De institutione musica III.8: De minoribus semitonio intervallis.
Philolaus, then, includes these and still smaller spaces in the following definitions. The diesis, he says, is the space by which the sesquitertian proportion is greater than two tones. The comma is the space by which the sesquioctave proportion is greater than two dieses, that is, two lesser semitones. The schisma is half a comma, the diaschisma half a diesis, that is, of the lesser semitone. From these it is gathered that, since the tone is divided principally into the lesser semitone and the apotome, it is divided also into two semitones and a comma; whence it comes about that it is divided into four diaschismata and a comma. The whole half of a tone, which is a semitone, consists of two diaschismata, which is one lesser semitone, and a schisma, which is half a comma. For since the whole tone is joined from two lesser semitones and a comma, if anyone wished to divide it wholly, he would make one lesser semitone and half a comma. But one lesser semitone is divided into two diaschismata, and half a comma is one schisma. It is rightly said, therefore, that the tone can be divided wholly in half into two diaschismata and one schisma, whence it comes about that the whole semitone is seen to differ from the lesser semitone by one schisma. The apotome differs from the lesser semitone by two schismata; for it differs by a comma. But two schismata make one comma.