De animae procreatione in Timaeo

Concerning which things, although you have heard frequent discourses, and have likewise read several arguments and disputes committed to writing upon the same subjects, it will not be amiss for me also to give a short account, after a brief repetition of Plato’s own words. God, said he, in the first place withdrew one part from the whole; which done, he took away the double of that; then a third part, sesquialter in proportion to the second, and triple to the first; then a fourth part, double to the second; next a fifth part, being the triple of the third; then a sixth, eight times the first; and lastly a seventh, being twenty-seven times the first. This done, he filled up the duple and triple intervals, retrenching also from thence certain other particles, and placing them in the midst of those intervals; so that in every interval

there might be two medieties, the one exceeding and being exceeded by one and the same part of the extremes, the other exceeding and being exceeded by the same number. Now in regard that from these connections in the first spaces there arose the intervals of sesquialters, sesquiterces, and sesquioctaves, he filled up all the sesquiterce intervals with sesquioctaves, leaving a part of each, so that the interval left of the part might bear the numerical proportion of 256 to 243. [*](Timaeus, p. 35 B.)

Here the question will be first concerning the quantity, next concerning the order, and in the third place concerning the force and virtue of the numbers. As to the quantity, we are to consider which he takes in the double and triple intervals. As to the order, whether they are to be placed in one row, according to the direction of Theodorus, or (as Crantor will have them) in the form of a Λ, placing the unit at the top, and the duples and triples apart by themselves in two several files. Lastly, we are to examine of what use and virtue they are in the structure and composition of the soul.

As to the first, we shall relinquish the opinion of those who affirm that it is enough, in proportions, to consider the nature of the intervals, and of the medieties which fill up their vacancies; and that the demonstration can be made out for any numbers whatsoever that have spaces sufficient to receive the aforesaid proportions. For this being granted, it makes the demonstration obscure, without the help of schemes, and drives us from another theory, which carries with it a delight not unbecoming philosophy.

Beginning therefore from the unit, let us place the duples and triples apart; and there will be on the one side, 2, 4, 8; on the other 3, 9, 27; —seven numbers in all, proceeding forward by

multiplication four steps from the unit, which is assumed as the common base. --- For not only here, but upon other occasions, the sympathy of the quaternary number with the septenary is apparent. There is this peculiar to that tetractys or quaternary number thirty six, so much celebrated by the Pythagoreans, which is more particularly worthy admiration,—that it is composed of the first four even numbers and the first four odd numbers; and it is the fourth connection made of numbers put together in order. The first connection is of one and two; the second of odd numbers. --- For placing the unit, which is common to both, before, he first takes eight and then twenty-seven, as it were pointing out with the finger where to place each particular sort.

[These places are so depraved in the original, that the sense is lost.]

But it belongs to others to explain these things more accurately and distinctly; while we content ourselves with only what remains, as peculiarly proper to the subject in hand.

For it was not out of vain-glory, to boast his skill in the mathematical sciences, that Plato inserted in a treatise of natural philosophy this discourse of harmonical and arithmetical medieties, but believing them both apt and convenient to demonstrate the structure and composition of the soul. For some there are who seek these proportions in the swift motions of the spheres of the planets; others rather in the distances, others in the magnitude of the stars; others, more accurate and nice in their enquiry, seek for the same proportions in the diameters of the epicycles; as if the Supreme Architect, for the sake of these, had adapted the soul, divided into seven parts, to the celestial bodies. Many also there are, who hither transfer the inventions of the Pythagoreans, tripling the distances of bodies from the middle. This is done by placing the unit next the fire; three next the Antichthon,

or earth which is opposite to our earth; nine next the Earth; 27 next the Moon; 81 next to Mercury; 243 upon Venus; and 729 upon the Sun. The last (729) is both a tetragonal and cubical number, whence it is, that they also call the sun a tetragon and a cube. By this way of tripling they also reduce the other stars to proportion. But these people may be thought to dote and to wander very much from reason, if there be any use of geometrical demonstration, since by their mistakes we find that the most probable proofs proceed from thence; and although geometers do not always make out their positions exactly, yet they approach the nearest to truth when they say that the diameter of the sun, compared with the diameter of the earth, bears the proportion of 12 to 1; while the diameter of the earth to that of the moon carries a triple proportion. And for that which appears to be the least of the fixed stars, the diameter of it is no less than the third part of the diameter of the earth, and the whole globe of the earth to the whole globe of the moon is as twenty-seven to one. The diameters of Venus and the earth bear a duple, the globes or spheres of both an octave proportion. The width of the shadow which causes an eclipse holds a triple proportion to the diameter of the moon; and the deviation of the moon from the middle of the signs, either to the one or the other side, is a twelfth part. Her positions as to the sun, either in triangular or quadrangular distances, give her the form when she appears as in the first quarter and gibbous; but when she comes to be quite round, that is, when she has run through half the signs, she then makes (as it were) a kind of diapason harmony with six notes. But in regard the motions of the sun are slowest when he arrives at the solstices, and swiftest when he comes to the equinoxes, by which he takes from the day or adds to the night, the proportion holds thus. For the first thirty days after the winter solstice, he adds to the day a sixth part of the length whereby the longest night exceeds the shortest; the next thirty days he adds a third part; to all the rest till the equinox he adds a half; and so by sextuple and triple distances he makes even the irregularity of time.

Moreover, the Chaldaeans make the spring to hold the proportion of a diatessaron to autumn; of a diapente to the winter, and of a diapason to the summer. But if Euripides rightly divides the year, where he says,

Four months the parching heats of summer reign,

And four of hoary winter’s cold complain;

Two months doth vernal pride the fields array,

And two months more to autumn tribute pay,

then the seasons shall be said to change in octave proportion.

Others there are, who fancy the earth to be in the lowest string of the harp, called proslambanomenos; and so proceeding, they place the moon in hypate, Mercury and Venus in the diatoni and lichani; the sun they likewise place in mese, as in the midst of the diapason, a fifth above the earth and a fourth from the sphere of the fixed stars.

But neither doth this pleasant conceit of the latter come near the truth, neither do the former attain perfect accuracy. However, they who will not allow the latter to depend upon Plato’s sentiments will yet grant the former to partake of musical proportions; so that, there being five tetrachords, called ὑπάτων, μέσων, συνημμένων, διεζευγμένων, and ὑπερβολαίων, in these five distances they place all the planets; making the first tetrachord from the Moon to the Sun and the planets which move with the Sun, that is, Mercury and Venus; the next from the Sun to the fiery planet of Mars; the third between this and Jupiter; the fourth from thence to Saturn; and the fifth from Saturn to the sphere of the fixed stars. So that the sounds and notes which bound the five tetrachords bear the same proportion with the intervals

of the planets. Still further, we know that the ancient musicians had two notes called hypate, three called nete, one mese, and one paramese, thus confining their scale to seven standing notes, equal in number to the number of the planets. But the moderns, adding the proslambanomenos, which is a full tone in descent from hypate, have multiplied the scheme into the double diapason, and thereby confounded the natural order of the concords; for the diapente happens to be before the diatessaron, with the addition of the whole tone in the bass. Whereas Plato makes his addition in the upper part; for in his Republic[*](X. p. 617 B.) he says, that every one of the eight spheres rolls about a Siren which is fixed upon each of the tuneful globes, and that they all sing one counterpoint without diversity of modulation, taking every one their peculiar concords, which together complete a melodious consort.

These Sirens sing for their pleasure divine and heavenly tunes, and accompany their sacred circuit and dance with an harmonious song of eight notes. Nor was there necessity of a fuller chorus, in regard that within the confines of eight notes lay the first bounds and limits of all duple and triple proportions; the unit being added to both the even and odd numbers. And certainly from hence it was that the ancients raised their invention of nine Muses; of which eight were employed in celestial affairs, as Plato said; the ninth was to take care of things terrestrial, and to reduce and reform the inequality and confusion of error and jarring variance.

Now then consider whether the soul does not roll and turn and manage the heavens and the celestial bodies by means of those harmonious concords and equal motions that are wrought and fermented within her, being herself most wise and most just. And such she became by virtue of harmonical proportions, whose images representing

things incorporeal are imprinted into the discernible and visible parts and bodies of the world. But the chief and most predominating power is visibly mixed in the soul, which renders her harmonious and obedient to herself, the other parts unanimously yielding to her as the most supreme and the divinest part of all. For the Sovereign Artificer and Creator finding a strange disorder and erroneous confusion in the motions of the decomposed and unruly soul, which was still at variance with herself, some things he divided and separated, others he brought together and reconciled to a mutual sympathy, making use of harmony and numbers. By virtue of which, the slightest and meanest of insensible substances, even stocks and stones, the rinds of trees, and sometimes even the rennets of beasts, by various mixtures, compositions, and temperatures, may become the charming objects of the sight, or afford most pleasing perfumes and wholesome medicaments for the relief of mankind, or be wrought and hollowed to send forth pleasing musical sounds. And for this reason it was that Zeno of Citium encouraged and persuaded youth to frequent the theatres, there to observe the variety of melodious sounds that proceeded from horns or cornets, wooden hautboys, flutes and reeds, or any other musical instruments to which the contrivance of art had rightly applied the reason of number and proportion. Not that we will here maintain, with the Pythagoreans, that all things resemble number, for that requires a long discourse to prove it. But where mutual society and sympathy arise out of discord and dissimilitude, that the cause of this is moderation and order, produced by the power of harmony and number, was a thing not concealed even from the poets. And these give to what is friendly and kind the epithet evenly fitted; while, on the other side, men of rugged and malicious dispositions they called unevenly tempered, as if enmity and discord were nothing but a sort of a disproportion. For this reason, he who writes Pindar’s elegy gives him this encomium,

To foreigners agreeable, to citizens a friend;[*](Ἄρμενος ἦν ξείνοισιν ἀνὴρ ὅδε, καὶ φίλος ἀστοῖς)

the poet plainly inferring complacency of humor and the aptitude of a person to fit himself to all tempers to be an excellency aspiring to virtue itself. Which Pindar himself also testifies, saying of Cadmus, that he listened to true music from Apollo himself.[*](See Boeckh’s note on Pindar, Frag. 8. The quotation from Pindar is corrupt; but the sense given above is derived from other quotations of the same passage. (G.)) Nor must we believe that the theologists, who were the most ancient philosophers, ordered the pictures and statues of the Gods to be made with musical instruments in their hands because they thought the Gods no better than pipers or harpers, but to signify that no work was so becoming to the Gods as accord and harmony.

Now then, as it would be absurd and ridiculous for any man to search for sesquiterces, sesquialters, and duples in the neck, or belly, or sides of a lute or harp,—though every one of these must also be allowed their symmetry of length and thickness,—the harmony and proportion of concords being to be sought for in the sound; so it is most probable that the bodies of the stars, the distances of spheres, and the swiftness of the motions and revolutions, have their sundry proportions, as well one to another as to the whole fabric, like instruments of music well set and tuned, though the measure of the quantity be unknown to us. However, we are to imagine that the principal effect and efficacy of these numbers and proportions, which the Supreme Architect made use of, is that same agreement, harmony, and consent of the soul with itself, by means of which she replenished the heavens themselves, when she came to actuate and perform her office there, with so

many infinite beauties, and by which she governs the earth by virtue of the several seasons, and other alterations wisely and artificially measured and varied as well for the generation as preservation of all terrestrial productions.