De animae procreatione in Timaeo

Of which the easy reconciliation of his seeming incongruities and contradiction of himself may serve for the first proof. For indeed no men of judgment would have objected to the most Bacchanalian sophister, more especially to Plato, the guilt of so much inconvenience and impudent rashness in a discourse by him so elaborately studied, as to affirm the same nature in one place never to have been created, in another to have been the effects of generation;—in Phaedrus to assert the soul eternal, in Timaeus to subject it to procreation. The words in Phaedrus need no repetition, as being familiar to nearly every one, wherein he proves the soul to be incorruptible in regard it never had a beginning, and to have never had a beginning because it moves itself. But in Timaeus, God, saith he, did not make the soul a junior to the body, as now we labor to prove it to have been subsequent to the body. For he would never have suffered the more ancient, because linked and coupled with the younger, to have been governed by it; only we, guided I know not how by chance and inconsiderate rashness, frame odd kind of notions to ourselves. But God most certainly composed the soul excelling the body both in seniority of origin and in power, to be mistress and governess of her inferior servant. [*](Timaeus, p. 34 B.)

And now what other or better reconciliation of these seeming contrarieties than his own explanation, to those that are willing to apprehend it? For he declares to have been without beginning the never procreated soul, that moved all things confusedly and in an irregular manner before the creation of the world. But as for that which God composed out of this and that other permanent and choicest substance, making it both prudent and orderly, and adding of his own, as if it were for form and beauty’s sake, intellect to sense, and order to motion, and which he constituted prince and chieftain of the whole,—that he acknowledges to have had a beginning and to have proceeded from generation. Thus he likewise pronounces the body of the world in one respect to be eternal and without beginning, in another sense to be the work of creation. To which purpose, where he says that the visible structure, never in repose at first but restless in a confused and tempestuous motion, was at length by the hand of God disposed and ranged into majestic order,—where he says that the four elements, fire and water, earth and air, before the stately pile was by them embellished and adorned, caused a prodigious fever and shivering ague in the whole mass of matter, that labored under the combats of their unequal

Again, when he says that the body was younger than the soul, and that the world was created, as being of a corporeal substance that may be seen and felt,—which sort of substances must necessarily have a beginning and be created,—it is evidently demonstrable from thence that he ascribes original creation to the nature of bodies. But he is far from being repugnant or contradictory to himself in these sublimest mysteries. For he does not contend, that the same body was created by God or after the same manner, and yet that it was before it had a being,—which would have been to act the part of a juggler; but he instructs us what we ought to understand by generations and creation. Therefore, says he, at first all these things were void of measure and proportion; but when God first began to beautify the whole, the fire and water, earth and air, having perhaps some prints and footsteps of their forms, lay in a huddle jumbled all together,—as probable it is that all things are, where God is absent,—which then he reduced to a comely perfection varied by number and order. Moreover, having told us before that it was a work not of one but of a twofold proportion to bind and fasten the bulky immensity of the whole, which was both solid and of a prodigious profundity, he then comes to declare how God, after he had placed the water and the earth in the midst between the fire and the air, incontinently closed up the heavens into a circular form. Out of these materials, saith he, being four in number, was the body of the world created, agreeing in proportion, and so amicably corresponding together, that being thus embodied and confined within their proper bounds, it is impossible that any dissolution should happen from their own contending force, unless he that riveted the whole frame should go about

Now that Plato had this belief concerning these things, and did not for contemplation’s sake lay down these suppositions concerning the creation of the world and the soul,—this, among many others, seems to be an evident signification that, as to the soul, he avers it to be both created and not created, but as to the world, he always maintains that it had a beginning and was created, never that it was uncreated and eternal. What necessity therefore of bringing any testimonies out of Timaeus? For the whole treatise, from the beginning to the end, discourses of nothing else but of the creation of the world. As for the rest, we find that Timaeus, in his Atlantic, addressing himself in prayer to the Deity, calls God that being which of old existed in his works, but now was apparent to reason. In his Politicus, his Parmenidean guest acknowledges that the world, which was the handiwork of God, is replenished with several good things, and that, if there be any thing in it which is vicious and offensive, it comes by mixture of its former incongruous and irrational habit. But Socrates, in the Politics, beginning to discourse of number, which some call by the name of wedlock, says: The created Divinity has a circular period, which is, as it were, enchased and

The first pair of these numbers consists of one and two, the second of three and four, the third of five and six; neither of which pairs make a tetragonal number, either by themselves or joined with any other figures. The fourth consists of seven and eight, which, being added all together, produce a tetragonal number of thirty-six. But the quaternary of numbers set down by Plato have a more perfect generation, of even numbers multiplied by even distances, and of odd by uneven distances. This quaternary contains the unit, the common original of all even and odd numbers. Subsequent to which are two and three, the first plane numbers; then four and nine, the first squares; and next eight and twenty-seven, the first cubical numbers (not counting the unit). Whence it is apparent, that his intention was not that the numbers should be placed in a direct line one above another, but apart and oppositely one against the other, the even by themselves, and the odd by themselves, according to the scheme here given. In this manner similar numbers will be joined together, which will produce other remarkable numbers, as well by addition as by multiplication.

By addition thus: two and three make five, four and nine make thirteen, eight and twenty-seven make thirty-five. Of all which numbers the Pythagoreans called five the nourisher, that is to say, the breeding or fostering sound, believing a fifth to be the first of all the intervals of tones which could be sounded. But as for thirteen,

Admit a right-angled parallelogram, A B C D, the lesser side of which A B consists of five, the longer side A C contains seven squares. Let the lesser division be unequally divided into two and three squares, marked by E; and the larger division in two unequal divisions more of three and four squares, marked by F. Thus A E F G comprehends six, E B G I nine, F G C H eight, and G I H D twelve. By this means the whole parallelogram, containing thirty-five little square areas, comprehends all the proportions of the first concords of music in the number of these little squares. For six is exceeded by eight in a sesquiterce proportion (3:4), wherein the diatessaron is comprehended. And six is exceeded by nine in a sesquialter proportion (2:3), wherein also is included the fifth. Six is exceeded by twelve in duple proportion (1:2), containing the octave; and then lastly, there is the sesquioctave proportion of a tone in eight to nine. And therefore they call that number which comprehends all these proportions harmony. This number is 35, which being multiplied by 6, the product is 210, which is the number of days, they say, which brings those infants to perfection that are born at the seventh month’s end.

To proceed by way of multiplication,—twice 3

Now these numbers aforesaid being endued with all these properties, the last of them, which is 27, has this peculiar to itself, that it is equal to all those that precede together; besides, that it is the periodical number of the days wherein the moon finishes her monthly course; the Pythagoreans make it to be the tone of all the harmonical intervals. On the other side, they call thirteen the remainder, in regard it misses a unit to be half of twenty-seven.

But since the numbers proposed did not afford space

Now the more readily to find out these means Eudorus hath taught us an easy method. For after you have proposed the extremities, if you take the half part of each and add them together, the product shall be the middle, alike in both duple and triple proportions, in arithmetical mediety.

Now Plato laid down this for a position, that the intervals of sesquialters, sesquiterces, and sesquioctaves having once arisen from these connections in the first spaces, the Deity filled up all the sesquiterce intervals with sesquioctaves, leaving a part of each, so that the interval left of the part should bear the numerical proportion of 256 to 243.[*](Timaeus, p. 36 A.) From these words of Plato they were constrained to enlarge their numbers and make them bigger. Now there must be two numbers following in order in sesquioctave proportion.

But first of all, we shall better understand what this leimma or remainder is and what was the opinion of Plato, if we do but call to mind what was frequently bandied in the Pythagorean schools. For interval in music is all that space which is comprehended by two sounds varied in pitch. Of which intervals, that which is called a tone is the full excess of diapente above diatessaron; and this being divided into two parts, according to the opinion of the musicians, makes two intervals, both which they call a semitone. But the Pythagoreans, despairing to divide a tone into equal

This being thus demonstrated, let us see whether the sesquioctave will admit a division into two equal parts; which if it will not do, neither will a tone. However, in regard that 9 and 8, which make the first sesquioctave, have no middle interval, but both being doubled, the space that falls between causes two intervals, thence it is apparent that, if those distances were equal, the sesquioctave also might be divided into equal parts. Now the double of 9 is 18, that of 8 is 16, the intermedium 17; by which means one of the intervals becomes larger, the other lesser; for the first is that of 18 to 17, the second that of 17 to 16. Thus the sesquioctave proportion not being to be otherwise than unequally divided, consequently neither will the tone admit of an equal division. So that neither of these two sections of a divided tone is to be called a semitone, but according as the mathematicians name it, the remainder. And this is that which Plato means, when he says, that God, having filled up the sesquiterces with sesquioctaves, left a part of each; of which the proportion is the same as of 256 to 243. For admit a diatessaron in two numbers comprehending sesquiterce proportion, that is to say, in 256 and 192; of which two numbers, let the lesser 192 be applied to the lowermost extreme, and the bigger number 256 to the uppermost extreme of the tetrachord. Whence we shall demonstrate that, this space being filled up by two sesquioctaves, such an interval remains as lies between the numbers 256 and 243. For the lower string being forced a full tone upward, which is a sesquioctave, it

Others, placing the two extremes of the diatessaron, the acute part in 288, and the lower sound in 216, in all the rest observe the same proportions, only that they take the remainder between the two middle intervals. For the base, being forced up a whole tone, makes 243; and the upper note, screwed downward a full tone, begets 256. Moreover 243 carries a sesquioctave proportion to 216, and 288 to 256; so that each of the intervals contains a full tone, and the residue is that which remains between 243 and 256, which is not a semitone, but something less. For 288 exceeds 256 by 32, and 243 exceeds 216 by 27; but 256 exceeds 243 by 13. Now this excess is less than half of the former. So it is plain that the diatessaron consists of two tones and the residue, not of two tones and a half. Let this suffice for the demonstration of these things. Nor is it a difficult thing to believe, by what has been already said, wherefore Plato, after he had asserted that the intervals of sesquialter, sesquiterce, and sesquioctave had arisen, when he comes to fill up the intervals of sesquiterces with sesquioctaves, makes not the least mention of sesquialters; for that the sesquialter is soon filled up, by adding the sesquiterce

Having therefore shown the manner how to fill up the intervals, and to place and dispose the medieties, had never any person taken the same pains before, I should have recommended the further consideration of it to the recreation of your fancies; but in regard that several most excellent musicians have made it their business to unfold these mysteries with a diligence more than usually exact,—more especially Crantor, Clearchus, and Theodorus, all born in Soli,—it shall suffice only to show how these men differed among themselves. For Theodorus, varying from the other two, and not observing two distinct files or rows of numbers, but placing the duples and triples in a direct line one before another, grounds himself upon that division of the substance which Plato calls the division in length, making two parts (as it were) out of one, not four out of two. Then he says, that the interposition of the mediums ought to take place in that manner, to avoid the trouble and confusion which must arise from transferring out of the first duple into the first triple the intervals which are ordained for the supplement of both. --- But as for those who take Crantor’s part, they so dispose their numbers as to place planes with planes, tetragons with tetragons, cubes with cubes, opposite to one another, not taking them in file, but alternatively odd to even. [Here is some great defect in the original.]