Page:Philosophical Review Volume 1.djvu/170

 CCORDING to Chinese tradition, the progression of fifths, which was the origin of their scale, was carried on by its inventors, Ling-lun and the Emperor Hoang-ti, until it yielded a system of twelve notes separated by hemitones, like the duodecimal chromatic scale of European music. This is the system of the twelve Lu, which according to Chinese ideas is the foundation of the whole art of tone, and which they recognize not only in theory, but in some of their instrumental forms.

Let us suppose the derivation of pipes one from another by the two-thirds measurement, which gives first the five and then the seven step scale, to be continued until twelve pipes are formed, the derivatives being doubled as before whenever necessary to keep the whole series of sounds within an octave. The theoretical result of this process would be the following interval order:

consisting of Pythagorean semitones alternating with an interval almost exactly the size of the diatonic semitone, $16⁄15$ (= 112 cents); the compass of the whole twelve notes being a Pythagorean semitone less than an octave. The sounds of twelve pipes obtained one from another by this extension of the fifth progression constitute what is known in Chinese theory as the system of the twelve Lu. The hemitones of the order are regarded as Rh