De institutione musica V.18: Quemadmodum Ptolomaeus et Aristoxeni et Archytae tetrachordorum divisiones reprehendat.
But Ptolemy reproves both divisions of the tetrachords in the following way. First, that of Archytas: because the second string from the highest in the chromatic genus, that is 1792, is so placed that it makes no superparticular proportion either to the highest, 1512, or to the one next to the lower, 1944, although Archytas held the superparticular comparisons in such esteem that he took them up even in the reckoning of the consonances. Next, because sense finds the first proportion from the lowest string in the chromatic to be greater than Archytas made it. For in the chromatic genus he made 1944 stand to 2016 in the sesquivigesimal-septimal proportion, whereas, according to the usual melody of the chromatic genus, it ought to have been the sesquivigesimal-prime (21 to 20). Likewise in the enharmonic genus the proportion which the first from the lowest holds according to the division of Archytas ought to be far smaller than it is found in the other genera. Yet he sets it equal to the other genera, since he makes the first proportions from the low in the three genera all sesquivigesimal-septimal. Aristoxenus he blames because, in the soft chromatic and the hemiolic chromatic, he set the first and second proportions from the lowest string so that they differ from one another by a very little, and by as much as sense cannot discern. For the first proportion in the division of the soft chromatic according to Aristoxenus is 8, and in the hemiolic chromatic 9. But 8 and 9 differ by a difference of one unit. The whole tone is of 24 units according to his setting, of which the unit is one twenty-fourth. The first proportions from the low, therefore, of the soft chromatic and the hemiolic chromatic differ from each other by the twenty-fourth part of a tone, which, because of the smallness of the difference, the hearing perceives in no way. He also reproves Aristoxenus because he made only two divisions of the diatonic genus, dividing it into the soft and the spirited, though other species of the diatonic genus can also be found.