, then major-third division yields unique dissonance. Harmonic divisions complete.", "supplement-067": "* Zarlino, Terza Parte, chapter 52, folio 254.", "supplement-069": "No usable diatonic sound between second’s notes: closest possible. Imagine solid bodies: sounds touch/collide. Ear offended like eye by mismatched colors. Syncope confirms old idea: syn together, copto I strike. Brossarda says note strikes beat/conductor’s hand. Secondary effect: note strikes another sound; clash felt in beat and hand.", "supplement-071": "Sound collision resembles Father Pardie’s solid-body propositions: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": "First effect prepared dissonance; second unprepared.", "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": "B rests; consonance A strikes. A stops, B moves C where A could go. A seems to transfer motion. Immovable D struck by F forces return to G. F rebounds.", "supplement-083": "Nearest consonance governs dissonance movement; acts by degree of perfection.", "supplement-084": "Perfect cadence octave A/D, representing fundamental, forces seventh B/F down. Irregular fifth D/A, less perfect like cadence itself, forces sixth F/B up.7 strikes 8, descends;6 strikes 5, ascends. Third C/G aids both offspring, softens harshness. Chapter II page 53.", "supplement-085": "Example most perfect prepared/unprepared dissonance treatment; ignore missing chord-fill sounds. Perfect chord sole principle; added sound dissonant* only against nearest consonance. That consonance governs movement; dissonance has no independent power. Added irregular-cadence sixth, approved by experience, must rise; always major here. Arrangement parallels descending seventh in perfect cadence. Both second/inverted seventh against neighbor; both soften on generating third.", "supplement-087": "Progressions arbitrary, including consonances before unprepared dissonance and C as possible A destination? They are good, even best. Enough.", "supplement-088": "Three cadences of last three chapters contain all essentials: chords, progression, true modulation. Consonance in perfect; added sound makes seventh containing dissonances. Great-sixth also reduces seventh. Study cadences; all later 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": "Minor third may rise octave if seventh implied alongside it; next chord must reach consonance naturally resolving that implied 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": "Minor-third discussion includes derived dissonances from changed bass arrangement. Concerns melodic taste: octave admitted only by supposition. More in Book III.", "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: tempo may change mid-air. Beat note value changes? Put new value in parentheses above staff. Same value? Unnecessary. See example.", "supplement-475-mouvement": "Change of tempo: beat values in parentheses.", "supplement-167": "Second: incomplete key signatures force “sol” instead of “ut,” “ré” instead of “la.” Movable singing syllables, not fixed pitches. Show correct transpositions, then explain faulty notation.", "supplement-169": "TURN THE PAGE for the continuing example. Its explanation follows.", "supplement-170": "EXPLANATION.", "supplement-171": "One major signature without signs; should be one minor too. French leave D/A minor indistinct, call tonic “ré” or “la.” Error long known, reform feared because old scores. Frere* tried same-name minor tonics but added sharp instead of needed flat. D minor flat marks minor sixth; his sharp gives major sixth, destroys minor order. Prefer “la” over “ré” and natural order preserved. Thanks still owed for thought.", "supplement-172": "Better model all minor keys on A octave. Sing minor tonic “la,” major tonic “ut.” Movable labels, no fixed-pitch substitution.", "supplement-174": "Reflection came late: page 158 says minor tonic “ré.” Original aim follow usage, avoid tedious reform of seemingly trivial matters. But omitted flat from D minor through last flat-minor key contradicts rule. Otherwise would stay silent. Most musicians ignore simplification proposals; almost all rely only on experience, may reject unfamiliar explanations. End digression.", "supplement-175": "French omit minor-key flat; nearly all Italians omit major-key sharp, A through last sharp key.", "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": "Correct signatures: major tonic “ut,” minor tonic “la.” Missing major sharp: tonic “sol.” Missing minor flat: tonic “ré.” Cannot distinguish modes? Method useless; call last sharp “si,” last flat “fa.” Still awkward with missing signs and finding last sign. Prescribed ordering helps.", "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, example’s first staff: cue below B belongs in middle of space, marking C. Not on 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. Replace “one cannot here make the …” with “one cannot here distinguish second degree from sixth degree, nor tonic from 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 example as shown.", "supplement-478-p222": "Page 222 corrected. Sixth part. Continuo bass. Fundamental bass. Irregular cadences A, B.", "supplement-217": "Page 227. Second example: 3 after label G means G forms third of second note F. Third example: 5 after H means H forms fifth of second note F.", "supplement-218": "Page 229, line 9: replace “Chapter XVI” with “Chapter XIII”.", "supplement-219": "Page 231, line 2: P → D. Second paragraph, line 2: start new paragraph at G. Last continuo-bass measure: use example below.", "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. Next-to-last fundamental-bass measure: use example below.", "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. Each staff begins with C. Dot missing at its right.", "supplement-229": "Page 245: second paragraph, line 5; third and fourth paragraphs. Also page 247. Repeated “by fives” and “by fours” should read “from fifth to fifth” and “from fourth to fourth”, or simply “by fifths”, “by fourths”.", "supplement-230": "Page 252. Remove first G label. Sharp below E labelled G belongs with 6 above same note. Line 2: “chiffrez” → “chiffrée” (French form of “figured”). Line 3: “which makes a mediant heard there” → “which is heard there requires only perfect chord”.", "supplement-231": "Start new paragraph with “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. E labelled F needs ♭.", "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. C label belongs below first note of measure, not second.", "supplement-238": "Page 267. First D in example needs label A below.", "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 4–5. Delete “although seventh is suitable only in preparing irregular eleventh”.", "supplement-244": "Page 278. Continuo-bass example: A above first note of next-to-last measure.", "supplement-245": "Page 281. First example: ♯ left of C note; another ♯ right of word “Ut” (C). Second example: remove ♯ from 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. Example’s first staff, second note: ♯ replaces ♮. Move ♮ to next note at same degree.", "supplement-249": "Page 288, line 6: replace “Chapter XXXI” with “Chapter XXIX, page 274”.", "supplement-250": "Page 290. Remove last three paragraphs. Replace with: To confirm this book’s rules, see discussion of establishing rules, Book II, Chapter XVIII, page 25. Chromatic motion possible in major keys. Major third of dominant falls semitone, becomes seventh of another dominant. Or fourth degree rises semitone to leading note of new key.", "supplement-251": "Page 293. Use following example.", "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": "Tritone sometimes on note other than fourth degree. Diminished fifth sometimes on note other than leading note. Then not chord’s defining feature. Accompaniment only. Modulation requires alteration. Some sevenths in preceding sequence likewise altered from ordinary proportion. Know required chord and current key: no worry about alteration. Natural voice’s successive degrees within key or mode’s octave determine ordinary or altered intervals in chord.", "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. Figured bass, second measure: remove 6 above G. Next-to-last measure: move 6 below A to above A. Last paragraph: “figures above” → “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 …” → “distinguish major thirds from minor thirds, major sixths from minor sixths …”. Small type, fifth line from bottom: diminished seventh, 4½ tones. Wrong examples C–B♭, G–F. Replace with C♯–B♭, G♯–F.", "supplement-268": "Page 367. Above example’s second staff: “Minor thirds”.", "supplement-269": "Page 368. Major-sixths example, fourth measure: remove ♯ beside D.", "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 from bottom. Measure 5: figure 4 → 3. Next-to-last measure: add F as shown.", "supplement-480-p382": "Page 382 chord with F added.", "supplement-273": "Page 383. Fourth staff from bottom. Measure 5 chord: arrange as shown.", "supplement-480-p383": "Fifth measure on page 383: corrected chord.", "supplement-275": "Same page. Missing figures for chords and fingering. Follow correct opening to supply them. Exception to watch: page 387, second staff begins 3. Change to 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. Whole example: replace G clef with C clef on first line. First three measures as shown.", "supplement-480-p399": "Corrected first three measures of page 399, C clef on the first line.", "supplement-279": "Page 400. Fifth chord: arrange as shown.", "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. Fourth measure, second chord: use following version.", "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. Measure 6, second chord: ♮ replaces ♯ beside F.", "supplement-291": "Same page. Figure cannot distinguish small-sixth chord here or elsewhere. Upper part contains all chords: recognize it there.", "supplement-292": "Page 423. Fifth chord: use following version.", "supplement-481-p423": "Corrected fifth chord on page 423.", "supplement-294": "Page 424. Count chord measures backward. Fourth measure: use following version.", "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. “naturel” (“natural”) → “nature”. Example’s 4 means tritone; 6 means small sixth. Both need bar. Author absent during printing. Signs not yet customary in printing. Printers thought them unimportant. But barred 6 identifies small-sixth chord, not major sixth as some claim. Aim: one figure names complete chord. Many figures confuse. Four sixth chords need distinct signs where possible. Little care given so far. Barred 6 used merely for major sixth, assuming accompanying third and fourth. Not always true. Often major sixth needs figure because new transposed modulation requires sharps absent from signature. Not necessarily chord meant here. Small sixth itself often minor. Custom alone authorizes signs. Barred 5, written 5̸, means diminished fifth. Undermines claim same bar elsewhere must mean major or augmented. Better new signs clearly identify complete chords. Not interval sometimes minor, sometimes major—especially when same interval admits different accompaniments.", "supplement-300": "Chapter mainly serves future. Rules also compensate for past faults.", "supplement-301": "Page 430, line 11: delete “&”. Combine upper parts on one staff for accompaniment.", "supplement-302": "Most music and harpsichord masters struggle to abandon prejudices. Do not expect everyone’s approval. Cannot accept our conclusions? Inform public. Give us means to improve work to desired perfection.", "supplement-303": "SUPPLEMENT ENDS.", "catalogue-title": "CATALOGUE\nOther music-theory books printed in France. Copies available.", "catalogue-001": "La Gamme du Si. The Si Scale. Author: Nivers.", "catalogue-002": "Music for children.", "catalogue-003": "Music lessons. Author: Berthet.", "catalogue-004": "Music principles. Questions and answers.", "catalogue-005": "Dupont commissioned an engraved version. More extensive.", "catalogue-006": "Very easy principles. Learn to sing any music at sight. Author: L’Affillard. Edition 5. Dedicated to Duke of Burgundy.", "catalogue-007": "— Same book. Edition 6. Dedicated to nuns.", "catalogue-008": "Musical transposition. Every method. Author: Frere. Supplement to all other methods.", "catalogue-009": "Music-principles chart. Author: Fleury.", "catalogue-010": "Easy method. Author: Monteclair. Detailed principles. Several lessons for one voice and two voices.", "catalogue-011": "— Music lessons. Four groups. Summary of principles.", "catalogue-012": "Composition treatise. Author: Nivers.", "catalogue-013": "New composition treatise. Author: Masson.", "catalogue-014": "Treatise. Author: de la Voye-Mignot. Quarto format. Rare.", "catalogue-015": "Treatise. Author: Father Parran. Quarto format. Rare.", "catalogue-016": "Music dictionary. Author: de Brossard. Folio format. Bound.", "catalogue-017": "Harpsichord principles. Author: de Saint-Lambert.", "catalogue-018": "— Accompaniment treatise. For harpsichord and all other instruments.", "catalogue-019": "Another accompaniment treatise. Author: Boyvin.", "catalogue-020": "Accompaniment treatise. Author: Couperin.", "catalogue-021": "Accompaniment treatise. Author: Dandrieu.", "catalogue-022": "Flute principles. Author: Hotteterre-le-Romain.", "catalogue-023": "Theorbo method. Author: Michel-Ange.", "catalogue-024": "Another theorbo method. Author: Fleury.", "catalogue-025": "— Chart of all musical chords. For accompaniment.", "catalogue-026": "Theorbo accompaniment treatise. Author: Campion.", "catalogue-027": "Art of playing preludes. Author: Hotteterre-le-Romain. Quarto format.", "catalogue-028": "Guitar method. Author: Desrosiers.", "catalogue-029": "Learn violin. Method by Monteclair.", "catalogue-030": "Violin principles. Questions and answers. Author: Dupont.", "catalogue-031": "Plainchant method. Author: Nivers.", "catalogue-032": "Another method. Examples in every chant tone. Special studies of music and plainchant.", "catalogue-033": "Chant tones. Those used in Rome and Paris.", "catalogue-034": "Choir ritual. Practical plainchant." }, "sourceSha256": "89d40bc079fbeaed6901dd7734992dfb505dd7dc4a75b379577888a193f82360" }