Free Pythagoras: His Life and Teaching, a Compendium of Classical Sources by James Wasserman, Thomas Stanley, Henry L. Drake, J Daniel Gunther Page B

call Decad quasi Dechad. 354 Wherefore they say that ten is a perfect number, even the most perfect of all numbers; comprehending in itself all difference of numbers, all reasons, species, and proportions. For if the nature of the universe be defined according to the reasons and proportions of numbers—andthat which is produced, and increased, and perfected, proceeds according to the reasons of numbers—and the Decad comprehends every reason of number, and every proportion, and all species: Why should not nature itself be termed by the name of Ten, the most perfect number? Hitherto Moderatus.
    Thus, from the symbolical use of numbers proceeded a multiplex variety of names, attributed to them by Pythagoras and his followers. Of which we shall now speak more particularly, beginning with the Monad.

CHAPTER 1
    V OICE , I TS K INDS
    O f human voice, those of the Pythagorean school said that there are (as of one genus) two species. One they properly named Continuous, the other Diastematic (intermissive), framing appellations from the accidents pertaining to each. The diastematic they conceived to be that which is sung and rests upon every note, and manifests the mutation which is in all its parts. It is free from confusion and divided and disjoined by the magnitudes which are in the several sounds, as accumulated but not mixed up. The parts of the voice, being applied mutually to one another, may easily be separated and distinguished, and are not destroyed together. Such is the musical kind of voice, which to the knowing, manifests all sounds of what magnitude everyone participates. For if a man use it not after this manner, he is not said to sing, but to speak. 590
    The other kind they conceived to be continuous, by which we discourse one to another, and read. We are not constrained to use any manifest distinct tensions of sounds, but to connect the discourse till we have finished that which we intended to speak. For if any man, in disputing or apologizing or reading, makes distinct magnitudes in the several sounds, taking off and transferring the voice from one to another, he is not said to read but to sing.
    Human voice, having in this manner two parts, they conceived that there are two places which each in passing possesses. The place of continuous voice—which is by nature infinite in magnitude—receives its proper term from that wherewith the speaker began until he ends; that is the place from the beginning of his speech to his conclusive silence; so that the variety thereof is in our power. But the place of diastematic voice is not in our power, but natural. And this likewise is bounded by different effects. The beginning is that which is first heard, the end that which is last pronounced. For from thence we begin to perceive the magnitude of sounds, and their mutual commutations, from whence first our hearing seems to operate.
    Whereas it is possible there may be some more obscure sounds perfected in nature which we cannot perceive or hear. As for instance, in things weighed there are some bodies which seem to have no weight, such as straws, bran, and the like. But when, as by the adding together of such bodies some beginning of ponderosity appears, then we say they first come within the compass of static. So, when a low sound increases by degrees, that which first of all may be perceived by the ear we make the beginning of the place which musical voice requires.

CHAPTER 5
    T HE D IVISION OF THE D IAPASON , A CCORDING TO THE D IATONIC K IND
    T his Diatonic kind seems naturally to have these degrees and progresses: hemitone , tone and tone (half-note, whole note, and whole note). This is the system Diatessaron, consisting of two tones, and that which is called a hemitone. Then another tone being inserted, Diapente is made, being a system of three tones and a hemitone. Then, in order after this, there being another diatessaron, that is to say, another sesquitertia. So that in the more ancient Heptachord, all fourths from