Plutarch · a new plain-English translation from the Greek
Since the things often said and written piecemeal in various places by those expounding Plato's opinion about the soul, which he held (as we ourselves used to conjecture), you think ought to be gathered into one and given this discourse its own separate treatise — a subject not otherwise easy to handle, and one that, because it runs counter to most of the followers of Plato, needs some justification — I shall first set out the text as it is written in the Timaeus:
"Of the indivisible essence that is ever in the same state, and of that essence which becomes divisible in connection with bodies, he blended a third form of essence in between, out of both, concerning the nature of the Same, and again of the Different; and in this way he composed it in the middle, between the indivisible and that which is divisible in connection with bodies. And taking these three, being three, he blended them into one form, forcing the nature of the Different, which resists mixture, into union with the Same, mingling it together with the essence; and having made one whole again out of three, he distributed this whole into the portions to which it was fitting, each of these portions being a mixture of the Same, the Different, and the Essence. And he began to divide as follows" — how many differences these words have furnished to interpreters would be an immense task to go through at present, and, since you have already met with most of them together, would besides be superfluous.
But since, among the most reputable men, Xenocrates won some over by declaring the essence of the soul to be number itself, moved by itself, while others attached themselves to Crantor of Soli, who mixed the soul out of the intelligible nature and the nature concerned with sensible, opinable things — I think that once these views are uncovered, their clarification will provide us something like a starting point. The argument concerning both is brief.
Some think that nothing but the generation of number is signified by the mixing of the indivisible and the divisible essence: for the one, they say, is indivisible, and multitude is divisible, and out of these number arises, the one setting a limit to multitude and imposing a boundary on the unlimited, which they also call the indefinite dyad. And Zaratas, the teacher of Pythagoras, used to call this the mother of number, and the one its father; and for this reason those numbers are better which most resemble the monad. But this number is not yet soul, for it lacks the moving and the moved. But when the Same and the Different are mixed together — of which the one is a principle of motion and change, the other of rest — soul came to be, being no less a power of stopping and being stopped than of moving and being moved.
Those around Crantor, on the other hand, supposing that it is above all the soul's own function to judge both intelligible and sensible things, and the differences and likenesses that arise among these both in themselves and toward one another, say that the soul is compounded out of all things, so that it may know all things; and that these are four: the intelligible nature, ever in the same state and in the same way; the nature concerned with bodies, which is passive and changeable; and further the nature of the Same and of the Different, because each of those two natures partakes of both otherness and sameness. All these thinkers alike suppose that the soul did not come to be in time and is not something generated, but has several powers, and that Plato, resolving its essence into these for the sake of theoretical exposition, represents it in his account as coming to be and being blended together; and that he thinks the same about the cosmos as well — knowing that it is eternal and ungenerated, but that it is not easy for one to learn the manner in which it is arranged and administered without first presupposing, at the outset, either its generation or the coming together of the generative factors — this being the path he takes in Plato's Timaeus.
Such being the general opinions stated, Eudorus thinks that neither side is wholly without a share of the plausible; but to me both seem to miss Plato's own view, if probability is to be the standard, since they are not expounding their own private doctrines but trying to say something consistent with his.
For the mixture said to be made out of the intelligible and the sensible essence does not make clear in what way this, more than anything else one might name, is the generation of soul specifically. For this cosmos itself, and each of its parts, is composed out of bodily essence and intelligible essence, of which the one furnished matter and substrate, the other form and shape, to what came to be; and while the thing shaped by participation in and likeness to the intelligible is at once tangible and visible, the soul escapes all sensation. Indeed Plato never called the soul a number, but always motion, self-moved, and "the fountain and source of motion"; it is by number and ratio and harmony that he has ordered its essence, which underlies and receives the fairest form generated in it by these.
I think it is not the same thing for the soul to be composed according to number and for its essence to be number: since it is composed according to harmony, and harmony is not essence, as he himself demonstrated in his treatise On the Soul. And manifestly these thinkers have also missed the point about the Same and the Different: they say that the one contributes the power of rest, the other of motion, to the generation of the soul, whereas Plato himself, in the Sophist, sets down Being, the Same, and the Different, and besides these Rest and Motion — each differing from each, and being five in number, existing apart from one another and distinguished. These thinkers in common, and most of those who make use of Plato, out of fear and to console themselves, contrive and force and twist everything, supposing that they must veil over and deny some terrible and unspeakable thing — both the generation of the cosmos and that of its soul, and their coming-into-being — as though these had not existed from eternity, nor had the infinite span of time been of this character. This has been treated separately elsewhere, and for now it will suffice to say only this: that they confuse, or rather utterly abolish, the argument and reasoning that Plato himself admits he used, most ambitiously and beyond his years, against the atheists. For if the cosmos is ungenerated, then gone, for Plato, is the claim that the soul, being older than the body, takes the lead in every change and motion, established as guide and first author, as he himself has said. But who the soul is, and of what the body then consisted, when the soul is said to have come to be prior to and older than it, the argument will show as it proceeds; for this point, being misunderstood, seems to cause the greatest perplexity and disbelief regarding the true opinion.
First, then, I shall set forth the view I myself hold on these matters, supporting it by probability and softening, as far as possible, the unfamiliarity and paradox of the argument; then I shall bring in the very words of the text, joining together at once the exposition and the proof.
For this is how the matter stands, at least in my judgment. "This cosmos," says Heraclitus, "neither any god nor any man made" — as if he feared that, if we deny it to a god, we might suspect that some man had become the cosmos's craftsman. It is better, then, to follow Plato and say and sing that the cosmos came to be from god: "for it is the fairest of things that have come to be, and he the best of causes"; but that the essence and matter out of which it came to be was not itself generated, but always lay underlying, available to the craftsman for the arrangement and ordering of itself, and for assimilation to him, as far as it was possible to provide. For generation is not out of what is not, but out of what is not in a good or sufficient condition — as with a house, a garment, or a statue. For disorder existed before the generation of the cosmos; and this disorder was not incorporeal, nor motionless, nor soulless, but had its corporeal element shapeless and unformed, and its motive element erratic and irrational — and this was the disharmony of a soul possessing no reason. For god made neither body out of the incorporeal, nor soul out of the soulless, but just as we require of a man skilled in harmony and rhythm, not that he produce sound or movement, but that he produce sound that is tuneful and movement that is well-rhythmed, so god produced neither the tangible and resistant quality of body nor the imaginative and motive quality of soul himself; rather, taking over both principles — the one dim and dark, the other turbulent and unreasoning — both incomplete in what was fitting and unbounded, he arranged and ordered and fitted them together, and out of them wrought the fairest and most perfect living creature.
The essence of body, then, is nothing other than what he calls the all-receiving nature, the seat and nurse of things generated. But the indeterminacy belonging to soul he has called, in the Philebus, a privation of number and ratio, consisting in deficiency and excess and difference and unlikeness, having in itself neither limit nor measure; whereas in the Timaeus, the nature blended together with the indivisible and said to become divisible in connection with bodies should not be supposed to mean multitude in units and points, nor lengths and breadths — things that belong to bodies and pertain to bodies rather than to soul — but rather that disorderly and indefinite, yet self-moving and motive, principle, which in many places he calls Necessity, but in the Laws he outright calls a disorderly and maleficent soul. For this was soul by itself, before it partook of mind and reasoning and harmonious order, so that it might become the soul of the cosmos. For indeed that all-receiving, material magnitude possessed extension and interval and room, but was deficient in due measure of beauty and shape and form; and it obtained these, so that the manifold bodies and instruments of earth and sea and sky and stars, of plants and animals, might come to be once it was set in order.
But those who take the Necessity spoken of in the Timaeus, and, in the Philebus, the disproportion and indeterminacy concerned with the more and the less, deficiency and excess, and attribute them to matter rather than to soul — where will they place the fact that matter is always said by Plato to be shapeless and formless, and bereft of every quality and power of its own, and is likened to odorless oils, which perfumers take as a base for their scents? For it is not possible that Plato supposed the qualityless — that which is by itself inert and without inclination — to be the cause and principle of evil, and called it foul and maleficent indeterminacy, and again called Necessity a thing much at odds with and resistant to god. For the Necessity that "turns back" the heaven, as is said in the Statesman, and unwinds it in the contrary direction, and the "innate desire," and that trait bred together long ago with its nature, partaking of much disorder before it arrived at the present cosmos — whence did this come to attach itself to things, if the substrate was qualityless matter, devoid of any cause whatsoever, while the craftsman was good and wished to assimilate everything to himself as far as possible, and there was nothing third besides these? For it is the very perplexities of the Stoics that overtake us, when we introduce evil out of what is not, without cause and without generation; since, among the things that are, it is not likely that either the good or the qualityless furnishes the essence and origin of evil. But Plato did not suffer the same fate as the later thinkers, nor did he, like them, overlook the intermediate third principle and power between matter and god; rather he endured the strangest of arguments, making — I do not know how — the nature of evils an episode arising spontaneously, by accident. For they do not allow Epicurus's atom to swerve even a hairsbreadth, on the ground that this introduces motion without cause out of what is not; yet they themselves say that so great an evil and misfortune, together with countless other absurdities and difficulties concerning the body, having no cause among their first principles, came to be as a mere consequence.
Plato was not so; rather, freeing matter from all responsibility for the difference of things, and placing the cause of evils as far as possible from god, he wrote this about the cosmos in the Statesman: "from him who put it together it possesses all that is good, but from its former condition it has whatever harsh and unjust things occur in heaven, and these it both has itself and produces in living creatures." And going on a little further he says: "as time goes on, and forgetfulness arises in it, the affection of the ancient disharmony prevails more strongly, and it runs the risk of being dissolved and sinking back again into the boundless region of unlikeness" — but unlikeness does not pertain to matter, which is qualityless and indifferent. But along with many others, Eudemus too, in ignorance, mocks Plato, as though he did not do well in declaring that which is so often called by him mother and nurse to be also the cause and principle of evils. For Plato calls matter mother and nurse, but calls the cause of evil the motive element of matter — that disorderly and irrational, yet not soulless, motion which becomes divisible in connection with bodies, and which in the Laws, as has been said, he called a soul opposed and antagonistic to the beneficent one. For soul is the cause and principle of motion, but mind is the cause of order and concord within motion. For god did not raise matter up out of idleness, but brought to rest that which was being disturbed by an unreasoning cause; nor did he furnish nature with the origins of change and of the affections, but, since it already existed amid every kind of affection and disorderly change, he removed its great indefiniteness and disorder, using harmony and proportion and number as his instruments — whose function is not, by change and motion, to furnish things with the affections and differences of otherness, but rather to make them steadfast and stable, and like to those things which are ever in the same state and in the same way. Such, then, is Plato's thought, at least in my own opinion.
The first proof is the resolution of the alleged and apparent inconsistency and discrepancy of Plato with himself. For not even a drunken sophist — let alone Plato — could reasonably be charged with such confusion and unevenness, in the very arguments about which he was most in earnest, as to declare the same nature to be at once ungenerated and generated: ungenerated in the Phaedrus, with respect to the soul, but generated in the Timaeus. Now the doctrine in the Phaedrus is on nearly everyone's lips, establishing the soul's imperishability by its being ungenerated, and its being ungenerated by its self-motion; but in the Timaeus he says, "as for the soul, we are not undertaking to describe it as coming later than we now attempt — so, too, the god contrived it to be younger, for he would not have allowed the elder to be ruled..."
"...older than younger, but bound them together and let it go. But somehow we, sharing largely in what is casual and random, speak in this loose way too; he, however, constituted the soul as prior to and older than the body both in coming-to-be and in excellence, as mistress and ruler of what is to be ruled." And again, having said that "turning within itself it began a divine beginning of an unceasing and intelligent life," he says, "the body of heaven, then, came to be visible,"
"while the soul itself is invisible, but partakes of reasoning and harmony, having come to be, among things that always exist as objects of intellect, the best of things generated by the best cause." Here, calling god "best of things that always exist" and the soul "best of things generated," by this very clear distinction and opposition he has stripped from it its eternity and its being ungenerated.
What other correction of this is there, then, besides the one he himself provides for those willing to accept it? For he declares the soul to be ungenerated insofar as it moves everything in a discordant and disorderly way before the generation of the cosmos, but generated and subject to becoming again insofar as it is that which god, having fashioned it out of this disorderly substance together with that abiding and best substance, made intelligent and ordered like a form, and, having furnished from himself understanding for its perceptive part and order for its motive part,
established it as ruler of the whole. For in the same way he declares the body of the cosmos too to be in one sense ungenerated and in another generated: for when he says, "all that was visible was not at rest but was moving in disorder when god took it in hand to set it in order," and again, "the four kinds, fire and water and
earth and air, before the universe came to be set in order by them, caused a shaking in matter and were shaken by it because of their irregularity," he plainly represents the bodies as already existing and underlying before the generation of the cosmos. But when again he says that the body came to be younger than the soul and that the cosmos is generated because it is visible and tangible and has body,
and things of this sort, coming into being and generated, were plainly evident to everyone, he is clearly attributing generation to the nature of body. Yet it is far from the case that he is saying the opposite and contradicting himself so blatantly on the greatest matters. For he does not say that the same body both comes to be by god and exists before it comes to be in the same sense and as the same thing; that would be the statement of a man out of his mind. But
what one must understand by "generation" too, he himself teaches. "For before this," he says, "all these things were in a condition without reason or measure; but when the ordering of the universe was undertaken, fire first, and water and earth and air, though having certain traces of themselves, were nevertheless disposed altogether as anything is likely to be when god is absent from it — thus then, being of such a nature,
these were first given distinct shape by means of forms and numbers." And having said still earlier that it was the work not of one proportion but of two to bind together the mass of the universe, being solid and having depth, and having explained that god, placing water and air between fire and earth, bound and constituted the heaven, "from these," he says, "being four in such number,
the body of the cosmos was generated, agreeing through proportion, and it obtained friendship out of these, so that, having come together into the same thing with itself, it became indissoluble by anything else except by him who bound it together" — teaching most clearly that god was father and craftsman not simply of body nor of mass and matter, but of commensurability, beauty, and likeness in respect to body. These same things,
then, one must think also concerning soul: that the one part was neither generated by god nor is the soul of the cosmos, but is a certain power, self-moved and ever-moving, of an irrational and disorderly motion and impulse belonging to imagination and opinion; while the other part god himself, having harmonized it with the appropriate numbers and ratios, established as ruler of the cosmos once it had come to be, this part being generated. That he had in mind precisely these things and not merely for the sake of theoretical exposition, even though the cosmos had not come into being, he nonetheless posited a constitution and generation for the soul as well — this among many other things is evidence: that the soul is said by him to be both ungenerated, as has been said, and generated, whereas the cosmos is said always to have come into being and to be generated, but never ungenerated nor eternal. As for the passages in the
Timaeus, why should one need to cite them? For the whole treatise, entire, is about the generation of the cosmos, from beginning to end. As for the other dialogues, in the Atlanticus, Timaeus in his prayer names the one "who long ago came to be in deed, and now in speech, a god"; in the Statesman the stranger from Elea, Parmenides' follower, says that the cosmos, put together by god, "partakes of many good things, but if
there is anything base or difficult, it has this mixed in from its former condition of disharmony and irrationality"; and in the Republic, concerning the number which some call the "nuptial" number, Socrates, beginning to speak, says, "there is, for a generated divine thing, a period which a perfect number encompasses," calling nothing else "generated divine thing" than the cosmos. In the same way, as regards form and shape it remains constant,
while what comes to be about bodies is divisible, as a receptacle and matter, and the mixture is a common product completed from both. The undivided substance, then, ever remaining the same and in the same condition — not through smallness, as the smallest of bodies do — must be understood as escaping division: for its simple, unaffected, and pure and single-formed character is called "partless" and "undivided,"
by which, in some way touching the composite, divided, and differing things, it stops their multiplicity and settles them into a single condition through likeness. But as for the substance that becomes divisible about bodies, if one wishes to call it "matter," as a nature underlying and participating in that other substance, using the term homonymously, it makes no difference to the argument; but those who insist that a corporeal matter is mixed with
the undivided substance go wrong, first, because Plato uses none of that substance's own names for it — he is accustomed always to call that one "receptacle," "all-receiving," and "nurse," not as divisible about bodies, but rather as body divided into particulars. Next, how will the generation of the soul differ from that of the cosmos, if for both the constitution came to be out of matter and the intelligibles alike?
Yet Plato himself, as if pushing away from the soul any generation out of body, says that the corporeal element was placed by god within the soul, and only afterward wrapped about it from outside; and in general, having in his account first completed the soul, he only later introduces the hypothesis about matter, having needed nothing of it earlier, when he was generating the soul, as though it came to be
without matter. Similar objections can be made against the followers of Posidonius too; for they have not distanced themselves far from matter: having accepted that the substance of limits is said to be divisible about bodies, and mixing this with the intelligible, they declared the soul to be the form of that which is extended in every direction, constituted according to number and comprehending harmony — for the objects of mathematics are ranked between the primary intelligibles and
the objects of sense, and since the soul possesses the eternity of the intelligibles and the passibility of the objects of sense, it is fitting for its substance to exist in between. For it escaped even these men's notice that god, using the limits of bodies later, after the soul had already been completed, for the shaping of matter, was defining and enclosing its scattered and unconnected character by means of surfaces fitted together out of triangles.
Still more absurd is it to make the soul a form: for the one is ever-moving, the other unmoved; and the one is unmixed with the sensible, the other bound up with body. Moreover, god became an imitator of the form, as of a model, while he was the craftsman of the soul, as of a finished work. And that Plato does not posit number as the substance of the
soul, but rather as that which is ordered by number, has already been said. Common to both these views is this: that neither in limits nor in numbers does there inhere any trace of that power by which the soul is naturally able to judge the sensible; for the participation in the intelligible principle has produced in it mind and the capacity for thought, while opinions and beliefs and the imaginative and passible element come from
the qualities pertaining to body — something one could not conceive as arising simply out of units, or lines, or surfaces. And indeed, not only the souls of mortal things possess a cognitive power of the sensible, but also that of the cosmos, he says, "revolving upon itself, whenever it touches something whose substance is scattered, and whenever it touches something undivided, speaking as it is moved through the whole of itself
concerning that with which a thing is the same and that from which it differs, and in relation to what especially, and how and in what way it happens, according to what comes to be, that each thing stands and is affected in relation to each other thing" — in these words he is at once sketching an outline of the ten categories, and he makes this still clearer in what follows: "true reasoning," he says, "whenever it concerns the sensible and
the circle of the different, moving rightly, reports it throughout the whole soul, opinions and beliefs come to be firm and true; but whenever it concerns the rational and the circle of the same, running smoothly, makes it known, knowledge is necessarily brought to completion; and if anyone ever calls that in which these two come to be, in respect of existing things, by any other name than soul, he will say anything sooner
than the truth." Whence, then, did the soul get this apprehensive and opinion-forming motion directed at the sensible, distinct from that intellective motion which issues in knowledge? It is difficult to say, unless we hold firmly that here he is constituting not simply soul but the soul of the cosmos, out of underlying elements — both the better substance, the undivided one, and the
inferior one, which he has called divisible about bodies — this latter being none other than the opinion-forming, imaginative motion sympathetic with the sensible, not generated but subsisting eternally, just like the other. For the nature that possesses the intellective element also possessed the opinion-forming element; but the one is unmoved, unaffected, and established about the ever-abiding substance, while the other is divisible and wandering, inasmuch as it is in contact with matter that is being carried about and scattered.
For the sensible had not yet obtained order but was shapeless and indefinite, and the power ordered in relation to it had neither articulate opinions nor all its motions ordered, but for the most part dreamlike and erratic ones, disturbing what has bodily form, except so far as by chance it happened to fall in with the better; for it was in between the two and had a nature sympathetic and akin to both,
clinging on its perceptive side to matter, and on its judging side to the intelligibles. He himself, in fact, makes this fairly clear too by his very names: "let this," he says, "reckoned by my vote, be given as a summary statement — that being, and space, and becoming are three, existing separately three ways, even before heaven came to be." For he calls matter "space," as it were a seat, at times
and also "receptacle"; and that which is intelligible he calls "being"; and "becoming," while the cosmos had not yet come to be, he calls no other substance than that which exists in changes and motions, ranked between that which stamps the impression and that which receives it, transmitting here the images from there. For these reasons it was called "divisible," and also because the perceiving element must be distributed and coextend together with the sensible, and the imagining element with the imagined —
for the sensory motion, being proper to the soul, moves toward the sensible outside it; whereas mind itself, in itself, was abiding and unmoved, but coming to be within the soul and gaining mastery, turns it back upon itself and completes the circular motion around that which remains, ever touching most closely upon being. For this reason the association of the two has proved hard to blend, mixing the
divisible with the undivided and the everywhere-carried with that which is nowhere movable, and forcing the one to come together with the other into the same thing. But "the different" was not motion, just as "the same" was not rest, but rather a principle of difference and dissimilarity; for each descends from its own separate principle, the same from the one, the different from the dyad; and here for the first time they are mixed together concerning the
soul, bound together by numbers and ratios and harmonic means, and it makes the different, coming to be within the same, into difference, and the same, within the different, into order, as is clear in the primary powers of the soul: these are the judging power and the moving power. Motion, then, straightaway displays itself concerning the heaven, in the sameness the difference
by the revolution of the fixed stars, and in the difference the sameness by the order of the planets — for among the fixed stars the same prevails, while among the bodies near the earth the opposite holds. Judgment has two principles: mind, from the same, directed toward universals, and sense-perception, from the different, directed toward particulars. Reasoning is mixed
out of both, becoming intellection among the intelligibles and opinion among the sensibles, using as its intermediary instruments imaginations and memories, of which some produce the different within the same and others the same within the different. For intellection is a motion of the intellecting subject about that which remains, while opinion is a stationary state of the perceiving subject about
that which moves; and imagination, being an interweaving of opinion with sensation, he places in memory; and the same in turn moves the different again in the difference between before and now, touching at once upon difference and sameness. One must take the fusion that occurred concerning the body of the cosmos as an image of the proportion by which he fitted together the soul. For there, the extremes were fire and
earth, having a nature difficult to blend with one another, or rather altogether unmixable and unstable; whence, placing between them air before fire and water before earth, he first mixed these with one another, and then through these he mixed and harmonized those with these and with one another. Here again, the same and the different,
...the opposing powers and contrary extremities, he brought together, not by themselves, but by means of another substance placed between them—setting the indivisible substance before Sameness, and the divisible before Difference, adapting each appropriately to each—and then, blending with those already mixed substances, he wove the whole together into a single form of soul, as far as was possible, making one thing resembling out of different things, one out of many. Some do not do well
to say, as certain people do, that the nature of Difference was said by Plato to be hard to mix, not because it is unreceptive but rather fond of change, while the nature of Sameness, being stable and hard to alter, does not easily admit mixture but is repelled and flees it, so that it may remain simple, pure, and unchanged. But those who make this charge fail to recognize that Sameness is the form of things that are disposed alike,
while Difference is the form of things disposed differently; and the function of the latter, wherever it touches, is to separate, to alter, and to make many things out of one; while the function of the former is to bring together and to unite through likeness, gathering a single shape and power out of many things. These, then, are powers of the soul of the universe as a whole; but those powers that enter into mortal and passible instruments—being themselves imperishable powers of perishable bodies—in
these the character of the dyadic and indeterminate portion appears more prominently, while the character of the simple and monadic portion sinks more dimly out of sight. Yet one could hardly easily conceive of any human passion entirely free of reasoning, nor any movement of thought entirely without desire or love of honor or of feeling pleasure or pain attaching to it. For this reason, among philosophers some make the passions to be forms of reasoning, holding that every desire
and grief and anger are judgments; while others declare that the virtues themselves are passions—for indeed, they say, courage is a kind of fear, temperance a kind of pleasure, and justice a kind of self-interest. And further, since the soul is at once contemplative and practical, and contemplates both universals and particulars—understanding the former, as it seems, and perceiving the latter by sense—the common
reasoning faculty, always encountering Sameness in connection with Difference and Difference in connection with Sameness, attempts by definitions and divisions to separate the one from the many, and the indivisible from the divisible, yet is unable to remain purely within either, because the very principles themselves are interwoven and intermingled with one another in alternation. And it is for this reason that god constructed, out of the indivisible
and the divisible substance, a receptacle common to Sameness and Difference, so that order might arise amid difference—for this was what had to come about, since apart from these, Sameness would have had no difference, and so no motion and no coming-into-being; while Difference would have had no order, and so no coherence and no coming-into-being either. For even if it belongs to Sameness to be different from the
Different, and to the Different in turn to be the same as itself, such a mutual participation produces nothing generative by itself, but requires some third thing, a kind of matter, to receive and be disposed by both. And this is the substance which he first established, defining the unlimited character of that which is in motion around bodies by reference to the stability that belongs to intelligible things. Just as there is a sound that is inarticulate and without meaning, while speech is a meaningful
utterance of sound conveying thought, and harmony is that which arises out of pitches and intervals—a single pitch being one and the same, while an interval is a difference and otherness between pitches, and when these are mixed together, song and melody come to be—so too the passible part of the soul was indeterminate and unmeasured, until it was bounded by the introduction of a limit and a form upon the divisible and manifold character of its motion. Having grasped both Sameness
and Difference, through the likenesses and unlikenesses of numbers producing agreement out of difference, it becomes the intelligent life of the universe, and a harmony, and a reasoning that leads a persuasion mingled with necessity—which most people call fate, Empedocles calls Love together with Strife, Heraclitus calls "the backward-turning harmony of the universe, as of the bow and the lyre," Parmenides calls Light and Darkness, Anaxagoras calls Mind and the Unlimited,
and Zoroaster calls god and daemon, naming the one Oromasdes and the other Areimanios. Euripides, however, did not use the disjunctive correctly in place of the conjunctive when he wrote: "whether it be necessity of nature or mind of mortals, O Zeus"—for indeed both necessity and mind are the single power that pervades all things. The Egyptians, then, in their myth-making, hint at this darkly, when Horus is condemned in a lawsuit: to the father is assigned
breath and blood, but to the mother flesh and fat. Of the soul, nothing is pure or unmixed or left apart from the rest—"for hidden harmony is stronger than visible," as Heraclitus says—in which the differences and otherness the mingling god has hidden and submerged; yet it is still made manifest, in its irrational part by turbulence, in its
rational part by good order, in its senses by compulsion, and in its intellect by self-mastery. The defining faculty embraces the universal and the indivisible on account of kinship, while conversely the dividing faculty is drawn toward particulars, on account of the divisible; the whole soul rejoices in the unchanging owing to Sameness, and desires the change it needs owing to Difference. Not least
do the difference between the beautiful and the shameful, and that between the pleasant and the painful, and again the enthusiasms and agitations of lovers and their inner battles between love of beauty and unrestraint, reveal the mixed nature composed both of the divine and impassible and of the mortal portion, subject to passion in connection with bodies—of which he himself names the one
innate desire for pleasures, and the other an imported opinion reaching after the best. For the soul brings forth the passible element from itself, but it partakes of intellect from the superior principle that enters into it from outside. And this twofold association is not absent even from the nature that surrounds the heaven, but, inclining now to one side, now to the other, it is at present set upright by the revolution of Sameness, which holds mastery and steers the universe rightly; but there will
come a certain portion of time—and it has already come many times—in which the intelligent part is blunted and falls into slumber, filled with forgetfulness of what is properly its own, while the part accustomed to body from the beginning and sympathetic with it draws the soul along, weighs it down, and reverses the course it takes to the right of the universe; yet it cannot break free from it entirely, but again recovers the better part and looks back up toward the pattern, with god turning it about and
guiding it aright together. In this way it is shown to us from many directions that the soul is not wholly the work of god, but, possessing within itself an innate portion of evil, has been set in order by god—who, by defining the unlimited by means of the one, so that a substance might come to be that partakes of limit; and by mingling order, change, difference, and likeness through the power of Sameness and of Difference, has, so far
as was possible, produced a fellowship and friendship among all these with one another, by means of numbers and harmony. Concerning these matters, even though you have often heard of them and encountered them in many discourses and writings, it will not be amiss for me too to go through them briefly, setting forth first Plato's own words: "He took away one portion first from the whole, and after this he took away a portion double of that; and a third, half again as much as the second
but three times the first; a fourth double the second; a fifth three times the third; a sixth eight times the first; and a seventh twenty-seven times the first. After this he went on to fill up the double and triple intervals, cutting off still more portions from that original mass and placing them in between these, so that in each interval there were two means, the one exceeding and being exceeded by
the same fraction of the extremes, and the other exceeding and being exceeded by the same number as the extremes; and out of these bonds there arose, within the previous intervals, intervals of one and a half, of four thirds, and of nine eighths; and with the interval of nine eighths he filled up all the intervals of four thirds, leaving over in each of them a fraction, the interval of this fraction, remaining as number to number, having
its terms as two hundred fifty-six to two hundred forty-three." In these matters the inquiry concerns, first, the quantity of the numbers; second, their order; and third, their power. Regarding the quantity, one must ask what the numbers are that he takes among the double and triple intervals; regarding the order, whether all should be set out along a single line, as
Theodorus does, or rather, as Crantor does, in the shape of a Λ, with the first number placed at the apex and, apart from the doubles on one side and apart from the triples on the other, arranged in two rows beneath. And regarding the use and the power, what these numbers accomplish when taken up for the composition of the soul. First, then, concerning the first point, we shall set aside those who say that as regards the ratios themselves
it is enough to observe the nature possessed by the intervals and by the means that fill them up, whatever numbers one may suppose to occupy the places receptive of the aforesaid proportions, since the teaching is completed in the same way regardless. For even if what they say is true, it makes learning dim without examples, and it shuts out another kind of contemplation that has a charm not without philosophy. If, then, beginning from the monad,
we set out the doubles and triples in turn, as he himself lays down, they will come in this order, at one point the second, the fourth, and the eighth, at another the third, the ninth, and the twenty-seventh—seven numbers in all, counting the unit in common, proceeding as far as the fourth term by multiplication. For not only here, but in many other places, the affinity of the number four with the number seven
becomes evident. Now the tetraktys celebrated by the Pythagoreans, the six and the thirty, seems to have this marvel: that it is composed of the first four even numbers and the first four odd numbers, and comes to be as the fourth pairing of the numbers successively added together; for the first pairing is that of one and two, the second that of three and four,
the third that of five and six—of which none makes a square number, either by itself or together with the others—while the pairing of seven and eight, though it is the fourth, when added to the earlier pairings yields thirty-six, a square number. But the tetraktys of the numbers set forth by Plato has a more complete origin, since the even numbers are multiplied by even intervals and the odd
by odd intervals; it contains the unit, which is the common source of even and odd, and beneath it two and three, the first plane numbers; four and nine, the first square numbers; and eight and twenty-seven, the first cube numbers—the unit being placed outside the reckoning, by which it is also clear that he wishes them to be arranged not on a single straight line
but rather alternately and separately, the even numbers set alongside one another and again the odd numbers alongside one another, as has been described above. In this way the pairings of like numbers will correspond to like numbers, and will produce conspicuous numbers both by addition and by multiplication with one another. By addition, thus: two and three make five, four and nine make thirteen, and eight and
twenty-seven make thirty-five. Of these numbers the Pythagoreans called the five "nurse," that is, a musical tone, believing that among the intervals of the whole tone the fifth was the first that could be sounded; and they called the thirteen "remainder," following Plato, recognizing the impossibility of dividing the tone into equal parts; and the thirty-five they called "harmony," because it is composed of two first cubes, arising from
an even and an odd number, and out of four numbers, six and eight and nine and twelve, which contain the arithmetic and the harmonic proportion. But this power will be made clearer by means of a diagram. Let there be a rectangular parallelogram ABCD, having as one of its sides AB five, and the side AD seven; and when
the shorter side is cut into two and three at the point K, and the longer side into three and four at the point L, let straight lines be drawn from the points of section, cutting one another, at K M N and at L M O, and making the area A K M L six, the area K B O M nine, the area
L M N D eight, and the area M O C N twelve; and the whole parallelogram contains thirty-five, the ratios of the first musical concords, in the numbers of the areas into which it has been divided. Now the six and the eight are in the ratio of four to three, in which is the interval of a fourth; and the six and the nine are in the ratio
of three to two, in which is the interval of a fifth; and the six and the twelve are in the ratio of two to one, in which is the interval of the octave. And the ratio of the tone, which is nine to eight, is also present, in the nine and the eight; and for this reason they called the number that contains these ratios "harmony." This number, taken six times, produces the number two hundred and ten, the number of days
in which seven-month infants are said to be brought to full term. Again, from another starting point, by multiplication: twice three makes six, four times nine makes thirty-six, and eight times twenty-seven makes two hundred and sixteen; and six is a perfect number, being equal to its own parts, and is called "marriage" because of the union of even and odd; moreover it is composed
of the source and of the first even number and the first odd number. And thirty-six is the first number that is both square and triangular—square from the six, and triangular from the eight—and it comes about by the multiplication of two square numbers, four multiplied by nine, and also by the addition of three cubes, for one and eight and twenty-seven
added together make the number written above. It is further an oblong number from two sides, twelve taken three times or nine taken four times. If, then, the sides of the figures are set out—six of the square, eight of the triangle, and of the parallelograms, nine of the one and twelve of the other—they will produce the ratios of the concords. For there will be
the twelve to the nine, a fourth, as nete to paramese; to the eight, a fifth, as nete to mese; and to the six, an octave, as nete to hypate. And the cube of 216 is derived from six and is equal to its own perimeter. Since the numbers set out have such powers, a peculiar property belongs to the last of them,
27: that the sum of all the numbers before it is equal to it alone, and it is also the period of the moon. And among the melodic intervals the Pythagoreans place the tone in this number; that is why they call the thirteen a leimma ("remainder"), for it falls short of the half by a unit. That these numbers also contain the ratios of the concords is easy to learn. For the ratio of two to one, in which lies the octave, is double; the ratio of three to two, in which lies the fifth, is sesquialter; the ratio of four to three, in which lies the fourth, is sesquitertian; the ratio of nine to three, in which lies the octave-plus-a-fifth, is triple;
and the ratio of eight to two, in which lies the double octave, is quadruple. There is also the ratio of nine to eight, in which lies the tone, which is superoctave (epogdoic). If, then, the unit, being common to both, is counted together with the even numbers and with the odd, the whole series of numbers yields the total of the decad — for the numbers from one up to ten,
added together, make fifteen, a triangular number from the pentad; while the odd series yields forty, produced by addition from thirteen and twenty-seven, the numbers by which the mathematicians clearly measure the melodic intervals, calling the one a diesis and the other a tone; and produced by multiplication through the power of the tetraktys — for when each of the first four numbers is taken four times over, there result four,
eight, twelve, and sixteen: these together make forty, and they contain the ratios of the concords. For the sixteen is sesquitertian to the twelve, double to the eight, and quadruple to the four; and the twelve is sesquialter to the eight and triple to the four. These ratios comprise the fourth, the fifth, the octave, and the double octave. The forty is also equal to two squares and two cubes taken together: for one, four, eight, and twenty-seven — cubes and squares — add up to forty when combined. So the Platonic tetraktys is far more varied in its arrangement than the Pythagorean, and more complete. But
since the means being introduced find no room among the numbers as first laid down, it was necessary to take larger terms in the same ratios; and we must say what these are. But first, concerning the means: of these, the one that exceeds by an equal number and is exceeded by an equal number is now called arithmetic; the one that exceeds and is exceeded by the same fraction of the extremes is called sub-contrary ("harmonic"). The terms of the
arithmetic mean are 6, 9, and 12: for nine exceeds six by the same number by which it is exceeded by twelve. The terms of the sub-contrary mean are 6, 8, 12: for eight exceeds six by two and is exceeded by twelve by four, and two is a third part of six, while four is a third part of twelve. It follows, then,
that in the arithmetic mean the middle term is exceeded and exceeds by the same fraction of the extremes, whereas in the sub-contrary mean it falls short by one fraction of the extremes and exceeds by the same fraction — for there, the three is a third part of the middle term, but here the four and the two are each a third part of the respective extreme; hence it has been called sub-contrary. They also name this the harmonic mean,
because it provides the primary concords for its terms: for the greatest term to the least gives the octave, the greatest to the middle gives the fifth, and the middle to the least gives the fourth — because when the greatest of the terms is set at nete and the least at hypate, the middle term becomes the one at mese, which
makes the fifth to the greatest and the fourth to the least, so that the eight falls at mese, the twelve at nete, and the six at hypate. As for the method by which they take the said means, Eudorus demonstrates it simply and clearly. Consider first the case of the arithmetic mean. If you set out the extremes and take
half of each and add them together, the sum will be the mean, alike in the case of doubles and of triples. In the case of the sub-contrary mean, among doubles, if you set out the extremes and take a third of the lesser and a half of the greater, the sum becomes the mean; among triples, conversely, you must take
a half of the lesser and a third of the greater, for the sum thus produced becomes the mean. For example, let 6 be the least term and 18 the greatest in a triple ratio: if you take half of the six, namely three, and a third of the eighteen, namely six, and add them, you will get nine, which exceeds and is exceeded by the same fraction of the extremes. In this way
the means are obtained. But they must be inserted there and made to fill out the double and triple intervals. Of the numbers set out, some have no room at all in between, and others not enough; so by increasing them, while keeping the same ratios, they create room sufficient for the said means. And first, taking six in place of one as the smallest term, since six is the first
number to have both a half and a third part, they made all the terms set out below six times as large, as has been described, so that they would admit both means in both the double and the triple intervals. Since Plato speaks of "the sesquialter, sesquitertian, and superoctave intervals that arose from these bonds," in the previous intervals all the sesquitertian ratios were filled out by the interval of a superoctave, leaving over,
in each case, a fraction — and since this fractional interval, when left over, has its terms in the ratio of number to number, namely 256 to 243, it was on account of this expression that they were compelled once more to raise the numbers and make them larger. For it was necessary that two superoctave intervals follow in succession; but since six neither has a superoctave of itself, nor, if it were divided, could it be split into fractional parts without the learning becoming hard to follow, since the units would have to be broken into fractions, the very nature of the matter dictated the multiplication — just as in a change of key the whole diagram is stretched proportionally together with the first of the numbers. Now Eudorus, following Crantor, first took 384, which arises when six is multiplied by 64; and he was led to these numbers by the fact that 64 has 72 as its superoctave.
But it agrees better with what Plato says to posit half of this number; for its leimma will have the ratio, in numbers, that Plato states, namely 256 to 243, when 192 is set as the first number. But if double this number is set as the first, the leimma will have the same ratio but a doubled numerical value, the one that 512 has to 486: for 512 is the sesquitertian of 384, just as 256 is the sesquitertian of 192. And the reduction to this number is not without reason, but it also furnished Crantor's school with their justification: for 64 is both a cube derived from the first square
and a square derived from the first cube; and when multiplied by three — the first odd number, the first triangular number, and the first perfect number, and also sesquialter — it produces 192, which itself also has a superoctave, as we shall show. But first, so that you may better grasp what the leimma is and what Plato's intention is, let us briefly recall what is customarily said in the Pythagorean schools.
An interval in melody is anything comprehended between two notes unlike in pitch. One of these intervals is the so-called tone, by which the fifth is greater than the fourth. Some musical theorists suppose that when this is divided in two it makes two intervals, each of which they call a semitone; but the Pythagoreans denied that it could be cut into equal parts, and
since the two parts are unequal, they call the smaller one the leimma, because it falls short of the half. Hence, of the concords, some make the fourth consist of two tones and a semitone, others of two tones and a leimma. The theorists of hearing seem to be borne out by sense-perception, the mathematicians by demonstration, and the method of the latter is as follows: it was observed by means of instruments
that the octave has the double ratio, the fifth the sesquialter, the fourth the sesquitertian, and the tone the superoctave. It is possible even now to test the truth of this, either by hanging two unequal weights from strings, or by making, out of two pipes of equal bore, one double the length of the other: for of the pipes, the longer
will sound lower, as hypate to nete; and of the strings, the one stretched with double the weight will sound higher than the other, as nete to hypate — and this is the octave. Likewise, lengths and weights taken in the ratio of three to two will produce the fifth, and four to three the fourth, of which the latter has the sesquitertian ratio, the former
the sesquialter. And if the inequality of weights or lengths is as nine to eight, it will produce the interval of a tone, not a concord but, so to speak, merely melodic, in that the notes, if struck one after another, sound sweet and pleasing, but if struck together, harsh and unpleasant; whereas among the concords, whether struck together or in alternation, the
perception welcomes the combined sound gladly. Moreover, they demonstrate this also through ratio. For in harmony the octave is composed of the fifth and the fourth, and in numbers the double ratio is composed of the sesquialter and the sesquitertian: for twelve is sesquitertian to nine, sesquialter to eight, and double to six.
The double ratio, then, is compounded of the sesquialter and the sesquitertian, just as the octave is compounded of the fifth and the fourth; but there, the fifth is greater than the fourth by a tone, and here, likewise, the sesquialter is greater than the sesquitertian by a superoctave. It appears, then, that the octave has the double ratio,
the fifth the sesquialter, the fourth the sesquitertian, and the tone the superoctave. Now that this has been demonstrated, let us examine whether the superoctave ratio is naturally divisible in two; for if it is not, neither is the tone. Since nine and eight, the first numbers to produce the superoctave ratio, have no interval between them, but when both are doubled, the number that falls
in between produces two intervals, it is clear that if these two intervals were equal, the superoctave would be divided in two. But in fact, when doubled, nine becomes eighteen and eight becomes sixteen, and between these falls seventeen, so that of the two intervals one is greater and the other smaller: the first is a seventeenth part greater, the second a sixteenth part greater. So
the superoctave is divided into unequal parts; and if this is so, so too is the tone. Neither of the two parts resulting from its division is therefore a semitone, but it has rightly been called a leimma by the mathematicians. And this is what Plato means when he says: "filling up the sesquitertian intervals with superoctaves, the god left over a fraction of each of them, whose ratio is that which 256
bears to 243." For let the fourth be taken in two numbers containing the sesquitertian ratio, 256 and 192: of these, the lesser, 192, is to be set at the lowest note of the tetrachord, and the greater, 256, at the highest. It must be shown that when this interval is filled up with two superoctaves,
there remains an interval of the same size as that which, in numbers, 256 has to 243. For when the lower note is raised by a tone, which is a superoctave, it becomes 216; and when this in turn is raised by another tone, it becomes 243: for this exceeds 216 by 27, and 216 exceeds 192 by 24,
of which the 27 is an eighth part of 216, and the 24 is an eighth part of 192. Hence of these three numbers, the greatest is a superoctave of the middle, and the middle of the least; and the interval from the least to the greatest — that is, from 192 to 243 — is a double tone, being filled up
by two superoctaves. If this is subtracted, there remains, of the whole interval, the part left between 243 and 256, namely 13 — which is why they called this number the leimma. I myself think that Plato's meaning is most clearly shown by these numbers. But others, setting the terms of the fourth with the higher note at 288 and the lower
at 216, work out the rest proportionally in the same way, except that they take the leimma as lying between two tones: for when the lower is raised by a tone, it becomes 243; and when the higher is lowered by a tone, it becomes 256 — for 243 is a superoctave of 216, and 288 a superoctave of 256 — so that each of the intervals is a full tone, and what remains between
...between 243 and 256, which is not a semitone but less than one. For 288 exceeds 256 by 27 (and a fraction more), while 243 exceeds 216 by 27, and 256 exceeds 243 by 13; and this excess is less than half of either of those other excesses. Hence the fourth is found to consist of two tones and a leimma, not two and a half tones.
This, then, is the demonstration of these matters. But it is not very difficult to see, from what has been said, why Plato, after stating that intervals in the ratios of 3:2, 4:3, and 9:8 arise, and that the 4:3 ratios are filled up by the 9:8 ratios, made no mention of the 3:2 ratios but passed over them. For the 3:2 ratio, too, is filled up when a 9:8 interval is added to a 4:3 interval.
Now that these points have been demonstrated, I would, for the sake of practice, have left it to you yourselves to fill in the intervals and insert the means, even if no one had done this before; but since this has in fact been worked out by many good men, especially Crantor, Clearchus, and Theodorus of Soli, it is not without use to say a little about their disagreement on the matter. For Theodorus, not making two rows as they did, but arranging the doubles and the triples in succession on a single straight line, argues first from the so-called division of the substance according to length, which makes two portions out of one, not four out of two; and then he says that the insertions of the means ought to take their place in this way, since otherwise there will be confusion and disorder, and immediate transpositions into the first triple out of the first double, when each ought to be filled up separately.
Crantor and his followers, on the other hand, are supported by the positions of the numbers—plane matched against plane, square against square, and cube against cube—and by taking them not in sequence but alternating even and odd. For, placing the monad, which is common to both series, first, he takes the eight and then next the twenty-seven, all but showing us what place he assigns to each kind. These matters, then, it is more fitting for others to work out precisely; what remains belongs properly to the subject before us.
For Plato did not introduce the arithmetic and harmonic means as a display of mathematical theory in a physical hypothesis that had no need of them, but because this reasoning is especially appropriate to the constitution of the soul. And yet some seek the proportions in question in the speeds of the wandering spheres, others rather in their distances, some in the sizes of the stars, while those who think themselves extremely precise look for them in the diameters of the epicycles—supposing that the demiurge fitted the soul to the heavens for the sake of these things, divided as it is into seven portions.
Many also transfer the Pythagorean scheme to this subject, tripling the distances of the bodies from the center. This works out as follows: for fire the unit is set at one; for the counter-earth, three; for the earth, nine; for the moon, twenty-seven; for Mercury, eighty-one; for Venus, two hundred forty-three; and for the sun itself, seven hundred twenty-nine—which is at once a square and a cube, and this is why they sometimes call the sun 'the square' and 'the cube.'
In this way they force the other bodies also into the pattern of tripling, straying far indeed from what is reasonable—if there is any value at all in geometrical demonstrations. And they show that those who set out from that other starting point are far more plausible to compare with them, though even these do not achieve complete precision but speak only approximately: that the ratio of the sun's diameter to the earth's diameter is twelve to one; that the earth's diameter, in turn, is three times the moon's diameter; that the faintest visible of the fixed stars has a diameter no less than a third of the earth's diameter; that the whole sphere of the earth stands to the whole sphere of the moon as twenty-seven to one; that the diameters of Venus and the earth are in the ratio of two to one, while their spheres are in the ratio of eight to one; that the breadth of the eclipse-shadow is three times the moon's diameter; and that the moon deviates in latitude from the circle of the zodiac by twelve degrees on either side.
Its relations to the sun, at triangular and square distances, take the forms of half-moon and gibbous phases; and having traversed six signs, it renders the full moon like a kind of consonance, the octave within a span of six tones. As for the sun's motions, which are smallest around the solstices and greatest around the equinox—through which it subtracts from the day and adds to the night, or the reverse—the ratio is as follows: in the first thirty days after the winter solstice, it adds to the day a sixth of the excess by which the longest night exceeds the shortest day; in the next thirty days, a third; and half in the remaining days up to the equinox, the irregularity being equalized over intervals of time in the ratios of six to one and three to one.
The Chaldeans say that spring stands to autumn in the ratio of a fourth, to winter in the ratio of a fifth, and to summer in the ratio of an octave. And if Euripides is right in distinguishing four months of summer and an equal number of winter, and two of dear autumn and an equal number of spring, then the seasons change through the interval of an octave.
Some, assigning to the earth the place of the added note, to the moon the hypate, and moving Mercury and Venus among the notes called parhypate and lichanos, maintain that the sun itself, as the mese, holds together the octave, being distant from the earth by a fifth and from the fixed stars by a fourth. But neither does the ingenuity of these men touch upon any truth, nor do the others attain complete accuracy.
To those, then, who do not think these views are dependent on Plato's own thought, the following will seem to hold entirely to musical reasoning: that, there being five tetrachords—the hypaton, meson, synemmenon, diezeugmenon, and hyperbolaion—the planets are arranged within five intervals. Of these, one runs from the moon to the sun and to those that move together with the sun, Mercury and Venus; a second runs from these to fiery Mars; a third lies between this and Jupiter; then next comes the interval to Saturn; and the fifth, finally, runs from this to the sphere of the fixed stars—so that the notes bounding the tetrachords stand in the same ratio as the wandering stars.
Moreover, we know that the ancients set two hypatai, three netai, one mese, and one paramese, so that the fixed notes were equal in number to the planets. But the moderns, having placed the proslambanomenos—differing by a tone from the hypate—on the low side, made the whole system a double octave, but did not preserve the natural order of the consonances; for the fifth comes before the fourth, once a tone has been added below the hypate.
Plato, however, is clearly adding at the high end: for he says in the Republic that each of the eight spheres revolves, and that upon each stands a Siren who sings, each sending forth a single note, and that out of all of them a single harmony is blended together; and these Sirens, released to sing, chant and celebrate the divine, an eight-stringed melody of the sacred circuit and dance. For eight, too, was the number of the first terms of the double and triple ratios, when the unit is counted in with each series.
The elder tradition has handed down to us nine Muses as well: eight of them, as in Plato, concerned with the heavens, and the ninth charming the things around the earth, calling them back and settling into order the irregularity and confusion that arise from wandering and diversity. Consider, then, whether it is not the soul—having become most prudent and most just—that guides the heavens and the heavenly bodies by the melodies and motions proper to it; and it has become such through the ratios that constitute harmony, of which images exist reaching even into the incorporeal, in the visible and seen parts and bodies of the cosmos. The first and most sovereign power is visibly blended into the soul and renders it consonant and obedient to itself, with the best and most divine part always in harmony with all the rest.
For the demiurge, taking over disorder and discord in the motions of the unharmonized and unintelligent soul as it was at variance with itself, marked off and separated some elements, and gathered and arranged others together, employing harmonies and numbers. By these same means, even the most inert bodies—stones, wood, the bark of plants, the bones of animals, and rennets—when blended and fitted together, produce marvelous appearances in statues and marvelous powers in drugs and instruments. For this reason Zeno of Citium used to urge the young men to go and observe flute-players closely, to see what a sound is given off by horns and wood and reeds and bones when they partake of proportion and consonance.
For the claim that all things resemble number, in accordance with the Pythagorean pronouncement, requires an argument; but that in all the things among which, out of difference and dissimilarity, some fellowship and concord with one another has come to be, the cause of this is measure and order, insofar as they partake of number and harmony—this has not escaped the poets, who call things that are dear and friendly 'articulate,' and enemies and foes 'unfitted,' on the ground that difference is a kind of disharmony. The poet who composed the funeral ode for Pindar wrote: 'this man was fitted to strangers and dear to his townsmen'—clearly regarding good fittingness as virtue; just as Pindar himself somewhere says that Cadmus heard the god display true music. And the ancient theologians, the oldest of philosophers, used to place musical instruments in the hands of the images of the gods—not supposing that the gods somehow play the lyre or the flute, but thinking that no work of the gods is so fitting as harmony and consonance.
Just as, then, a man who looks for the ratios of 4:3, 3:2, and 2:1 in the yoke of the lyre, or in its sound-box, or in its pegs, is ridiculous—for while it is true that these parts, too, must be made proportionate to one another in length and thickness, that harmony itself is to be observed in the notes—so likewise it is reasonable that the bodies of the stars, the intervals of their circles, and the speeds of their revolutions, like the parts of an instrument, stand to one another and to the whole in fixed ratios and due measure, even though the precise quantity escapes us. As for those ratios which the demiurge employed, and the numbers, we should consider their work to be the very melodiousness and harmony of the soul with itself, by which, having come to be present in the heavens, it has filled them with countless blessings, and has ordered the things around the earth—with seasons and changes possessing due measure—in the best and most beautiful way for both the generation and the preservation of the things that come to be.