De institutione musica I.33: Quo sint modo accipienda, quae dicta sunt.
All the matters, however, that are to be treated more carefully hereafter, I now attempt summarily and briefly, so that meanwhile these things may accustom the mind of the reader on a certain surface, who will descend to the inner knowledge by the later treatment. It was the custom of the Pythagoreans that, when something was said by their master Pythagoras, no one dared to ask the reason of it, but the authority of the teacher was the reason for them; and this went on as long as the learner’s mind, strengthened by firmer teaching, found the reason of these same things itself with no teacher. So now also we commend what we propose to the reader’s trust, that he may hold that the diapason consists in the double, the diapente in the sesquialter, the diatessaron in the sesquitertian, diapente and diapason in the triple, the double diapason in the quadruple proportion. Afterwards both the reason will be explained more carefully, and in what ways the musical consonances are also gathered by the judgment of the ears, and all the other things said above a fuller treatise will set out: that the tone makes the sesquioctave proportion and cannot be divided into two equal parts, as no proportion of that kind, that is, of the superparticular; that the diatessaron consonance consists of two tones and a semitone; that there are two semitones, a greater and a lesser; that the diapente is contained in three tones and a lesser semitone; that the diapason is filled up by five tones and two lesser semitones, and does not in any way reach six tones. All this I shall prove later both by the reason of numbers and by the judgment of the ears. And so much for this.