the note of generation, Koung, coincided with any one of the first seven Lu, and they were named from the notes of the scale that fell upon these when Koung was at Huang-chung. Thus the identification of Koung with the Lu Huang-chung was called a modulation or intonation in Koung, its identification with the Lu Ku-hsi a modulation in Kio, since when Koung is at Huang-chung, Kio is at Ku-hsi. Although for the cases when Koung falls on one of the intermediate Lu no nomenclature referring to the primal form of coincidence seems to have been used, they must nevertheless have been conceived as intermediate modulations, and it is for this reason perhaps that we hear less of them.
Thus with the idea of each of the twelve possible embodiments of the scale in the Lu became combined the notion of another, in notes bearing definite relations of pitch (which might be unison) to those of the first. Now this conception of the relation in pitch between two embodiments of the same scale is exactly what is known in European music as a Key. The various possible identifications of the scale with different selections of Lu came therefore through the mingling with them all of the notion of one primal scheme of coincidence, to be so many keys. Had an association between the scale and the first seven Lu not been formed in the Chinese mind, had the various embodiments of the scale in sets of Lu been conceived each for itself, their music would have possessed what might be called a system of transposition, but not a system of keys. To the conception of Key the idea of the definite reference of one set of pitches embodying a scale to another is essential.
A relation emerges whenever we regard any two things from the point of view of either. The two relations of fatherhood and sonship appear in considering the same two beings according as we regard one with reference to the other or the second with reference to the first. The embodiment of the scale from the point of view of which we consider another we shall here call the referred scale, the embodiment with regard to which we consider it the scale of reference. The relation between them may be conceived after two manners which we may call respec-
