Again as in China, the notes of the diatonic scale were associated primarily with certain of the elements of this order, and with the same elements as in the system of the Lu, Fa (= Koung), being identified with the lowest pitch of the whole three-octave interval order. Exactly as in China, again, the Greeks permitted all possible relative positions of the scale and the duodecimal octave; and since the same conception of their primary relation (Fa = lowest note of the octave) that persisted in China formed a part also of the Greek theory, their transpositions of the scale came to be united likewise into a duodecimal system of keys. To this striking list of theoretical similarities must be added a no less striking difference between Greek and Chinese nomenclature. Although the keys to be named were identical, the intervals involved between corresponding notes being those of unison or of one, two, etc., up to eleven hemitones, yet the method of naming them was, in a manner, opposite in the two systems. The Chinese proceeded by designating the note of the scale of reference upon which, or (hypothetically) the notes upon the semitone between which, a certain note (Koung) of the referred scale should fall. The nomenclature of the Greeks was derived from that of their ancient Schemata, or, as we should now call them, modes. These were the different sequences of tones and hemitones between octaves of each different note of the scale. Giving to the notes of the diatonic order their modern names, between octave repetitions of Do the following sequence of tones and hemitones is included: T T H T T T H; between octave repetitions of Sol, the following: T T H T T H T. The first was called by the Greeks the Lydian scheme, the second the Hypo-Phrygian: and other like names were given to the others. Since their keys involved an interval of pitch of a certain number of hemitones between two embodiments of the scale, the note Fa of the scale of reference fell in each either upon some note of the referred scale, or halfway between two. In the former case the key was given the old name of the scheme or mode bounded by that note; in the latter case the name of the mode bounded by the next note below the intermediate pitch with which Fa coincided, a vari-
