De institutione musica V.9: Demonstratio secundum Ptolomaeum diapason et diatessaron consonantiam esse.
He proves, however, that a certain symphony is made from the diapason and diatessaron in this way: the diapason consonance produces such a union of the voice that one and the same string seems to sound, and the Pythagoreans also agree on this. Wherefore, if any consonance is added to it, it is kept whole and inviolate. For it is added to the diapason consonance as to a single string. Let there be, then, a diapason consonance contained between the hypate meson and the nete diezeugmenon. These two agree with each other and are joined in sound so that they strike the ear as one voice, as of one string, not as a mixture of two. Whatever consonance, then, we join to this diapason consonance is preserved whole, because it is joined as to a single little voice and string. If, therefore, the hypate meson and the nete diezeugmenon have each a diatessaron joined above them, as the nete hyperboleon is joined to the nete diezeugmenon and the mese to the hypate meson, each will sound with each: the mese with the nete diezeugmenon, and the same mese with the hypate meson; likewise the nete hyperboleon with the nete diezeugmenon and with the hypate meson. Likewise, if both diatessaron consonances are let down toward the lower side, the hypate hypaton will hold the diatessaron consonance to the hypate meson, and the paramese to the nete diezeugmenon, and the hypate hypaton will sound with the hypate meson and with the nete diezeugmenon, and the paramese with the nete diezeugmenon and with the hypate meson; but in such a way that the lower, which is to its nearest neighbor, keeps the diatessaron consonance, and to the farther one the diatessaron and diapason; for example, the hypate hypaton to the hypate meson a diatessaron, to the nete diezeugmenon a diatessaron and diapason. Likewise the nete hyperboleon, which is the higher, to the nete diezeugmenon nearest to it keeps a diatessaron consonance, to the hypate meson a diatessaron and diapason.