De institutione musica I.17: In quibus primis numeris semitonium constet.
What the whole semitone is, or by what first numbers it is constituted, I shall now explain more clearly. For what was said about the division of the tone was not meant to show the measures of the semitones, but rather to show that we said the tone cannot be divided into two equal parts. The diatessaron, which is a consonance of four notes and three intervals, consists of two tones and not a whole semitone. Let the following description be set down: 192, 216, 243, 256. If, then, the number 192 is compared with 256, the sesquitertian proportion arises and the diatessaron concord will sound. But if we compare 216 with 192, it is a sesquioctave proportion. For their difference is 24, which is the eighth part of 192. It is therefore a tone. Again, if 243 is compared with 216, there will be another sesquioctave proportion. For their difference, 27, is shown to be the eighth part of 216. There remains the comparison of 256 to 243, whose difference is 13, which, made eight times, does not appear to fill the half of 243. It is therefore not a semitone, but less than a semitone. For it would rightly be thought a whole semitone only if their difference, which is 13, made eight times, could equal the half of the number 243; and the true lesser semitone is the comparison of 243 to 256.