Pythagoras: His Life and Teaching, a Compendium of Classical Sources (22 page)

CHAPTER 14

T
HE
D
ECAD

T
en, according to the Pythagoreans, is the greatest number—as well for that it is the Tetractys, as that it comprehends all arithmetical and harmonical proportions.
⁵⁶¹
Pythagoras said that ten is the nature of number: because all nations, Greeks and Barbarians, reckon to it; and when they arrive at it, return to the Monad.
⁵⁶²

Names of the Decad:

World
, because according to the Decad all things are ordered in general and particular.
⁵⁶³
The Decad comprehends all numbers, the world all form;
⁵⁶⁴
for the same reason it is termed also Sphere.
⁵⁶⁵

Heaven
,
⁵⁶⁶
because it is the most perfect term of number, as heaven is the receptacle of all things.
⁵⁶⁷
The Decad being a perfect number, the Pythagoreans desired to apply to it those things which are contained in Heaven—where finding but nine (the orbs, the seven planets, and the heaven of Fixed Stars, with the earth), they added an Antichthon (another earth opposite to this) and made Ten; by this means they accommodated them to the Decad.
⁵⁶⁸

Fate
,
⁵⁶⁹
because there is no property neither in numbers nor beings, according to the composition of number, which is not seminally contained in the Decad.
⁵⁷⁰

Age
.
⁵⁷¹

Power
,
⁵⁷²
from the command it has over all other numbers.
⁵⁷³

Faith, Necessity.
⁵⁷⁴

Atlas
, for as Atlas is fabled to sustain heaven with his shoulders, so the Decad holds all the spheres as the diameter of them all.
⁵⁷⁵

Unwearied, God, Phanes, Sun, Urania, Memory, Mnemosyne
.
⁵⁷⁶

First Square
, because it is made of the first four numbers: one plus two plus three plus four.
⁵⁷⁷

[“key-bearer”], as the magazine and confinement of all proportions,
⁵⁷⁸
or
[“branch-bearer”], because other numbers branch out of it.
⁵⁷⁹

[“the absolute”], because it perfects all number, comprehends within itself all the nature of even and odd, moved and unmoved, good and ill.
⁵⁸⁰

CHAPTER 15

D
IVINATION BY
N
UMBERS

U
pon the near affinity which Pythagoras (following Orpheus) conceived to be between the gods and numbers, he collected a kind of Arithmancy. This he not only practiced himself, but communicated to his disciples—as is manifest from Iamblichus, who cites this fragment of the Sacred Discourse, a book ascribed to him.

“Concerning the gods of Pythagoras, son of Mnesarchus, I learned this when I was initiated at Libeth in Thrace, Aglaophemus administering the rites to me. Orpheus, son of Calliope, instructed by his mother in the Pangaean mountain, said that number is an eternal substance, the most provident principle of the universe: heaven, and earth, and middle nature; likewise the root of divine beings, and of gods and daemons.”
⁵⁸¹

Hence (says Iamblichus) it is manifest that Pythagoras received from the traditions of Orpheus the doctrine that numbers hold the determinate essence of the gods. By these numbers he framed a wonderful system of divination and service of the gods. This had the closest affinity to numbers, as may be evinced from hence (for it is requisite to give an instance for confirmation of what we say).

The student of Pythagoras, Abaris, performed those kinds of sacrifices to which he was accustomed, and diligently practiced divination after the ways of the Barbarians by victims (principally of cocks, whose entrals they conceived to be most exact for inspection). Pythagoras, not willing to take him away from his study of truth; yet, in order to direct him by a safer way, without blood and slaughter (moreover esteeming the cock sacred to the Sun), taught Abaris to find out all truth by the science of arithmetic.
⁵⁸²
Thus says Iamblichus, who writes elsewhere that Pythagoras, instead of the art of divining by sacrifices, taught that kind of prediction which is by numbers, conceiving that to be more sacred and divine, and more agreeable to the celestial nature of the gods.

This hint some have taken to impose upon the world, under the name of Pythagoras, an
Onomantic
kind of arithmetic—assigning particular numbers to the letters of the alphabet, to the planets, to the days of the week, and to the signs of the Zodiac. They thereby resolve questions concerning nativities, victory, life or death, journeys, prosperity or adversity. Such a system is set down by Fludd,
⁵⁸³
who adds that Apollonius has delivered another way of divination according to the Pythagorean doctrine; affirming that future things may be prognosticated by virtue of a wheel invented by Pythagoras. Hereby is treated of life and death, of fugitives, of litigious business, of victories, of the sex of children unborn, and infinite others of the like kind. But concerning the exposition of the wheel, and the true position of numbers, therein the ancient authors have written very inconstantly. So that the truth of its composition cannot be comprehended otherwise than by conjecture. What ancient authors he means I know not. The citation of Apollonius I doubt to be no less an assumption than the wheel itself, which Trithemius and others acknowledge to be an invention of later times.
⁵⁸⁴

M
USIC

T
he Pythagoreans define music as an apt composition of contraries, a union of many, and consent of differents.
⁵⁸⁵
For it not only coordinates rhythms and modulation, but all manner of systems. Its end is to unite, and aptly conjoin. God is the reconciler of things discordant, and his chief work—according to music and medicine—is to reconcile enmities. In music consists the agreement of all things, and the aristocracy of the universe. For what is harmony in the world, in a city is good government, in a family temperance.

Of many sects (says Ptolemy) that were conversant about harmony, the most eminent were two: the Pythagorean and Aristoxenian.
⁵⁸⁶
Pythagoras judged it by reason, Aristoxenus by sense.
⁵⁸⁷
The Pythagoreans, not crediting the relation of hearing in all those things wherein it is requisite, adapted reasons to the differences of sounds, contrary to those which are perceived by the senses. So that by this criterion (reason), they gave occasion of calumny to such as were of a different opinion.
⁵⁸⁸

Hence the Pythagoreans named that which we now call Harmonic, “Canonic”; not from the canon or instrument, as some imagine, but from rectitude—since reason finds out that which is right by using harmonic canons or rules.
⁵⁸⁹
Even of all sorts of instruments framed by harmonic rules (pipes, flutes, and the like), they call the exercise canonic; which, although it be not canonic, yet is so termed because it is made according to the reasons and theorems of canonic. The instrument therefore seems to be so denominated from its canonic affection.

A follower of canonic doctrine is a “harmonic” who is conversant by ratiocination about that which consists of harmony. Musicians and harmonics differ. Musicians are those harmonics who begin from sense; but canonics are Pythagoreans, who are also called harmonics. Both sorts are termed by the general name, Musicians.

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.