tively individual and representative. Either we may recognize the relation subsisting between each individual note in the one embodiment and one in the other, or we may take a single note of the scale as standard of comparison and regard the interval between its two positions as the representative of the same interval between all other pairs of corresponding notes. In either case the recognition of unison (identity) as a possible form which the relations concerned may take is necessary for systematic completeness.
The nomenclature we have just described indicates that it is the latter simpler manner of regarding keys that obtained in China. The compound relation of pitch in whose recognition a Key consists was there conceived by means of that between corresponding notes of the two embodiments of the scale concerned. In naming the fundamental keys of their music, the Chinese used Koung as a note of comparison and stated the interval between its two pitches by giving the note of the scale of reference upon which the Koung of the referred scale falls.
In both of the two theories of music which have in succession developed themselves upon European soil, that of the later Greeks and that of modern times, the element of key has a conspicuous place. In the former the representative conception of key, which had been developed in China, received another embodiment; and this still persists in the music of modern Europe. But as we shall see, the origin of the modern system of modulation in the conception of small displacements in pitch in the notes of a diatonic order has given it a character fundamentally individual.
That the practical limit of the fifth progression is an octave of twelve approximate hemitones was known to the Greek theorist, Aristoxenus (fourth century B.C.); and like the Chinese the later Greeks laid down as the entire system of distinctions of pitch to be recognized in their music, a series of twelve notes separated by hemitones and repeated in the octave above and the octave below.[1]
- ↑ This range of pitch was increased by three hemitones in the system of fifteen scales of transposition (Tonoi or Tropoi) recorded by Alypios (360 A.D.).
