Jean-Philippe Rameau · section 9 of 109

Chapter six

On Compound Intervals, Especially the Ninth and Eleventh

We have already observed in Chapter III, Article III, p. 7, that in practice compound intervals are always regarded as their simple forms. We must, however, except the ninth and eleventh, which harmony admits only under these names, because their progression and the construction of their chords differ entirely from those of the second and fourth, of which they may be called compound forms. The ninth and eleventh may represent the second and fourth, just as these may represent the others: since the octave introduces no variety into harmony, a sound may freely be transposed one or more octaves higher or lower, provided it always remains above the lower sound of the particular interval in question. Nevertheless, we cannot avoid distinguishing different chords by different names, above all by giving a chord that is primary in its kind the name of the interval that contains all the sounds composing it. Although the fifth is the primary object of all chords, we nevertheless call a chord a seventh chord when that interval contains the others within its compass. The same custom applies to the ninth for the same reason, while the names second and fourth are given only to inverted chords. Consequently the eleventh chord, which is primary in its kind like the seventh and ninth chords, and likewise contains within its compass every interval in its chord, must be distinguished from an inverted chord by the name of the interval it naturally forms. We shall see the proof in the following chapter, Articles III and IV: the ratios of the second and fourth occur throughout the chords that must be formed from these intervals, whereas when the ninth and eleventh must sound in them, the former ratios are no longer involved, but those of the latter intervals. This will be still easier to judge once we know the origin of chords; but it was appropriate to prepare the reader for names that might otherwise have caused surprise. We shall discuss them more fully in Book II, Chapters X and XI.