De institutione musica III.4: Diapason consonantiam a sex tonis commate excedi et qui sit minimus commatis numerus.
IV. But if we seek to place this difference in whole numbers, since a third part added to the part that is two thirds makes a full unit—which third part is half of the same two thirds—if I add to the same the half of the whole difference, which is 2,384⅓, the whole sum becomes 7,153, which a while ago held the proportion of the comma. For the comma is that by which six tones exceed the consonance of the octave, which is contained in the first 7,153 units. As, then, we added the half of the difference to make it grow to 7,153, so let us also join their own halves to all the terms A, B, C, D, and the same proportion as above will be in all. And the same difference will arise between five tones and twice the fourth as is the difference between six tones and the consonance of the octave, namely 7,153 units. From this it is gathered that five tones exceed twice the fourth, and six tones one octave, by the same comma, which is found in the first 7,153 units. The description set below will make this plain.
The former numbers with their halves.
