derivative from it, since the proportion of the two (1 : 23) embodies the fundamental ideas, unity, duality, and triplicity. The continued application of this proportion gives, as a natural progression of notes, those corresponding, through the sizes of their sources, to the numerical series
123(23)2(23)3, etc.
Let us suppose such a progression by upward fifths to be carried on until a series of five notes be formed, the pipes being doubled, that is, the lower octave of a note being taken, whenever necessary to keep the compass of the series within an octave. The following interval-order would be the theoretical result, the initial note occupying the lower extreme:
1st3d5th2d4th
(cents) 204 204 294 204
Of these two intervals, the smaller is that called in European music the major tone (98); and the larger is an interval (3227) closely approximating to a minor third (316 cents). The primary scale of Chinese theory consists of notes at these intervals repeated in octaves above and below. This extension introduces no new interval into the order, the compass of the above four being just 294 cents less than an octave. The complete order consists, therefore, of approximate minor thirds, alternating first with one and then with two tones. To these five notes and their octave repetitions were given the following names: the note from which the order can be derived by a progression of fifths, that one, namely, which lies below the sequence of two tones was called Koung; the note between the two tones was called Chang; that above them, Kio; the note below the isolated tone was called Tche; that above it, Yu. Were the fifth progression carried on two steps further, still keeping it within the octave, two more major tones would be introduced, giving the following order:
1st3d5th7th2d4th6th
(—294—)
204 204 204 90 204 204
KChKiTY
