Jean-Philippe Rameau · section 15 of 109

BOOK TWO. On the Nature and Properties of Chords, and Everything That Can Serve to Make Music Perfect

CHAPTER ONE · On the Fundamental Sound of Harmony and Its Progression

Since we have sufficiently explained in Book I, Chapter III, Article I, p. 5, what the fundamental sound is and the place it must occupy in harmony, we shall chiefly concern ourselves here with determining its progression.

The part in which this fundamental sound prevails is called the bass, because that sound is always the deepest and lowest. Here is how Zarlino* explains the subject: just as the earth serves as the foundation of the other elements, so the bass has the property of supporting, establishing, and strengthening the other parts. It is therefore regarded as the base and foundation of harmony, whence its name bass, as if to say base and support. Having supposed that, if the earth failed, all this beautiful order of nature would fall into ruin, he says likewise that, if the bass failed, the whole musical piece would be filled with dissonance and confusion. When composing a bass, then, we must make it proceed by somewhat slow and separated movements—that is, farther apart than those of the other parts—so that they can proceed by conjunct movements, especially the part forming the soprano, because this is its property, and so forth. Yet compare so clear and accurate a definition of harmony's fundamental part with this author's rules and examples: contradictions will be found everywhere, keeping us perpetually doubtful and uncertain.

Yet a principle on which everything rests cannot be established too firmly, and losing sight of it for a moment is to destroy it. Without departing from the principle just proposed, we shall therefore reinforce it with that of the whole string, whose first divisions contain consonances that together form perfect harmony. If we can assign a progression to the part represented by this whole string, it can only be through those consonant intervals given by its first divisions. Each sound will thus always agree with its predecessor; and each, in turn, being able to bear a chord like that received from these first divisions, will readily represent the whole string that is the principle and foundation of that chord. This defines Zarlino's proposition concerning the separated intervals by which he says the bass must proceed, since they cannot be consonant unless they are separated. If he also says they must be slow, this is only relative to the other parts, which must be diatonic: in this way the upper parts can make several movements in passing from one consonance to another while the bass makes only one. In establishing our rules, however, we shall make every part proceed by equal movements, to keep matters simple and clear at first. The octave must not be confused with the progression we have just assigned to the bass: it does not matter whether the fundamental sound is raised or lowered by several octaves, provided it always remains beneath the other parts. Rather, the fifth must first be regarded as the interval most suited to it. Indeed, no final cadence or conclusion of a melody is heard without this progression being its primary object. Consult anyone with some feeling for harmony: whatever the kind of melodic conclusion heard, they feel compelled to make the bass proceed by this interval. What we say of the fifth must also be understood of the fourth, which always represents it. People whose voices are low enough naturally descend a fifth in these conclusions; those who cannot do so ascend a fourth. This plainly proves both the power of the octave, always represented in either sound forming it, and the relationship between the fourth and fifth arising from its division. The fifth is always preferred as soon as the voice permits it, yet it is not destroyed when the fourth is substituted for it. Next, to keep the listener in a pleasing suspense, since the fifth consists of two thirds, the bass may proceed by one or more thirds, and consequently by the sixths representing them. All cadences are reserved for the fifth alone and the fourth representing it. The entire progression of the fundamental bass must therefore be confined to these consonances. If dissonance sometimes obliges this bass to ascend only a whole tone or semitone, this arises from a license introduced by the interrupted cadence, which we shall discuss later. Moreover, observe that this whole tone or semitone ascending, not descending, is the inversion of the seventh then sounding between the two sounds forming it. We shall even see in Book III, Chapter XI that, except in the interrupted cadence, progression by a third and fourth can be understood as implied there.

* Zarlino, Istitutioni Harmoniche, third part, chapter 58, fols. 281 and 282.

We should be disposed in favor of this principle if it can hold good everywhere; nor has it been advanced without certainty of its success.