Aristoxenus 350-320 B.C., a pupil of Aristotle, disavowed the whole Pythagorean scheme, and the philosophers ranged themselves in two opposing schools, the Pythagoreans who determined intervals by proportional numbers, and the Aristoxenians who relied upon the judgment of the ear.
Somewhere in the period embraced by the lives of Ion and Aristoxenus, for it was a period of high intellectual activity with the Greeks (Sophocles, Pericles, Plato, Aristotle and other famous men were living), somewhere we have to place the Disjunct, or Greater System Complete. It consists of fifteen notes,—
3 | 1 | |||
| a—— | b ‿ c——d—— | e | ‿ f——g—— | a |
| * | ||||
| 2 | 4 | |||
| —— | b ‿ c——d—— | e | ‿ f——g—— | a |
then there was an alternative arrangement ultimately admitted, making conjunction at a*, allowing b flat instead of b, causing that tetrachord to end on d, and placing the tone of disjunction between the d and e. Very noticeable this as shewing how popular feeling hankered after the old way of Terpander. This later arrangement of the Greek scale, comprising the two octaves, comes to us from Euclid’s reputed treatise on Music, now attributed to Cleonidas, writing about 120 A.D.
Thus was the scale completed. The order of the growth of the scale is shewn by the figures, 1, 2, 3, 4 over the several tetrachords.