Rameau Jean-Philippe. Treatise on Harmony

Translated with an introduction and notes by P. Gossett. — New York: Dover Publications, 1971. — 627 p.The Traité de l'harmonie of Jen-Philippe Rameau is one of the most important books in the history of Western music. Written while Rameau was still a relatively obscure organist and music master at Clermont-Ferrand, the book received but one printing during Rameau's life, in 1722, shortly before he settled in Paris. The Traité was immediately recognized as a profound advance in musical theory, however, and it established Rameau's reputation as a theorist. His book was the first to codify those principles of tonality that were to dominate the music of the West for almost two centuries. Even today the theories of Rameau remain the basis for the study of harmony.
Rameau's Traité de l'harmonie is divided into four books, the first of which presents the mathematical basis from which Rameau sought to derive his theories. Book Two may be considered the most important section of the Traité; in it Rameau generates his entire harmonic system from fundamental principles, explaining intervals, chords, and modes — everything, in fact, essential to musical composition in tonal style. Working from the principles developed in Books One and Two, Book Three treats the practical rules of composition, including such topics as harmonic modulation and chord progressions. Book Four concerns the practical art of accompaniment on harpsichord or organ, including the realization of a figured bass. Corrections added by Rameau in a supplement are included in the text, and all the musical examples have been reset in modern musical notation. In addition, two pages from a unique copy of the first issue of the first edition are given in facsimile. The translator's introduction discusses the history of the work, Rameau's mathematics, and his place in the history of music theory.On the Relationship between Harmonic Ratios and Proportions.
On Music and Sound.
On the different ways in which the relationship between Sounds can be known to us.
On the origin of Consonances and on their relationships.
Remarks on the properties of the Harmonic and Arithmetic Proportions.
On the origin of Dissonances and on their relationships.
On doubled Intervals, and especially on the Ninth and the Eleventh.
On Harmonic Division, or on the origin of Chords.
On the inversion of Chords.
Remarks on all the preceding Chords.
Remarks on the different Ratios which can be given to a single Chord.
How to relate the Ratios given by the Divisions to the Vibrations and to the Multiplication of Lengths.
On the Nature and Properties of Chords and on Everything which may be used to make Music perfect.
On the fundamental Sound of Harmony and on its progression.
On the Chords appropriate to fundamental Sounds and on their progression.
On the nature and properties of the Octave.
On the nature and properties of the Fifth and the Fourth.
On the Perfect Cadence, in which the nature and properties of all the Intervals are found.
On the Deceptive Cadence.
On the Irregular Cadence.
On the imitation of Cadences by inversion.
On how to avoid Cadences while imitating them.
On Chords by supposition with which we may also avoid Cadences while imitating them.
On the Fourth and the Eleventh.
On Chords by borrowing with which we may avoid Perfect Cadences while imitating them.
Rule for the progression of Dissonances, derived from the progression of fundamental Chords.
Remarks on the progression of Thirds and Sixths.
On occasions when the Seventh should be suppressed from the Ninth Chord.
On dissonant Consonances, in which the Fourth is discussed together with the false idea of it that exists because of superfluous Rules.
On License.
Observations on establishing Rules, in which the method of composing a Fundamental Bass is taught.
Continuation of the preceding Chapter, in which it appears that Melody arises from Harmony.
On the properties of Chords.
On the Modes.
On the origin of our liberty to pass from one Mode or from one Key to another.
On the properties of Modes and Keys.
On Meter.
On the usefulness of this new way of indicating different Meters.
On the number of Measures each Air should contain, and on their characteristic Movements.
How to proceed when setting Words to Music.
On Design, Imitation, Fugue, and on their properties.
On those Intervals which should be classified as major and minor; as just or perfect; as augmented and diminished.
Principles of Composition.
Introduction to practical Music.
On the Fundamental Bass.
On the Perfect Chord, with which Composition in four Parts begins.
On the succession of Chords.
On several Rules which must be observed.
On the Seventh Chord.
Remarks on Dissonance.
On Key and Mode.
On how to Modulate harmonically when the Bass is given a diatonic progression.
On the Basso Continuo.
On the progression of the Bass, which simultaneously determines the progression of the Chords; how we may relate a derived Chord to its Fundamental.
Continuation of the Rules drawn from the preceding Example.
On the Perfect Cadence.
On the Leading Tone, and on how all Dissonances are resolved.
On the Eleventh, called the Fourth.
On the irregular Cadence.
On the different progressions of a Bass which are related to one another in such a way that the Harmony in the upper Parts does not change at all.
On how to prepare Dissonances.
On occasions when Dissonances cannot be prepared.
A precise enumeration of the different progressions of the Bass, according to the different. Dissonances used there.
On the Chord of the Second.
On Keys and Modes in general.
On how to pass from one Key to another; i.e., on how to Modulate.
Continuation of the Rules contained in the preceding Chapter.
How to know which Chords must be given to the Bass Notes in any progression.
How to use the Seventh on every Note of a Key in a diatonic progression.
How the same Dissonance may occur in several consecutive Chords on different Notes; how it may be resolved by Notes which appear to be foreign.
On all Licenses, beginning with the Deceptive Cadence.
On the Chord of the augmented Fifth.
On the Ninth Chord.
On the Eleventh Chord, called the.
On the Chord of the augmented Seventh.
On the Chord of the augmented Second and on its derivatives.
On Chromaticism.
On how to make use of everything we have discussed hitherto.
On Composition in two Parts.
On False Relations.
On how to write a Melody above a Bass.
On ornamented Melody or Supposition.
On how to compose a Fundamental Bass below a Treble.
How to compose a Basso Continuo below a Treble.
Useful Remarks concerning the preceding Chapter.
Rules to be observed in a Composition in two, three, and four Parts.
On Design, Imitation, and Fugue.
Principles of Accompaniment.
How to recognize the Intervals from the arrangement of the Keyboard.
On the difference between major and minor Intervals; and between those which are perfect and those which are augmented or diminished.
On the Position of the Hand and on the Arrangement of the Fingers.
On how to find Chords on the Keyboard.
Useful Remarks concerning all the Chords.
On Keys and Modes.
On the order which must be followed for the succession of Chords found within the Octave of each Key.
General Rules.
On the different Chords which should follow the Seventh Chord when the Bass Note remains on the same degree.
On the Chord of the Second.
On Chords of the Sixth.
On the Chord of the augmented Second and on its derivatives.
On Chords by Supposition.
Observations on the relations between all the preceding Chords.
On how to prepare and resolve all Dissonances, from which we shall come to know the Key in use and the Chords which each Note of this Key should bear.
On Chromaticism.
Recapitulation of the various successions of Chords.
Rules which are necessary in order to accompany properly.
On how to figure a Basso Continuo, and on how to know which Chords each figure denotes.
How to tell which Bass Notes should bear a Chord.