De institutione musica V.13: Quemadmodum Aristoxenus intervalla consideret.
What Aristoxenus thinks of these matters must be briefly explained. Since he establishes no treatment by reason but leaves it to the judgment of the ears, he marks the voices themselves with no numbers by which to gather their proportions, but takes the difference between them as the middle term, so as to place his speculation not in the voices themselves but in that by which they differ from one another—very imprudently, for he thinks he knows the difference of voices of which he establishes no magnitude or measure. He accordingly proposes that the diatessaron consonance is of two tones and a semitone, the diapente of three tones and a semitone, and the diapason of six tones—which was shown in the earlier volumes to be impossible.