De institutione musica IV.11: Monochordi hypaton per tria genera partitio et totius dispositio descriptionis.
Now, therefore, the hypaton tetrachord is to be divided through the three kinds. I take the half of hypate meson, that is 6,144, which is 3,072. If I add this to the same, there will be 9,216, which is proslambanomenos, keeping the consonance of the fifth to hypate meson. If from the same hypate meson, that is 6,144, I take away the third part, which is 2,048, and add it to the same, there will be 8,192, and this is B, hypate hypaton. Hypate meson is therefore in the consonance of the fifth to proslambanomenos, and of the fourth to hypate hypaton. From this hypate meson, that is 6,144, let the eighth part be taken; it will be 768. If anyone joins this to the same, there will be 6,912, which is E, lichanos hypaton diatonos, holding to hypate meson the proportion of a tone.
Again, from 6,912 let the eighth part be taken. It is 864. If this is joined to the same, there will be 7,776, which is C, parhypate hypaton diatonos, keeping to lichanos hypaton diatonos the distance of a tone, and to hypate meson that of two tones. There remains, then, a semitone between parhypate hypaton diatonos and hypate hypaton, that is between 7,776 and 8,192. And such is the hypaton tetrachord of the diatonic kind; the chromatic we divide by this method. I take the difference of hypate meson and of lichanos hypaton diatonos, that is 6,144 and 6,912. It is 768. I divide this in half, so that I make two semitones; it will be 384. I add this to 6,912, so that three semitones are made; they will be 7,296. This will be F, lichanos hypaton chromatice, distant from hypate meson by three semitones. There remain, then, two semitones, one between lichanos hypaton chromatice and parhypate hypaton chromatice, that is between 7,296 and 7,776, and the other between parhypate hypaton chromatice and hypate hypaton, that is between 7,776 and 8,192. There remains the enharmonic kind, of which the division, after the pattern above, is as follows. Since parhypate hypaton diatonos or parhypate hypaton chromatice, which is marked by the units 7,776, is distant two tones from hypate meson, the same will be in the enharmonic kind lichanos hypaton enarmonios, which differs from hypate meson by two whole tones. There remains, then, from the consonance of the fourth a semitone, which is between lichanos hypaton enarmonios and hypate hypaton, that is between 7,776 and 8,192. This we divide into two dieses thus. I take the difference of that which is lichanos hypaton enarmonios and hypate hypaton, that is 416. I take the half of this; it is 208. I add this to 7,776; it will be 7,984, and let this be D, parhypate hypaton enarmonios. There are, then, two dieses, one between lichanos hypaton enarmonios and parhypate hypaton enarmonios, that is between 7,776 and 7,984, the other between parhypate hypaton enarmonios and hypate hypaton, that is between 7,984 and 8,192. The last tone is contained between proslambanomenos and hypate hypaton, that is between 9,216 and 8,192. The hypaton tetrachord has therefore been divided according to the three kinds, diatonic, chromatic, enharmonic. If to the tetrachords above, the hyperboleon, diezeugmenon, synemmenon and meson, this is added, the whole and perfect description of the regular monochord divided through all the three kinds is made.