Note 3 — § 10. Aristoxenus.
Reading edition
Harm. p. 37, 19 Meib. houtô gar hoi men tôn harmonikôn legousi barytaton men ton Hypodôrion tôn tonôn, hêmitoniô de oxyteron toutou ton Mixolydion, toutou de hêmitoniô ton Dôrion, tou de Dôriou tonô ton Phrygion: hôsautôs de kai tou Phrygiou ton Lydion heterô tonô. Westphal (Harmonik und Melopöie p. 165) would transfer the words hêmitoniô ... Mixolydion to the end of the sentence, and insert oxyteron before ton Dôrion. The necessity for this insertion shows that Westphal's transposition is not in itself an easy one. The only reason for it is the difficulty of supposing that there could have been so great a difference in the pitch of the Mixo-lydian scale. As to this, however, see p. 23 (note).
The words Hypophrygion aulon have also been condemned by Westphal (Aristoxenus, p. 453). He points out the curious contradiction between pros tên tôn aulôn trypêsin blepontes and the complaint ti d' esti pros ho blepontes ... ouden eirêkasin. But if pros tên ... blepontes was a marginal gloss, as Westphal suggests, it was doubtless a gloss on aulon, and if so, aulon is presumably sound. Since the aulos was especially a Phrygian instrument, and regularly associated with the Phrygian mode (as we know from Aristotle, see p. 13), nothing is more probable than that there was a variety of flute called Hypo-phrygian, because tuned so as to yield the Hypo-phrygian key, either by itself or as a modulation from the Phrygian.
In this scheme the important feature—that which marks it as an advance on the others referred to by Aristoxenus—is the conformity which it exhibits with the diatonic scale. The result of this conformity is that the keys stand in a certain relation to each other. Taking any two, we find that certain notes are common to them. So long as the intervals of pitch were quite arbitrary, or were practically irrational quantities, such as three-quarters of a tone, no such relation could exist. It now became possible to pass from one key to another, i. e. to employ modulation (metabolê) as a source of musical effect. This new system had evidently made some progress when Aristoxenus wrote, though it was not perfected, and had not passed into general use.