De institutione musica IV.1: Vocum differentias in quantitate consistere.
Although we have set out in order, in the treatment of the preceding book, everything that was to be demonstrated, I do not regret briefly presenting the same things again to be gathered in the memory, with a certain variety of treatment, so that when these have returned to memory we may come to the division of the rule, to which the whole intention tends. If there were rest of all things, no sound would strike the hearing, and this would be because, all motions ceasing, things would excite no stroke among themselves. For there to be a voice, therefore, a stroke is needed. But for there to be a stroke, a motion must necessarily precede. For a voice to be, therefore, motion must be. But every motion has in itself both swiftness and slowness. If the motion is slow in striking, the sound is made deeper. For as slowness is next to standing still, so deepness is next to silence. A swift motion, however, yields a high note. Besides, what is low grows toward the middle by tension, and what is high decreases toward the middle by relaxation. Hence it comes about that every sound seems to be composed as if of certain parts. But every joining of parts is made by a certain proportion. The joining of sounds, therefore, is constituted by proportions. Proportions, however, are chiefly considered in numbers. The simple proportion of numbers is found either in multiples or in superparticulars or in superpartients. According to the multiple or superparticular proportions, voices are heard as consonant or dissonant. Consonant are those which, struck together, join a sweet and blended sound among themselves. Dissonant are those which, struck together, do not yield a sweet or blended sound. With these things so premised, let us say a few things about proportions.