r
in their arrangement of the tetrachord. In the enharmonic, the
tetrachord consists of two tones and two "dieses." A diesis is a quarter
tone; hence in a semitone there are included two dieses. In the
chromatic there are two semitones arranged in succession, and the third
interval is a tone and a half. In the diatonic, there are two
consecutive tones, and the third interval of a semitone completes the
tetrachord. Hence, in the three classes, the tetrachords are equally
composed of two tones and a semitone, but when they are regarded
separately according to the terms of each class, they differ in the
arrangement of their intervals.

4. Now then, these intervals of tones and semitones of the tetrachord
are a division introduced by nature in the case of the voice, and she
has defined their limits by measures according to the magnitude of the
intervals, and determined their characteristics in certain different
ways. These natural laws are followed by the skilled workmen who fashion
musical instruments, in bringing them to the perfection of their proper
concords.

[Illustration]

5. In each class there are eighteen notes, termed in Greek [Greek:
phthongoi], of which eight in all the three classes are constant and
fixed, while the other ten, not being tuned to the same pitch, are
variable. The fixed notes are those which, being placed between the
moveable, make up the unity of the tetrachord, and remain unaltered in
their boundaries according to the different classes. Their names are
proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon,
paramese, nete diezeugmenon, nete hyperbolaeon. The moveable notes are
those which, being arranged in the tetrachord between the immoveable,
change from place to place according to the different classes. They are
called parhypate hypaton, lichanos hypaton, parhypate meson, lichanos
meson, trite synhemmenon, paranete synhemmenon, trite diezeugmenon,
paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

[Illustration]

6. These notes, from being moveable, take on different qualities; for
they may stand at different intervals and increasing distances. Thus,
parhypate, which in the enharmonic is at the interval of half a semitone
from hypate, has a semitone interval when transferred to the chromatic.
What is called lichanos in the enharmonic is at the interval of a
semitone from hypate; but when shifted to the chromatic, it goes two
semitones away; and in the