Hoc in volumine haec opera continentur

proportionately, therefore the whole tone will not be divided into equal parts. The paranete and lichanos will be obtained through consonantiae consonances in this manner. Let the mese be b; let the diatessaron fourth be instituted at i, c; and let the diapente fifth be completed at i, d, with a, c. Therefore, the tone is b, d. Again, let the diatessaron be extended at e, with a, b; and let the diapente be completed at i, f, with a, b, e. Therefore, the tone is f, d, and the ditone major third is f, b. The lichanos therefore will be f; in a similar manner, the paranete will be obtained, [but] the parypate and trite do not divide it into equal parts. Let the mese be b, the lichanos be c, and the hypate be d. Let the diapente be extended from b to f. Therefore, the tone is f, d, and let the diatessaron be extended from f to e. Therefore, the interval is f, d, and c, e. Let the common [segment] d, c be proposed; therefore, f, c is equal to d, e. However, it is a diatessaron [from] f to e; therefore, no proportional mean intervenes [between] them, [i.e.,] f, e, for it is a superparticular interval, and it is equal; d, f is equal to c, e. Therefore, no mean intervenes for d, c, which is from the hypate to the lichanos. Therefore, the parypate does not distribute it into equal parts. Similarly, neither will the trite describe the canon of the called immutable systema system.

A decorative initial letter 'I' is depicted. I. The immutable canon, which is also the lowest sound, is called the bombyx drone/reed instrument. Let the length of the canon, which is also the string, be a, b, and let it be distributed into four equal parts by c, d, e. Therefore, a, b will be the lowest sound, the bombyx. This [part] a, b is the sesquitertius ratio of 4:3 of c, b. Thus, c, b will be consonant to a, b in a diatessaron toward the acute part; and a, b will be the proslambanomenos, therefore c, b will be the hypaton diatonos. Again, because it is quadruple of e, b, e, b will be the nete hyperbolaeon. For I divided c, b in half at f; therefore, c, b is double that of f, b. Thus, c, b resonates with f, b in a diapason octave; therefore, f, b will be the nete hypemenon. I took the third part of d, b, [which is] d, g, and it will be sesqualter ratio of 3:2, [with] d, b to g, b; therefore, d, b will resonate with g, b in a diapente; therefore, d, b is the nete diezeugmenon. I placed g, h equal to g, b; therefore, h, b will resonate with g, b in a diapason, so that h, b is the hypate meson. I took the third part of h, b, [which is] h, k; it will be sesqualter, [with] h, b to k, b; and therefore k, b will be the paramese. I took l, k equal to k, b; [so] l, b will be the hypate gravis. Therefore, all the sounds of the immutable system will be taken in the canon. It remains to take the others: I was cutting e, b into eight [parts] and placed one equal to them, [which is] e, m, and therefore m, b will be the sesquioctave ratio of 9:8 of e, b. Again, I was dividing m, b into eight [parts] and placed one equal to them, [which is] n, m; therefore, n, b will be a whole tone lower than m, b. But m, b [is lower] than b, e; therefore, n, b will be the trite hyperbolaeon, [and] m, b the hyperbolaeon diatonus. I took the third part of n, b and placed one equal to them, n, x; and therefore x, b will be sesquitertius of n, b, resonating in diatessaron in gravity, making x, b the trite diezeugmenon. Again, I was taking the half part of x, b, [and] I made [it] equal to them, x, o; and therefore, by e, [it is] consonant, [with] o, b to x, b; therefore, o, b will be the parhypate meson, and I placed o, p equal to x, o; and therefore p, b will be the parhypate hypaton. I was taking, indeed, the fourth part of b, c, [which is] c, r, and therefore r, b is the medium diatonus.