De institutione musica V.17: Quomodo Archytas tetrachorda dividat eorumque descriptio.
Archytas, establishing everything by reason, not only neglected to observe the sense of the ears in the first consonances, but also, in the division of the tetrachords especially, followed reason, yet in such a way that he neither effectively worked out what he sought, nor did the reasoning he proposed agree with sense. For he held that there are three genera, enharmonic, diatonic and chromatic, in which he set the same lowest and highest sounds, making the lowest sound in all the genera 2016 and the highest 1512. Between these, in the three genera, he places the string nearest to the lowest as that which is 1944, so that 2016 to it has the sesquivigesimal-septimal proportion (28 to 27). After this, below the high string, but third from the lowest, he places in the enharmonic genus the one that is 1890, to which 1944 is joined in the sesquitricesimal-quintal proportion (36 to 35). And the same 1890 is constituted to the highest, that is 1512, in the sesquiquartal proportion. Likewise in the diatonic genus he places as third from the lowest string and second from the highest the one that is 1701, to which 1944 is joined in the sesquiseptimal proportion, and 1701 itself to the highest 1512 in the sesquioctave. In the chromatic genus, as third from the lowest and second from the highest he places the string which to 1701, the second in the diatonic genus, has the proportion that 256 has to 243. This is 1792, which is set as second from the highest. And the second from the highest in the diatonic genus, that is 1701, has to the second from the highest in the chromatic genus, that is 1792, the proportion that 243 has to 256. The form of these tetrachords divided according to the opinion of Archytas is shown by the description below.