Jean-Philippe Rameau · section 3 of 109

Table Explaining Essential Terms

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A

ACCOMPANIMENT. See Book Four. page 363

CHORD. There is only one chord from which the others arise. All can be reduced to a division by thirds through inversion. Chapter VII, Book I. 102. 114. 126. 127 and 128

The principle of every chord resides in a single sound. 5. 127 and 133

There are only the perfect chord and the seventh chord. 45. 61. 378 and 379

Nothing is easier than using consonant and even dissonant chords through the fundamental rules of harmony, from which every imaginable melody may be drawn, and so forth. This always reveals the sounds needed to complete the chords. 72 and 73

The seventh chord is always contained in chords by supposition. 74 and 75

Every dissonant chord consists only of combined consonances. 95

To draw sound conclusions, examine not only how chord sounds affect the bass but also how they affect one another. page 96

Every bass note moving by consonant intervals may receive a consonant chord [printed “Conso-sonant”]. 395

See Perfect, Rule, Consonance, and Octave.

HIGH-PITCHED. This is the proper name for high sounds, just as low-pitched names low sounds.

High sounds are contained in the low sound. 3 and 5

B

FUNDAMENTAL BASS, or FUNDAMENTAL SOUND. The fundamental bass cannot subsist unless it always prevails below the other parts. page 134

See Imply and Suppose.

The only intervals assigned to fundamental-bass progression are the third, fifth, and seventh. 49 through 51

Its most perfect progression descends by thirds, fifths, and sevenths. 132

The most perfect of these is the fifth, which seems to return to its source, and so forth. page 129

This progression forms the perfect cadence. 57

Dissonance can be prepared and resolved only in one of these progressions. 81. 87 and 110

When the fundamental bass ascends by these same intervals, the dissonance cannot be prepared. 84 through 87

Descending a fifth and ascending a fourth are equivalent in these progressions. 185

Zarlino compares the bass to the earth and says it must move slowly and by separate steps. 49

The intervals used for fundamental-bass progression must also accompany it. 52

The fundamental bass produces a very good effect in choruses. 138

See Cadence, Principle, and Progression.

C

CADENCE. A perfect cadence is formed by a fundamental bass descending a fifth or ascending a fourth. page 50

The perfect cadence proves where dissonance belongs. 53

Definition of the perfect cadence. 54

It determines every interval’s progression except the octave and fifth, and so forth. page 55

Example of the perfect cadence. 57

Zarlino says music would be confused without a bass and that a perfect cadence’s bass should descend a fifth, yet forgets this bass in almost all his examples. 58

A cadence is called interrupted when the dominant ascends diatonically in the bass or other parts. 61 through 63

This cadence is admitted only by license. 110

Benefits obtainable from it. 271 and 272

A cadence is called irregular when the bass ascends a fifth, and so forth. It contains a dissonance with irregular progression, but that dissonance can always be omitted. See the Supplement.

A cadence is called imperfect when the perfect cadence’s bass is absent but can be implied. 257

Knowing all these cadences is essential to understanding harmony. See the Supplement.

Inverting these cadences creates harmonic variety and produces melody. 67

Ways to maintain a long sequence of melody and chords without any conclusion. page 68

Distinguishing a cadence from its imitation. 68 and 69

Evading cadences by imitating them. 70

The example is written correctly in the Supplement.

Progression of chords by supposition originates in the first three cadences. 75 and 77

Modulation derives from the perfect cadence. 144. 145 and 148

The perfect cadence suffices to explain every musical rule. 129

CANON. Definition of canon. 359 through 362

CENTER. The principle of harmony may be regarded as the harmonic center. 127

CLASH. Sounds clash in a way related to the collision of solid bodies. See the Supplement.

This clash occurs between a dissonance and its nearest consonance. Ibid.

COMMA. Determining how many commas make up a whole tone. 27

A ratio much smaller than the comma is needed to form the intervals. Ibid.

CHROMATIC. The chromatic genus arises from semitone progression. In harmony it occurs chiefly between the sixth and seventh notes of minor keys. page 293

Making the tonic a tonic dominant reveals the chromatic. 70

A part moving by semitones has a chromatic progression.

COMPOSE. COMPOSITION. In music, this means inventing pleasing melodies and combining sounds to good effect; giving each sound an appropriate progression; understanding the relationships among all intervals and chords; in short, putting into practice everything that can make music perfect.

Composition should first be taught in 4 parts. 239 and 240

Qualities required for good composition. 143 and 162

Accompaniment is, in a sense, necessary for reaching an understanding of composition sooner. 140

CONJUNCT. Conjunct progression or steps include diatonic and chromatic motion.

See Diatonic and Chromatic.

CONSONANCE. An interval whose combined sounds greatly please the ear. All consonances consist of thirds, fourths, fifths, and sixths. “Consonant progression” means that the melody moves by one of these intervals.

Origin of consonances, their order there, order of perfection, and mutual relationships. pages 3. 4. 5. 15 and 16

There are only three primary consonances. 13 and 14

There are dissonant consonances. 96 and 102

COUNTERPOINT means composition. Among practitioners, it means music composed on a particular subject, ordinarily taken from church chant.

Counterpoint is divided into simple, figured, and other types. See Monsieur de Brossard’s Dictionary.

Plainchant was composed before good modulation was understood and constantly violates the natural order. To fit harmony to it, one must follow rules sharing the defects of that plainchant, since it is their object.

Nevertheless, many musicians still favor these rules without considering their principle. Those sensitive to true harmony regard them as extraneous, since good modulation supplies simpler, sounder rules that ensure correctness, provided the subject—as it absolutely should—follows good modulation. See Plainchant below, and for further satisfaction Book II, Chapters XVIII, XIX, and XXI.

STRING. A string stretched to produce a sound teaches us the relationships between sounds. page 2

Divide this string according to the natural sequence of numbers to obtain every necessary harmonic benefit. 3. 4. 15. 16 and 21

Sound relates to sound as string relates to string. 3

People commonly say “beautiful strings” to express beauties found in harmony and melody.

BODY. Unity, the principle of numbers, represents the sounding body from which relationships between sounds are proved. 18

D

DIATONIC. Diatonic progression moves the melody through successive degrees of the natural voice, following the scale or perfect diatonic system. page 23

See System and Progression.

DISJUNCT. Disjunct progression includes consonant and dissonant motion.

See Consonance and Dissonance.

DISSONANCE. Intervals that in some way strike against the ear. “Dissonant progression” means melodic movement by one of these intervals.

Origin and relationships of dissonances. 22. 24 and 27

The seventh chord is the origin of all dissonant chords. 31 and 38 through 45. 96. 98 and 101

All dissonances are major or minor, like the thirds from which they originate and whose properties they consequently follow. 45. 55. 81 and 130

The leading note is the origin of all major dissonances. 56 and 137

A major dissonance is such only when joined by the minor dissonance. 137

The seventh is the origin of all minor dissonances. 98

Dissonance must be used with great discretion. 142

Reflection on resolving dissonances. 137

See Cadence, Division, Ratio, Progression, Prepare, Resolve, Fundamental Bass, Second, Seventh, and Tritone.

DOMINANT. Definition of dominant. page 56

Distinctions among dominants. 68. 69 and 200

E

BORROWING. A new practical term distinguishing a kind of chord usable only in minor keys. pages 43. 79. 80 and 81

Proof of this borrowing. 282 through 285. See Second.

EXPERIENCE. See Music.

F

FUNDAMENTAL. See Fundamental Bass.

FUGUE. A musical ornament whose only principle is good taste. page 358

Fugue may have been invented for four-part pieces. 331

For more on this subject, read Book III, Chapter XLIII.

G

LOW-PITCHED. See High-Pitched.

H

HARMONY. Several sounds combined to affect the ear agreeably.

Harmony is perceived only at the first instant of each beat. page 134

Melody comes from harmony. 23. 138 and 139

Perfect harmony consists in four parts. 140 and 141

Harmonic progression comes from arithmetic progression. 17 and 20

See Cadence, String, Proportion, Melody, Meter, Music, Number, and Principle.

I

IMITATION. Definition of imitation. 193 and 332

IMPERFECT. This term applies to variable consonances such as the third and sixth, and should also apply to cadences inverted from the perfect cadence. See Cadence.

Some inversions of the perfect chord are called imperfect chords. 35

INTERVAL. Definition and names of intervals. 2

Distinguishing inverted intervals from uninverted ones through arithmetic operations. 17

Formation of intervals. 27. See Ratio and Tritone.

IRREGULAR. See Cadence.

L

LICENSE. Origin of musical licenses. page 110

LENGTH. See Ratio.

M

MELODY. The tune of a single part. Music is commonly called melodious when each part’s melody matches the beauty of the harmony.

As far as can be judged, ancient music was founded on melody alone. pages 142. 143 and 146

Zarlino explains this perfectly well. 142

See Cadence and Harmony.

METER. Descartes says animals could dance in meter. 150

Meter may be derived from the principle of harmony. Ibid.

Useful practices for training the ear in meter. 151

The numbers 2, 3, and 4 alone suffice to indicate every meter. Ibid.

Using the same signs for movements with equal and unequal beats prevents their distinction. 156

A note before the clef may indicate each beat’s value by its own duration, thus distinguishing slow from fast tempo. 152

This pre-clef note can identify the key and also facilitate solmization without concern for the number of sharps or flats after the clef. page 158

MODE. It determines not only the diatonic progression of sounds within an octave, but also an order among chords, which can consist only of those octave’s sounds.

Modes are derived from the perfect diatonic system. 143 and 144

There are only two modes. 143

Errors of the ancients and Zarlino in establishing modes, and the probable cause of Zarlino’s error. 145 through 148

Understanding modulation greatly helps determine whether music is well composed. 135. See Cadence, Key, Tritone, Third.

MUSIC. What music is and what it consists of. 1

Although hearing alone may judge music’s effects, the mind can grasp its properties only with reason’s help. 125

Experience presents many chords, but reason unites them all in one; reason must therefore govern our judgments. 126

Musical experience alone cannot convince us. page 106

But reason can supply what is missing. 114

Music is subordinate to arithmetic. 18 and 19

While arithmetic progression must increase, harmonic progression must decrease. 11

To apply the natural numerical sequence to harmony, imagine that numbers indicate divisions of unity, and so forth. 11 and 19

What a good musician must observe in creating works. 143

See Mode.

N

NUMBER. All harmony’s power has been attributed to numbers. page 3

Only three consonant numbers form the perfect chord. 34 and 35

Observations on the power of three. 35

A number multiplied geometrically always represents, so to speak, the same sound, and so forth. 7

The number 5 can represent unity. 13

The number 3, where the fourth arises, cannot head a chord without inverting its natural order. 21 and 22

If numbers are understood as divisions of unity, everything becomes simple, familiar, precise, just, and correct. page 21

See String, Body, and Music.

TONIC NOTE. LEADING NOTE. See Sound and Leading.

NINTH. Difference between ninth and second. 28 and 78

The ninth interval and its chord derive from the fifth. 32

This chord proves that the seventh can resolve to the octave. 118 and 119

When a ninth chord sounds above a tonic, avoid adding the seventh. 94

See Eleventh, Seventh, Suppose, and Tritone.

O

OCTAVE. Definition and properties of the octave. pages 6 through 17, and also 54

All chord variety arising from inversion comes from the octave’s power. 15 and 16

The octave should be called aequisonance rather than consonance. 7. 15 and 16

See Principle and Simulated.

ELEVENTH. Difference between eleventh and fourth. 28 and 77

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

The eleventh chord is extremely harsh in its ordinary form, so its middle sounds are usually removed. We then call it heteroclite. page 76

See Suppose.

P

PERFECT. The perfect chord consists of the fifth and the two thirds.

Chords arising from inversion of the perfect chord. pages 34. 35 and 36

Any chord besides the perfect chord must consist of the perfect chord plus one of its parts. 31. See Cadence.

PLAINCHANT. Plainchant suits harmony only in keys conforming to the perfect system. Its melody could be made easier and more flowing. 147

PREPARE. This term means that a minor dissonance must be preceded by a consonance on the same degree. This is not, however, a universal rule. 84 through 87

Dissonance need not always be prepared on weak beats, and major dissonance can never be prepared. 86

Dissonance absolutely must be prepared by a consonance. 123 and 125

PRINCIPLE. Harmony’s principle resides in a single sound. 5 and 127

The fundamental sound, or principle, uses its octave as a second endpoint to which all intervals generated by its division must answer, showing more clearly that it is their beginning and end. page 8

Everything agreeing with the principle agrees equally with its octave. Ibid.

The principle is implied in its octave. 8 and 9

Always seek the principle in fundamental chords. 117

The principle resides not merely in fundamental chords, but more precisely in their lowest sound. 133

Since the foundation or principle can subsist only within its octave, chords exceeding that span must employ this foundation by supposition. 32 and 33

See Suppose.

Zarlino knew this principle but lost sight of it in his operations and rules. 18 through 21

Dissonance derives its principle from the perfect chord, and so forth; that chord derives its principle from its lowest sound, and so forth. 109

See Viol and Center.

PROGRESSION. While fundamental-bass progression must be consonant, upper-part progression must be diatonic. page 52

One part may be given the progression belonging to another. Ibid.

Dissonance must move diatonically, and the sounds preceding and following it must be consonant. Ibid.

See Fundamental Bass, Cadence, String, Harmony, Music, Proportion, Ratio, Consonance, Dissonance, Chromatic, Diatonic, Conjunct, and Disjunct.

PROPORTION. A relationship between two or more sounds compared together.

Harmonic or arithmetic proportion gives consonances an especially pleasing order. 4

The ratio 2 to 4, giving the octave, affects the ear much like 2 to 2, giving the unison. 7

Harmonic proportion or progression derives from arithmetic proportion; their relationship. 17 and 20

Faults apparently caused by favoring harmonic over arithmetic proportion. 18. 19 and 20

Sound ideas about harmony supplied by arithmetic proportion. 21 and 22

The difference between harmonic and arithmetic proportions partly caused the ancients’ errors in arranging modes. page 147

Q

FOURTH. Origin of the fourth. pages 10 and 11

Although the fourth can produce a seventh through its squares, it cannot divide that seventh harmonically. 31

The fourth in second and small-sixth chords is consonant. 99 and 102

See Number, Eleventh, and Tritone.

FIFTH. Origin of the fifth and its precedence over the fourth. 10 and 11

The fifth is the first consonance, excluding the octave. 5

The fifth and thirds compose all chords. 29. 30. 31 and 32

The fifth is the primary object of all chords. 12. 32 and 54

The fifth cannot serve as the limit of intervals. 13

No chord is complete without the fifth, hence without the two thirds composing it. 30

The fifth alone can generate through its squares an interval exceeding an octave; the resulting chord is tolerable only because the fifth divides it harmonically. 32

The first bass note of a descending fifth or ascending fourth may, and indeed should, bear a seventh chord. page 69

Anyone somewhat sensitive to harmony hears a melodic conclusion with an almost irresistible urge to make the bass descend a fifth, and so forth. 50

In harpsichord accompaniment, consecutive fifths between right-hand upper parts are sometimes almost unavoidable. They create a connection in chord progression whose habit is more easily acquired by tolerating this small fault than by strictly enforcing compositional rules.

I call it a small fault, if it is a fault at all in accompaniment: it does not destroy the harmonic foundation, and Italians use it without scruple in such cases.

See Fundamental Bass, Simulated, Tritone, and Cadence.

R

RATIO. Different ratios assignable to one chord. pages 26 and 46

Vibration ratios match division ratios; length ratios are their inversions. pages 47 and 48

Catalogue of natural and inverted ratios for all intervals. page 26

See String.

INVERT. INVERSION. In music, rearranging the natural order of sounds relative to one another in forming perfect harmony.

Inversion comes from the octave’s power. 7. 15 and 16

Most theorists have considered interval inversion merely as the difference between one interval and another. 16

Zarlino understood interval inversion but forgot chord inversion. 20 and 111

Distinguishing inverted and uninverted intervals through arithmetic operations. 17

Inversion is the key to all harmonic variety. 10 and 114

Knowledge of inverted chords developed only over time. 132

Inversion becomes clearer as we penetrate harmony’s secrets. 11

Some musicians believe chords by supposition can be inverted because they misunderstand the principles of both these chords and inversion.

See Suppose.

OCTAVE EQUIVALENT. Definition of an octave equivalent. page 6

RULE. Rules derive from principles, not principles from rules. 113 and 126

Rules originating in fundamental harmony hold only within the chords assigned to that harmony. 90 and 91

Seek a derived chord’s properties in its fundamental chord. 103

The rule requiring every dissonance to be prepared by a consonance has no exception. 104

Proof of errors in modern rules. 105 through 109, and 132

Faults of commentators on the first rules. 125 and 143

The fundamental bass determines every rule concerning consonances. 128 and 129

Different principles behind the rule allowing a syncopated bass beneath a dissonance. 107 and 108

See Cadence and Counterpoint.

S

RESOLVE. In music, this means every dissonance must be followed diatonically by a consonance.

Major dissonances must resolve upward by semitone; minor ones downward diatonically. pages 55 and 130

SECOND. Minor dissonance is always recognized in a second or seventh. page 100

The second is an inverted seventh, as shown in the squares on page 38.

Origin of the augmented second and how it borrows its foundation from the fundamental sound. 41 through 44

This borrowing generates as many chords as a tonic dominant’s seventh chord. 80. 283. 284. 404 and 405

See Seventh.

SEMITONE. This word derives from Greek and means half-tone.

The semitone provides all the ornament of harmony and melody. It always governs major-dissonance progression. Zarlino, after discussing it successfully, abandons it where it is felt most strongly. 55 through 57

The minor semitone distinguishes major from minor thirds, hence all intervals classed as major, minor, augmented, or diminished. 27

Distinguishing major and minor whole tones and semitones, and so forth, is useless in practice. 364

See Leading and Tritone.

LEADING. Definition of the leading note. 56 and 217

The leading note identifies the current key. 258

See Dissonance.

SEVENTH. The seventh is the origin of all dissonances: without it, the major dissonance is merely a consonance. The squares on page 38 show this: adding the seventh to the perfect chord produces all dissonances.

T

BEAT. See Meter.

TERM. Some musicians err because they do not understand the force of terms. page 124

THIRD. Origin of thirds. 12. 13 and 14

The fifth and thirds compose all chords. 29 through 32

Thirds may be regarded as the sole object of all chords. 33 through 44

The third is distinguished as major or minor. page 130 and the demonstration on page 4

The third is the only consonance that can resolve dissonance in natural, fundamental harmony. 53 and 121

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

The major third must ascend; the minor third must descend. 55. 88 and 89

Every interval classed as major, minor, augmented, or diminished must follow the properties of these thirds. 55 and 130

The third of the fundamental sound or tonic determines the mode’s kind. There are therefore only two modes, major and minor. 143

Only thirds and sixths should be distinguished as major and minor. 165

Descartes erred about the origin of the minor third and sixths. 14

Thirds partake of consonance and dissonance. 87

The major third may descend. 90

Minor thirds and minor sixths may ascend in harmony inverted from the fundamental. 91 through 93 and the Supplement.

TONE / KEY. French “ton” has two practical meanings that must be distinguished. First, it names the distance between two compared sounds: the whole-tone interval, theoretically distinguished as major or minor. 22 and 23

This distinction is useless in practice. 364 and 367

Different ratios for minor and major whole tones cause corresponding differences in all interval ratios except the octave and augmented seventh. 25 and 26

Second, “ton,” meaning key, often takes the place and properties of “mode.” Hence the sound determining modulation’s order within its octave is called the tonic note.

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

Consonances determine not only chord construction and fundamental-bass progression, which also governs the upper parts, but also how to pass between keys or modes. Ibid.

Distinguishing key from mode. pages 149 and 198

Determining whether a note bearing a perfect chord is tonic, and the consequences for choosing chords. 264 and 265

See Meter.

TRANSPOSE. There are only two modes, one beginning on C and the other on A. A mode or key is called transposed when another note serves as its first degree.

Most Italians omit the principal sharp required after the clef in transposed major modes; almost all French musicians omit the principal flat required in transposed minor modes. See the Supplement.

Order of sharps and flats in transposed modes. Ibid.

Avoiding the need to count post-clef sharps and flats when solmizing, and the difficulties that counting causes beginners. Ibid.

Monsieur Frere erred in his new notation for transposed minor modes. Ibid.

TRITONE. The augmented fourth contains three whole tones, hence its name. It often represents a perfect fourth altered only by modulation, and is then no longer the tritone usually imagined. The same applies to fifths, seconds, sevenths, and ninths that modulation sometimes alters. Understanding modulation greatly helps avoid confusion; see page 236.

Masson called a fourth altered by modulation a tritone, although that fourth was not dissonant. 65 and 66

V

VIBRATION. See Ratio.

VIOL. Evidence from musical instruments concerning the principle and its octave. page 6

Z

ZARLINO or ZARLIN. Celebrated music author whom Monsieur de Brossard calls the Prince of Modern Musicians.

Errors in Zarlino’s rules partly arose because he considered only two sounds at once. page 89

This author judges perfectly the astonishing effects the ancients attributed to their music. 142

See Invert, Cadence, Principle, Mode, and Semitone.

End of the Table of Terms.