able by the fact that the notes most frequently used in both horn and Samien songs are those which fall within the primitive system of the Lu, from d' to c''#. As in the theory so in the practice of Chinese music so far as the evidence of our collection of songs goes, this octave takes the position of first importance.
We have seen that the Chinese regard their scales as results of the same process of the derivation of pipes which, carried as far as primitive workmen can, produces the system of the Lu. In this account of the origin of their five and seven step octaves, the Chinese base them upon an achievement of theoretical grasp and practical skill which must certainly be assigned to a much later date than the appearance of scales in their music. Moreover, the choice of five or seven steps is still unexplained, for the fifth progression affords scales of any number up to twelve. Evidently the opposite derivation is the true one. Just as the Pythagorean use of the progression of fifths did not create, but was the result of the Greek scale of his time, so in China the same progression became the foundation of theory through the fact that by its use an accurately determinate form could be given to the scale of five alternate approximate tones and thirds (and perhaps of seven approximate tones) which was already in use among them.[1] For these ancient octave forms themselves another origin must be sought: we may, perhaps, surmise that they are what may be called the natural precipitates of all simpler melody. That these natural interval orders can be formed by a progression of fifths is a wonderful fact: wonderful, too, it must have been to these primitive theorists to see the generative powers of the fifth progression exhaust themselves in the formation of an interval order of twelve equal semitones. In their eyes the fifth progression became the natural foundation of all music. From it their scales came to be regarded as derived, and, to its limit, the system of the twelve Lu, an origin not alone mathematical was ascribed; they were obtained by Hoang-ti from the mysterious symbols
- ↑ In the Arabian scale just mentioned, the fifth progression is again applied to determine an interval order otherwise produced.
