1. 1. 1. Teacher: The word "modus"—what foot is it?

Student: A pyrrhic.

Teacher: How many time-units does it have?

Student: Two.

Teacher: And "bonus"—what foot is it?

Student: The same as "modus."

Teacher: Then "modus" is the same thing as "bonus."

Student: No.

Teacher: Then why the same?

Student: Because they are the same in sound but different in meaning.

Teacher: So you grant that the sound is the same when we say "modus" and "bonus."

Student: As far as the sound of the letters goes I see that they differ, but in everything else they are equal.

Teacher: Now then, when we pronounce "pone" as a verb and "pone" as an adverb—apart from the difference in meaning, does the sound seem to you to differ at all?

Student: It differs entirely.

Teacher: Wherein does it differ, since both consist of the same time-units and the same letters?

Student: It differs in this, that they carry the accent on different syllables.

Teacher: And to what art, in the end, does it belong to discern such things?

Student: I am used to hearing these things from the grammarians, and that is where I learned them; but whether this is proper to that same art, or borrowed from elsewhere, I do not know.

Teacher: We will look into that later. For now I ask this: if I were to strike a drum or a string as quickly and rapidly as we say "modus" or "bonus," would you recognize that they had the same time-units, or not?

Student: I would recognize it.

Teacher: Then you would call it a pyrrhic foot.

Student: I would.

Teacher: And from whom did you learn the name of this foot, if not from the grammarian?

Student: I admit it.

Teacher: So will the grammarian be the judge of all sounds of this kind? Or did you learn these beats by yourself, and merely hear from the grammarian the name to give them?

Student: That is so.

Teacher: And did you dare to transfer the name that grammar taught you to a thing that you confess does not belong to grammar?

Student: I see that the name was given to the foot for no other reason than the measure of its time-units; so wherever I recognize that measure, why should I not dare to transfer the term to it? Yet even if other names must be given—when sounds have the same measure but do not belong to the grammarians—why should I trouble myself over names, when the thing is plain?

Teacher: Nor do I wish that. But still, when you see countless kinds of sounds in which fixed measures can be observed—kinds that, as we admit, are not to be assigned to the discipline of grammar—do you not think there is some other discipline that contains whatever is rhythmical and crafted in sounds of this kind?

Student: It seems probable to me.

Teacher: What do you suppose its name is? For I think it is not news to you that a certain all-power of song is usually granted to the Muses. This, unless I am mistaken, is what is called music.

Student: I think so too.

1. 2. 2. Teacher: But now let us decide to trouble ourselves not at all about the name. Let us simply inquire, if you please, as carefully as we can, into the whole power and account of this discipline, whatever it is.

Student: Let us inquire by all means; for I greatly desire to know all of this, whatever it is.

Teacher: Then define music.

Student: I do not dare.

Teacher: Can you at least approve my definition?

Student: I will try, if you state it.

Teacher: Music is the science of measuring well. Does it not seem so to you?

Student: It might seem so, perhaps, if it were clear to me what this "measuring" itself is.

Teacher: This word, "to measure" (modulari)—have you never heard it, or heard it anywhere except in connection with singing or dancing?

Student: That is indeed so. But because I see that "modulari" is derived from "modus" (measure), and that in all well-made things a measure must be kept—while many things in singing and dancing, however much they please, are utterly worthless—I want to grasp most fully what this "measuring" itself really is, since in this almost single word the definition of so great a discipline is contained. For what is to be learned here is not the sort of thing that any singers and stage-players know.

Teacher: That earlier point—that a measure must be kept even in things done outside of music, and yet that in music it is called "modulation"—need not trouble you, unless perhaps you are unaware that the delivery of an orator is properly called "diction" (dictio).

Student: I am aware of it; but where is this leading?

Teacher: To this: that even your servant, however unpolished and rustic, when he answers you with so much as a single word as you ask him a question—do you grant that he is saying something?

Student: I grant it.

Teacher: Is he, then, an orator?

Student: No.

Teacher: Then he did not use "diction" when he said something, although we grant that "diction" is derived from "saying" (dicere).

Student: I concede it; but I ask too where this is leading.

Teacher: To this, of course: that you may understand that "modulation" can belong to music alone, even though "measure," from which the word is bent, can be present in other things as well—just as "diction" is properly assigned to orators, although everyone who speaks says something, and "diction" is named from "saying."

Student: Now I understand.

1. 2. 3. Teacher: Then that point you made afterward—that there are many worthless things in singing and dancing, and that if we take the name of "modulation" to apply to them this almost divine discipline is cheapened—was observed by you very cautiously indeed. And so let us examine first what it is to measure, and then what it is to measure well; for it was not pointlessly added to the definition. Finally, the fact that "science" is set down there must not be slighted either; for by these three terms, unless I am mistaken, that definition is made complete.

Student: Let it be so.

Teacher: So, since we admit that "modulation" is named from "measure," does it seem to you that we need fear lest the measure be either exceeded or not fulfilled, except in things that come about by some motion? Or, if nothing is moved, can we dread that something may be done apart from measure?

Student: In no way.

Teacher: Then "modulation" is not unfittingly called a certain skill in moving, or at any rate that by which it comes about that something is moved well. For we cannot say that anything is moved well if it does not keep a measure.

Student: We cannot, indeed; but then we will be forced again to understand this "modulation" as present in all well-made things. For I see that nothing is well done except by moving well.

Teacher: What if perhaps all these things come about through music, even though the name of "modulation" is more in use—and not undeservedly—in instruments of every kind? For I believe it seems to you that one thing is some object turned on a lathe, of wood or silver or whatever material, and another the very motion of the craftsman when those things are being turned.

Student: I agree that they differ greatly.

Teacher: So is the motion itself sought for its own sake, and not for the sake of the thing that is to be turned on the lathe?

Student: That is clear.

Teacher: Again: if someone moved his limbs for no other reason than that they might be moved beautifully and gracefully, would we say he was doing anything but dancing?

Student: So it seems.

Teacher: When, then, do you judge that some thing excels and, as it were, holds the mastery—when it is sought for its own sake, or when for the sake of something else?

Student: Who denies that it is when it is sought for its own sake?

Teacher: Now take up again what we said earlier about modulation; for we had set it down as a kind of skill in moving. See where this name ought rather to have its seat: in that motion which is, as it were, free—that is, sought for its own sake and pleasing of itself—or in that which is in a way servile. For all things that do not exist for themselves but are referred to something else are, as it were, servile.

Student: In that one, of course, which is sought for its own sake.

Teacher: Then it is now probable that the science of measuring is the science of moving well, in such a way that the motion is sought for its own sake and on that account pleases of itself.

Student: Probable indeed.

1. 3. 4. Teacher: Then why was "well" added, since modulation itself cannot exist unless something is moved well?

Student: I do not know, and I cannot tell how it slipped away from me; for this question had stuck in my mind as something to be asked.

Teacher: There could be no controversy at all about this word, so that, removing the "well" that was set down, we would define music simply as the science of measuring.

Student: Who indeed would put up with it, if you wanted to unravel the whole thing that way?

Teacher: Music is the science of moving well. But because anything can already be said to be moved well that is moved rhythmically, keeping the measures of time-units and intervals (for it already pleases, and on this account is now not unfittingly called modulation), it can happen that this rhythm and measure pleases when it ought not—as when someone, singing most sweetly and dancing beautifully, wants for that very reason to be wanton when the matter calls for seriousness. He certainly is not using rhythmical modulation well; that is, he is using badly, that is unfittingly, the motion that can already be called good because it is rhythmical. Hence it is one thing to measure, another to measure well. For modulation is to be reckoned to belong to any singer who only does not err in those measures of voice and sound, but good modulation belongs to this liberal discipline, that is, to music. But if even that motion does not seem good to you, because it is inept—though you admit it is artfully rhythmical—let us hold to that principle of ours, to be kept everywhere, that a quarrel over a word may not torment us when the thing is clear enough; and let us not care at all whether music is described as the science of measuring or of measuring well.

Student: I do indeed love to pass over and despise quarrels of words; yet this distinction does not displease me.

1. 4. 5. Teacher: It remains for us to ask why "science" is in the definition.

Student: Let it be so; for I remember that the order demands this.

Teacher: Answer, then: does it seem to you that the nightingale measures its voice well in the spring part of the year? For that song is both rhythmical and most sweet, and, unless I am mistaken, it suits the season.

Student: So it certainly seems.

Teacher: Is it skilled in this liberal discipline?

Student: No.

Teacher: You see, then, that the word "science" is altogether necessary to the definition.

Student: I see it plainly.

Teacher: Tell me, then, I beg you: do not all those seem to you like that nightingale who, led by a kind of instinct, sing well—that is, do so rhythmically and sweetly—even though, when questioned about the numbers themselves, or about the intervals of high and low notes, they cannot answer?

Student: I think they are very much alike.

Teacher: And what of those who gladly listen to such singers without that science? Since we see elephants, bears, and several other kinds of beasts moved by song, and the very birds delighting in their own voices (for they would not do this so intently, without any external advantage in view, were there not some pleasure in it)—are they not to be compared to cattle?

Student: I think so; but this reproach reaches almost the whole human race.

Teacher: It is not as you think. For great men, even if they do not know music, either wish to accommodate the common people, who differ little from cattle and whose number is enormous—which they do most modestly and prudently (but this is not the place to discuss it now)—or, after great cares, for the sake of relaxing and restoring the mind, take some pleasure from these things most temperately. To enjoy such pleasure now and then is most modest; but to be captivated by it, even now and then, is base and unseemly.

1. 4. 6. Student: No.

Teacher: How, then, do they differ?

Student: In that in these people I see there is a certain art, but in the nightingale only nature.

Teacher: What you say is verisimilar; but does it seem to you that this is to be called art, even if they do it by a kind of imitation?

Student: Why not? For I see that imitation is so important in the arts that, if it were removed, almost all of them would perish. For teachers offer themselves to be imitated, and this very thing is what they call teaching.

Teacher: Does it seem to you that art is a kind of reason, and that those who use art use reason? Or do you think otherwise?

Student: It seems so.

Teacher: Whoever, then, cannot use reason does not use art.

Student: This too I concede.

Teacher: Do you think dumb animals, which are also called irrational, can use reason?

Student: In no way.

Teacher: Then either you will say that magpies, parrots, and crows are rational animals, or you have rashly called imitation by the name of art. For we see these birds sing and utter many things after a human fashion, and do so only by imitating—unless you believe otherwise.

Student: How you have brought this about, and how far it tells against my answer, I do not yet plainly understand.

Teacher: I had asked you whether you would say that lyre-players and flute-players, and other men of this kind, have an art, even if what they do in playing they attained by imitation. You said it was an art, and you affirmed that imitation is so important that, if it were removed, almost all the arts seemed to you to be in peril. From this it can now be gathered that everyone who attains something by imitating uses an art—even if perhaps not everyone who uses an art has learned it by imitating. But if all imitation is art, and all art is reason, then all imitation is reason. Yet an irrational animal does not use reason; therefore it does not have art. But it has imitation; therefore imitation is not art.

Student: I said that many arts consist of imitation; I did not call imitation itself an art.

Teacher: The arts, then, that consist of imitation—do you not judge that they consist of reason?

Student: On the contrary, I think they consist of both.

Teacher: I do not object; but in which do you place science—in reason, or in imitation?

Student: This too in both.

Teacher: Then you will grant science to those birds from which you do not withhold imitation.

Student: I will not grant it; for I said that science is in both in such a way that it cannot be in imitation alone.

Teacher: Well then, does it seem to you that it can be in reason alone?

Student: It seems so.

Teacher: Then you think that art is one thing and science another, since science can be in reason alone, but art joins imitation to reason.

Student: I do not see that this follows. For I had said that not all the arts, but many, consist of reason and imitation together.

Teacher: Well then, will you also call "science" that which consists of these two together, or will you attribute to it only the part that is reason?

Student: For what prevents me from calling it science, when imitation is joined to reason?

1. 4. 7. Teacher: Since we are now treating of the lyre-player and the flute-player, that is, of musical matters, I want you to tell me whether what these men do by imitation is to be attributed to the body—that is, to a certain compliance of the body.

Student: I think it is to be attributed to mind and body together—though the very word you used is set down quite properly, when you called it a compliance of the body; for the body can comply with nothing but the mind.

Teacher: I see that you very cautiously refused to grant imitation to the body alone. But will you deny that science belongs to the mind alone?

Student: Who would deny it?

Teacher: Then in no way will you be allowed to attribute the science in the sounds of strings and flutes to reason and imitation together. For that imitation, as you confessed, is not without the body, whereas you said that science belongs to the mind alone.

Student: From what I have conceded to you, I admit that this is established; but what of it? For the flute-player too will have science in his mind. For when imitation, which I granted cannot be without the body, is added to him, it will not take away what he embraces with his mind.

Teacher: It will not take it away, indeed; nor do I affirm that all who handle these instruments lack science, but I say that not all have it. For we have turned this question over in order to understand, if we can, how rightly science is set in that definition of music; and if all flute-players and lyre-players, and any others of that kind, have it, then I think nothing is cheaper than this discipline, nothing more abject.

1. 4. 8. Student: Why should I not grant it?

Teacher: Now then: do you grant the sense of hearing to the mind, to the body, or to both?

Student: To both.

Teacher: And memory?

Student: I think it is to be attributed to the mind. For even if we perceive through the senses something that we commit to memory, memory is not on that account to be thought to be in the body.

Teacher: This is perhaps a great question, and not suited to the present discussion. But what is enough for our purpose is this: I think you cannot deny that beasts have memory. For swallows return to their nests after a year, and of the she-goats it was most truly said, and the she-goats themselves, remembering, return to their stalls. And the dog is recorded to have recognized its hero-master when his own household had already forgotten him. And we could note countless instances, if we wished, by which what I say is plain.

Student: I do not deny it either, and I am keenly waiting to see how it helps you.

Teacher: In nothing else than this: that whoever attributes science to the mind alone, and withholds it from all irrational animals, has placed it neither in sense nor in memory (for the one is not without the body, and both are present even in a beast), but in the understanding alone.

Student: This too I wait to see how it helps you.

Teacher: In nothing else than this: that all who follow the senses, and commit to memory what pleases in them, and, moving the body accordingly, add a certain power of imitation, do not have science—however skillfully and learnedly they seem to do many things—if they do not hold the very thing they profess or display in the purity and truth of the understanding. But if reason shows that these stage-workers are of this kind, there will be, I think, no reason for you to hesitate to deny them science, and on this account by no means to grant them music, which is the science of measuring.

Student: Unfold this; let us see what sort of thing it is.

1. 4. 9. Teacher: The quicker or slower nimbleness of the fingers, I believe, you would assign not to science but to practice.

Student: Why do you believe that?

Teacher: Because earlier you attributed science to the mind alone, whereas this, though commanded by the mind, you see belongs nevertheless to the body.

Student: But since it is the knowing mind that commands this of the body, I think it should be attributed rather to the knowing mind than to the serving limbs.

Teacher: Do you not judge that it can happen that one man surpasses another in science, while that less skilled man moves his fingers far more easily and readily?

Student: I do.

Teacher: But if the quick and ready motion of the fingers had to be attributed to science, each man would excel in it just so far as he was more knowing.

Student: I concede it.

Teacher: Note this too. For I suppose you have sometimes observed carpenters, or workmen of that kind, striking the same spot again and again with an adze or an axe, and bringing the blow nowhere but where the mind intends; and when we try this and cannot manage it, they often laugh at us.

Student: It is as you say.

Teacher: So, when we cannot do this, are we ignorant of what ought to be struck, or how much ought to be cut away?

Student: Often we are ignorant of it, often we know it.

Teacher: Suppose, then, that someone knows everything carpenters ought to do, and knows it perfectly, yet has less skill in the work itself, but can dictate many things to those very men who work most easily, more shrewdly than they could judge by themselves—do you deny that this happens by practice?

Student: I do not deny it.

Teacher: Then not only the speed and ease of moving, but even the very manner of motion in the limbs, is to be attributed to practice rather than to science. For if it were otherwise, each man would use his hands the better the more skilled he was—a thing we may refer to flutes and lyres as well, lest we suppose that what the fingers and joints do there, because it is difficult for us, comes about by science rather than by practice and diligent imitation and exercise.

Student: I cannot resist; for I too am accustomed to hear that physicians, most learned men, are often surpassed by the less skilled in cutting, or in some way compressing, limbs—in what is done by hand and knife. This kind of treatment they call surgery, a word that signifies well enough a certain manual, workmanlike practice of healing. Go on, then, to the rest, and now finish this question.

1. 5. 10. Teacher: This remains, I think: that we find, if we can, that these very arts which please us through the hands—so that they were masters of that practice—followed not science directly, but sense and memory. So you may not perhaps tell me that it can indeed happen that science is present without practice, and often greater than it is in those who excel in practice; but that even those men could not have come merely to that practice without any science.

Student: Proceed; for it is clear that this is owed.

Teacher: Have you never listened to stage-players of this kind rather attentively?

Student: More, perhaps, than I would wish.

Teacher: How do you think it comes about that the unskilled crowd often hisses a flute-player who puts forth trifling sounds, and again applauds one who plays well—and indeed is moved the more, and the more eagerly, the more sweetly the playing is done? Must we believe that the common people do this through the art of music?

Student: No.

Teacher: How then?

Student: I think it comes about by nature, which has given to all the sense of hearing by which these things are judged.

Teacher: You think rightly. But now see this too: whether the flute-player himself is also endowed with this sense. If so, his judgment, following it, can move his fingers when he has breathed into the flute, and note whatever has sounded conveniently enough to his liking and commit it to memory, and by repeating it accustom his fingers to be carried there without any trembling or error—whether he receives from another what he is to play, or finds it himself, with nature, of which we have spoken, leading and approving. And so, when memory follows sense, and the joints follow memory, now tamed and prepared by practice, he plays when he wishes the better and more pleasantly the more he surpasses in all those things which reason taught us above we have in common with beasts: namely the appetite for imitating, sense, and memory. Have you anything to say against this?

Student: I have nothing. Now I desire to hear what sort of discipline that is which I see has been most subtly vindicated from the knowledge of the basest minds.

1. 6. 11. Teacher: What has been done is not yet enough, and I will not let us pass on to its explanation, unless—just as we have agreed that stage-players can satisfy the pleasure of popular ears without this science—it is likewise established that there can in no way be stage-players who are students of music and skilled in it.

Student: It would be wonderful if you brought this about.

Teacher: Easily indeed; but I need you to be more attentive.

Student: For my part I have never, so far as I know, been more remiss in listening since this conversation took its start; but now, I admit, you have made me much more alert.

Teacher: I am grateful—though you do yourself the greater favor. So answer, if you please: does it seem to you that a man knows what a gold solidus is, if, wishing to sell it at a fair price, he reckons it to be worth ten coins?

Student: To whom would it seem so?

Teacher: Now come, tell me, which is to be held the more precious: what is contained in our own understanding, or what is granted to us by chance through the judgment of the unskilled?

Student: There is no doubt for anyone that the former far excels all the rest—things which are not even to be thought our own.

Teacher: Then do you deny that all science is contained in the understanding?

Student: Who denies it?

Teacher: And so music too is there.

Student: I see that this follows from its definition.

Teacher: And the applause of the people and all those theatrical rewards—do they not seem to you to be of that kind which is set in the power of fortune and the judgment of the unskilled?

Student: I judge that nothing is more fortuitous and exposed to chance, and more subject to the dominion and whims of the mob, than all those things.

Teacher: Then would stage-players sell their songs at this price, if they knew music?

Student: I am moved not a little by this conclusion, but I have something to object. For that seller of the solidus does not seem comparable to the player; for the player, on receiving applause or whatever money is lavished on him, does not lose the science—if he happens to have any—by which he delighted the people, but goes home heavier by a coin and gladder for men's praise, with that same discipline safe and whole. He would be a fool, indeed, to despise those advantages, without which he would be much more obscure and poorer, while having gained them he would be no less learned.

1. 6. 12. Teacher: See, then, whether by this very point we establish what we want. For I believe it seems to you that the thing for the sake of which we do something is much more excellent than the very thing we do.

Student: That is clear.

Teacher: He, then, who sings or learns to sing for no other reason than to be praised by the people, or by any man at all—does he not judge that the praise is better than the song?

Student: I cannot deny it.

Teacher: And the man who judges badly about some thing—does he seem to you to know it?

Student: In no way, unless perhaps he is in some way corrupted.

Teacher: Then he who truly thinks that something better which is worse, beyond all doubt lacks science of it.

Student: That is so.

Teacher: When, therefore, you have either persuaded me or shown me that any stage-player has gained or displays whatever ability he has, not in order to please the people for the sake of gain or fame, I will grant that someone can both have the science of music and be a stage-player. But if it is most probable that there is no stage-player who does not set and propose to himself the end of his profession in money or glory, you must admit either that stage-players do not know music, or that praise—and whatever other fortuitous advantages there are—is more to be sought from others than understanding from ourselves. [And because they seek praise and advantages from others and do not seek understanding from us, since they prefer what is cheaper to what is more precious, it is clear that they do not have the science of it.]

Student: I see that, having conceded the earlier points, I must yield to these as well. For it can in no way seem to me that such a man could be found on the stage—one who loves his art for its own sake and not for advantages laid up outside it—when scarcely such a man is found in the gymnasium; although, if any such person exists or has existed, then it is not that the musicians are to be despised, but that the stage-players might sometimes seem worthy of honor. So now, if you please, unfold this great discipline, which can no longer seem cheap to me.

1. 7. 13. Teacher: I will do it—or rather you will do it. For I will do nothing but ask and question you; and you, by answering, will unfold this whole thing, whatever it is, which you now seem to seek without knowing it. So now I ask you: can anyone run both for a long time and swiftly?

Student: He can.

Teacher: And both slowly and swiftly?

Student: In no way.

Teacher: Then "long" is one thing, "slow" another.

Student: Quite another.

Teacher: Likewise I ask what you think is contrary to length of time, as swiftness is to slowness.

Student: No customary word comes to me. So I see nothing to set against "long-lasting" except "not long-lasting," so that the contrary of what is called "long" is "not long"—since if I were unwilling to say "swiftly," and said "not slowly" instead, nothing else would be meant.

Teacher: You speak truly. For nothing of the truth is lost when we speak this way. For even if there is such a word as you say did not come to you, either it is unknown to me, or it does not come to mind at present. So let us proceed by calling these two pairs of contraries in this way: "long" and "not long," "slow" and "swift." And first let us discuss the long-lasting and the not-long-lasting, if you please.

Student: Let it be so.

1. 8. 14. Teacher: Is it clear to you that what is done over a long time is said to be done "long," and what is done over a short time "not long"?

Student: Clear.

Teacher: A motion, then, that is done, for example, in two hours—does it not have twice the time of one that is done in a single hour?

Student: Who would doubt this?

Teacher: Then what we call "long" or "not long" admits of measures and numbers of this kind, so that one motion is to another as two to one—that is, so that one has twice as much as the other has once; another likewise to another as three to two, that is, so that it has three parts of time for the other's two. And so one may run through the remaining numbers, so that the spans are not indefinite and undetermined, but two motions hold to each other some number: either the same, as one to one, two to two, three to three, four to four; or not the same, as one to two, two to three, three to four; or one to three, two to six, and whatever measure anything can hold to itself.

Student: Make this plainer, I beg.

Teacher: Return, then, to those hours, and what I thought was said enough when I had spoken of one hour and of two, consider it throughout. For surely you do not deny that some motion can be made in the time of one hour, and another in two.

Student: It is true.

Teacher: And do you not admit that one is of two hours, another of three?

Student: I admit it.

Teacher: And is it not clear that one is made in three hours, another in four; and again one in one, another in three; or one in two, another in six?

Student: It is clear.

Teacher: Then why should that other point not also be clear? For this is what I was saying when I said that two motions can hold to each other some number, as one to two, two to three, three to four; one to three, two to six, and any others you may wish to count. For once these are known, it is within one's power to pursue the rest, whether seven to ten, or five to eight, and whatever there is at all in two motions having their parts measured against each other in such a way that they can be said to be so-many to so-many—whether the numbers are equal, or one greater and the other less.

Student: Now I understand, and I concede that it can be so.

1. 9. 15. Teacher: This too, I think, you understand: that every measure and limit is rightly to be preferred to immoderateness and the infinite.

Student: It is most clear.

Teacher: Two motions, then, which hold to each other, as has been said, some numerical measure, are to be preferred to those which do not have it.

Student: This too is clear and follows; for those motions a certain fixed limit, and the measure that is in numbers, joins to each other—whereas those that lack it are surely not joined to each other by any rational principle.

Teacher: Let us call, then, if you please, those that are measured against each other "rational," and those that lack that measure "irrational."

Student: I agree.

Teacher: Now consider this: whether there seems to you to be greater concord among rational motions in those that are equal to each other than in those that are unequal.

Student: To whom would it not seem so?

Teacher: Further, among unequal motions, are there not some in which we can say by what fraction of itself the greater either equals the lesser or exceeds it—as two and four, or six and eight—and others in which the same cannot be said, as in these numbers, three and ten, or four and eleven? You surely see that in those two former numbers the greater equals the lesser by half of itself; in those again that I named afterward, the lesser is exceeded by the greater by a fourth part of the greater; but in these others, such as three and ten, or four and eleven, we do see some agreement, because they have parts of which it can be said "so-many to so-many"—but is it such as is in the former? For one cannot say in any way by what fraction the greater equals the lesser, nor by what fraction the greater exceeds the lesser. For no one could say what fraction of ten three is, nor what fraction of eleven four is. And when I tell you to consider what fraction it is, I mean a clean fraction, without any addition—such as a half, a third, a fourth, a fifth, a sixth, and so on; not so that thirds-of-an-ounce, half-ounces, and that kind of fractional cut be added.

Student: Now I understand.

1. 9. 16. Teacher: Then, of these unequal rational motions—since I have set forth two kinds, with numerical examples added—which do you judge are to be preferred to which: those in which that clean fraction can be named, or those in which it cannot?

Student: Reason seems to me to command that those be preferred in which it can be said, as was shown, by what fraction of itself the greater either equals the lesser or exceeds it, to those in which the same does not happen.

Teacher: Rightly. But do you also wish us to give these names, so that when it is afterward necessary to mention them we may speak more readily?

Student: I do indeed wish it.

Teacher: Let us then call those we prefer "co-numbered" (connumerati), and those to which we prefer them "out-numbered" (dinumerati): because the former not only are counted singly, but also measure and count themselves by that part by which the greater equals the lesser or exceeds it; whereas the latter are merely counted against each other one by one, but by that part by which the greater equals or exceeds the lesser they do not measure and count themselves. For in them one cannot say either how many times the greater contains the lesser, or how many times both the greater and the lesser contain that by which the greater exceeds the lesser.

Student: I accept these terms too, and, as far as I can, I will see that I remember them.

1. 10. 17. Teacher: Come now, let us see what division can be made of the co-numbered; for I judge it is evident. There is one kind of co-numbered in which the lesser number measures the greater—that is, the greater contains it some number of times, as we said the numbers two and four are: for we see that two is contained in four twice; it would be contained three times if we set against two not four but six, four times if eight, five times if ten. There is another kind, in which that part by which the greater exceeds the lesser measures both—that is, both the greater and the lesser contain it some number of times, which we have already seen in those numbers six and eight. For that part by which the lesser is exceeded is two, which you see is in the number eight four times, in the number six three times. So let us mark these motions too, which we are treating, and the numbers by which what we wish to learn in motions is illustrated, and signify them by names. For their distinction has already, unless I am mistaken, become apparent. Therefore, if it now seems good to you, let those in which the greater is made by multiplying the lesser be called "multiplied" (complicati); but the others, by an old name now, "sesquate" (sesquati). For it is called "sesqui" where two numbers are so related to each other that the greater has toward the lesser as many parts as the fraction of itself by which it goes beyond it: for if it is three to two, the greater goes beyond the lesser by a third of itself; if four to three, by a fourth; if five to four, by a fifth, and so on. The same principle holds in six to four, eight to six, ten to eight; and from there one may observe and explore this principle both in the following and in the larger numbers. The origin of this name I could not easily state—unless perhaps "sesqui" is said as though "se absque," that is, "apart from itself," because five to four is, apart from its fifth part, what the lesser is. On these matters I ask what seems to you.

Student: To me both that account of the measures and numbers seems most true, and the terms you have given seem to me fitting for recalling the things we have understood; and the origin of this name that you have now explained is not absurd, even if perhaps it was not the one that he followed who established the name.

1. 11. 18. Teacher: I approve and accept your view. But do you see that all these rational motions—that is, those that hold to each other some numerical measure—can go on through numbers to infinity, unless again a fixed principle restrains them and recalls them to a certain measure and form? For, to speak first of the equal ones themselves: one to one, two to two, three to three, four to four, and so on if I pursue it—what end will there be, since there is no end of number itself? For this power is in number, that every number named is finite, but unnamed it is infinite. And what happens with equal motions you can observe happening with unequal ones too, whether multiplied, or sesquate, or co-numbered, or out-numbered. For if you set one to two, and wish to remain in that multiplication, saying one to three, one to four, one to five, and so on, there will be no end; or if doubles alone, as one to two, two to four, four to eight, eight to sixteen, and so on, here too there is no end; and so triples alone, and quadruples alone, and whatever of these you wish to try, go on to infinity. So too the sesquate: for when we say two to three, three to four, four to five, you see nothing prevents pursuing the rest, with no end resisting—whether you wish to persevere in the same kind in this way, as two to three, four to six, six to nine, eight to twelve, ten to fifteen, and so on; in this kind, or in the others, no end occurs. What need is there now to speak of the out-numbered, when from what has already been said anyone can understand that in these too, rising step by step, there is no end? Or does it not seem so to you?

1. 11. 19. Student: What could be said truer than this? But now I most eagerly await to learn that principle which recalls this infinity to a fixed measure and prescribes a form that ought not to be exceeded.

Teacher: This too, like the rest, you will recognize that you yourself know, when you have answered truly to my questions. For first I ask you—since we are treating of rhythmical motions—whether we ought to consult the numbers themselves, so that whatever fixed and settled laws they show us, we may judge that these are to be observed and watched for in those motions.

Student: I agree indeed; for I think nothing can be done more orderly.

Teacher: Then let us take the start of this consideration, if you please, from the very beginning of numbers, and see—as far as the strength of our mind allows us to behold such things—what the principle is by which, although number proceeds through the infinite, as has been said, men have nevertheless made certain joints in counting, from which they return again to one, which is the beginning of numbers. For in counting we proceed from one up to ten, and from there return to one; and if you wish to pursue the multiplication by ten, so as to proceed in this way—ten, twenty, thirty, forty—the progression goes up to a hundred; if by the hundred—a hundred, two hundred, three hundred, four hundred—the joint at which one turns back is a thousand. What need is there now to seek further? You surely see what joints I mean, whose first rule is prescribed by the number ten. For as ten has one ten times, so a hundred has those same ten ten times, and a thousand has a hundred ten times; and so on, as far as one pleases to proceed, it will go in joints of this kind, as was predetermined in the number ten. Or do you not understand some of this?

Student: All is most clear, and most true.

1. 12. 20. Teacher: Let us then examine, as carefully as we can, what the principle is by which the progression from one up to ten, and from there the return again to one, comes about. So I ask you whether what we call a beginning can be the beginning of anything at all except of something.

Student: In no way can it.

Teacher: Likewise, what we call an end—can it be the end of anything except of something?

Student: This too it cannot.

Teacher: And do you think one can come from a beginning to an end except through some middle?

Student: I do not think so.

Teacher: So, for anything to be a whole, it consists of a beginning, a middle, and an end.

Student: So it seems.

Teacher: Tell me now, then, by what number a beginning, a middle, and an end seem to you to be contained.

Student: I judge that you want me to answer "three"; for there are three things you ask about.

Teacher: You judge rightly. So you see that there is a certain perfection in the number three, because it is whole; for it has a beginning, a middle, and an end.

Student: I see it plainly.

Teacher: And did we not learn from earliest childhood that every number is either even or odd?

Student: You speak truly.

Teacher: Recall, then, and tell me which we are accustomed to call an even number, and which an odd one.

Student: The one that can be divided into two equal parts is called even; the one that cannot, odd.

1. 12. 21. Teacher: You have it. Since, then, three is the first whole odd number—for it consists, as was said, of a beginning, a middle, and an end—must there not also be an even number that is whole and perfect, in which likewise a beginning, a middle, and an end are found?

Student: There must be indeed.

Teacher: But this number, whatever it is, cannot have an indivisible middle as the odd number has; for if it had, it could not be divided into two equal parts, which we said is proper to an even number. Now an indivisible middle is one, a divisible middle is two. And the middle in numbers is that from which both sides are equal to each other. Or has something been said obscurely, and you do not quite follow?

Student: On the contrary, these things too are clear to me; and as I seek a whole even number, four occurs to me first. For in two, how can those three things be found by which a number is whole—that is, a beginning, a middle, and an end?

Teacher: You have answered the very thing I wished, and what reason itself compels us to admit. So take up the treatment again from one itself, and consider; you will surely see that one has no middle and end precisely because it is only a beginning—or rather that it is a beginning because it lacks a middle and an end.

Student: It is clear.

Teacher: What, then, shall we say of two? Can we understand in it a beginning and a middle, since there cannot be a middle except where there is an end? Or a beginning and an end, since one cannot come to an end except through a middle?

Student: Reason presses me to confess it; and what to answer about this number I am quite uncertain.

Teacher: See whether this number too may be a beginning of numbers. For if it lacks a middle and an end—which, as you said, reason compels us to confess—what remains but that this too is a beginning? Or do you hesitate to set up two beginnings?

Student: I hesitate strongly.

Teacher: You would do well, if the two beginnings were set up over against each other; but as it is, this second beginning derives from that first one, so that the first is from nothing, while this is from the first. For one and one are two, and both are beginnings in this way: that all numbers indeed are from one, but because they come about through a kind of multiplication and joining, while the origin of multiplication and joining is rightly attributed to the number two—so it comes about that the first is found to be that beginning from which all numbers are, and the second that through which all numbers are. Unless you have something to argue against this.

Student: I have nothing; and I do not think on these things without wonder, although it is I who answer them when questioned by you.

1. 12. 22. Teacher: These things are inquired into more subtly and more deeply in the discipline that concerns numbers; but here let us return, as quickly as we can, to the work we set out to do. So I ask: two joined to one, what do they make?

Student: Three.

Teacher: Then these two beginnings of numbers, joined to each other, make a number that is whole and perfect.

Student: That is so.

Teacher: And what number do we set down in counting after one and two?

Student: That same three.

Teacher: The same number, then, which is made from one and two, is placed after both in order, so that no other can be set between.

Student: So I see.

Teacher: But you ought also to see that this can happen with none of the remaining numbers: that when you have marked any two numbers joined to each other in the order of counting, the one made from both should follow them with nothing set between.

Student: I see this too: for two and three, which are numbers joined to each other, make five in sum; yet five does not follow immediately, but four. Again, three and four make seven; but between four and seven, five and six are set in order. And the further I wish to go, the more are set between.

Teacher: Great, then, is this concord in the first three numbers: for we say one, two, and three, between which nothing can be set; and one and two are themselves three.

Student: Great indeed.

Teacher: And do you think this worthy of no consideration: that the tighter and closer this concord is, the more it tends toward a certain unity, and makes some one thing out of many?

Student: On the contrary, of the greatest; and somehow I both wonder at and love this unity that you commend.

Teacher: I much approve; but surely any coupling and connection of things makes some one thing most of all when both the middle agrees with the extremes and the extremes with the middle.

Student: So it must certainly be.

1. 12. 23. Teacher: Attend, then, so that we may see this in that connection. For when we say one, two, three, is not one surpassed by two by just as much as two is surpassed by three?

Student: It is most true.

Teacher: Tell me now, in this comparison, how many times have I named one?

Student: Once.

Teacher: Three, how many times?

Student: Once.

Teacher: And two?

Student: Twice.

Teacher: Once, then, and twice, and once—how many does that make in sum?

Student: Four.

Teacher: Rightly, then, does the number four follow those three; for to it is assigned this comparison by such proportion. How much this proportion is worth, you may begin to learn from this: that the unity which you said you love can, in ordered things, be brought about by this one thing, whose Greek name is "analogia"; some of our writers have called it "proportion" (proportio)—let us use that word, if you please, for I would not willingly, except by necessity, use Greek terms in Latin speech.

Student: It pleases me indeed; but go on where you had intended.

Teacher: I will. For what proportion is, and how much authority it has in things, we will inquire more carefully in its place in this discipline; and the further advanced you are in learning, the better you will know its power and nature. But you surely see—which for the present is enough—that those three numbers, whose concord you wondered at, could not be brought together in that same connection except through the number four. Therefore, that it should be set in order after them, so that that concord may be coupled more closely with these, you understand, has rightly been won; so that now there is not merely one, two, three, but one, two, three, four—a most amicably coupled progression of numbers.

Student: I agree entirely.

1. 12. 24. Teacher: But look at the rest, lest you suppose that the number four has nothing of its own, lacking to all the remaining numbers, that avails for this connection of which I speak—so that from one up to four there is a fixed number and a most beautiful manner of proceeding. For we had agreed earlier that one thing is made most of all from many when the middle agrees with the extremes and the extremes with the middle.

Student: That is so.

Teacher: When, then, we set down one and two and three, tell me what are the extremes and what is the middle.

Student: I see that one and three are the extremes, two the middle.

Teacher: Now answer: what is made from one and three?

Student: Four.

Teacher: And two, which is the single number in the middle—can it be compared except with itself? So tell me also what two twice makes.

Student: Four.

Teacher: So the middle agrees with the extremes, and the extremes with the middle. Therefore, just as three excels in this, that it is set after one and two, while consisting of one and two, so four excels in this, that it is counted after one and two and three, while consisting of one and three, or twice two: which is the agreement of the extremes with the middle, and of the middle with the extremes, in that which in Greek is called "proportion." Show whether you have understood this.

Student: I understand well enough.

1. 12. 25. Teacher: Try it, then, in the remaining numbers, whether what we said is proper to the number four is found there.

Student: I will. For if we set down two, three, four, the extremes compared make six; the middle compared with itself makes the same; yet not six, but five follows. Again I set down three, four, and five; the extremes make eight, and the middle taken twice as well; but between five and eight I see not one number now, but two—six and seven—set between. And by that same reckoning, the further I go, the larger these intervals become.

Teacher: I see that you have understood, and altogether know what has been said. But now, lest we linger, you surely observe that from one up to four a most just progression is made—whether because of the odd and the even number, since the first whole odd number is three and the first whole even number is four, as was treated a little before; or because one and two are beginnings, and as it were the seeds of numbers, from which three is made, so that there are now three numbers, which, when compared to one another in proportion, cause four to shine forth and be begotten, and is therefore rightly joined to them, so that up to it there is made that moderate progression which we seek.

Student: I understand.

1. 12. 26. Teacher: Well indeed. But do you remember at last what we had set out to inquire? For, I think, the question proposed was whether we could somehow find—since, in that infinity of numbers, fixed joints were established for those who count—what the cause was that the very first joint was in the number ten, which has the greatest force through all the rest; that is, why those who count, having proceeded from one up to ten, return again to one.

Student: I clearly recall that for the sake of this question we have gone about so much; but what we have accomplished that bears on solving it, I do not find. For all that reasoning of ours was concluded to this: that the just and moderate progression is not up to ten, but up to four.

Teacher: Then do you not see what sum is made from one and two and three and four?

Student: Now I see, I see, and I wonder at it all, and I confess that the question that arose has been solved: for one and two and three and four together are ten.

Teacher: Then it is fitting that those four first numbers, and their series and connection, be held more honorable than the rest among numbers.

1. 13. 27. Student: I can in no way deny it.

Teacher: What if someone were to clap rhythmically, so that one beat holds a single time-unit and another a double—the feet they call iambs—and were to continue and weave them together; while another danced to the same beat, moving his limbs according to those time-units? Would you not either even state the very measure of the time-units—that is, that in the motions the spans of single and double alternate, whether in that clapping which is heard or in that dancing which is seen—or at least take pleasure in the rhythm that you feel, even if you could not state the numbers of its measure?

Student: It is indeed as you say: for those who know these numbers feel them in the clapping and dancing, and readily say which they are; and those who do not know them and cannot name them do not deny, all the same, that they enjoy some pleasure from them.

1. 13. 28. Teacher: Since, then, it cannot be denied that to the very principle of this discipline—if indeed it is the science of measuring well—all motions belong that are well measured, and especially those that are not referred to anything else but keep in themselves the end of their beauty or delight; yet these motions, as you have now rightly and truly said in answer to me, if they are made over a long span of time, and in that very measure which is beautiful take up an hour or even more, cannot suit our senses. [Although the same foot in singing, the principle of comparison being kept, can sometimes be made with longer, sometimes with shorter, sounds.] Therefore, since music, proceeding in a way from its most hidden inner shrine, has placed certain traces even in our senses, or in the things that are perceived by us, must we not first pursue those very traces, so that we may be led more conveniently, if we can, and without any error, to that inner shrine of which I spoke?

Student: We must indeed; and I beg that we do so right now.

Teacher: Let us, then, leave aside those bounds of time stretched beyond the capacity of our sense, and discuss, as far as reason leads us, these short spans of intervals that charm us in singing and dancing. Unless perhaps you think those traces can be tracked in some other way, which, as has been said, this discipline has placed in our senses and in the things we are able to perceive.

Student: I think there is no other way at all.

2. 1. 1. Teacher: Attend carefully, then, and now at last receive, as it were, another beginning of our discussion. And first answer: whether you have learned well the distinction of short and long syllables that the grammarians teach; or whether—whether you know it or not—you would rather have us inquire as though we were wholly unschooled in these matters, so that reason may lead us to everything, rather than ingrained habit or prejudged authority compel us.

Student: I am clearly driven to prefer that, not only by reason itself, but also by my own inexperience in these syllables—for why should I hesitate to admit it?

Teacher: Come now, at least say this: whether you yourself have never on your own noticed that in our speech some syllables are uttered rapidly and very briefly, others more drawn out and at greater length.

Student: I cannot deny that I have not been deaf even to this.

Teacher: Now I would have you know that the whole of that knowledge which in Greek is called "grammar" and in Latin "literature" professes to be the guardian of records—either that alone, as the subtler reasoning teaches, or chiefly so, as even dull minds grant. So, for example, when you say "cano," or perhaps place it in a verse in such a way that you either lengthen the first syllable of this word in pronouncing it, or set it in a place in the verse where it ought to have been lengthened, the grammarian—that guardian of records, of course—will censure you, asserting no other reason why it ought to be shortened than that those who lived before us, whose books survive and are studied by the grammarians, used it short and not long. Here, then, whatever has force, the force of authority has. But the principle of music, to which the rational measuring of sounds and their rhythm belongs, does not care, except that a syllable that is in this or that place be shortened or lengthened according to the principle of its own measures. For if you set this word in the place where it is fitting to put two long syllables, and make the first, which is short, long in pronunciation, music takes no offense at all; for the time-units of the sounds that reached the ears were those that were owed to that rhythm. But the grammarian bids it be corrected, and bids you set there a word whose first syllable should be lengthened, according to the authority of our forebears, as was said, whose writings he guards.

2. 2. 2. Student: Very often indeed, so much so that I have almost never heard a verse without delight.

Teacher: If, then, someone, in a verse you delight to hear, were to lengthen or shorten syllables in a place where the principle of that same verse does not require it, could you be delighted in the same way?

Student: On the contrary, I cannot hear this without offense.

Teacher: There is, then, no doubt at all that, in the sound by which you say you are delighted, it is a certain measuring of numbers that delights you, and that, when this is disturbed, that delight cannot be presented to the ears.

Student: It is manifest.

Teacher: Tell me next, as far as the sound of the verse is concerned, what difference it makes whether I say Arma virumque cano, Troiae qui primus ab oris or qui primis ab oris.

Student: To me, indeed, both sound the same, as far as that measuring is concerned.

Teacher: But this came about by my pronunciation, with that fault, of course, which the grammarians call a barbarism. For "primus" is a long and a short syllable, whereas in "primis" both must be lengthened; but I shortened the last of them, so that your ears suffered no deception. Therefore it must be tried again and again, whether you can perceive, as I pronounce, what "long" and "not long" in syllables is, so that our discussion may proceed, by my asking and your answering, as we have set out. So now I will repeat the same verse in which I made the barbarism, and that syllable which I shortened—lest your ears be offended—I will lengthen, as the grammarians bid; and you report back to me whether that measuring of the verse affects your sense with the same pleasure. Thus let me pronounce it: Arma virumque cano, Troiae qui primis ab oris.

Student: Now indeed I cannot deny that I was offended by some misshapenness of sound, I know not what.

Teacher: Not without reason; for although no barbarism has been made, yet that fault has been made which both grammar and music censure: grammar, because that word, whose last syllable must be lengthened, was set in a place where one to be shortened ought to have been put; but music, only because some sound was lengthened in a place where it ought to have been shortened, and the time-unit owed, which the rhythmical measuring demanded, was not rendered. Therefore, if you now discern well enough what sense demands and what authority demands, it follows that we see why that very sense is sometimes delighted in sounds, whether lengthened or shortened, and sometimes offended; for this is what pertains to "long" and "not long." This is the part, I believe you remember, that we undertook to explain.

Student: I have both discerned that and I remember this, and I await most attentively what follows.

2. 3. 3. Teacher: What do you think follows, except that we begin to compare syllables with one another, and see what numbers they have toward each other—just as we treated of motions above, between us, at such length? For everything that sounds is also in motion; and syllables certainly sound. Or can any of this be denied?

Student: In no way.

Teacher: When, then, syllables are compared with one another, certain motions are compared with one another, in which certain numbers can be sought by the measure of their length of time.

Student: That is so.

Teacher: Can one syllable, then, be compared with itself? For singleness, unless you think otherwise, escapes all comparison.

Student: I think nothing otherwise.

Teacher: But do you deny that one can be compared with one, or one or two with two or three, and so on with more?

Student: Who would deny this?

Teacher: See this again: that any short syllable, pronounced briefly and for the least time, and ending as soon as it has burst forth, nevertheless takes up some span of time, and has a certain little duration of its own.

Student: I see that what you say is necessary.

Teacher: Tell me now, from what shall we begin number?

Student: From one, of course.

Teacher: Not absurdly, then, did the ancients call this least span of time, which a short syllable takes up, one time-unit; for we proceed from the short to the long.

Student: It is true.

Teacher: It follows now that you notice this too: since, as in numbers the first progression is from one to two, so in syllables, by which we proceed from the short to the long, the long ought to have double the time-units; and through this, if the span the short takes up is rightly called one time-unit, then the span the long takes up is rightly named two time-units.

Student: Quite rightly; for I agree that reason demands this.

2. 4. 4. Teacher: Come, now let us look at the comparisons themselves; for I ask what relation one short syllable seems to you to have to one short syllable, or what these motions are called among themselves. For you remember, unless I am mistaken, that in the earlier discussion we gave names to all motions that agree with one another by some rhythm.

Student: I remember that they were named equal; for they have the same amount of time to each other.

Teacher: But this comparison of syllables, by which they are now compared so as to have some numbers toward each other—do you think it is to be left without a name?

Student: I do not think so.

Teacher: Now know that the ancients called such a comparison of sounds a "foot." But how far reason allows the foot to proceed must be carefully observed. So tell me also: by what relation are a short and a long syllable compared to each other?

Student: I think this comparison flows from that kind of numbers which we called "multiplied"; for in it I see that single is compared to double—that is, the one time-unit of the short syllable to the two time-units of the long syllable.

Teacher: What if they are so ordered that the long is pronounced first, then the short? Does the principle of multiplied numbers not remain, just because the order has been changed? For as in that foot single is found toward double, so in this double toward single.

Student: That is so.

Teacher: And in a foot of two longs, are not two time-units compared with two time-units?

Student: It is manifest.

Teacher: From what principle, then, is this comparison drawn?

Student: From that of those called equal, of course.

2. 4. 5. Teacher: Come, now tell me: from when we began with two shorts to when we arrived at two long syllables, how many comparisons of feet have we treated?

Student: Four: for first it was spoken of two shorts, second of a short and a long, third of a long and a short, fourth of two longs.

Teacher: Can there be more than four, when two syllables are compared with each other?

Student: In no way; for since the syllables have received this measure, that a short has one time-unit and a long two, and since every syllable is either short or long, in what way can two syllables be compared and coupled to make a foot, except as either short and short, or short and long, or long and short, or long and long?

Teacher: Tell me also how many time-units the smallest foot of two syllables has, and how many the largest.

Student: The former two, the latter four.

Teacher: Do you see that the progression could be made only up to the number four, whether in feet or in time-units?

Student: I see it plainly, and I recall the principle of progression in numbers, and I feel that this same power is present here too, with great pleasure of mind.

Teacher: Do you not then judge that, since feet consist of syllables—that is, of distinct and, as it were, articulated motions that are in sounds, while syllables are stretched out by time-units—the progression of the foot too ought to go up to four syllables, just as you see it has already been made up to the number four, both in the feet themselves and in their time-units?

Student: I feel exactly as you say, and I recognize that this seems to belong to a perfect principle, and I demand it as owed.

2. 5. 6. Teacher: Come now, then, first, as the order itself demands, let us see how many feet of three syllables there can be, just as we found there are four of two.

Student: Let it be so.

Teacher: You remember that we began this account from a single short syllable, that is, of one time-unit, and understood well enough why it had to be so.

Student: I remember that, by that law of counting by which we begin from one, which is the beginning of numbers, it seemed good to us that we ought not to depart from it.

Teacher: Since, then, among feet of two syllables the first is the one that consists of two shorts (for reason compelled that one time-unit be joined to one time-unit before two), which, in the end, do you judge ought to be the first among feet of three syllables?

Student: Which, except the one made of three shorts?

Teacher: And how many time-units does this have?

Student: Three, of course.

Teacher: How, then, are its parts compared with each other? For every foot, because of that comparison of numbers, must necessarily have two parts that are compared with each other by some principle—I remember we treated this above; but can we divide this foot of three short syllables into two equal parts?

Student: In no way.

Teacher: How, then, is it divided?

Student: I see nothing else but that the first part has one syllable, the second two; or the first two, the second one.

Teacher: Tell me also from what rule of numbers this is.

Student: I recognize that it is from the kind of the multiplied.

2. 5. 7. Teacher: Come, now attend to this: three syllables in which one is long and the rest short—how many ways can they be varied, that is, how many feet can they make? Answer, if you have found out.

Student: I see there is one foot that consists of a long and two shorts; I understand no other.

Teacher: Does only that one seem to you to have a single long among three, which has it in the first place?

Student: I would in no way think that, since the two shorts can come first and the long last.

Teacher: Consider whether there is a third.

Student: There is plainly: for this long can also be set in the middle of the two shorts.

Teacher: See whether there is also a fourth.

Student: There cannot be at all.

Teacher: Can you now answer how many ways three syllables having in them one long and two shorts can be varied—that is, how many feet they can make?

Student: I can indeed: for they were varied three times, and made three feet.

Teacher: And these three feet—how they are to be ordered, do you now gather for yourself, or must you be led to this too, bit by bit?

Student: Does the order in which I discovered the variation itself displease you? For first I noted one long and two shorts, then two shorts and one long, last a short and a long and a short.

Teacher: Would it not displease you, indeed, that someone orders things so as to go from the first to the third, from the third to the second, rather than from the first to the second and then to the third?

Student: It displeases me utterly; but what such thing have you noticed here, I ask?

Teacher: Since you set first, in this threefold difference, that foot which has the long in the first place, because you sensed that the unity of the long syllable holds the primacy (for it alone is there single), and that on this account it ought to generate the order, so that the first foot is where it is first—you ought at the same time to have seen that it is second where it is second, and third where it is third. Or do you think you must still abide by that earlier view?

Student: On the contrary, I condemn it without hesitation; for that this is the better order—or rather that this is the order—who would not agree?

Teacher: Now then tell me by what rule of numbers these feet too are divided, and their parts compared with each other.

Student: I see that the first and the last are divided by an equal rule, because the one can be divided into a long and two shorts, the other into two shorts and a long, so that each part has two time-units, and on this account they are equal. But in the second, since it has the long syllable in the middle, whether it is assigned to the prior or the latter part, it is divided either into three and one, or into one and three time-units; and through this, in its division the principle of the multiplied numbers holds.

2. 5. 8. Teacher: I want you now to tell me by yourself, if you can, after those we have treated, which feet you think are to be ordered next. For first the four of two syllables were treated, whose order was drawn from the order of numbers, so that we began with short syllables. Then we undertook to treat the longer feet of three syllables, and, since it was easy from the earlier principle, we began with three shorts. What followed next, but that we should see how many forms one long with two shorts produces? It was seen; and three feet after that first were ordered, as had to be. Which follow next, ought you not now to see for yourself, lest we dig out everything by tiny little questions?

Student: You say rightly; for who would not see that those now follow in which there is one short and the rest long? To which short, because it is single, since by the earlier principle primacy is assigned to it, the first will certainly be where it is first, the second where it is second, the third where it is third, which is also the last.

Teacher: You discern, I think, by what principles too they are divided, so that their parts can be compared with each other.

Student: I discern it plainly: for the one that consists of one short and two longs cannot be divided except so that the prior part has three time-units, which contains a short and a long, and the latter two, which are in one long. But this third is in one respect equal to that prior one, in that it admits a single division; in another, unlike, because while that one is cut into three and two, this is cut into two and three time-units. For the long syllable, which holds the first part, is stretched over two time-units; there remain a long and a short, which is a span of three time-units. But the middle one, which has the short syllable in the middle, can admit a twofold division, because that same short can be assigned to either the prior or the latter part; therefore it is divided either into two and three, or into three and two, time-units. Thus the principle of the sesquate numbers possesses these three feet.

Teacher: Have we now considered all the feet of three syllables, or does something remain?

Student: I see one remaining, which consists of three longs.

Teacher: Treat, then, its division too.

Student: Its division is one syllable and two, or two and one—that is, two and four time-units, or four and two; so by the principle of the multiplied numbers the parts of this foot are compared with each other.

2. 6. 9. Teacher: Now let us see, in due sequence and order, the feet of four syllables, and tell me yourself which of these ought to be first, adding also the principle of its division.

Student: That of four shorts, of course, which is divided into two parts of two syllables, holding two and two time-units by the principle of equal numbers.

Teacher: You have it; so now proceed yourself, and pursue the rest. For I think there is now no need for you to be questioned point by point, since there is one principle for removing the short syllables in turn and putting longs in their place, until one comes to all longs; and for considering, when the shorts are removed and longs substituted, what variations they make and how many feet they produce—that syllable, of course, retaining the primacy of order which is single among the rest, whether long or short; for in all these you have already been exercised above. But where there are two shorts and two longs, which was not the case in the preceding, which do you judge ought to have the primacy?

Student: This too is now clear from the earlier cases. For the short syllable, which has one time-unit, holds unity more than the long, which has two. And therefore at every head and beginning we set the foot that consists of shorts.

2. 6. 10. Teacher: Nothing, then, prevents you from pursuing all these feet, with me listening and judging, not questioning.

Student: I will, if I can. For first, from the four shorts of the first foot, one short must be taken away, and in its place a long set in the first place, because of the dignity of unity. This foot is divided in two ways: either into a long and three shorts, or into a long and a short, and two shorts—that is, either into two and three, or into three and two, time-units. A long set in the second place makes another foot, which is rightly divided in one way—namely into three and two time-units, so that the prior part holds a short and a long, the latter two shorts. Further, a long set in the third place makes that foot which again is rightly divided in one way, but so that the prior part has two time-units in two short syllables, the latter three in a long and a short. A final long makes the fourth foot, which is divided in two ways, like the one where it is first: for it can be divided either into two shorts and a short and a long, or into three shorts and a long—that is, into two and three, or into three and two, time-units. But all these four feet, where a long is set variously with three shorts, have their parts compared with each other by the principle of the sesquate numbers.

2. 6. 11. It follows that, two shorts being taken away from the four shorts, we substitute two longs for them, and see how many forms and feet they can produce when the shorts and longs are each two. First, then, I see that two shorts and two longs are to be set down, because the beginning is more rightly from shorts. This foot has a twofold division: for it is divided either into two and four, or into four and two, time-units; so that either the two shorts hold the prior part and the two longs the latter, or two shorts and a long the prior, and the remaining long the latter. Another foot is made when those two shorts that we had set at the head are placed in the middle, as the order itself demands; and this foot's division is into three and three time-units: for a long and a short occupy the prior part, a short and a long the latter. But when they are placed at the end—for this follows—they make a foot of twofold division, whose prior part either has two time-units in one long and the latter four in a long and two shorts, or the prior four in two longs and the latter two in two shorts. The parts of these three feet, as concerns the first and third, are compared by the principle of the multiplied numbers; the middle has them equal.

2. 6. 12. Now next, those two shorts that were set joined together must be set apart: the smallest separation of them, from which we must also begin, is that they have one long syllable between them; the largest, that they have two. But when there is one between them, it happens in two ways, and two feet are produced. The prior of these ways is that there is a short at the head, then a long, then a short, and the long that remains. The other way is that the shorts are in the second and last places, and the longs in the first and third places: thus there will be a long and a short, and a long and a short. But that largest separation is when the two longs are in the middle, and one of the shorts is in the first, the other in the last place. And these three feet, in which the shorts are set apart, are divided into three and three time-units—that is, the first of them into a short and a long, and a short and a long; the second into a long and a short, and a long and a short; the third into a short and a long, and a long and a short. Thus there come about six feet, with two short and two long syllables set variously among themselves, as far as they can be.

2. 6. 13. It remains that, of the four shorts, three be taken away, and three longs set in their place: there will be one short; and because one short at the head, which three longs follow, makes one foot, set in the second place it makes the second, in the third the third, in the fourth the fourth. Of these four, the first two are divided into three and four time-units, the latter two into four and three, and all have their parts compared by the principle of the sesquate numbers. For the prior part of the first is a short and a long, holding three time-units; the latter, two longs in four time-units. The prior part of the second is a long and a short, hence three time-units; the latter, two longs, four time-units. The third has its prior part in two longs, four time-units; its latter part a short and a long hold, that is, three time-units. The fourth's prior part two longs likewise make, of four time-units; and the latter a long and a short, of three time-units. The remaining foot is of four syllables, where all the shorts are removed, so that the foot consists of four longs. This is divided into two and two longs according to the equal numbers, that is, into four and four time-units. You have what you wished to have unfolded by me; go on now to pursue the rest by asking.

2. 7. 14. Teacher: I will; but have you considered enough how far that progression up to the number four, which was demonstrated in the numbers themselves, holds also in these feet?

Student: I approve this principle of proceeding in these just as in those.

Teacher: And this: as feet were made by weaving syllables together, so must we judge that by weaving feet together something can be made that is no longer reckoned by the name of syllable or of foot?

Student: I judge so entirely.

Teacher: What, in the end, do you think this is?

Student: I judge it is a verse.

Teacher: What if someone wished to weave certain feet together endlessly, putting no measure and end to them, except either failure of voice, or some other interrupting chance, or the need of time to pass to something else? Will you still name it a verse, having twenty or thirty or even a hundred or more feet, as he wished and was able who wove them together in however long a continuation?

Student: It is not so; for I will not call it a verse either when I notice any feet mixed with any others, or many connected through an infinite length; but I will be able, by some discipline, to grasp both the kind and the number of feet—that is, which and how many feet make up a verse—and from it to judge whether a verse has struck my ears.

Teacher: But this discipline, whatever it is, establishes the rule and measure for verses not just as it pleases, but by some principle.

Student: It neither ought nor could be otherwise, if indeed it is a discipline.

Teacher: Let us investigate this principle, then, and attain it, if you please. For if we look only to authority, that will be a verse which some Asclepiades, I know not who, or Archilochus—ancient poets, of course—or the poetess Sappho, and the rest, by whose very names the kinds of verses are called, wished to be called a verse, who first observed and sang them. For there is the Asclepiadean verse, and the Archilochian, and the Sapphic, and the Greeks gave six hundred other authors' names to verses of different kinds. From which it can not absurdly seem to someone that, if anyone arranges as he wishes, as many feet as he wishes, and which he wishes, then—because no one before him established this order and measure for the feet—he will rightly and justly be called the founder and propagator of a new kind of verse. Or, if this license is shut off from a man, we must ask with complaint what those others, after all, did to deserve it, if, following no principle, they made the connection of feet that they pleased to connect be called and held a verse. Or does it seem otherwise to you?

Student: It is indeed as you say, and I agree entirely that a verse is generated by reason rather than by authority—which I ask that we now examine right away.

2. 8. 15. Teacher: Let us see, then, which feet are to be coupled to each other; next, what is made from these coupled (for a verse is not made by itself); finally, we will treat the whole principle of the verse. But do you think we can pursue these conveniently unless we hold the names of the feet? Although they have been arranged by us in such an order that they could be named by the names of their own order—for one can say the first, the second, the third, and so on for the rest. But because old terms are not to be despised, nor should we easily depart from custom, except where it opposes reason, we must use those names of the feet which the Greeks established, and which our own people now use in place of Latin ones: which let us so adopt that we do not seek the origins of the names. For that matter holds much talk and little usefulness. For you call bread, wood, and stone no less usefully in speaking because you do not know why these were so named.

Student: I feel exactly as you say.

Teacher: The first foot is called the pyrrhic, of two shorts, of two time-units, as fuga. The second, the iamb, of a short and a long, as parens, of three time-units. The third, the trochee, also called the choree, of a long and a short, as meta, of three time-units. The fourth, the spondee, of two longs, as aestas, of four time-units. The fifth, the tribrach, of three shorts, as macula, of three time-units. The sixth, the dactyl, of a long and two shorts, as Maenalus, of four time-units. The seventh, the amphibrach, of a short and a long and a short, as carina, of four time-units. The eighth, the anapest, of two shorts and a long, as Erato, of four time-units. The ninth, the bacchius, of a short and two longs, as Achates, of five time-units. The tenth, the cretic, or amphimacer, of a long and a short and a long, as insulae, of five time-units. The eleventh, the palimbacchius, of two longs and a short, as natura, of five time-units. The twelfth, the molossus, of three longs, as Aeneas, of six time-units. The thirteenth, the proceleusmatic, of four shorts, as avicula, of four time-units. The fourteenth, the first paeon, of a first long and three shorts, as legitimus, of five time-units. The fifteenth, the second paeon, of a second long and three shorts, as colonia, of five time-units. The sixteenth, the third paeon, of a third long and three shorts, as Menedemus, of five time-units. The seventeenth, the fourth paeon, of a fourth long and three shorts, as celeritas, of five time-units. The eighteenth, the ionic from the lesser, of two shorts and two longs, as Diomedes, of six time-units. The nineteenth, the choriamb, of a long and two shorts and a long, as armipotens, of six time-units. The twentieth, the ionic from the greater, of two longs and two shorts, as Iunonius, of six time-units. The twenty-first, the diiamb, of a short and a long, and a short and a long, as propinquitas, of six time-units. The twenty-second, the dichoree, or ditrochee, of a long and a short, and a long and a short, as cantilena, of six time-units. The twenty-third, the antispast, of a short and two longs and a short, as Saloninus, of six time-units. The twenty-fourth, the first epitrite, of a first short and three longs, as sacerdotes, of seven time-units. The twenty-fifth, the second epitrite, of a second short and three longs, as conditores, of seven time-units. The twenty-sixth, the third epitrite, of a third short and three longs, as Demosthenes, of seven time-units. The twenty-seventh, the fourth epitrite, of a fourth short and three longs, as Fescenninus, of seven time-units. The twenty-eighth, the dispondee, of four longs, as oratores, of eight time-units.

2. 9. 16. Student: I have these. Now discuss which feet are coupled to each other.

Teacher: You will judge this easily, if you judge equality and likeness to be more excellent than inequality and unlikeness.

Student: I think there is no one who does not so judge.

Teacher: This principle, then, must be followed first and above all in weaving feet together, and one must not deviate from it at all, except when there is some most just cause.

Student: I agree.

Teacher: You will not hesitate, then, to weave pyrrhic feet together with each other, nor iambs, nor trochees (which are also called chorees), nor spondees; and so you will surely couple the rest of their own kind to each other without any hesitation: for there is the highest equality when feet of the same kind and name follow one another. Or does it not seem so to you?

Student: It can in no way seem otherwise to me.

Teacher: And do you not approve this: that some feet are to be mixed with others, equality being kept? For what can be more pleasant to the ears than when they are both charmed by variety and not cheated of equality?

Student: I approve well enough.

Teacher: Do you think any feet are to be held equal except those that are of the same measure?

Student: I think so.

Teacher: And are they to be thought of the same measure except those that take up the same amount of time?

Student: It is true.

Teacher: The feet, then, that you find of the same number of time-units, you will weave together without offense to the ears.

Student: I see that it follows.

2. 10. 17. Teacher: Rightly indeed; but the matter still holds some question. For although the amphibrach is a foot of four time-units, some deny that it can be mixed with dactyls, or anapests, or spondees, or proceleusmatics—for these are all feet of four time-units; and not only do they deny that it can be mixed with these, but they think that even from itself alone, repeated and connected to itself, the rhythm does not proceed rightly and, as it were, lawfully. Their opinion we ought to consider, lest it have some reason that it would be fitting to follow and approve.

Student: I desire and am altogether eager to hear what they bring forward. For it moves me not a little that, when there are twenty-eight feet that reason has pursued, this one alone should be excluded from the continuation of rhythms, though it holds as much span in time as the dactyl and the others you enumerated as equal, which no one is forbidden to connect.

Teacher: But, that you may be able to discern this, you must consider the other feet, how their parts are compared with one another; for thus you will see that something new and singular happens to this one alone, so that it has not been judged unfit for rhythms without cause.

2. 10. 18. Student: I see, first, that the pyrrhic has as much in the raising as in the setting-down. The spondee too, the dactyl, the anapest, the proceleusmatic, the choriamb, the diiamb, the dichoree, the antispast, the dispondee, are divided by the same principle: for in these the beat sets down as much time as it raises. I see, second, that the iamb has the principle of single and double—a principle I discern also in the choree, the tribrach, the molossus, and in each ionic. Now this amphibrach's raising and setting-down (for it itself occurs to me in order, for which I seek the others as equal) consists of the principle of single and triple. But I find no other at all following whose parts are compared with each other by so great an interval. For when I consider those in which there is one short and two longs—that is, the bacchius, the cretic, and the palimbacchius—I see the raising and setting-down in these made by the principle of the sesquialter number. The same principle is in those four in which there is one long and three shorts, which are named in order the four paeons. There remain the four epitrites, likewise named in order, whose raising and setting-down the sesquitertian number contains.

2. 10. 19. Teacher: Does the cause then seem to you too little just, why this foot is not admitted to the rhythmical series of sounds—namely that the parts of it alone differ so far from each other that one is single, the other triple? For a certain nearness of parts is the more worthy of approval the closer it is to equality. And so, in that rule of numbers, when we proceed from one up to four, nothing is nearer to each than itself. Therefore that is to be approved first of all in feet, when their parts have the same amount with one another; next, the coupling of single and double stands out in one and two; the sesquialter coupling appears in two and three; the sesquitertian, now, in three and four. But single and triple, although held by the law of the multiplied numbers, do not yet cohere with each other in that order: for we do not count three after one, but one comes to three with two set between. This is the principle by which the amphibrach foot is judged to be excluded from that coupling of which we are inquiring—which, if it is approved by you, let us see the rest.

Student: It is approved indeed, for it is most manifest and most certain.

2. 11. 20. Teacher: Since, then, it pleases us that, however they stand in their syllables, yet if they are of the same span in time, feet can rightly and without loss of equality be mixed together—except only the amphibrach—it can not unreasonably be asked whether those are rightly mixed which, though they are equal in time, do not nevertheless agree in the same beat that compares the parts of a foot with each other by raising and setting-down. For the dactyl, the anapest, and the spondee are not only of equal time-units, but are also beaten equally: for in all of them the raising claims for itself as much as the setting-down. And so these are mixed with one another more justly than either ionic with the other six-time-unit feet. For each ionic is beaten to single and double—namely comparing two time-units to four. With these the molossus too agrees in this respect. But the rest are beaten to an equal amount; for in these three time-units are assigned to the raising and to the setting-down. Therefore, although all are lawfully struck—for those three by the principle of single and double, and the other four by equal parts—yet because this mixture makes an unequal beat, I rather think it may rightly be rejected; unless you have something against this.

Student: I incline rather to that view. For how an unequal beat does not offend the sense, I do not know; and if it does offend, this surely cannot happen without a fault in this mixture.

2. 11. 21. Teacher: But know that the ancients judged these feet were to be mixed, and composed verses by their mixture. Yet, lest I seem to press you with authority, receive some of these verses, and see whether they offend the hearing. For if they not only do not offend, but even delight, there will be no reason to disapprove this mixture. The verses I want you to attend to are these: At consona quae sunt, nisi vocalibus aptes, pars dimidium vocis opus proferet ex se; pars muta soni comprimet ora molientum; illis sonus obscurior impeditiorque, utcumque tamen promitur ore semicluso. I think this is enough for judging what I want. So tell me, I beg, whether this rhythm has at all charmed your ears.

Student: On the contrary, nothing seems to me to run and sound more festively.

Teacher: Consider the feet, then; you will surely find that, since there are five verses, the first two run on ionics alone, while the latter three have a dichoree mixed in—though all together delight our sense by a common equality.

Student: I have already noticed this, and the more easily as you pronounced it.

Teacher: Why, then, do we hesitate to agree with the ancients—conquered not by their authority but now by reason itself—who judge that those feet which are of the same time can reasonably be mixed, if they have a lawful, though different, beat?

Student: I yield now entirely; for that sound does not let me object anything.

2. 12. 22. Teacher: Attend likewise to these verses: Volo tandem tibi parcas, labor est in chartis, et apertum ire per auras animum permittas. Placet hoc nam sapienter, remittere interdum aciem rebus agendis decenter intentam.

Student: This too is enough.

Teacher: Especially since these verses are crude, which I fashioned on the spot out of necessity. Nevertheless, in these four too I ask the judgment of your sense.

Student: What else can I say here too than that they sounded beautifully and harmoniously?

Teacher: Do you perceive too that the first two consist of the other ionic, which is called "from the lesser," and that the latter two have a diiamb mixed in?

Student: This too I perceived as you suggested it by pronouncing.

Teacher: And does it not move you that, in those verses of Terentianus, the dichoree is mixed with the ionic that is called "from the greater," while in these of ours the diiamb is mixed with the other ionic, named "from the lesser"? Or do you think it makes no difference?

Student: On the contrary, it does make a difference, and I seem to myself to see the very principle: for since the ionic from the greater begins with two longs, it demands rather to be coupled with one where the long is first—that is, the dichoree. But the diiamb, because it begins with a short, is more harmoniously mixed with the other ionic, which begins with two shorts.

2. 12. 23. Teacher: You understand well; so this too must be held: that this agreement also, apart from the equality of time-units, ought to have some force in mixing feet—not the most force, yet some. For that any foot of six time-units can be put for any other foot of six time-units, you may judge by questioning your sense thus: let the molossus be our first example, virtutes; the ionic from the lesser, moderatas; the choriamb, percipies; the ionic from the greater, concedere; the diiamb, benignitas; the dichoree, civitasque; the antispast, volet iusta.

Student: I have these.

Teacher: Weave all these together, then, and pronounce them; or rather, receive them as I pronounce them, so that your sense may be freer to judge. For, that I may convey to you the equality of the continued rhythm without any offense to the ears, I will pronounce this whole text three times, which I do not doubt is enough: Virtutes moderatas percipies, concedere benignitas civitasque volet iusta. Virtutes moderatas percipies, concedere benignitas civitasque volet iusta. Virtutes moderatas percipies, concedere benignitas civitasque volet iusta. Has anything in this course of feet cheated your ears of equality or sweetness?

Student: In no way.

Teacher: Did anything delight you? Although this indeed follows in this kind, that everything delights which has not offended.

Student: I cannot say that I was affected otherwise than seems so to you.

Teacher: You approve, then, that all these feet of six time-units can rightly be coupled and mixed with one another.

Student: I approve.

2. 13. 24. Teacher: Do you fear nothing—that someone might judge that these feet could sound so equally only when compared in this order, but that if you alter the order they cannot do the same?

Student: It does bring up something; but it is not hard to test.

Teacher: Do that, then, when you have leisure: you will find nothing other than that your sense is charmed by manifold variety and a single equality.

Student: I will; although by this example there is no one who does not foresee that this will necessarily happen.

Teacher: You judge rightly; but, as concerns our purpose, I will run through these with the beat added, so that about this too you can decide whether something limps or nothing does; and that you may at the same time test something about that change of order which we said would bring no limping—now change the order itself, and let me sound out and beat the same feet set in another arrangement than I set them, as you please.

Student: Let the first be the ionic from the lesser, the second the ionic from the greater, the third the choriamb, the fourth the diiamb, the fifth the antispast, the sixth the dichoree, the seventh the molossus.

Teacher: Bend your ear, then, to the sound, and your eyes to the beat; for the beating hand must not be heard but seen, and one must note sharply how much delay of time is in the raising, how much in the setting-down.

Student: I am wholly here, as far as I am able.

Teacher: Receive, then, with the beat, that arrangement of yours: Moderatas, concedere, percipies, benignitas, volet iusta, civitasque, virtutes.

Student: I do feel that this beat in no way limps, and raises as much as it sets down; but I greatly wonder how those feet could be beaten by it whose division consists of the principle of single and double, as both ionics and the molossus are.

Teacher: What do you nevertheless think happens here, when in these three time-units are raised and as many set down?

Student: I see nothing else here at all but that the long syllable—which in the ionic from the greater and in the molossus is the second, and in the ionic from the lesser the third—is divided by the beat itself; so that, since it has two time-units, it gives one of them to the prior part and the other to the latter, and thus the raising and the setting-down each obtain three time-units.

2. 13. 25. Teacher: Nothing else at all can be said or understood here. But why should not that amphibrach too, which we were casting out entirely from this rhythm, be mixed on this condition with the spondee, dactyl, and anapest, or, continued by itself, produce something rhythmical in music? For by a similar principle the middle syllable of this foot too, which is long, can be divided by the beat, so that, when it has given single time-units to each side, the raising and the setting-down claim for themselves not now one and three, but two time-units each—unless you have something to object.

Student: I have nothing to say, except that this too is to be admitted.

Teacher: Let us, then, beat something ordered and woven of feet of four time-units, with which it is mixed, and in the same way test by the sense whether anything unequal offends. And so attend to this rhythm, repeated three times with the beat for ease of judging: Sumas optima, facias honesta. Sumas optima, facias honesta. Sumas optima, facias honesta.

Student: Now, I beg, spare my ears; for even with the beat not added, by itself the course of these feet limps most violently at that amphibrach.

Teacher: What, then, must we think is the cause that in this foot what was possible in the molossus and the ionics cannot happen? Is it because in those the sides are equal to the middle? For in an even number, where the middle is equal to its sides, six is the first to occur. Therefore those feet of six time-units, since they have two time-units in the middle and two each in the sides, willingly let that middle, in a way, fall into the sides, to which it is joined by a most amicable equality. But the same will not happen in the amphibrach, where the sides are unequal to the middle, since in those there are single time-units, in this two. To this is added that in the ionics and the molossus, when the middle is dissolved into the sides, three time-units each result, in which again, the middle being even, equal sides are found—which likewise fails in the amphibrach.

Student: The matter is as you say; and not without reason does the amphibrach offend the hearing in that series, while these even delight.

2. 14. 26. Teacher: Come, now, begin yourself from the pyrrhic itself, and, according to the principles stated above, explain as briefly as you can which feet ought to be mixed with which.

Student: None with the pyrrhic; for no other is found of the same number of time-units. The choree could go with the iamb, but it must be avoided because of the unequal beat, since the one begins from single, the other from double. So the tribrach can be accommodated to either. The spondee, dactyl, anapest, and proceleusmatic I see are friendly to one another and capable of being coupled: for they agree not only in time-units but also in beat. But the amphibrach, once excluded, could by no principle be brought back, which the equality of time-units could not help, since its division and beat are discordant. With the bacchius go the cretic, and the first, second, and fourth paeons. With the palimbacchius, it is manifest that the same cretic, and the first, third, and fourth paeons, agree both in time-units and in beat. Therefore with the cretic and the first and fourth paeons—since their division can begin from both two and three time-units—all the other feet of five time-units can be coupled without any limping. Now, that among all those that consist of six time-units there is a certain wonderful concord with one another has been discussed enough; since even those do not sound discordantly in beating against the others which the condition of their syllables compels to be divided otherwise—so great is the force of equality with the middle of the sides. Further, since there are four feet of seven time-units, called epitrites, I find that the first and second can be coupled with each other: for the division of both begins from three time-units, and therefore they differ neither in span of time nor in beat. Again the third and fourth are willingly joined to each other, because each in dividing begins from four time-units, and so are both measured and beaten equally. There remains the foot of eight time-units called the dispondee, for which, as for the pyrrhic, there is no equal. You have from me what you asked and I could do. Go on to the rest.

Teacher: I will; but after so long a discussion let us breathe a little, and recall those verses which weariness itself a little while ago suggested to me on the spot: Volo tandem tibi parcas, labor est in chartis, et apertum ire per auras animum permittas. Placet hoc nam sapienter, remittere interdum aciem rebus agendis decenter intentam.

Student: It pleases me indeed, and I willingly obey.

3. 1. 1. Teacher: This third discussion demands that, since enough has been said about a certain friendship and concord of feet, we see what is produced from these woven and continued together. So first I ask you whether feet coupled together—those that ought to be coupled—can create a certain perpetual rhythm, where no fixed end appears: as when musicians strike footboards and cymbals with their feet, in fixed rhythms indeed, and ones that are joined with pleasure to the ears, yet in a perpetual flow, so that, if you do not hear the flutes, you can in no way mark there how far the connection of feet runs on, and from where one returns again to the head—as if you wished to run through a hundred or more pyrrhics, or other feet that are friends to one another, in a continuous connection as far as you pleased.

Student: Now I understand, and I concede that there can be a certain connection of feet in which it is fixed up to how many feet one must proceed, and from there return.

Teacher: Do you doubt that this is of that kind (and you concede that this differs from that earlier one), since you do not deny that there is a fixed discipline of making verses, and you have confessed that you have always heard verses with pleasure?

Student: It is manifest both that this is so, and that it differs from that earlier kind.

3. 1. 2. Teacher: Since, then, things that are distinct in reality must be distinguished by terms as well, know that that earlier kind of coupling is called by the Greeks "rhythm," and this other "meter"; in Latin the former might be called "number" (numerus), the latter "measuring" or "measure" (mensio, mensura). But because these names among us have wide application, and we must be careful not to speak ambiguously, we more conveniently use the Greek ones. Yet you see, I think, how rightly each name is given to these things. For since the former rolls on by fixed feet, and one errs in it if discordant feet are mixed, it is rightly called "rhythm," that is "number"; but because the rolling itself has no limit, and it is not settled at which foot some end stands out, it ought not, for lack of any measure of the continuation, to be called "meter." But this other has both: for it runs on by fixed feet, and is terminated by a fixed limit. And so it is not only "meter," because of its marked end, but is also "rhythm," because of the rational connection of feet. Therefore every meter is rhythm, but not every rhythm is also meter. For the name "rhythm" in music has so wide an application that this whole part of it which pertains to "long" and "not long" is named rhythm. But that, when the thing is clear, one should not be busy about the name, has pleased both the learned and the wise. Do you think anything is to be objected or doubted about what I have said?

Student: On the contrary, I agree entirely.

3. 2. 3. Teacher: Now then consider this with me: whether, just as every verse is a meter, so every meter is also a verse.

Student: I do consider it, but I do not find what to answer.

Teacher: To what do you think this has happened to you? Is it because the question is about terms? For we cannot answer when questioned about names as about things belonging to a discipline, because things are implanted in common in the minds of all, whereas names are given as each one pleased, and their force rests chiefly on authority and custom—whence too there can be a diversity of languages, but there surely cannot be of things established in truth itself. From me, then, receive what you yourself could in no way answer: the ancients called meter not only verse. So, as far as concerns you, see and answer—for it is no longer about names—whether between these two there is some difference: that a certain number of feet is closed off by a fixed end in such a way that it matters nothing to the thing where some joint occurs before one comes to the end; while another is not only closed off by a fixed end, but also, before the end, in a certain fixed place, some division of it stands out, so that it is, as it were, made up of two members.

Student: I do not understand.

Teacher: Attend, then, to these examples: Ite igitur, Camoenae fonticolae puellae, quae canitis sub antris mellifluos sonores, quae lavitis capillum purpureum Hippocrene fonte, ubi fusus olim spumea lavit almus ora iubis aquosis Pegasus, in nitentem pervolaturus aethram. You surely discern that the upper five little verses have the part of speech ended in the same place—that is, at the choriamb foot, to which a bacchius is joined to complete the little verse (for these eleven consist of the choriamb and bacchius feet); but the rest, except one, namely ora iubis aquosis, do not have the part of speech ended in the same place.

Student: I discern that indeed, but I do not see where it leads.

Teacher: To this, of course: that you may understand that this meter does not have, as it were, a lawful place where the part of speech is ended before the end of the verse; for if it were so, all would have this joint in the same place, or at least most rarely among them would one be found that did not have it; but as it is, since there are eleven, six are so and five are not so.

Student: This too I accept, and I still await where the reasoning is tending.

Teacher: Attend, then, also to this most well-known line: Arma virumque cano, Troiae qui primus ab oris. And, not to make it long, since the poem is most familiar, examine the lines one by one, from this verse up to whichever you wish; you will find the part of speech ended at the fifth half-foot—that is, at two feet and a half: for these verses consist of feet of four time-units; so this end of the part of speech of which we are treating is, as it were, lawfully at the tenth time-unit.

Student: It is manifest.

3. 2. 4. Teacher: Now then you understand that between those two kinds which I had set forth before these examples there is some difference: that one meter, before it is closed off, has no fixed and settled joint, as we examined in those eleven little verses; but another has one, as in the heroic meter the fifth half-foot sufficiently indicates.

Student: Now what you say is clear.

Teacher: But you ought to know that by the learned ancients, in whom there is great authority, that earlier kind was not called a verse; rather, a verse has now been defined and named as that which consists of two members, as it were, joined by a fixed measure and principle. But do not trouble yourself much over the name, which, unless it were pointed out to you by me or anyone else, you could in no way answer if questioned about it. But to what reason teaches, direct your mind especially and above all—as to this very thing we are now treating: for reason teaches that between these two kinds there is some difference, by whatever terms they are named; and so this you could say if rightly questioned, trusting in truth itself, whereas that other you could not say except by following authority.

Student: I have now most plainly come to know these things, and I now reckon how highly you value this, of which you so often admonish me.

Teacher: These three names, then, which we will necessarily use for the sake of discussion, I would have you commit to memory: rhythm, meter, verse. They are distinguished thus: that every meter is also rhythm, but not every rhythm is also meter; likewise every verse is also meter, but not every meter is also verse. Therefore every verse is rhythm and meter; for this, I judge, you see follows.

Student: I see it indeed; for it is clearer than light.

3. 3. 5. Teacher: First, then, if you please, let us discuss rhythm in which there is no meter; then meter where there is no verse; finally the verse itself, as far as we can.

Student: I agree indeed.

Teacher: Take, then, from the very head pyrrhic feet, and weave a rhythm from these.

Student: Even if I could do this, what limit will there be?

Teacher: It is enough that you stretch it (for we do this for the sake of example) up to ten feet; for the verse does not proceed beyond this number of feet, which will be carefully treated in its place.

Student: You have indeed proposed to me not many feet to couple; but you seem to me not to recall that you have already distinguished well enough what lies between the grammarian and the musician, when I answered you that I have no knowledge of long and short syllables, which is handed down by the grammarians—unless perhaps you permit me to present this rhythm not in words but by some beat: for I do not deny that I can have the judgment of the ears for regulating the measures of time; but which syllable should be lengthened or shortened, which rests on authority, I am wholly ignorant of.

Teacher: I admit that we have, as you say, distinguished the grammarian from the musician, and that in this kind you have confessed your ignorance. So receive from me this kind of example: Ago celeriter agile quod ago tibi quod anima velit.

Student: I have it.

3. 3. 6. Teacher: By repeating this, then, as often as you please, you will make this rhythm as long as you wish, although these ten feet suffice for an example. But I ask this: if someone tells you that this rhythm consists not of pyrrhics but of proceleusmatic feet, what will you answer?

Student: I am quite at a loss; for where there are ten pyrrhics, I measure five proceleusmatics; and the doubt is the greater because we are consulted about a rhythm, which of course flows perpetually. For eleven pyrrhics, or thirteen, and any odd number, cannot have a whole number of proceleusmatics. If, then, there were a fixed end in this rhythm of which we are treating, we could at least say there that it runs by the pyrrhic rather than the proceleusmatic, where all whole proceleusmatics would not be found; but as it is, both the infinite itself confounds our judgment, and so does it when feet are indeed counted but proposed to us in an even number, as these ten are.

Teacher: But even about that odd number of pyrrhics, what seemed clear to you is not clearly seen. For what if, eleven pyrrhic feet being proposed, the rhythm be said to have five proceleusmatics and a half-foot? Can it be resisted, when we find many verses closed off by a half-foot?

Student: I have already said that I do not know what can be said about this matter.

Teacher: Do you not also know this, that the pyrrhic is prior to the proceleusmatic? Since a proceleusmatic is made of two pyrrhics; just as one is prior to two, and two to four, so the pyrrhic is prior to the proceleusmatic.

Student: It is most true.

Teacher: When, then, we fall into this ambiguity, that in a rhythm both the pyrrhic and the proceleusmatic can be measured, to which shall we give the primacy: to the prior, of which the latter consists, or to the latter, of which the prior does not consist?

Student: No one will doubt that it must be given to the prior.

Teacher: Why, then, do you hesitate to answer, when consulted about this matter, that this rhythm should be named pyrrhic rather than proceleusmatic?

Student: Now I do not hesitate at all: I am ashamed not to have quickly noticed so manifest a reason.

3. 4. 7. Teacher: Do you see that by this reasoning this too is established: that there are certain feet which cannot continue a rhythm? For what was found about the proceleusmatic, from which the pyrrhic takes the primacy, this I think is found about the diiamb and the dichoree and the dispondee too—unless it seems otherwise to you.

Student: What else can seem to me, when, that reason being proved, I cannot disprove what follows?

Teacher: Look at these too, and compare and judge. For it seems that, when such uncertainty arises, the foot by which one runs ought rather to be distinguished by the beat: so that if you wish to run by the pyrrhic, you must raise one time-unit and set down one; if by the proceleusmatic, two and two. Thus both the foot will appear, and none of the feet will be shut out from the continuation of a rhythm.

Student: I favor this view more, which lets no foot be exempt from this weaving.

Teacher: You do rightly; and that you may approve this the more, consider what we can answer about the tribrach foot, if someone should nonetheless contend that this rhythm runs not by the pyrrhic or the proceleusmatic, but by the tribrach.

Student: I see that the judgment must be brought back to that beat: so that if there is one time-unit in the raising and two in the setting-down—that is, one and two syllables—or the contrary, two in the raising and one in the setting-down, the rhythm is said to be tribrach.

3. 4. 8. Teacher: You understand rightly. So now tell me whether the spondee foot can be joined to a pyrrhic rhythm.

Student: In no way; for an equal beat will not be continued, since the raising and setting-down hold single time-units in the pyrrhic, but two each in the spondee.

Teacher: Then it can be joined to the proceleusmatic.

Student: It can.

Teacher: And when it is joined to it—being asked whether the rhythm is proceleusmatic or spondaic, what shall we answer?

Student: What do you think, except that the primacy must be given to the spondee? For since this dispute is not decided by the beat—for in both we raise and set down two time-units each—what else remains but that the one reign which is prior in the very order of feet?

Teacher: I approve well enough that you have followed reason; and you see, I judge, what follows.

Student: What, in the end?

Teacher: What do you think, except that no other foot can be mixed with a proceleusmatic rhythm? For whatever is mixed with it must be of the same number of time-units (for otherwise it cannot be mixed), and the name of the rhythm must be transferred to it. For all are prior to it that consist of the same number of time-units. And since reason compels us to give the primacy to those that are found prior—that is, to name the rhythm from it—it will no longer be a proceleusmatic rhythm, with some other four-time-unit foot mixed in, but spondaic or dactylic or anapestic. For the amphibrach is rightly removed from the coupling of these numbers.

Student: I admit it is so.

3. 4. 9. Teacher: Now then consider in order the iambic rhythm, since we have discussed enough the pyrrhic and the proceleusmatic, which is produced by doubling the pyrrhic. So I would have you say which foot you judge should be mixed with this, so that the iambic rhythm may keep its name.

Student: Which, except the tribrach, which agrees both in time-units and in beat; and because it is later, cannot prevail in the reign? For the choree is indeed later, and of the same number of time-units, but is not beaten in the same way.

Teacher: Come, now look at the trochaic rhythm, and answer the same about this too.

Student: I answer the same: for the tribrach can harmonize with this too not only in span of time but also in beat. And who does not see that the iamb must be avoided? Which, even if it were beaten equally, would still, when mixed, carry off the primacy.

Teacher: And to a spondaic rhythm which foot, in the end, shall we couple?

Student: Indeed in this there is the most ample supply: for I see that the dactyl and the anapest and the proceleusmatic can be mixed with it, with no inequality of time-units, no limping of the beat, no removal of primacy hindering.

3. 4. 10. Teacher: I see now that you can easily pursue the rest in order; so, my questioning being set aside—or rather, as if questioned about all of them—answer briefly and as clearly as you can, how each of the remaining feet, with others lawfully mixed in, keeps its own name in the rhythm.

Student: I will; for it is no trouble at all, so great a light of principles having gone before. With the tribrach none will be mixed; for all that are equal to it in time-units are prior. The anapest can go with the dactyl; for it is both later, and runs equally in time and beat; and the proceleusmatic is coupled with each by the same principle, of course. Now with the bacchius the cretic, and of the paeons the first, second, and fourth, can be mixed. Further, with the cretic itself all the five-time-unit feet that come after it are rightly mixed, but not all by the same division. For some are divided into two and three, others into three and two time-units. But this cretic can be divided either way, because the middle short is assigned to either part. The palimbacchius, however, since its division, beginning from two time-units, ends in three, has all the paeons harmonious and capable of being coupled, except the second. Of the trisyllables the molossus remains, from which first the six-time-unit feet begin, all of which can be joined to it, partly because of the principle of single and double, partly because of that division of the long syllable which the beat showed us, which grants single time-units to each part, because in the number six the middle is equal to the sides. For which cause both the molossus and both ionics are struck not only into single and double, but also into equal parts through three time-units each. Hence it comes about that to all the six-time-unit feet in turn all the later feet of the same number of time-units can be coupled; and the antispast alone, which would have none mixed with it, remains. These the four epitrites follow, of which the first admits the second, the second none, the third the fourth, the fourth none. There remains the dispondee, which will itself too make a rhythm alone, because it finds neither any later nor any equal. And so of all the feet there are eight that make a rhythm with no other mixed in: the pyrrhic, the tribrach, the proceleusmatic, the fourth paeon, the antispast, the second and fourth epitrite, and the dispondee; the rest allow those that are later than themselves to be coupled with them, so that they keep the name of the rhythm, even if fewer are counted in that series. This is, I think, enough unfolded and arranged by me as you wished; it is now yours to see what remains.

3. 5. 11. Teacher: Nay, with me yours too; for we both inquire. But what, in the end, do you judge remains that pertains to rhythm? Is not this to be considered: whether some measure of a foot, although it does not exceed eight time-units, which the dispondee holds, nevertheless exceeds the number of four syllables?

Student: Why, I ask?

Teacher: Nay, you—why do you ask me rather than yourself? Or does it not seem to you that, without any deception or offense to the ears, whether as concerns the beat and division of feet, or as concerns the span of time, two shorts can be put for one long syllable?

Student: Who would deny this?

Teacher: From this, then, it comes that for an iamb or a choree we put a tribrach, and for a spondee a dactyl or anapest or proceleusmatic, when we put two shorts either for its second or for its first, or four for both.

Student: I agree.

Teacher: Do this same thing, then, in any ionic, or in some other four-syllable foot of six time-units, and set two shorts for any one of its longs. Does anything of the measure perish, or resist the beat?

Student: Nothing at all.

Teacher: Consider, then, how many syllables there come to be.

Student: I see there come to be five.

Teacher: You surely see that the number of four syllables can be exceeded.

Student: I see it indeed.

Teacher: And if for the two longs that are there you put four shorts, must not six syllables be measured in one foot?

Student: It is so.

Teacher: And if you dissolve all the longs of any epitrite into shorts, must we doubt even about seven syllables?

Student: In no way.

Teacher: And the dispondee itself? Does it not make eight, when we set two shorts for all the longs?

Student: It is most true.

3. 5. 12. Teacher: What, then, is the principle by which we are compelled both to measure feet of so many syllables, and yet, by the principles treated before, to confess that the foot which is applied to rhythms does not exceed four syllables? Do these not seem to you to be at war with each other?

Student: On the contrary, very much so; and how this can be reconciled I do not know.

Teacher: This too is easy, if you again question yourself whether it was reasonably agreed between us a little while ago that the pyrrhic and the proceleusmatic ought to be decided and distinguished by the beat, lest there be any foot of lawful division that does not make a rhythm—that is, that a rhythm be named from it.

Student: I do remember this, and I do not find why I should regret that it pleased me; but where is this leading?

Teacher: Because, of course, all these feet of four syllables, except the amphibrach, make a rhythm—that is, hold the primacy in a rhythm, and bring it about in use and name; but those that have more than four syllables can indeed, many of them, be put for these, yet cannot by themselves make a rhythm and keep the name of a rhythm; and therefore I would not think these should even be called feet. Therefore that contradiction which was troubling us is now, I think, composed and laid to rest, since one may both put more syllables than four for some foot, and yet not call a foot anything except that by which a rhythm is brought about. For some manner of progression in syllables had to be established for the foot. And that manner could best be established which, transferred from the very principle of numbers, settled on four. And so a foot could be of four long syllables. But when we set eight shorts for it, since they have as much span in time, they can be put for the other. But because they exceed the lawful progression—that is, the number four—they are forbidden to be put for themselves, and to produce a rhythm, not by the judgment of the ears, but by the law of the discipline. Unless you are preparing to object something.

3. 5. 13. Student: I am preparing indeed, and I will do it now. For what was preventing the foot from proceeding up to the number eight in syllables, since we see that the same number can be admitted to a rhythm? Nor does it move me that you say it is admitted for another; rather, this the more prompts me to ask—or rather to complain—that the one which can stand for another is not also admitted under its own name.

Teacher: It is no wonder that you are deceived here; but the explanation of the truth is easy. For—to pass over the many things already argued before on behalf of the number four, why the progression of syllables ought to be made up to it—suppose I have now yielded to you and consented that the length of a foot ought to be stretched up to eight syllables: can you resist that there can now be a foot of eight long syllables? For certainly, to whatever number of syllables a foot comes, not only the one that consists of shorts comes to it, but also the one that consists of longs. Whence it comes about that, applying again that law which cannot be abrogated, by which two shorts may be put for one long, we stretch on to sixteen syllables. And there, if you again wish to set the foot's increase, we set out into thirty-two shorts; here too your reasoning compels you to bring the foot, and again that law to set the double number of shorts for the longs; and so no limit will be established.

Student: Now I yield to the reasoning by which we advance the foot up to the number of four syllables. But that for these lawful feet there ought to be put feet of more syllables, so long as two shorts occupy the place of one long, I do not refuse.

3. 6. 14. Teacher: It is easy, then, for you to see and concede this too: that some feet are put for those in whose hands is the primacy of a rhythm, and others that are set together with these. For where two shorts are doubled for single longs, we set another in place of the one that holds the rhythm—as a tribrach for an iamb or trochee, or a dactyl or anapest or proceleusmatic for a spondee. But where the same does not happen, whatever of the lower feet is mixed in is put not for it but with it—as the anapest with the dactyl, but the diiamb or dichoree with either ionic; and the rest likewise by their own right with the others. Or does it seem to you too little clear, or false?

Student: Now I understand.

Teacher: Answer, then, whether those that are put for others can also themselves by themselves make a rhythm.

Student: They can.

Teacher: All of them?

Student: All.

Teacher: Then a foot of five syllables too can make a rhythm under its own name, because it can be put for a bacchius or cretic or any paeon.

Student: It cannot, indeed; but we no longer call that a foot, if I remember well enough that progression up to the number four. But when I answered that all can, I answered, of course, that feet can.

Teacher: I praise too your diligence and vigilance in retaining the name. But know that to many it has seemed that even feet of six syllables should be named; but beyond that, so far as I know, it has pleased no one. And those to whom this pleased denied that such long feet ought to be applied to producing a rhythm or a meter by themselves. And so they did not even give them names. Therefore that manner of progression is most true which comes up to four syllables; since all these feet, which when divided cannot become two, when joined could make a foot. And so those who proceeded up to the sixth syllable dared to transfer only the name of "foot" to those that exceeded the fourth; but to the primacy that is in rhythms and meters they in no way allowed them to aspire. But when shorts are doubled for longs, one comes even to the seventh and eighth syllable, as reason has now shown; to which number no one has stretched a foot. But since I see it is agreed between us that any foot of more than four syllables, when we put two shorts for a long, can be put not with these lawful feet but for them, and cannot by themselves create a rhythm—lest what is to be ended by reason go on to infinity, and since I think enough has now been argued between us about rhythm—let us pass on to meters, if you please.

Student: I agree indeed.

3. 7. 15. Teacher: Tell me, then, whether you judge that meter is made by feet, or feet by meter.

Student: I do not understand.

Teacher: Do feet joined together create a meter, or are feet created when meters are joined?

Student: Now I know what you mean, and I think that meter is made by feet joined together.

Teacher: Why, in the end, do you think this?

Student: Because you said that this lies between rhythm and meter: that in rhythm the weaving of feet has no fixed end, but in meter it has; so that this weaving of feet is understood to belong both to rhythm and to meter, but there it stands infinite, here finite.

Teacher: Then one foot is not a meter.

Student: It is not.

Teacher: And one foot and a half?

Student: Not even this.

Teacher: Why? Is it because meter is made of feet, and there cannot be said to be feet where there are fewer than two?

Student: It is so.

Teacher: Let us, then, inspect those meters which I mentioned a little while ago, and see of what feet they consist; for it is not fitting that you should still be untrained in noticing this kind of thing. They are these: Ite igitur, Camoenae fonticolae puellae, quae canitis sub antris mellifluos sonores. I think these are enough for what we intend; now measure them, and report what feet they have.

Student: I cannot at all; for I think those are to be measured which can be lawfully coupled with one another, and I cannot extricate myself here. For if I make the first a choree, an iamb follows, which is equal in time-units but is not beaten alike; if a dactyl, no other follows that is equal to it even in time-units; if a choriamb, the same difficulty arises, for what remains agrees with it neither in time-units nor in beat. So either this is not a meter, or what was argued between us about the coupling of feet is false; for what else to say I do not find.

3. 7. 16. Teacher: That it is a meter—both because it is more than a foot and has a fixed end—is proved by the judgment of the ears themselves. For it would not sound with such sweet equality, nor be beaten with so harmonious a motion, if there were not in it that rhythm which surely can be only in this part of music. But that what we agreed on between us is false, I wonder that you should think; for nothing is more certain than numbers, nor more orderly than that mention and arrangement of feet. For from the very principle of numbers, which in no way deceives, was expressed whatever we have seen in them to avail both for charming the ears and for obtaining the primacy in a rhythm. But look rather, when I often repeat quae canitis sub antris, and charm your sense with that rhythm: what difference is there between this, and if I were to add at the end of it some short syllable, and likewise repeat it the same way: quae canitis sub antrisve?

Student: Each glides pleasantly into my ears; yet this latter one, to which you added a short syllable, I am compelled to admit holds more span and time, since it has been made longer.

Teacher: And when I repeat that earlier one, quae canitis sub antris, in such a way that after the end I am silent for nothing—does the same pleasantness reach you?

Student: On the contrary, something halting, I know not what, offends me—unless perhaps you have drawn out that last syllable more than the other longs.

Teacher: So whether it is the very thing that is drawn out longer, or the silence, do you judge that it has some span in time?

Student: How could it be otherwise?

3. 8. 17. Teacher: You judge rightly. But tell me also how much span you think it is.

Student: It is altogether difficult to measure this.

Teacher: You speak truly; but does it not seem to you that that short syllable measures it—the one which, when we added it, our sense desired neither any drawing-out of the last long beyond the usual, nor any silence, in the repetition of that meter?

Student: I agree entirely; for as you pronounced and repeated that earlier one, I was repeating this latter one to myself, in step with you; and so I felt that the same span of time fell to both, since my final short agreed with your silence.

Teacher: You ought, then, to hold that these spans of silence are fixed in meters. So when you find that something is lacking to a lawful foot, you must consider whether it is compensated by a measured and counted silence.

Student: I hold this now; pursue the rest.

3. 8. 18. Teacher: I see now that we ought to inquire into the measure of the silence itself; for in this meter, where after the choriamb we found a bacchius, because one time-unit was lacking for it to be of six time-units like the choriamb, the ears most easily perceived it, and in the repetition compelled us to interpose a silence of as great a span as a short syllable would take up. But if a spondee is set after the choriamb, two time-units must be passed by us, with silence, as we return to the head, as in this: quae canitis fontem. For I believe you now feel that one must be silent, so that, when we return to the head, the beat does not limp. But that you may be able to test how great the measure of this silence is, add one long syllable, so that it becomes quae canitis fontem vos; and repeat this with the beat: you will see that the beat takes up as much time as it took in the former, since there two longs were set after the choriamb, here three. Hence it appears that a silence of two time-units is interposed there. But if an iamb is set after the choriamb, as in this: quae canitis locos, we are compelled to be silent for three time-units; which, that it may be tested, are added either by another iamb, or by a choree, or by a tribrach, so that it becomes quae canitis locos bonos, or quae canitis locos monte, or quae canitis locos nemore. For when these are added, since the repetition moves us pleasantly and evenly without silence, and, the beat being applied, these three are found each to hold as much span as that one in which we were silent, it becomes manifest that the silence there is of three time-units. After the choriamb one long syllable can be set, so that four time-units are kept silent. For the choriamb can be divided in such a way too that the raising and setting-down agree by single and double. An example of this meter is quae canitis res. To which, if you add either two longs, or a long and two shorts, or a short and a long and a short, or two shorts and a long, or four shorts, you will fill out a foot of six time-units, so that it is repeated with no silence desired. Such are: quae canitis res pulchras, quae canitis res in bona, quae canitis res bonumve, quae canitis res teneras, quae canitis res modo bene. These being known and granted, I believe it now appears to you sufficiently that one cannot be silent for less than one time-unit, nor ought one to be silent for more than four. For this is that very moderate progression of which much has already been said; and in all feet no raising or setting-down takes up more than four time-units.

3. 8. 19. Student: I have learned it and I agree.

Teacher: Trusting me, or seeing for yourself that these things are true?

Student: For myself indeed, although it is as you say that I recognize these things to be true.

3. 9. 20. Teacher: Come, then, now that we have found from where meter begins, let us also find how far it proceeds. For meter begins from two feet, whether full of sound itself, or with a silence counted in to fill out what is lacking. So you must now look back to that fourfold progression, and report to me up to how many feet we ought to stretch a meter.

Student: This indeed is easy. For reason teaches well enough that there are eight feet.

Teacher: And do you recall that we said the learned called that a verse which consists of two members measured and coupled by a fixed principle?

Student: I remember well.

Teacher: Since, then, it was said that a verse consists not of two feet but of two members, and since it is manifest that a verse has not one foot but several, does not the matter itself show that a member is longer than a foot?

Student: It does indeed.

Teacher: But if the members in a verse were equal, could they not be reversed, so that the first part might without distinction become the last, and the last the first?

Student: I understand.

Teacher: Then, that this may not happen, and that it may appear and be distinguished well enough in a verse that one member is that with which it begins, another that with which it ends, we cannot refuse that the members ought to be unequal.

Student: In no way.

Teacher: Let us consider this first in the pyrrhic, if you please, in which I believe it now seems to you that a member cannot be less than three time-units, since this is the first thing that is more than a foot.

Student: I agree.

Teacher: How many time-units, then, will the smallest verse possess?

Student: I would say six, did not that reversal call me back. So it will have seven: because a member cannot have less than three; but to have more is not yet forbidden.

Teacher: You understand rightly. But tell me how many pyrrhic feet seven time-units have.

Student: Three and a half.

Teacher: So a silence of one time-unit is owed, while one returns to the beginning, that the span of a foot may be filled out.

Student: It is owed indeed.

Teacher: With this counted in, how many time-units will there be?

Student: Eight.

Teacher: So, as the smallest foot, which is also the first, cannot have less than two, so the smallest verse, which is the first, cannot have less than eight time-units.

Student: It is so.

Teacher: And the largest verse, than which none ought to be larger—of how many time-units, in the end, ought it to be? Will you not see at once, if we turn our mind to that progression of which so much has so often been said?

Student: Now I understand that a verse cannot be larger than thirty-two time-units.

3. 9. 21. Teacher: And about the length of a meter? Do you judge that it ought to be larger than a verse, when meter, in what is its smallest, is just so much less than the smallest verse?

Student: I do not judge so.

Teacher: Since, then, meter begins from two feet, a verse from four—the one from the span of two feet, the other from four with a silence counted in—but meter does not exceed eight feet: since a verse too is a meter, must it not exceed not the same number of feet?

Student: It is so.

Teacher: Again, since a verse is not longer than thirty-two time-units, and a meter too is the length of a verse—if it does not have such a coupling of two members as is prescribed in a verse, but is only closed off by a fixed end, and ought not to be longer than a verse—is it not manifest that, as a verse ought not to exceed eight feet, so a meter ought not to exceed thirty-two time-units?

Student: I agree.

Teacher: There will then be the same span of time, and the same number of feet, for both meter and verse, and a certain common boundary beyond which neither ought to proceed—although meter is ended by quadrupling the feet from which it begins to be, and a verse by quadrupling the time-units from which it too begins to be; so that, the manner of growing being kept by that fourfold principle, meter shares with verse in feet, and verse with meter in time-units.

Student: I understand and approve; and I am delighted that this concord and agreement holds so.

4. 1. 1. Teacher: Let us return, then, to the consideration of meter, on account of whose progression and length I was compelled to deal with you somewhat about the verse, whose treatment has been set for us in a place later on. But first I ask whether you would not reject this: that poets, and the grammarians who judge them, have held that the last syllable, which ends a meter—whether it is long or short—matters nothing to the thing.

Student: I reject it entirely; for it does not seem to me to be reasonable.

Teacher: Tell me, I beg, what is the smallest meter in the pyrrhic.

Student: Three shorts.

Teacher: How much, then, must be kept silent while it is repeated?

Student: One time-unit, which is the span of one short syllable.

Teacher: Come, now beat this meter, not with the voice but with a beat.

Student: I have done it.

Teacher: Now beat an anapest in this way too.

Student: This too I have done.

Teacher: What difference seemed to you to be between them?

Student: None at all.

Teacher: And can you say the cause why it is so?

Student: It seems to me to appear well enough: for what in the one is referred to silence, in the other is referred to the drawing-out of the last syllable; for the last short there is beaten in the same way as the long here, and after just as great an interval one returns to the head. But there one rests until the span of the pyrrhic foot is filled, here until the long syllable is filled. So in each the delay is equal, with which interposed we return.

Teacher: Not absurdly, then, did they hold that the last syllable of a meter, whether long or short, matters nothing to the thing: for where there is an end, silence follows, as far as concerns the meter itself which is ended. Or do you think that in this case they ought to have considered any repetition or return to the head, and not only that, because it ends, as if nothing were thereafter to be said?

Student: Now I agree that the last syllable is to be taken indifferently.

Teacher: Rightly. But if this comes about because of the silence, since the end is considered as if the one who has ended will thereafter sound nothing, and on this account, the span of time in the rest itself being most ample, it matters nothing what syllable is set there—does it not follow that the very indifference of the last syllable, which is granted because of the ample span, avails to this: that, whether there be a short syllable there or a long, the ears claim it for themselves as a long?

Student: I see plainly that it follows.

4. 2. 2. Teacher: Do you see this too: that when we say the smallest pyrrhic meter is three short syllables, so that one is silent for the span of one short while we return to the beginning, it matters nothing whether we repeat this meter or anapest feet?

Student: I perceived this indeed a little while ago by that beating.

Teacher: Do you not, then, think that whatever is confused here must be distinguished by some principle?

Student: I think so entirely.

Teacher: Tell me whether you see any other principle that distinguishes these, except that the smallest pyrrhic meter is not the one that seemed to you to be in three shorts, but in five. For the equality of the anapest does not let us be silent, after one foot and a half, for the delay of the half-foot owed to filling out the foot, and so return to the beginning, and establish this as the smallest meter in the pyrrhic, as has now been shown; so after two feet and a half we must be silent that one time-unit, if we want to be free of confusion.

Student: For why are two pyrrhics not the smallest meter in the pyrrhic, and four short syllables rather—after which there is no need to be silent—than five, after which there is?

Teacher: Watchfully indeed; but you do not guard against the proceleusmatic excluding you from this, as the anapest does from that.

Student: You speak truly.

Teacher: Does this manner, then, please you, in five shorts, with a silence of one time-unit?

Student: It pleases me indeed.

Teacher: It seems to me you have forgotten how we said, in the case of rhythm, that one can distinguish whether one runs by the pyrrhic or the proceleusmatic.

Student: You remind me well; for we found that these rhythms are to be distinguished from one another by the beat; so now I no longer fear this proceleusmatic, which by applying the beat I shall be able to distinguish from the pyrrhic.

Teacher: Why, then, did you not see that the same beat should be applied, so that the anapest might be distinguished from those three shorts—that is, a pyrrhic and a half-foot, after which one would have to be silent one time-unit?

Student: Now I understand, and I return to the road, and I affirm that the smallest meter in the pyrrhic is three short syllables, which, with the silence counted in, take up the time of two pyrrhics.

Teacher: Do your ears, then, approve this kind of rhythm: Si aliqua, bene vis, bene dic, bene fac, animus, si aliquid, male vis, male dic, male fac, animus, medium est.

Student: They approve it well enough, especially since I have now recalled how they ought to be beaten, lest the anapest feet be confused with the pyrrhic meter.

4. 2. 3. Teacher: See these too: Si aliquid es, age bene, male qui agit, nihil agit, et ideo, miser erit.

Student: These too insinuate themselves sweetly, except in one place, where the end of the third is coupled with the beginning of the fourth.

Teacher: That is exactly what I desired from your ears. For not without reason is the sense offended, when it expects single time-units of all the syllables with no silence interposed; and this expectation the meeting of two consonants, "t" and "n," surely cheats, which compel the preceding vowel to be long and extend it into two time-units—the kind of syllable the grammarians call long by position. But because of that indifference of the last syllable, no one finds fault with this meter, though sincere and severe ears condemn it even without an accuser. For see, I beg, how great the difference is, if for what is male qui agit, nihil agit one says male qui agit, homo perit.

Student: This indeed is clear and whole.

Teacher: Let us, then, observe this for the sake of the sincerity of music, which the poets do not observe for the ease of singing: that whenever, for example, it is necessary for us to interpose some meters in which nothing is owed to a foot to be compensated by silence, we set those last syllables which the law of that rhythm demands; lest, with some offense to the ears and falseness of measure, we return from the end to the beginning. We grant them, however, to end such meters as if they would thereafter say nothing, and therefore to set the last syllable, whether long or short, with impunity; for in a continuation of meters they are most plainly convicted by the judgment of the ears that they ought not to set as last any syllable except the one that is to be set by the very right and principle of the meter. And this continuation happens when nothing is owed to a foot on account of which we are compelled to be silent.

Student: I understand, and I am grateful that you promise such examples as the sense will suffer no injury from.

4. 3. 4. Teacher: Come, now report in order about these pyrrhics too: Quid erit homo qui amat hominem, si amet in eo fragile quod est? Amet igitur animum hominis, et erit homo aliquid amans. How do these seem?

Student: What, except that they run most sweetly and most soundly?

Teacher: And these? Bonus erit amor, anima bona sit; amor inhabitat, et anima domus. Ita bene habitat, ubi bona domus; ubi mala, male.

Student: These too, continued, I receive most sweetly.

Teacher: Now look at three and a half feet: Animus hominis est mala bonave agitans. Bona voluit, habet; mala voluit, habet.

Student: These too, with a silence of one time-unit interposed, are pleasant.

Teacher: Four full pyrrhics follow; receive these and judge: Animus hominis agit ut habeat ea bona, quibus inhabitet homo, nihil ibi metuitur.

Student: In these too there is a fixed and pleasant measure.

Teacher: Now hear nine short syllables; hear and judge: Homo malus amat et eget; malus etenim ea bona amat, nihil ubi satiat eum.

Student: Now bring forth five pyrrhics.

Teacher: Levicula fragilia bona, qui amat homo, similiter habet.

Student: Now this is enough, and I approve; now add a half-foot.

Teacher: I will: Vaga levia fragilia bona, qui amat homo, similis erit eis.

Student: Quite well; now I await six pyrrhics for it.

Teacher: Hear these too: Vaga levicula fragilia bona, qui adamat homo, similis erit eis.

Student: It is enough; add a half-foot.

Teacher: Fluida levicula fragilia bona quae adamat anima, similis erit eis.

Student: It is enough, and it is well; now give seven pyrrhics.

Teacher: Levicula fragilia gracilia bona, quae adamat animula, similis erit eis.

Student: Let a half-foot be added to these; for this stands elegantly.

Teacher: Vaga fluida levicula fragilia bona, quae adamat animula, fit ea similis eis.

Student: I see that eight feet now remain, so that we may at last escape these tiny things. For although the ears approve by a certain natural measure what you sound, I would not have you seek so many short syllables, which, unless I am mistaken, woven together, are harder to find in the joining of words than if it were allowed to mix longs with them.

Teacher: Nothing escapes you; and to prove to you my gladness that we are at last permitted to pass on from here, I will compose the meter that remains of this kind with a happier thought: Solida bona bonus amat, et ea qui amat habet. Itaque nec eget amor, et ea bona Deus est.

Student: I have most fully the completed meters of the pyrrhic. The iambics follow, of which one or two examples for each suffice for me, which it is a delight to hear with no interruption.

4. 4. 5. Teacher: I will indulge you. But these that we have now finished—how many are they?

Student: Fourteen.

Teacher: And how many do you believe the iambics will be?

Student: Likewise fourteen.

Teacher: And if in them I wished to put a tribrach for an iamb, would not the variety be more manifold?

Student: It is manifest indeed; but I desire to hear these examples in iambs alone, lest we make it long; for that two shorts can be put for any long syllable is an easy lesson.

Teacher: I will do what you wish, and I am grateful that you lessen my labor by a ready understanding; but lend your ear to the iambic.

Student: I am here; begin.

Teacher: Bonus vir beatus. Malus miser, sibi est malum. Bonus beatus, Deus bonum eius. Bonus beatus est, Deus bonum eius est. Bonus vir est beatus, videt Deum beate. Bonus vir et sapit bonum, videns Deum beatus est. Deum videre qui cupiscit, bonusque vivit, hic videbit. Bonum videre qui cupit diem, bonus sit hic, videbit et Deum. Bonum videre qui cupit diem illum, bonus sit hic, videbit et Deum illic. Beatus est bonus, fruens enim est Deo; malus miser, sed ipse poena fit sua. Beatus est videns Deum, nihil cupit plus; malus bonum foris requirit, hinc egestas. Beatus est videns Deum, nihil boni amplius; malus bonum foris requirit, hinc eget miser. Beatus est videns Deum, nihil boni amplius vult; malus foris bonum requirit, hinc egenus errat. Beatus est videns Deum, nihil boni amplius volet; malus foris bonum requirit, hinc eget miser bono.

4. 5. 6. Student: The trochee follows; bring forth the trochaics, for these stand excellently.

Teacher: I will, and in the same way as the iambics: Optimi non egent. Veritate, non egetur. Veritas sat est, semper haec manet. Veritas vocatur ars Dei supremi. Veritate factus est mundus iste quem vides. Veritate facta cuncta quaeque gignier videmus. Veritate facta cuncta sunt omniumque forma veritas. Veritate cuncta facta cerno; veritas manet, moventur ista. Veritate facta cernis omnia, veritas manet, moventur omnia. Veritate facta cernis ista cuncta, veritas tamen manet, moventur ista. Veritate facta cuncta cernis optime, veritas manet, moventur haec, sed ordine. Veritate facta cuncta cernis ordinata, veritas manet, novans movet quod innovatur. Veritate facta cuncta sunt, et ordinata sunt, veritas novat manens, moventur ut noventur haec. Veritate facta cuncta sunt, et ordinata cuncta, veritas manens novat, moventur ut noventur ista.

4. 6. 7. Student: I see the spondee follows; for the trochee too has satisfied the ears.

Teacher: These are the meters of the spondee: Magnorum est, libertas. Magnum est munus libertatis. Solus liber fit, qui errorem vincit. Solus liber vivit, qui errorem iam vicit. Solus liber vere fit qui erroris vinclum vicit. Solus liber vere vivit qui erroris vinclum iam vicit. Solus liber non falso vivit qui erroris vinclum iam devicit. Solus liber iure ac vere vivit qui erroris vinclum magnus devicit. Solus liber iure ac non falso vivit qui erroris vinclum funestum devicit. Solus liber iure ac vere magnus vivit qui erroris vinclum funestum iam devicit. Solus liber iure ac non falso magnus vivit qui erroris vinclum funestum prudens devicit. Solus liber iure ac non falso securus vivit qui erroris vinclum funestum prudens iam devicit. Solus liber iure ac non falso securus iam vivit qui erroris vinclum tetrum ac funestum prudens devicit. Solus liber iure ac non falso securam vitam vivit qui erroris vinclum tetrum ac funestum prudens iam devicit.

4. 7. 8. Student: I have nothing to ask about the spondee either; let us come to the tribrach.

Teacher: Indeed. But since all four of the earlier feet of which we have spoken have produced fourteen meters each, which together are fifty-six, more are to be expected from the tribrach. For in those, when the span of a half-foot is in silence, no more than one syllable is kept silent; but in this, when we are silent, do you judge that one ought to be silent only for the span of one short syllable, or can the delay of two shorts too be contained in the silence? Since no one would doubt that its division is twofold: for it either begins from one and ends at two, or, beginning from two on the contrary, is terminated by one. So this must produce twenty-one meters.

Student: It is most true. For they begin from four shorts, so that we are silent for two time-units; then there are five, where we are silent for one; third, six, where nothing is to be kept silent; fourth, seven, where again two time-units are to be kept silent; then eight, where one; sixth, nine, where none. And so, as single syllables are added, until one comes to twenty-four syllables, which are eight tribrachs, twenty-one meters in all are completed.

Teacher: You have followed the reasoning most readily; but do you judge that examples are to be brought forth by us everywhere, or is it to be thought that those we set under those first four feet will give light enough to the rest?

Student: In my judgment, enough.

Teacher: Nor do I now require any judgment but yours. Nevertheless, since you now know excellently that in pyrrhic meters, the beat being changed, tribrachs can be beaten, I ask whether the first pyrrhic meter can also have the meter of the tribrach.

Student: It cannot; for a meter ought to be larger than a foot.

Teacher: And the second?

Student: It can: for the four shorts are two pyrrhics, one tribrach and a half-foot, so that there we are silent for no time-units, here for two.

Teacher: So, the beat being changed, you have in the pyrrhics examples of the tribrach too, up to sixteen syllables—that is, up to five tribrachs and a half-foot—with which you must be content; for the rest you can weave together yourself, whether by voice or by some beat, if indeed you still judge that rhythms of this kind are to be tested by the sense of the ears.

Student: I will do what seems best; let us see what remains.

4. 8. 9. Teacher: The dactyl follows, which can be divided once. Or do you think otherwise?

Student: No, it is so.

Teacher: What fraction of it, then, can be in silence?

Student: Half, of course.

Teacher: And if, a trochee being set after the dactyl, someone wished to be silent for one time-unit, which is owed in a short syllable to filling out the dactyl, what shall we answer? For we cannot say that one ought not to be silent for less than the span of a half-foot. For the reasoning treated above had persuaded us that one ought to be silent not for less but for more than the time of a half-foot. For surely less than a half-foot is kept silent in the choriamb, where a bacchius is set after the choriamb itself, of which the example is fonticolae puellae. For you recognize that here we are silent for the span of one short syllable, which is owed to filling out six time-units.

Student: You speak truly.

Teacher: A trochee being set, then, after the dactyl, will it be allowed to be silent even for one time-unit?

Student: So I am compelled to admit.

Teacher: Who, in the end, would compel you, if you remembered the earlier points? For this has happened to you: that you have forgotten what was shown about the indifference of the last syllable, and how the ears claim the last as a long where there remains a span over which it may be stretched, even if it is short.

Student: Now I understand: for surely, if the ears take the last short syllable as long when a silence remains, as we have learned by the earlier reasoning and examples, it will matter nothing whether a trochee or a spondee is set after the dactyl. So when the repetition is to be distinguished by silence, one ought to put one long syllable after the dactyl, so that we are silent for the span of two time-units.

Teacher: And if a pyrrhic is set after the dactyl, do you think it is rightly done?

Student: Not rightly: for it matters nothing whether it is the same or an iamb, since it must be taken for an iamb because of the last syllable, which the ears require to be long, because a silence remains. But that an iamb ought not to be set after a dactyl, because of the difference of raising and setting-down—neither of which ought in the dactyl to have three time-units—who would not understand?

4. 9. 10. Teacher: Excellently and consistently throughout. But what, in the end, seems to you about the anapest? Is the reasoning the same?

Student: Quite the same.

Teacher: Now then let us consider the bacchius, if you please, and tell me what its first meter is.

Student: I think it is four syllables—one short and three longs, of which two belong to the bacchius, but the last one to the beginning of that foot which can be set with the bacchius, so that what is owed to it is in silence; yet in some example I would like to test this by the ears.

Teacher: It is easy indeed to add examples, by which, however, I do not think you can be delighted as by the earlier ones; for these feet of five time-units, like those of seven, do not run so sweetly as those that are divided either into equal parts, or into single and double, or into double and single—so great is the difference between sesquate motions and equal or multiplied ones, of which we treated enough in that first discussion of ours. And so these feet, namely of five and seven time-units, prose takes up the more willingly the more disdainfully the poets do; which can be seen more easily in the examples you asked for. For these are: Laborat magister docens tardos. Turn this over, with a silence of three time-units interposed, which, that you might more easily feel it, I therefore set a long syllable after three feet, which is the beginning of a cretic, which can be set with a bacchius. Nor did I give an example for the first meter, which is of four syllables, lest one foot should not be enough to remind your sense how much you ought to be silent after it and one long. This now, see, I will utter, and repeat myself, so that in my silence you may feel three time-units: Labor nullus, amor magnus.

Student: It appears well enough that these feet are more harmonious for prose, and there is no need to run through the rest with examples.

Teacher: You speak truly; but does it seem to you that, when one must be silent, only one long can be set after the bacchius?

Student: Not at all; but also a short and a long, which is the first half-foot of that same bacchius: for if we were allowed to begin a cretic, because it can be set with that same bacchius, how much more will it be allowed to do this with the bacchius itself—especially since we will not have set down the whole of the cretic that is equal in time-units to the first part of the bacchius?

4. 10. 11. Teacher: Now then, if you please, with me listening and judging, run through the rest yourself, and set forth what is put after a full foot, when the remainder is filled by silence, in all the feet that remain.

Student: What you require is now, I think, most brief and most easy; for what was said of the bacchius can be said also of the second paeon. After the cretic one may put both a single long, and an iamb, and a spondee, so that either three time-units, or two, or one are kept silent. And what was said of this falls also on the first and last paeons [because of the two divisions]. Now after the palimbacchius it is fitting that either a single long or a spondee be set, so in this meter too either three time-units or one will be kept silent. The same is the condition of the third paeon. Indeed, wherever a spondee, there an anapest too is rightly set. But after the molossus, as concerns its division, we set either a single long, so that we are silent for four time-units, or two, so that we are silent for two. But since it has been tested both by reckoning and by reason that all six-time-unit feet can be ordered with it, there will be a place after it for an iamb too, and three time-units will remain to be kept silent; there will be one for a cretic, and one will be kept silent; on this condition there will be one for a bacchius too. But if we dissolve the first of the cretic and the second of the bacchius into two shorts, there will be one for the fourth paeon. And what I have said of the molossus, I would say of the other six-time-unit feet too. Now I judge the proceleusmatic is to be referred to the others that consist of four time-units, except when we set three shorts after it; which is as if we set an anapest, because of the last syllable, which with the silence is usually taken as a long. But to the first epitrite an iamb is rightly joined, and a bacchius and a cretic and a fourth paeon. Let this be said of the second too, so that either four or two time-units are kept silent. The two remaining epitrites the spondee and the molossus can rightly follow, so that one may dissolve the first of the spondee, and the first or second of the molossus, into two shorts. So in these meters either three time-units or one will be kept silent. There remains the dispondee, after which, if we set a spondee, four time-units must be kept silent; if a molossus, two, the license remaining of dissolving a long into two shorts, whether in the spondee or in the molossus, except the last. You have what you wished me to run through—unless perhaps you will correct something.

4. 11. 12. Teacher: Nay, not I, but you, when you have applied your ear to judging. For I ask you whether, when I say and beat this meter, Verus optimus, and this, Verus optimorum, and this, Veritatis inops—your sense receives this third as pleasantly as those earlier ones; which, by repeating them and beating them with the due silences, it will easily judge.

Student: It is manifest that it receives those pleasantly, this unpleasantly.

Teacher: Then an iamb is not rightly set after a dichoree.

Student: It is so.

Teacher: But that it can rightly be set after the others, whoever repeats these meters with the discipline of interposing silences will agree: Fallacem cave. Male castum cave. Multiloquium cave. Fallaciam cave. Et invidum cave. Et infirmum cave.

Student: I feel what you say, and I approve.

Teacher: See also whether nothing offends you when, a silence of two time-units interposed, this meter, repeated, goes on unequal. For does it sound as these do? Veraces regnant. Sapientes regnant. Veriloqui regnant. Prudentia regnat. Boni in bonis regnant. Pura cuncta regnant.

Student: On the contrary, these are equal and sweet, but that one absurd.

Teacher: So we will hold this in the meters of six-time-unit feet: that the dichoree is badly closed by an iamb, and the antispast by a spondee.

Student: We will hold it indeed.

4. 11. 13. Teacher: And will you not approve the cause why it is so, if you notice that a foot is divided by raising and setting-down into two parts, so that, if there is some middle syllable in it, whether one or two, either it is assigned to one part, the prior or the latter, or it is divided between both?

Student: I know that, and it is true; but what of it?

Teacher: Attend to this too which I will say, and then you will see more easily what you ask. For I judge it is manifest to you that some feet are without middle syllables, as the pyrrhic and the rest of two syllables; others in which the middle agrees in span either with the prior part, or with the last, or with both, or with neither: with the prior, as in the anapest, or the palimbacchius, or the first paeon; with the last, as in the dactyl, or the bacchius, or the fourth paeon; with both, as in the tribrach, or the molossus, or the choriamb, or any ionic; with neither, as in the cretic, or the second and third paeons, or the diiamb, dichoree, antispast. For the feet that can be divided into three equal parts have their middle part agreeing with the first and the last; but those that cannot, either with the first only, or with the last, or with neither.

Student: This too I know equally, and I await where it tends.

Teacher: Where, in the end, do you think, except that you may see that an iamb is badly set with silence after a dichoree, because its middle is equal neither to the prior part nor to the last, and on that account discords from the raising and setting-down? This is understood of the spondee too, which likewise does not like to be set with silence after an antispast. Or is anything to be said by you against this?

Student: For my part nothing—except that this offense which is made to the ears, when these feet are so placed, is made in comparison with that sweetness which delights the hearing when these feet are set with silence after the other six-time-unit feet. For if, the others being kept silent, you consulted me how they sounded, examples being added, an iamb set after a dichoree, or a spondee after an antispast, with silence—I will say what I feel: perhaps I would approve and praise them.

Teacher: I do not resist you indeed. Yet it is enough for me that this placement offends in comparison with such rhythms, but ones sounding better, as you say; for it is to be disapproved on this ground: that, since those feet too are of the same kind, which we confess glide more pleasantly closed by these half-feet, it ought not to have differed from them. But does it not seem to you, by this reasoning, that an iamb ought not to be set with silence after a second epitrite either? For in this foot too the iamb holds the middle place so that it is equal in time-units neither to the prior nor to the latter part.

Student: The earlier reasoning compels me to concede it.

4. 12. 14. Teacher: Come now, render me the number of all the meters, if you please, that we have now treated—that is, of those which begin from their full feet, and are closed off either by their full feet, so that we do not interpose silence when one returns to the head, or by feet not full, with silence, which yet reason taught to agree with them; the number beginning from two not-full up to eight full, yet so that thirty-two time-units are not exceeded.

Student: What you impose is laborious indeed, yet it is worth the labor. But I remember that a little while ago we had already come to seventy-seven meters from the pyrrhic up to the tribrach, since those feet of two syllables produced fourteen each, which together are fifty-six. But the tribrach produced twenty-one, because of its twofold division. To these seventy-seven, then, we add the fourteen of the dactyl and as many of the anapest: for if set full, with no silence, the meter beginning from two up to eight feet, they bear seven each; but with half-feet added, with silence, the meter beginning from one foot and a half-foot reaching to seven and a half, another seven each. And now all become a hundred and five. But the bacchius cannot carry its meter up to eight feet, lest it pass thirty-two time-units, nor can any foot of five time-units; but these can come up to six. The bacchius, then, and the second paeon, which is equal to it not only in time-units but also in division, proceeding from two feet up to six, when ordered whole without silence, bear five meters each; but with silence, beginning from one half-foot and reaching to five half-feet, another five each when one long is set after them, and likewise five when a short and a long; so they create fifteen each, which reduced to a sum are thirty. And now all the meters become a hundred and thirty-five. But the cretic, and those divided equally with it, the first and fourth paeons, since after them one may put both a single long, and an iamb, and a spondee, and an anapest, come to seventy-five: for since there are three feet, they create five each without silence, but twenty with silence, which together, as said, become seventy-five, which added to the previous sum complete two hundred and ten. The palimbacchius and the third paeon, which agrees with it in division, bear five whole without silence; but with silence, five with one long, five with a spondee, five with an anapest. These we add to the larger sum, and we have all the meters two hundred and fifty.

4. 12. 15. The molossus and the other six-time-unit feet, which with it make seven, create four each whole; but with silence, since after each of them can be set a single long, and an iamb, and a spondee, and an anapest, and a bacchius, and a cretic, and a fourth paeon, they complete twenty-eight each, which together become a hundred and ninety-six, which taken with those fours complete two hundred and twenty-four; but from this eight are to be deducted, because an iamb after a dichoree and a spondee after an antispast are badly ordered. There remain two hundred and sixteen, which added to the larger sum make all the meters four hundred and sixty-six. The proceleusmatic could not be reckoned with the feet to which it agrees, because of the half-feet that are set after it in greater number. For both one long syllable can be set after it with silence, as after the dactyl and its consorts, so that two time-units are kept silent, and three shorts so that one time-unit is kept silent; whereby it comes about that the last short is taken for a long. The epitrites produce three meters each whole, the meter beginning from two feet, reaching to four; for if you add a fifth, you will exceed thirty-two time-units, which one ought not. But with silence the first and second epitrites give three each, an iamb being set after, three with a bacchius, three with a cretic, three with a fourth paeon; which become, with those three that are without silence, thirty. But the third and fourth epitrites produce three before silence, three with a spondee, and three with an anapest, three with a molossus, three with an ionic from the lesser, three with a choriamb; which become, together with those three that they produced without silence, thirty-six. So all the epitrites bear sixty-six meters; which, with the twenty-one of the proceleusmatic, added to the previous sum, make five hundred and fifty-three. The dispondee remains, itself too producing three whole; but with silence applied, three with a spondee, and three with an anapest, three with a molossus, three with an ionic from the lesser, three with a choriamb; which taken in sum with those three that it creates whole, become eighteen. So all the meters will be five hundred and seventy-one.

4. 13. 16. Teacher: They would be, were not three to be taken away, because after the second epitrite it was said that an iamb is badly set. But this stands well; so now tell me how this meter touches your ear: Triplici vides, ut ortu Triviae rotetur ignis.

Student: Most sweetly.

Teacher: Can you say of what feet it consists?

Student: I cannot; for I do not find how those I measure agree with one another. For whether I set a pyrrhic at the head, or an anapest, or a third paeon, they do not agree with those that follow; and I find here indeed a cretic after the third paeon, so that a long syllable remains, which the cretic does not refuse to have set after it; but this meter could not rightly consist of these feet except with a silence of three time-units interposed; whereas now nothing is kept silent, when, repeating it, it charms the hearing.

Teacher: See, then, whether it ought to begin from a pyrrhic, then let us measure a dichoree, then a spondee, which completes the time-units, of which two are at the beginning. The head can likewise be held by an anapest, then a diiamb be measured, so that the last long, set with the four time-units of the anapest, completes six time-units, which agree with the diiamb; from which you may understand that the parts of feet are set not only at the end but also at the head of meters.

Student: Now I understand.

4. 13. 17. Teacher: And if I take away one last long, so that the meter is such: Segetes meus labor—do you not notice that it is repeated with a silence of two time-units? From which it is manifest both that some part of a foot can be set at the beginning of a meter, and some at the end, and some in silence.

Student: This too is manifest.

Teacher: But this happens if you measure a whole dichoree in this meter; for if a diiamb, and an anapest is set at the head, you discern that a part of a foot is set at the beginning, which now has four time-units, while the two that are owed are kept silent at the end. From which we learn that a meter can begin from a part of a foot, and end at a full foot, but never without silence.

Student: This too is clear.

4. 13. 18. Teacher: And can you measure this meter, and say of what feet it consists? Iam satis terris nivis, atque dirae grandinis misit Pater, et rubente dextera sacras iaculatus arces.

Student: I can set a cretic at the head, and measure two remaining feet of six time-units, one an ionic from the greater, the other a dichoree, and be silent for one time-unit which is joined to the cretic so that six time-units are completed.

Teacher: Something was lacking to your consideration: for when the dichoree is at the end, a silence remaining, its last syllable, which is short, is taken for a long. Or will you deny this?

Student: On the contrary, I admit it.

Teacher: It is not fitting, then, to set a dichoree at the end, except when no silence follows in the repetition, lest now not a dichoree but a second epitrite be perceived.

Student: It is manifest. How, then, shall we measure this meter?

Student: I do not know.

4. 14. 18. Teacher: Attend, then, whether it sounds well when I pronounce it so as to be silent for one time-unit after the first three syllables: for thus nothing will be owed at the end, so that a dichoree can fittingly be there.

Student: It sounds most pleasantly.

4. 14. 19. Teacher: Let us, then, add this too to the art: that we be silent, when we ought, not only at the end but also before the end. And we ought to do so when what is owed to filling out the time-units of feet is either unfittingly kept silent at the end because of a final short, as in the case mentioned; or when two not-full feet are set, one at the head, the other at the end, such as this: Gentiles nostros inter oberrat equos. For you felt, I think, that after five long syllables I was silent for a delay of two time-units, and just as much must be kept silent at the end, while one returns to the head. For if you measure this meter by the law of six time-units, the first will be a spondee, the second a molossus, the third a choriamb, the fourth an anapest. Two time-units, then, are owed to the spondee to fill out a six-time-unit foot, and to the anapest; so two are kept silent after the molossus before the end, and two after the anapest at the end. But if by the law of four time-units, there will be one long at the head, then we measure two spondees, then two dactyls, and after that one long will conclude. And so we are silent for two time-units after the double spondee before the end, and two at the end, so that both feet may be filled, whose halves we set at the head and at the extreme.

4. 14. 20. Sometimes, however, what is owed to two not-full feet set at the beginning and end is rendered by the final silence alone, if it is only so much that it does not exceed the span of a half-foot, such as these two: Silvae laborantes, geluque flumina constiterint acuto. For the former of these begins from a palimbacchius, then runs out into a molossus, and is terminated by a bacchius: so two time-units are kept silent; one of which, when you have rendered to the bacchius and the other to the palimbacchius, six time-units everywhere will be filled. But this latter is begun by a dactyl, then proceeds into a choriamb, is closed by a bacchius: so one must be silent for three time-units; one of which we will repay to the bacchius, two to the dactyl, so that in all there are six time-units.

4. 14. 21. But what is owed to filling out the last foot is rendered before what is owed to the one set at the beginning. Nor do the ears allow it to be done otherwise at all. And no wonder: for when we repeat it, what is utterly last is joined to the head. So in this meter that was mentioned, flumina constiterint acuto, since three time-units are owed to filling out the six, if you wish to render them not by silence but by voice, and they can be rendered by an iamb, by a choree, or by a tribrach, since all hold three time-units—the sense itself in no way permits them to be rendered by a choree, in which the long syllable is prior and the short latter: for that ought to sound first which is owed to the last bacchius, that is, the short syllable, not the long, which is owed to the first dactyl. One may test this by these examples: Flumina constiterint acuto gelu. Flumina constiterint acute gelida. Flumina constiterint in alta nocte. Who doubts that those two are repeated sweetly, but this third in no way?

4. 14. 22. Likewise, when single time-units are owed to single less-than-full feet, if you wish to render them by voice, the sense does not allow them to be compressed into one syllable—an altogether wonderful justice. For it is not fitting that what is to be rendered separately should not also be set down separately. Therefore in that meter Silvae laborantes, geluque, if you add one long for the silence at the end, as in Silvae laborantes gelu duro, the ears do not approve it, as they do approve when we say Silvae laborantes gelu et frigore. Which you feel most fully when you repeat each.

4. 14. 23. Likewise, when two less-than-full feet are set, the larger ought not to be set at the beginning rather than at the end; for the hearing condemns this too, as if you say Optimum tempus adest tandem, so that the first foot is a cretic, the second a choriamb, the third a spondee, so that we are silent for three time-units, of which two are owed to the last spondee to fill out six, and one to the first cretic. But if it is said thus, Tandem tempus adest optimum, the same delay of three time-units being interposed in silence, who would not feel that it is repeated most pleasantly? So either the less-than-full foot at the end ought to be of as great a span as that at the beginning, as that Silvae laborantes, geluque; or the smaller at the beginning and the larger at the end, as is Flumina constiterint acuto. And not without reason, because where there is equality, there is no discord; but where the number is unequal, if we come from the smaller to the larger, as is usual in counting, the order itself again makes concord.

4. 14. 24. From which this too follows: that when the less-than-full feet of which we are treating are set, if silence is interposed in two places—that is, before the end and at the end—just so much is kept silent before the end as is owed to the last, and just so much at the end as is owed to the first; because the middle tends toward the end, but from the end one must return to the beginning. But if the same is owed to each, there is no dispute that as much must be kept silent before the end as at the end. And one ought to be silent only where a part of speech is terminated. But in those rhythms which are made not by words but by some beat or breath, or even by the tongue itself, there is no distinction in this matter after what voice or beat one is silent, provided only that a lawful silence intervene according to the principles stated above. So a meter can begin from two less-than-full feet too, provided that the joined span of both is not less than that of one foot and a half could be; for we said above that two less-than-full feet are rightly set when what is owed to both does not pass the span of a half-foot. An example is Montes acuti; so that we are silent either for three time-units at the end, or one time-unit after the spondee and two at the end. For otherwise this meter cannot be conveniently measured.

4. 15. 25. Let this too be in the discipline: that when we are silent before the end, a part of speech should not be terminated there by a short syllable, lest, according to that often-mentioned rule, the sense take it for a long, a silence following. So in this meter Montibus acutis we cannot be silent for one time-unit after the dactyl, as we could in the earlier one after the spondee, lest now not a dactyl but a cretic be perceived; and so the meter would seem to consist not of two less-than-full feet, which we are now demonstrating, but of a full dichoree and a final spondee, with a silence of two time-units to be rendered at the end.

4. 15. 26. But this is to be noted: that for a less-than-full foot set at the beginning, what is owed is rendered by silence either in that same place, as is Iam satis terris nivis atque dirae, or at the end, as Segetes meus labor. But for a less-than-full foot set at the end, what is owed is restored by silence either in that same place, as in that Ite igitur Camoenae, or in some middle place, as in this: Ver blandum viget arvis, adest hospes hirundo. For the one time-unit owed to the last bacchius can be kept silent either after the whole rhythm, or after the first foot of that rhythm, the molossus, or after the second, the ionic from the lesser. But what is owed perhaps to less-than-full feet in the middle can be rendered only in that same place: as is Tuba terribilem sonitum dedit aere curvo. For if we measure this meter so as to make the first an anapest, the second any ionic in five syllables (the long, of course, whether first or last, being dissolved into two shorts), the third a choriamb, the last a bacchius—there will be three time-units owed, one to be rendered to the last bacchius, and two to the first anapest, so that six may be completed. But this whole span of three time-units can be kept silent at the end. But if you begin from a whole foot, the first five syllables being measured as any ionic, a choriamb follows; then you will no longer find a whole foot; therefore one must be silent for the span of one long; which counted in, the other choriamb will be filled; the remaining bacchius being about to close the meter, to which the one owed time-unit you will keep silent at the end.

4. 15. 27. Whence I think it is now clear that, when one is silent in the middle places, either those time-units are restored that are owed at the end, or those that are owed where one is silent. But sometimes it is not necessary to be silent in the middle, when the meter can be measured otherwise, as in the one we set down a little before. But sometimes it is necessary, as in this: Vernat temperies, aurae tepent, sunt deliciae. For it is manifest that this rhythm runs by feet either of four time-units or of six. If of four, one must be silent for one time-unit after the eighth syllable, and two at the end; let a spondee be measured first, a dactyl second, a spondee third, a dactyl fourth—a silence being counted in after the long, because not after a short—a spondee fifth, a dactyl sixth, the last long by which the rhythm is closed, to which the two owed time-units are kept silent at the end. But if we measure here feet of six time-units, the first will be a molossus, the second an ionic from the lesser, the third a cretic which becomes a dichoree with a silence of one time-unit joined, the fourth an ionic from the greater and the last long, after which four time-units will be kept silent. It could be otherwise, so that one long is set at the beginning, which an ionic from the greater follows, then a molossus, then a bacchius, which would become an antispast with a silence of one time-unit joined; the last choriamb would close the meter, so that a silence of four time-units at the end is rendered to the one long set at the beginning. But the ears reject this measuring; because a part of a foot set at the beginning, unless it has been greater than a half, is not rightly rendered to it, after a full foot, by a final silence where it is owed; but with other feet interposed, we know indeed how much is owed, yet it is not grasped by the sense to be silent for so great a span, unless less is owed in silence than was set in sound: because when the voice has finished the greater part of a foot, the smaller part that remains easily occurs wherever it may.

4. 15. 28. Therefore, of the meter we set down under this example, Vernat temperies, aurae tepent, sunt deliciae: since there is one necessary measuring, which we have mentioned—if after its tenth syllable one time-unit is kept silent, and four at the end—there is another, voluntary, if one wishes after the sixth syllable to be silent for two time-units, and one after the eleventh, and two at the end: so that there is a spondee at the beginning, a choriamb follows it, a silence of two time-units is counted to the third spondee, so that it becomes either a molossus or an ionic from the lesser, the fourth bacchius, a silence of one time-unit likewise joined, becomes an antispast, the rhythm is terminated in the voice by the fifth choriamb, two time-units at the end being rendered by silence to the spondee set at the beginning. There is likewise another. For, if you wish, after the sixth syllable you will be silent one time-unit, and one after the tenth, as much after the eleventh, and two at the end: so that the first is a spondee, the second a choriamb, the third a palimbacchius becomes an antispast, one time-unit of silence being counted in, the fourth spondee becomes a dichoree, one time-unit being interposed and one time-unit of silence following, the last choriamb closes the rhythm, so that we are silent two time-units at the end, which are owed to the first spondee. There is a third measuring too, if after the first spondee one time-unit is kept silent, and the rest as kept in the one just above; except that in the end of this one one time-unit will be kept silent, because that spondee which is usually set at the beginning has, by a following silence of one time-unit, become a palimbacchius, so that nothing more than one time-unit is owed to it, to be kept silent at the end. Whence you now perceive that silences are interposed in meters—some necessary, some voluntary; necessary indeed, when something is owed to filling out feet; voluntary, when the feet are full and whole.

4. 15. 29. But what was said above, that one ought not be silent for more than four time-units, was said of the necessary silences, where owed time-units are filled out. For in those we have named voluntary silences, one may even sound a foot and be silent for a foot; which, if we do it at equal intervals, will not be a meter but a rhythm, no fixed end appearing from which to return to the head. So if, for example, you wish to distinguish by silences, so that after the first foot you are silent for the time-units of another foot, this is not to be kept up perpetually. But one may, with any variety of counted-in silences, draw out a meter up to the lawful time-units, as in this: Nobis verum in promptu est, tu si verum dicis. Here one may be silent for four time-units after the first spondee, and another four after the two following; but after the three final ones nothing will be kept silent, for now thirty-two time-units are terminated. But it is much more fitting, and in a way more just, that one be silent either only at the end, or also in the middle and at the end—which can be done by subtracting one foot, so that it is thus: Nobis verum in promptu est, tu dic verum. This too is to be held in the meters of the other feet: namely that by necessary silences, whether final or middle, what is owed is rendered, so that the feet may be filled; but that one ought not be silent for more than the part of a foot which the raising or setting-down takes up. But by voluntary silences both parts of feet and whole feet may be kept silent, as we have shown by the examples given above. But let the principle of interposing silences be treated thus far.

4. 16. 30. Now let us say a few things about the mixing of feet, and about the coupling of the meters themselves; since much has already been said when we inquired which feet ought to be mixed with one another; and as concerns the coupling of meters, some things are to be said when we begin to discuss verses; for feet are joined and mixed with one another according to the rules we opened up in the second discussion. But in this it is to be known that each of the kinds of meter which have already been celebrated by the poets had its own authors and inventors, from whom we are forbidden to wrench away certain fixed laws they have set; for it is not fitting, when they have fixed them by reason, to change anything there, although according to reason we might do so without offense to the ears. The knowledge of this is handed down not by art but by record, whence it is believed rather than known. For if some Phaliscus, I know not who, composed meters so that they sound thus: Quando flagella ligas, ita liga, vitis et ulmus uti simul eant, we cannot know this, but only believe it by hearing and reading. That is a matter of the discipline which pertains to us: to see whether this consists of three dactyls and a final pyrrhic, as most who are unskilled in music claim—for they do not feel that a pyrrhic cannot be set after a dactyl—or whether, as reason teaches, the first foot in this meter is a choriamb, the second an ionic with the long syllable dissolved into two shorts, the last an iamb, after which three time-units will be kept silent: which half-learned men could feel, if it were pronounced and beaten by a learned man according to each law. For thus they would judge by natural and common sense what the standard of the discipline prescribed.

4. 16. 31. Nevertheless, that that poet wished these rhythms to be unchangeable must be kept when we use this meter: for it does not cheat the hearing—although it would equally cheat nothing if we set either a diiamb for the choriamb, or the ionic itself with no dissolution into shorts, or whatever else would agree. In this meter, then, nothing will be changed; not by that principle by which we avoid inequality, but by that by which we observe authority. Reason indeed teaches that some meters are established as unchangeable—that is, in which nothing ought to be changed, as is this very one of which we have spoken enough; others changeable, in which one may set some feet for others, as is Troiae qui primus ab oris, arma virumque cano. For here one may set an anapest for a spondee in any place. Others neither wholly unchangeable nor wholly changeable, as is Pendeat ex umeris dulcis chelys, et numeros edat varios, quibus assonet omne virens late nemus, et tortis errans qui flexibus. For you see that here spondees and dactyls can be set everywhere, except the last foot, which the author of the meter wished always to be a dactyl. And in these three kinds you see that authority has some force.

4. 16. 32. But as to what, in the mixing of feet, pertains to reason alone judging about the things that are perceived: it is to be known that those parts of feet which are set unpleasantly after certain feet, a silence remaining—as an iamb after a dichoree and a second epitrite, and a spondee after an antispast—are also badly set after other feet with which these have been mixed; for it is manifest that an iamb is well set after a molossus, as this example, often repeated with a silence of three time-units at the end, indicates: Ver blandum viret floribus; but if you set a dichoree first for the molossus, as is Vere terra viret floribus, the hearing rejects and condemns this. This too is easy to test in the rest, with the sense examining. For the principle is most certain, that when feet capable of being coupled are coupled with one another, those parts ought to be joined at the end which agree with all set in that series, lest among allies, in a way, some discord arise.

4. 16. 33. This is the more to be wondered at: that, although a spondee sweetly closes both a diiamb and a dichoree, yet when these two feet, whether alone or mixed in any way with others capable of being coupled, are in one series, a spondee cannot, with the sense approving, be set at the end. For who would doubt that the ears gladly receive these repeated singly: Timenda res non est, and likewise separately, Iam timere noli? But if you join them thus, Timenda res, iam timere noli, I would not wish to hear it except in prose. And it is no less absurd if you connect another in any place, such as a molossus in this way: Vir fortis, timenda res, iam timere noli; or thus, Timenda res, vir fortis, iam timere noli; or even thus, Timenda res, iam timere vir fortis noli. The cause of which absurdity is that the diiamb foot can also be beaten to double and single, as the dichoree to single and double; but the spondee is equal to the double part of these; but when the one draws it to the first, the other to the last, some discord arises; and so reason takes away the wonder.

4. 16. 34. No less a marvel does the antispast produce: with which, if no other of the feet, or at any rate only a diiamb, is mixed, it allows the meter to be closed by an iamb, but when set with others in no way; and with a dichoree indeed because of the dichoree itself, so this I do not wonder at. But with the other feet of six time-units, why it rejects the mentioned foot of three time-units at the end, I do not know—there is some cause more hidden, perhaps, than that it can be drawn out and shown by us; but that it is so I prove by these examples. For these two meters, Potestate placet, Potestate potentium placet, no one doubts are sweetly repeated singly with a silence of three time-units at the end. But these unpleasantly with the same silence: Potestate praeclara placet. Potestate tibi multum placet. Potestate iam tibi sic placet. Potestate multum tibi placet. Potestatis magnitudo placet. As concerns the sense, it has done its duty in this question, and has indicated both what it received and what it hissed off; but about the cause why it is so, reason must be consulted. And mine indeed, in such great obscurity, sees nothing else but that the antispast has its prior half in common with the diiamb—for each begins from a short and a long—but its latter half with the dichoree, for both are ended by a long and a short. And so the antispast, set either alone, as having its own prior half, or with the diiamb, with which it has it in common, allows there to be an iamb at the end of the meter; and with the dichoree it would allow it, if such a termination agreed with that same dichoree; but with the rest it does not allow it, with which it is not joined by such a fellowship.

4. 17. 35. But as concerns the coupling of meters, it is enough for the present to see that diverse meters can be coupled with one another, which yet agree in beat, that is, in raising and setting-down. They are diverse either in quantity, as when larger are coupled with smaller, such as these, namely: Iam satis terris nivis atque dirae grandinis misit Pater, et rubente dextera sacras iaculatus arces, terruit urbem. For this fourth, which is terminated by one choriamb and one long at the end, you see how small it is, set under the three earlier ones equal to one another. Or in feet, as these: Grato Pyrrha sub antro, cui flavam religas comam. For you discern that the earlier of these two consists of a spondee and a choriamb, and a last long, which was owed to the spondee to fill out six time-units; but this latter of a spondee and a choriamb, and two last shorts, which likewise with the first spondee fill out six time-units. These are equal, then, in time-units, but in feet hold some diversity.

4. 17. 36. There is also another difference of these couplings: that some are so coupled that they wish no silences interposed between them, as these two most recent; others demand that something be kept silent between them, as these: Vides ut alta stet nive candidum Soracte, nec iam sustineant onus silvae laborantes, geluque flumina constiterint acuto. For if these are repeated singly, the first two demand that one time-unit be kept silent at the end, the third two, the fourth three. But coupled, they compel one passing from the first to the second to be silent for one time-unit, from the second to the third two, from the third to the fourth three. But if from the fourth you return to the first, you will be silent for one time-unit. And the principle of returning to the first is the same as that of passing to another such coupling. This kind of coupling we rightly call a "circuit" (circuitus), which in Greek is called a "period." A circuit, then, cannot be less than one that consists of two members—that is, of two meters; nor did they wish it to be larger than one that proceeds up to four members. So one may call the smallest two-membered, the middle three-membered, and the last four-membered. Since we are going to treat of this whole kind more carefully, as I said, in that discussion which we will have about verses, for now let this in the meantime be enough.

4. 17. 37. Student: Let it be so.

5. 1. 1. Teacher: What a verse is was inquired among the learned ancients with no small struggle, nor was the fruit lacking. For the thing was discovered, and committed to writing for the knowledge of posterity, made firm by a weighty and certain authority and also by reason. They noticed, then, that there is some difference between rhythm and meter, so that every meter is rhythm, but not every rhythm is also meter. For every lawful connection of feet is rhythmical; and since meter has this, it can in no way fail to be rhythm, that is, fail to be number. But because it is not the same thing to roll on with lawful feet but no fixed end, and likewise to proceed with lawful feet but be restrained by a fixed end, these two kinds had also to be distinguished by terms—so that the former is now called rhythm only, by its proper name, while this other is called rhythm in such a way that it is also called meter. Again, since of those rhythms that are closed off by a fixed end—that is, of meters—some are those in which no account is taken of a certain division about the middle, others in which it is carefully taken, this difference too had to be noted by terms. Therefore the kind of rhythm where this account is not taken was properly called "meter"; but where it is taken, they named it "verse." The origin of which name reason itself will perhaps show us as we proceed. Nor should you think this so prescribed that it is not also permitted to call those meters verses. But it is one thing when we misuse a name, by the license of a certain nearness, another when we state a thing by its proper word. But let the mention of names be made thus far; in which, as we have already learned, the agreement of those conversing and the authority of antiquity have full force. The rest, if you please, let us investigate in our manner, with sense reporting and reason judging; so that you may recognize that even those ancient authors did not establish these things as if they had not been whole and perfect in the nature of things, but discovered them by reasoning, and noted them by naming.

5. 2. 2. Student: This indeed has already been made clear and proved to me before.

Teacher: And meter, which is manifestly made by the comparison of feet—must it be judged to be of that kind of thing which cannot be divided, when nothing indivisible can be stretched through time at all, and what consists of divisible feet would most absurdly be thought indivisible?

Student: In no way would I refuse that this kind admits division.

Teacher: But all things that admit division—are they not more beautiful if their parts agree by some equality than if they are discordant and dissonant?

Student: There is no doubt for anyone.

Teacher: And what number, in the end, is the author of equal division itself? Is it two?

Student: It is so.

Teacher: As, then, we have found that a foot is divided into two harmonious parts, and by that very thing delights the ear, if we also find such a meter, will it not rightly be preferred to the others that are not such?

Student: I agree.

5. 3. 3. Teacher: Rightly indeed. So now answer this: since in all things that we measure by some part of time, one thing precedes, another follows, one begins, another ends, does it not seem to you that there ought to be some difference between the preceding and beginning part, and that which follows and ends?

Student: I judge that there ought to be.

Teacher: Tell me, then, what difference there is between these two parts of a verse, of which one is cornua velatarum, the other vertimus antennarum. For not as the same poet has it, obvertimus, but if the verse is uttered thus, cornua velatarum vertimus antennarum—is it not made uncertain, by repeating it more often, which part is prior and which latter? For the same verse stands no less when it is uttered thus: Vertimus antennarum cornua velatarum.

Student: I see plainly that it becomes uncertain.

Teacher: Do you judge it should be avoided?

Student: I do.

Teacher: See, then, whether it is sufficiently avoided here. One part of the verse, and that the preceding one, is arma virumque cano; the other, following, Troiae qui primus ab oris; which differ so far from each other that, if you reverse the order and pronounce it this way, Troiae qui primus ab oris, arma virumque cano, it is necessary to measure other feet.

Student: I understand.

Teacher: But see whether this principle is kept in others. For of the same measure as the beginning part arma virumque cano you recognize is Italiam fato. Litora multum ille et. Vi superum saevae. Multa quoque et bello. Inferretque deos. Albanique patres. Not to be long, pursue the rest as far as you wish; you will find these prior parts of verses of the same measure—that is, articulated at the fifth half-foot. Most rarely indeed is this not so; so that the latter parts are no less equal to one another: Troiae qui primus ab oris. Profugus Lavinaque venit. Terris iactatus et alto. Memorem Iunonis ob iram. Passus dum conderet urbem. Latio genus unde Latinum. Atque altae moenia Romae.

Student: It is most manifest.

5. 3. 4. Teacher: Five and seven half-feet, then, divide the heroic verse into two members, which is most well known to consist of six feet of four time-units each; and without a harmony of two members—whether this or some other—there is no verse. In all of which reason has shown that this is to be kept: that the prior part cannot be set in the latter place, nor the latter in the prior. And if it is otherwise, it will no longer be called a verse, except by misuse of the name; it will be a rhythm and meter, such as it is not unbecoming most rarely to interpose in long poems that are woven of verses—such as that very one I mentioned a little before, cornua velatarum vertimus antennarum. Therefore a verse does not seem to me to be named, as some think, from the fact that from a fixed end one returns to the head of the same rhythm, so that the name is drawn from those who turn themselves while they return by the road; for this is seen to be common to them with those meters too which are not verses. But rather perhaps it found its name from the contrary, so that, as the grammarians called a verb that does not lay aside the letter "r" a deponent—as is "lucror" and "conqueror"—so that which is made of two members, neither of which can, the law of rhythms being saved, be set in the place of the other, because it cannot be turned, is called a "verse" (versus). But whichever of these origins of the term you may approve, or disapprove of both and seek another, or despise with me this whole kind of question, it matters nothing for the present. For since the thing signified by this name appears well enough, one need not labor over the root of the word. Unless you have something against this.

Student: For my part nothing; but go on to the rest.

5. 4. 5. Teacher: It follows that we inquire about the end of the verse. For they wished this too to be marked and distinguished by some difference—or rather reason itself did. Or do you not judge it better that the end, by which the rolling-on of rhythm is restrained, should stand out—the equality of time-units not being disturbed—rather than be confused with the other parts that do not make an end?

Student: Who doubts that this is better, which is more evident?

Teacher: Consider, then, whether some have rightly wished the marked end of the heroic verse to be a spondee foot. For in five other places one may set either this or a dactyl; but at the end only a spondee; for as for the trochee they suppose, it comes from the indifference of the last syllable, of which we have spoken enough in the meters. But according to these the iambic senarius will either not be a verse, or be without that prominence of the end; and both are absurd. For no one ever, whether of the most learned men or of the moderately or even slightly educated, has doubted that this is a verse: Phaselus ille quem videtis hospites; and whatever in words is formed with such rhythm: and the gravest authors, in proportion as they are the most skilled, have judged that no verse is to be thought to be without a marked end.

5. 4. 6. Student: You speak truly. So I claim that another mark of this end must be sought, and that this one which is set in the spondee is not to be approved.

Teacher: And this—do you doubt that, whatever it is, it is either in a difference of foot, or in a difference of time, or in both?

Student: How can it be?

Teacher: Which, in the end, of these three do you approve? For I—since to end the verse itself, that it may not run out longer than it ought, pertains to nothing but the measure of time—do not judge that this mark ought to be taken from anything other than time. Or does something else please you?

Student: On the contrary, I agree.

Teacher: Do you see this too: since time here cannot have a difference except that one is longer and another shorter, because when a verse is ended it is brought about that it not go on longer, the mark of the end ought to be in the shorter time?

Student: I do see it; but to what does the added word "here" pertain?

Teacher: To this, of course: that we do not everywhere take a difference of time as lying only in shortness and length. Or do you deny that the difference between summer and winter is a difference of time, or set it rather in a shorter or longer span, and not in the force of cold and heat, or of moisture and dryness, and any such other thing?

Student: Now I understand, and I agree that this mark of the end which we seek is to be drawn from the shortness of time.

5. 4. 7. Teacher: Attend, then, to this verse, Roma, Roma, cerne quanta sit deum benignitas, which is called trochaic, and measure it, and answer what you find about its members and the number of feet.

Student: About the feet I would answer easily: for it is clear that they are seven and a half. But about the members the matter is not quite plain, for I see a part of speech ended in many places; yet I think this division is at the eighth half-foot, so that the preceding member is Roma, Roma, cerne quanta, and the following sit deum benignitas.

Teacher: How many half-feet has it?

Student: Seven.

Teacher: Reason itself has led you entirely. For since nothing is better than equality, and one ought to seek it in dividing, if it cannot be obtained, its nearness must be sought, lest we stray too far from it. And so, since this verse has fifteen half-feet in all, it could not be divided more equally than into eight and seven; for the nearness in seven and eight is the same. But thus the mark of the end would not be kept in the shorter time, as reason itself prescribes it must be kept; for if the verse were such, Roma cerne quanta sit tibi deum benignitas, so that the member began in these seven half-feet, Roma cerne quanta sit, and the other were terminated in these eight, tibi deum benignitas, a half-foot could not close the verse: for eight half-feet make four whole feet. At the same time another deformity would befall: that we would measure not the same feet in the last member as in the first, and the prior member would rather be ended by the mark of the shorter time—that is, a half-foot—than the latter, to which this end is rightly owed. For in that, three trochees and a half, Roma cerne quanta sit; in this, four iambs would be scanned, tibi deum benignitas. But as it is, we both scan trochees in each member, and the verse is closed by a half-foot, so that the end holds the mark of the shorter span. For there are in the prior four, Roma, Roma cerne quanta; but in the latter three and a half, sit deum benignitas. Or are you preparing to object something?

Student: Nothing at all, and I gladly agree.

5. 4. 8. Teacher: Let us, then, hold these laws unshaken, if you please: that neither should the division of two members tending toward equality be lacking to a verse, as it is lacking to this, cornua velatarum obvertimus antennarum; nor should the equality of the members itself make a reversible, so to speak, division, as it does in this, cornua velatarum vertimus antennarum; nor, when this reversal is avoided, should the members depart too far from each other, but be as nearly equal as they can by the nearest numbers—lest we say these can be divided so that eight half-feet precede, cornua velatarum vertimus, and four follow, that is, antennarum. Nor should the latter member have an even number of half-feet, as is tibi deum benignitas, lest the verse, ended by a full foot, should not have an end marked by a shorter time.

Student: I have these now, and I commit them to memory as far as I can.

5. 5. 9. Teacher: Since, then, we now hold that a verse ought not to be ended by a full foot, how do you think the heroic verse is to be measured by us, so that both that law of members is kept and this mark of the end?

Student: I see that there are twelve half-feet; and because, to avoid that reversal, the members cannot have six half-feet each; and they ought not to depart far from each other, so as to be three and nine, or nine and three; nor should an even number of half-feet be given to the latter member, so as to be eight and four, or four and eight, lest the verse end by a full foot: the division must be made into five and seven, or seven and five. For both these numbers are the nearest odd ones, and the members certainly come closer to each other than they would in the numbers four and eight. And that I may hold this most firmly, I see that a part of speech is always or almost always terminated at the fifth half-foot, as in Virgil's first verse, arma virumque cano; and in the second, Italiam fato; and in the third, litora multum ille et; in the fourth likewise, vi superum saevae; and so on through almost the whole poem.

Teacher: You speak truly; but you must see what feet you measure, so that you dare to violate none of the earlier laws now established unshaken.

Student: Although the reasoning is plain enough to me, yet I am confused by its novelty. For we are not accustomed in this kind to scan anything but the spondee foot and the dactyl, which there is almost no one so unlearned that he has not heard, even if he is less able to do it. So this most widespread custom, if I now wish to follow it, that law of the end must be abrogated; for the preceding member would be closed by a half-foot, but the latter by a full foot, which ought to have been the contrary. But because it is most unjust to do away with that law, and in numbers I have already learned that it can happen that we begin from a not-full foot, it remains that we judge not a dactyl with a spondee, but an anapest, to be set here; so that the verse begins from one long syllable, then two feet, either spondees or anapests or alternating, terminate the upper member; then again three—either anapests, or a spondee in any place, or in all—and at the end one syllable, by which the verse is lawfully terminated. Do you approve this too?

5. 5. 10. Teacher: I too judge it most right; but these things are not easily persuaded to the people. For so great is the force of custom that, once ingrained, if it is born of a false opinion, nothing is more hostile to truth. For you understand that for making a verse it matters nothing whether in this kind an anapest is set with a spondee or a dactyl; yet for measuring rationally—which belongs not to the ears but to the mind—this is discerned by a true and certain reason, not by an irrational opinion; nor has it now been first found by us, but it was observed much earlier than this ingrained custom. So if they read those who were most learned in this discipline, whether in the Greek or in the Latin tongue, those who happen to hear this will not wonder too much—although it is shameful weakness that, to strengthen reason, the authority of men is sought, when nothing ought to be more excellent than the authority of reason and truth itself, which is surely better than any man. For it is not as in lengthening or shortening a syllable, where we seek nothing but the authority of the ancient men, so that, as they used the words by which we too speak, so we too may use them—because in a matter of this kind both to follow no observation is sloth, and to establish a new one is license; so in measuring a verse the ingrained will of men, and not the eternal reason of things, is to be considered, since we both naturally feel its moderate length first by the ear, then approve it by a rational consideration of numbers, and whoever judges that it must be ended by a marked end judges that it must be ended more surely than the other meters, and it is manifest that this end must be marked in a shorter time, since it restrains and bridles, in a way, the length of time.

5. 6. 11. Student: I see the members of this one distributed into five and seven half-feet, so that the prior is Phaselus ille, the latter quem videtis, hospites; but I discern the feet to be iambs.

Teacher: I ask, do you guard against nothing in terminating the verse with a full foot?

Student: You speak truly, and I do not know where I was. For who would not see that, as in the heroic, one must begin from a half-foot? Which, when it is done in this kind, we measure the verse not now by iambs but by trochees, so that a half-foot lawfully closes it.

5. 6. 12. Teacher: It is as you say; but see what you think you should answer about this one, which they call asclepiadean: Maecenas atavis edite regibus. For a part of speech is terminated at the sixth syllable, and not inconsistently, but in almost all verses of this kind. So its first member is Maecenas atavis, the second edite regibus, which by what principle it comes about can be doubted. For if you measure feet of four time-units in it, there will be five in the prior, but in the latter member four half-feet; but the law forbids that the latter member consist of an even number of half-feet, lest the verse be terminated by a full foot. It remains that we consider feet of six time-units, whence it comes about that each member consists of three half-feet. For, that the preceding member may be ended by a whole foot, one must begin from two longs; then a whole choriamb divides the verse, so that, another choriamb following too, the latter member is begun, a half-foot closing the verse in two short syllables: for so many time-units, with a spondee set at the head, fill out a foot of six time-units. Unless you have something against this.

Student: Nothing at all.

Teacher: Does it please you, then, that each member consists of the same number of half-feet?

Student: Why should it not please me? For that reversal is not to be feared here, because, the latter member being set in the place of the preceding, so that what is first becomes second, the same law of feet will not remain. Therefore there is no cause why the same number of half-feet should be denied to the members in this kind, since this equality can be kept without any fault of reversal, the law of a more marked end being kept too, when the verse is not terminated by a full foot, which it pleases me well should most constantly be kept.

5. 7. 13. Teacher: You have seen the thing itself entirely; so now, since reason has found that there are two kinds of verse, one in which the number of half-feet in the members is the same, the other in which it is unequal, let us carefully consider, if you please, in what way this inequality of half-feet is referred to a certain equality—by a somewhat more obscure, but indeed most subtle, reasoning of numbers. For I ask you: when I say two and three, how many numbers do I say?

Student: Two, of course.

Teacher: So both two is one, and three is one number; and whatever other we may name.

Student: It is so.

Teacher: Does it not seem to you from this that one can not absurdly be compared with any number? Since we could not say that one is two, but that two is in a way one; and likewise it can be said, not falsely, that three and four are one.

Student: I agree.

Teacher: Attend to another thing: tell me, two taken three times, what do they make in sum?

Student: Six.

Teacher: Are six and three the same amount?

Student: In no way.

Teacher: Now I would have you take three four times, and answer the sum.

Student: Twelve.

Teacher: You see likewise that twelve is more than four.

Student: And far more indeed.

Teacher: Now, not to linger, the rule must be fixed: from two onward, whatever two numbers you set up, the lesser multiplied by the greater must necessarily exceed it.

Student: Who would doubt this? For what is so small in the plural as two? Yet if I take this number a thousand times, it will so exceed a thousand that it becomes double.

Teacher: You speak truly; but set up one, and then any greater number, and, as we were doing in those, multiply the lesser by the greater—will the greater be surpassed in the same way?

Student: Not at all; rather, the lesser will be made equal to the greater. For one twice is two; and one ten times, ten; and one a thousand times, a thousand; and by whatever other number I multiply, one must be made equal.

Teacher: One, then, has a certain right of equality with the other numbers; not only that it is a number, whatever it is, but also that, taken so many times, it makes just as much.

Student: It is most manifest.

5. 7. 14. Teacher: Come now, turn your mind to the numbers of half-feet by which the members in a verse are made unequal, and you will find, by this reasoning we have treated, a certain wonderful equality. For, I think, the smallest verse with an unequal number of half-feet in two members has four and three half-feet, as in this: Hospes ille quem vides; whose first member, which is Hospes ille, can be cut equally into two parts of two half-feet each; but the second, which is quem vides, is so divided that one part has two half-feet, the other one; which is as though they were two and two, by that right of equality of which we have treated enough, which one has with all numbers. From which it comes about that, by this division, the upper member is in a way just as much as the latter. And so where there are four and five half-feet, as in this, Roma, Roma, cerne quanta sit, it is not so approved, and therefore it will be a meter rather than a verse, because the members are so unequal that they can by no section be referred to any law of equality. For you discern, I think, that the four half-feet of the upper member, Roma, Roma, can be parted into two each; but the five latter ones, cerne quanta sit, are divided into two and three half-feet, where equality appears by no right. For the five half-feet cannot in any way be worth as much, on account of the two and three, as four are worth; in the way we found earlier in a shorter verse that three half-feet are worth as much, on account of the one and two, as four are worth. Or have you not followed something, or does it not please you?

Student: On the contrary, all is manifest and settled.

5. 7. 15. Teacher: Come, now let us consider five and three half-feet, such as that little verse Phaselus ille quem vides; and let us see how this inequality is held by some right of equality: for all agree that this kind is not only a meter but also a verse. So when you have cut the first member into two and three half-feet, and the second into two and one, you join the little parts that you find equal in each, because we have two in the first member, and in the second there remain two little parts, one in the three half-feet of the prior member, the other in the one of the latter. These, then, we both join sociably, because one has fellowship with all, and in sum one and three make four, which is just as much as two and two. By this section, then, even five and three half-feet are brought to concord. But answer whether you have understood.

Student: Indeed, and I quite approve.

5. 8. 16. Teacher: It follows that we discuss the five and seven half-feet, such as those two most famous verses, the heroic and the one commonly called iambic, the senarius itself. For Arma virumque cano, Troiae qui primus ab oris is so divided that its first member is arma virumque cano, which is five, and the second Troiae qui primus ab oris, which is seven half-feet. And Phaselus ille quem videtis, hospites has its first member Phaselus ille in five half-feet, the second in seven, quem videtis, hospites. But that great fame labors under this law of equality. For when we have divided the upper five half-feet into two and three, but the latter seven into three and four, the little parts of three half-feet will indeed agree with each other; but if the two remaining ones so agreed that one of them consisted of one half-foot, the other of five, they would be joined by that law by which one can be joined with all numbers, and in sum would make six, which three and three also are; but as it is, because two and four are found, they will indeed yield a sum of six, but by no right of equality are two worth as much as four, so that they may be coupled in this kind of, so to speak, kinship. Unless perhaps someone says it is enough for some rule of equality that, as three and three, so two and four make six. Against which reasoning I do not think one should fight: for this too is some equality. But I would not wish that five and three half-feet should agree by greater harmony than five and seven. For the name of that verse is not so great as of these; and you see that in that one not only is there found, comparing one and three, as great a sum as is in two and two, but also that the parts are much more concordant when one and three are joined, because of that friendship of one with all the other numbers, than when two and four are coupled, as is the case in these. Or is anything obscure to you?

Student: Nothing at all. But somehow it offends me that these senarii, though they are more celebrated than the other kinds, and are said to hold a certain primacy among verses, have something less in the concord of their members than those verses of more obscure fame.

Teacher: Be of good cheer: for I will show you in them as great a concord as they alone of all have deserved to have, so that you may see they were not preferred without cause. But because the treatment itself is somewhat longer, though altogether more pleasant, it ought to remain for us as the last; so that when we have discussed the others as far as seems enough, then, freed from all care, we may come to scrutinize the inner shrines of these.

Student: It does please me; but now I would wish that those earlier things we undertook were explained, so that I might hear that more conveniently.

Teacher: By comparison with these that we discussed before, those things you await become sweeter.

5. 9. 17. Student: I see that the first member can be distributed into parts that have three half-feet each, the second into three and four. So, the equal ones being joined, six half-feet come about; but three and four are seven, and are not made equal to that number. But if we consider two and two in that part where there are four, and two and one in that part where there are three, then, the parts that have two each being joined, the sum is four; but those of which one has two, the other one, being joined—if we take these too as though they were four, because of the concord of one with the other numbers—make eight together, and exceed the sum of six more than when they had been seven.

5. 9. 18. Teacher: It is as you say; and therefore, this kind of coupling being separated from the law of verses, attend, as the order demands, now to those members of which the first has eight half-feet, the second seven. This coupling indeed has what we seek. For joining the half part of the preceding member with the larger part of the following, which is nearest to the half—since they are four half-feet each—I make the sum of the number eight. There remain, then, four half-feet of the prior, three of the latter member. Two from here and two from there, coupled, make four. Two again left over from here, and one from there, coupled by the law of that agreement by which one is equal to the rest, are in a way taken for four. So now eight agrees with the upper eight.

Student: But why do I not hear an example of this?

Teacher: Because it has been mentioned often; yet, lest you think it omitted in its place, it is this: Roma, Roma, cerne quanta sit deum benignitas; or this too: Optimus beatus ille qui procul negotio.

5. 9. 19. Student: This agreement is easy to recognize: for the upper member is divided into four and five half-feet, the latter into three and four. So the smaller part of the upper joined with the larger part of the latter makes the number eight; and the larger of the upper with the smaller of the latter, likewise eight: for that joining is four and four, this five and three half-feet. To this is added that, if you divide five into two and three half-feet, but three into two and one, another agreement appears, of two with two, and of one with three, because one is compared with all numbers by the law mentioned above. But unless reason deceives me, nothing further remains for us to inquire about the coupling of members: for now we have come to eight feet, which number, as we have learned well enough, it is not lawful for a verse to exceed. So now come, unfold the secrets of those senarii, the heroic and the iambic or trochaic, by which you have both stirred and deferred my eagerness.

5. 10. 20. Teacher: I will—or rather reason itself will, which is common to me and to you. But do you remember, I beg, that when we were treating of meters, we said, and proved well enough by the very sense, that those feet whose parts agree at the sesqui ratio—whether in two and three, as the cretic or the paeons, or in three and four, as the epitrites—being excluded by the poets because of their less graceful sound, more harmoniously adorn the gravity of prose, when clauses are bound up with them?

Student: I remember; but to what do these things look?

Teacher: Because I want us first to understand this: that, these kinds of feet being set apart from the poets' treatment, there remain only those whose parts agree at an equal amount, as is the spondee; or those at double, as the iamb; or those at both, as the choriamb.

Student: It is so.

Teacher: But if this is the poets' material, and prose is hostile to verses, no verse is to be made except from this kind of feet.

Student: I agree. For I see that poems are made more grand by verses than by the other meters of the lyric poets; but still I do not know where this reasoning tends.

5. 10. 21. Teacher: Do not hurry: for we are now discussing the excellence of senarius verses, and I wish first to demonstrate to you, if I can, that the most fitting senarii can be only of those two kinds which are also the most celebrated of all—of which one is the heroic, as Arma virumque cano, Troiae qui primus ab oris, which usage measures by a spondee and a dactyl, but the subtler reason by a spondee and an anapest; the other which is called iambic, and by the same reason is found trochaic. For I believe it is manifest to you that, by long syllables, unless shorts are interposed, the spans of sounds are in a way blunted; likewise, unless longs are interposed among shorts, they become too clipped and, as it were, tremulous; that neither is well tempered, although they fill the ears by the equality of time-units. Therefore neither those verses that have six pyrrhics and six proceleusmatics aspire to the dignity of the heroic, nor those that have six tribrachs aspire to that of the trochaic. To this is added that in these, which reason itself prefers to the rest, if you reverse the members, the whole will be so changed that we necessarily measure other feet too. And so they are, so to speak, more irreversible than those that consist either of all shorts or of all longs. And therefore, whether the members in these more temperate verses are ordered in five and seven, or seven and five half-feet, it matters nothing: for in neither of these orders can the verse be reversed without so great a change that it seems to run by other feet. But in those, if a poem has been begun with such verses whose prior members have five half-feet each, one ought not to mix in those in which the prior have seven, lest it now be allowed to reverse them all: for no change of feet calls back from reversal. But yet the heroics are allowed to interpose all spondees most rarely, which indeed this our later age has scarcely approved. But of the trochaics or iambics, although one may interpose a tribrach foot in any place, yet to have in poems of this kind a verse dissolved into all shorts has been judged most base.

5. 10. 22. The epitrite feet, then, being removed from the law of senarius verses—not only because they are more fit for prose, but also because, if there be six of them, they exceed thirty-two time-units, as the dispondees do; the feet of five time-units being removed too, because prose has claimed them more willingly for its clauses; the molossi likewise, and the others of six time-units, although they flourish most gracefully in poems, being excluded from this number of time-units of which we now treat—there remain the verses of all short syllables, which have either pyrrhics or proceleusmatics or tribrachs, and those of all longs, which have spondees. Which, although they are admitted to the senarius measure, must yet yield to the dignity and good tempering of those that are varied by shorts and longs, and on that account can much less be reversed.

5. 11. 23. But it can be asked why those senarii were judged better in which that subtle reason measures an anapest, and those in which a trochee, than if it measured a dactyl there and an iamb here. For—without prejudice to the verdict, since we are now treating of numbers—if a verse were thus, Troiae qui primus ab oris arma virumque cano, or of that other kind, Qui procul malo pius beatus ille, each of these would be no less a senarius, no less moderated by the tempering of short and long syllables, nor more capable of being reversed; and in each the members are so ordered that a part of speech is terminated at both the fifth and the seventh half-foot. Why, then, should those be thought better, if they be rather thus: Arma virumque cano, Troiae qui primus ab oris. Beatus ille qui procul pius malo? In which question I would more easily and readily say that it perhaps happened that these were noticed and frequented first; or, if that is not by chance, I believe it seemed better that the heroic be closed by two longs rather than by two shorts and a long, because the ears rest more conveniently on longs; but that other should have rather a long than a short syllable in its final half-foot. The matter indeed stands thus: that whichever of these were chosen first, would necessarily take away the place from the others, which could be made by reversing those same members. So if that was judged better whose example is Arma virumque cano, Troiae qui primus ab oris, then another kind would now be made ineptly by reversing it, as is Troiae qui primus ab oris, arma virumque cano. Which is to be understood of the trochaic kind too. For if Beatus ille qui procul negotio is more honorable, then the kind that would be made by reversing it, as is Qui procul negotio beatus ille, surely ought not to be made; yet if anyone dares and makes such verses, it is manifest that he will be making other kinds of senarii, than which these are better.

5. 11. 24. Student: I agree entirely; and now that equality of members, to which you made me most attentive a little while ago, I eagerly await to learn, if it is now permitted.

5. 12. 25. Teacher: Be wholly present, then, and answer whether it seems to you that any length can be cut into any number of parts.

Student: I am persuaded enough of this; nor do I think it can be doubted that every length, which is called a line, has its half, and through this can be cut crosswise into two lines; and because those two lines that are made by this section are without doubt lines, it is manifest that this can be done in them too. And so any length, however small, can be cut into any number of parts.

Teacher: Most readily and most truly. So now see whether it is rightly asserted that every length, stretched out toward the breadth that arises from it, is worth as much as the square of the breadth occupies. For if one proceeds into a broad space less or more than the line from which one proceeds is long, no square is made; but if just as much, nothing else than a square is made.

Student: I understand and agree: for what is truer?

Teacher: Then this follows, I think, as you see: that if, for a line, equal pebbles ordered lengthwise are set, that length does not come to the square form unless the pebbles have been multiplied by the same number—so that if, for example, you set two pebbles, you do not make a square unless two others are added to the breadth; but if three, six must be added, but the three distributed into two rows likewise crosswise into the breadth: for if they are added lengthwise, no figure is made. For length without breadth is no figure. And so by proportion one may consider the other numbers: for as twice two, and three times three, make square figures in numbers, so four times four, five times five, six times six, and so on infinitely in the rest.

Student: These too are settled and manifest.

Teacher: Attend now whether there is any length of time.

Student: Who would doubt that there is no time without some length?

Teacher: And a verse—can it fail to hold some length of time?

Student: On the contrary, it must hold one.

Teacher: What do we better set, for pebbles, in that length? The feet, which are necessarily distributed into two parts, that is, raising and setting-down; or the half-feet themselves rather, which hold single raisings and settings-down?

Student: I judge it more fitting that half-feet be set for those pebbles.

5. 12. 26. Teacher: Come, now mention how many half-feet the shorter member of the heroic verse has.

Student: Five.

Teacher: Give an example.

Student: Arma virumque cano.

Teacher: Do you, then, desire anything other than that the other seven half-feet agree with these five by some equality?

Student: Nothing else at all.

Teacher: And can seven half-feet complete some verse by themselves?

Student: They can indeed: for the first and smallest verse has so many half-feet, with a silence counted in at the end.

Teacher: You speak rightly; but, that it may be able to be a verse, how is it divided into two members?

Student: Into four and three half-feet, of course.

Teacher: Bring these single parts, then, to the law of the square, and see what four times four make.

Student: Sixteen.

Teacher: And three times three?

Student: Nine.

Teacher: And the whole together?

Student: Twenty-five.

Teacher: So seven half-feet, since they can have two members, each of their members being referred to the principle of squares, make in sum the number twenty-five; and this is one part of the heroic verse.

Student: It is so.

Teacher: The other part, then, which has five half-feet, since it cannot be divided into two members and ought to harmonize by some equality—is it not to be brought whole into a square?

Student: I judge nothing else at all, and now at last I recognize the wonderful equality. For five taken five times complete the same twenty-five. Not without reason, then, were the senarius verses made more celebrated and more noble than the rest: for it can scarcely be said how great the difference is between their equality in unequal members and that of all the others.

5. 13. 27. Teacher: My promise, then, did not deceive you—or rather, reason itself, which each of us follows, did not. So, to conclude this discussion at last, you surely discern that, although the meters are almost innumerable, yet there cannot be a verse except one terminated by two members harmonized with each other, either by the same number of half-feet, but not reversible, as is Maecenas atavis edite regibus; or by an unequal number of half-feet too, but yet joined by some equality, as are four and three, or five and three, or five and seven, or six and seven, or eight and seven, or seven and nine. For a trochaic verse can begin from a full foot, as is Optimus beatus ille qui procul negotio, and from a not-full one, as is Vir optimus beatus ille qui procul negotio; but it can in no way be terminated except by a not-full one. But these not-full feet—whether they have whole half-feet, as is that one I just set down; or less than a half-foot, as in that choriambic the two last shorts of Maecenas atavis edite regibus; or more than a half-foot, as at its head the two first longs, or at the end of another choriambic the bacchius, whose example is Te domus Evandri, te sedes celsa Latini—all these not-full feet are called half-feet.

5. 13. 28. But now not only are such poems made by verses, so that one kind is kept in them—such as those of the epic poets, or also of the comic poets; but the lyric poets make those circuits too, which the Greeks call "periods," not only by those meters which are not held by the law of verses, but also by verses. For that one of Flaccus, Nox erat, et caelo fulgebat luna sereno inter minora sidera, is a two-membered period, and consists of verses. These two verses cannot agree with each other unless each is referred to feet of six time-units. For the heroic measure does not harmonize with the iambic or trochaic measure, because the former feet are divided at an equal amount, the latter at double. Periods, then, are made either by all meters that are not verses, as those are which were discussed in the earlier discussion, when we treated of meters themselves; or by verses only, as those of which we have now spoken; or so that they are tempered both by verses and by other meters, such as that one: Diffugere nives, redeunt iam gramina campis, arboribusque comae. But in what order verses are set with other meters, or larger members with smaller, matters nothing to the pleasure of the ears, provided only that the period be not shorter than two-membered, not larger than four-membered. But now, if you have nothing to object, let there be an end of this discussion, so that hereafter, as concerns this part of music which is in the time-units of numbers, we may come, with all the sagacity we have, from these its sensible traces to the very resting-places where it is free from all body.

6. 1. 1. Teacher: Long enough, and indeed quite childishly, have we lingered through five books in the footprints of numbers as they pertain to the delays of time. This triviality of ours an obliging labor may perhaps easily excuse among kindly people—a labor we thought should be undertaken for no other reason than that young men, or men of any age whom God has endowed with good talent, might, with reason as guide, be torn away—not precipitately but by certain steps—from the senses of the flesh and from carnal letters, to which it is hard for them not to cling, and might cleave, by love of unchangeable truth, to the one God and Lord of all things, who presides over human minds with no nature set between. Whoever, then, reads those books will find that I have busied myself with grammatical and poetical matters, not by choice of dwelling there but by the necessity of traveling. But when he comes to this book, then, if—as I hope and humbly pray—God our Lord guides my purpose and will, and brings it to where it is aimed, he will understand that the lowly road, by which we now preferred to walk along with the weaker, while we ourselves are not very strong, rather than to fling those of fewer feathers headlong through freer airs, is the road of no lowly possession. So, as I judge, he will reckon that we have erred either not at all or not much, if indeed he is of the number of spiritual men. For the rest of the crowd—from the schools of clamoring tongues, rejoicing with vulgar lightness at the noise of applauders—if perchance they rush into these writings, will either despise them all, or will judge those five books enough for them; but this one, in which the fruit of those lies, they will either cast away as unnecessary, or put off as coming after the necessary. But as for the rest, who are not learned enough to understand these things—if, steeped in the sacraments of Christian purity, striving by the highest love toward the one and true God, they have flown over all childish things—I fraternally admonish them not to come down to these matters, and, when they have begun to labor here, not to complain of their slowness, not knowing that the journeys are hard and troublesome to their feet, while by flying they could pass over even what they have not learned. But if those read who can walk this road neither with weak nor with unexercised steps, and have no wings of piety by which to fly past these matters as neglected, let them not thrust themselves into an unsuitable business; but let them nourish, by the precepts of the most healthful religion and in the nest of Christian faith, the feathers by which, borne up, they may escape the labor and dust of this journey, burning rather with love of their homeland itself than of the winding roads. For these things have been written for those who, given over to secular letters, are entangled in great errors, and waste good talents on trifles, not knowing what delights them there. And if they noticed it, they would see by what they might escape those nets, and what the place of most blessed security is.

6. 2. 2. Teacher: Therefore you, with whom I now reason, my familiar friend, that we may pass from corporeal to incorporeal things, answer, if it seems good: when we pronounce this verse, Deus creator omnium, where do you judge those four iambs of which it consists, and the twelve time-units, to be? That is, in the sound only that is heard, or also in the sense of the hearer that belongs to the ears, or in the act too of the one pronouncing, or—because the verse is known—must we admit that these numbers are in our memory as well?

Student: In all of these, I think.

Teacher: Nowhere more?

Student: I do not see what else remains, unless perhaps there is some interior and higher power from which these proceed.

Teacher: I do not ask what is to be suspected; so, if these four kinds appear to you in such a way that you see no other equally manifest, let us, if you please, distinguish them from one another, and see whether they can each exist without one another. For I believe you will not deny that it can happen that in some place some sound of this kind exists, striking the air with such little delays and measures, whether by a dripping or by some other striking of bodies, where no hearer is present. And when this happens, is any of these four found besides that first kind, when the sound itself has these numbers?

Student: I see no other.

6. 2. 3. Teacher: What of that other, which is in the sense of the hearer? Can it exist if nothing sounds? For I do not ask whether those ears have the power of perceiving if anything sounds, which they surely do not lack if a sound is absent—for not even when there is silence do they differ in nothing from the deaf; but I ask whether they have the numbers themselves, even if nothing sounds. For it is one thing to have numbers, another to be able to perceive a rhythmical sound. For even if you touch a sentient part of the body with a finger, as often as it is touched, that number is felt by the touch; and when it is felt, the one feeling does not lack it; but whether—no one touching—not the sensation, but the number is present, is the same question.

Student: I could not easily say that the sense lacks such numbers established in itself, even before anything sounds; for it would not otherwise be either soothed by their harmony or offended by their absurdity. This very thing, then, whatever it is, by which we either assent or recoil, not by reason but by nature, when something sounds, I call the number of the sense itself. For this power of approving and disapproving does not then come to be in my ears when I hear a sound; for the ears lie open no otherwise to good sounds than to bad.

Teacher: See rather that these two are by no means to be confused. For if any verse is pronounced now more shortly, now more drawn out, it must hold not the same span of time, although the same principle of feet is kept. So, that it may charm the ears by its very kind, that power does it by which we adopt the harmonious and reject the absurd. But that it is perceived in a shorter time when it is uttered more quickly than when more slowly, makes no difference except how long the ears are touched by the sound. This affection of the ears, then, when they are touched by sound, is in no way the same as if they are not touched. For as to hear differs from not to hear, so to hear this sound differs from hearing another. This affection, then, is neither stretched beyond nor held within, since the measure of it is the sound that makes it. So there is one in an iamb, another in a tribrach; more drawn out in a more drawn-out iamb, shorter in a shorter; none in silence. And if it comes about by a rhythmical voice, it too must be rhythmical. Nor can it exist except when the sound that effects it is present: for it is like a footprint impressed in water, which is neither formed before you have pressed the body in, nor remains when you have drawn it out. But that natural power, a judicial one as it were, which is present in the ears, does not cease to be in silence, nor does the sound bring it to us, but is rather received by it, whether to be approved or disapproved. So these two, unless I am mistaken, are to be distinguished; and it must be admitted that the numbers which are in the very passion of the ears, when something is heard, are brought in by the sound and taken away by silence. From which it is gathered that the numbers which are in the sound itself can exist without these which are in the act of hearing, while these cannot exist without those.

6. 3. 4. Student: I agree.

Teacher: Attend, then, to this third kind, which is in the very use and activity of the one pronouncing; and see whether these numbers can exist without those that are in the memory. For even silently, within ourselves, we can run through some numbers by thinking, in the same delay of time in which they would be run through by voice as well. That these are in a certain activity of the mind is manifest; which, since it gives off no sound and brings no passion to the ears, shows that this kind can exist without those two, one of which is in the sound, the other in the hearer when he hears. But whether it would exist without the help of memory, we ask. Although, if the soul produces these numbers which we find in the beating of the veins, the question is solved: for it is manifest both that these are in an activity, and that we are helped toward them by no memory. But if it is uncertain about these, whether they belong to the acting soul, about those which we produce by the to-and-fro of the breath there is no doubt that there are numbers in intervals of time, and that the soul so produces them that, the will being applied too, they can be varied in many ways; and yet, that they may be produced, there is no need of any memory.

Student: It seems to me that this kind can exist without the other three. For, although I do not doubt that the various beatings of the veins and the intervals of breathing come about according to the temperament of bodies, yet who would dare to deny that they come about by the soul's acting? For this course, even if for the diversity of bodies it is quicker in some, slower in others, is nevertheless none unless the soul is present to do it.

Teacher: Consider, then, the fourth kind too, namely of those numbers that are in the memory: for if we draw them out by recollection, and, when we are carried off into other thoughts, leave them again as it were hidden away in their own secret places, it is not, I think, obscure that they can exist without the others.

Student: I do not doubt that they exist without the others; but yet, unless heard or thought, they would not be committed to memory; and therefore, although they remain when those cease, they are nevertheless impressed by those same ones going before.

6. 4. 5. Teacher: I do not resist you, and I would now ask which of these four kinds you at last judge most excellent—did I not think that, while we treat those, a fifth kind has appeared to us, from I know not where, which is in the very natural judgment of perceiving, when we are delighted by the equality of numbers, or, when they are erred in, are offended. For I do not despise what seemed to you: that without certain numbers lying hidden in it, our sense could in no way have done this. Or do you perhaps judge that this so great power belongs to some one of those four kinds?

Student: I think this kind is to be distinguished from all those. For it is one thing to sound, which is attributed to the body; another to hear, which the soul undergoes in the body from sounds; another to produce numbers, whether more drawn out or shorter; another to remember these; another to pass sentence on all these, whether by assenting or recoiling, as it were by a certain natural right.

6. 4. 6. Teacher: Come, now tell me which of these five most excels.

Student: This fifth, I think.

Teacher: You think rightly: for it could not judge about those unless it excelled. But again I ask, of the other four which do you most approve?

Student: That one, surely, which is in the memory; for I see that the numbers are there more lasting than when they sound, or are heard, or are produced.

Teacher: So you prefer the made to the making: for those that are in the memory, you said a little before, are impressed by those others.

Student: I would not wish to prefer them; but again, how I am not to prefer the more lasting to the less lasting, I do not see.

Teacher: Let that not move you. For things are not to be preferred to one another as the eternal to the temporal, just because they are abolished more slowly than those that pass in a shorter time. For the health of one day is surely better than the weakness of many days. And if we compare things to be chosen with things to be chosen, the reading of one day is better than the writing of many, if the same thing is read in one day that is written in several. So the numbers that are in the memory, although they last longer than those by which they are impressed, ought not to be preferred to those we produce, not in the body but in the soul; for both pass away, the one by ceasing, the other by forgetting. But those we produce seem to be taken away, even while we have not yet ceased, by the succession of those following, while the first yield place to the second, and the second to the third, and so on the earlier yield by passing to the later, until the ceasing itself destroys the last. But by forgetting many numbers at once are wiped away, though little by little; for not even do they themselves remain whole for any time. For what is not found in the memory after a year, for example, is already less even after one day; but this diminution is not felt; yet it is not falsely inferred from this, since surely it does not suddenly fly away whole the day before the year is completed; whence it is given to understand that from the time when it clings to the memory it begins to slip away. Hence is that which we often say, "I remember faintly," when after a time we seek to recall something by recollection, before it has wholly fallen away. Therefore each of these two kinds of numbers is mortal. Nevertheless the making are rightly preferred to the made.

Student: I accept and approve.

6. 4. 7. Teacher: Now then look at the three remaining, and set forth which of them too is best and to be preferred to the rest.

Student: This is not easy. For by that rule by which the making ought to be preferred to the made, I am compelled to give the palm to the sounding numbers: for these we feel when hearing, and when we feel these, these we undergo. These, then, make those that are in the passion of the ears when we hear; and these again, which we have by feeling, make others in the memory, to which, as made by them, they are rightly preferred. But here, because both to feel and to remember belong to the soul, I am not moved if I prefer something that comes about in the soul to something that likewise comes about in it. This confounds me: how sounding numbers, which are certainly corporeal, or in some way in the body, are to be praised more than those which, when we feel, are found to be in the soul. But again it confounds me how they are not to be praised more, since these make and those are made by these.

Teacher: Wonder rather that a body can do anything in the soul. For this perhaps it could not do, had not that body, which by the first sin was changed for the worse—which body it used to animate and govern with no trouble and with the highest ease—come to lie subject to corruption and death; which body yet has a beauty of its own kind, and by that very thing sufficiently commends the dignity of the soul, whose neither wound nor sickness has deserved to be without the honor of some comeliness. Which wound the highest Wisdom of God deigned to take on by a wonderful and ineffable mystery, when he took up man without sin, but not without the condition of a sinner. For he willed both to be born in human fashion, and to suffer and to die. None of these by desert, but by his most excellent goodness; so that we might beware rather of the pride by which we most deservedly fell into these things than of the insults which he, undeserving, received; and might with even mind pay the death we owe, if for our sake he was able to bear even one not owed; and whatever more hidden and more purified can be understood in such a mystery by the holy and the better. So it is no wonder that the soul, working in mortal flesh, feels the passion of bodies. Nor, because the soul itself is better than the body, must everything that comes about in it be thought better than everything that comes about in the body. For I believe it seems to you that the true is to be preferred to the false.

Student: Who would doubt it?

Teacher: But is there a tree that we see in dreams?

Student: In no way.

Teacher: But its form comes about in the soul, whereas the form of this one which we now see has come about in the body. So, since both the true is better than the false and the soul better than the body, the true in the body is better than the false in the soul. But as this is better insofar as it is true, not insofar as it comes about in the body, so that other is perhaps worse insofar as it is false, not insofar as it comes about in the soul. Unless you have something against this.

Student: Nothing indeed.

Teacher: Hear another point, which is, I think, nearer than better. For you will not deny that what is becoming is better than what is unbecoming.

Student: On the contrary, I admit it.

Teacher: But who would doubt that in the same garment in which a woman is becoming, a man can be unbecoming?

Student: This too is manifest.

Teacher: What, then, if this form of numbers is becoming in sounds, which glide into the ears, and unbecoming in the soul, when it has them by feeling and undergoing—is it greatly to be wondered at?

Student: I think not.

Teacher: Why, then, do we hesitate to prefer the sounding and corporeal numbers to those that are made from them, although they are made in the soul, which is better than the body? Because we prefer numbers to numbers, the effecting to the made, not body to soul. For bodies are the better the more rhythmical they are by such numbers. But the soul becomes better by lacking those which it receives through the body, when it turns itself away from the carnal senses and is reformed by the divine numbers of wisdom. For thus it is said in the holy Scriptures: I turned about, that I might know and consider and seek wisdom and number (See Eccl 7:25) Which must in no way be thought said of these numbers by which even shameful theaters resound; but of those, I believe, which the soul receives not from the body, but, having received them from the highest God, itself rather impresses on the body. Of what kind this is, is not to be considered in this place.

6. 5. 8. Student: What, then, is it that takes place in the hearer?

Teacher: Whatever that may be, which perhaps we cannot find out or explain—will it avail to make us doubt that the soul is better than the body? Or, when we admit this, will we be able to subject it to the body that works and imposes numbers, so that the body is the fashioner, and the soul the material from which and in which something rhythmical is fashioned? And if we believe this, we must necessarily believe the soul worse. Than which what more wretched, what more detestable, can be believed? Since these things are so, I will indeed try, as far as God deigns to help, to conjecture and discuss what lies hidden there. But if, because of the weakness of both or one of us, this turns out less according to my wish, either we ourselves at another, calmer time will investigate it, or we will leave it to be investigated by the more intelligent, or we will with even mind allow it to lie hidden; yet we ought not on that account to let these more certain things slip from our hands.

Student: I will hold this unshaken if I can; and yet I could wish that this hidden thing were not impenetrable to us.

6. 5. 9. Teacher: I will quickly say what I feel; but do you either follow, or even go ahead, if you can, where you notice me delaying and hesitating. For I do not think this body is animated by the soul except by the intention of the one acting. Nor do I judge that the soul undergoes anything from the body, but acts upon it and in it as upon something divinely subjected to its dominion; yet sometimes it works with ease, sometimes with difficulty, according as, for its merits, corporeal nature yields to it more or less. So whatever corporeal things are forced upon this body or set against it from without do something not in the soul but in the body itself, which either opposes or agrees with its work. And so, when it strives against what opposes, and with difficulty drives the matter subjected to it into the ways of its work, it becomes, from the difficulty, more attentive in its action; which difficulty, because of the attention, when it does not lie hidden from it, is said to be felt, and this is called pain or labor. But when what is brought in agrees, or lies near, it easily leads the whole, or as much of it as is needed, into the paths of its work. And this its action, by which it joins its body to a fitting body from without, because it is done more attentively on account of something newly arrived, does not lie hidden; but because of the agreement, it is felt with pleasure. But when those things are lacking by which it might repair the body's losses, want follows; and when, by this difficulty of action, it becomes more attentive, and such activity of its does not lie hidden from it, it is called hunger or thirst, or some such thing. But when what has been brought in is in excess, and from their burden arises difficulty of working, neither does this happen without attention; and when such action does not lie hidden, indigestion is felt; it also works attentively when it casts out the superfluous—if gently, with pleasure; if harshly, with pain. The diseased disturbance of the body too it works attentively at, seeking to come to the aid of what is failing and dissolving; and by this action not lying hidden it is said to feel diseases and sicknesses.

6. 5. 10. And, not to make it long, it seems to me that the soul, when it feels in the body, undergoes nothing from it, but acts more attentively in its passions, and that these actions—whether easy because of agreement, or difficult because of disagreement—do not lie hidden from it; and this whole is what is said to be feeling. But this sense, which is present even while we feel nothing, is an instrument of the body, worked by the soul with such a temperament that in it the soul is the more ready to act, with attention, upon the passions of the body, so as to join like to like and repel what is harmful. Further, it works, I think, something luminous in the eyes, something airy, most serene and most mobile, in the ears, something misty in the nostrils, something moist in the mouth, something earthy and as it were muddy in touch. But whether these things be conjectured by this distribution or another, the soul works these with quiet, if those things that are present have yielded, in the unity of health, by a certain familiar consent, as it were. But when those things are applied which affect the body with a certain otherness, so to speak, it puts forth more attentive actions, accommodated to their several places and instruments: then it is said to see, or hear, or smell, or taste, or feel by touching; with which actions it gladly associates the agreeable, and troublesomely resists the disagreeable. These activities, I think, the soul presents to the passions of the body when it feels, not that it receives those same passions.

6. 5. 11. Student: Nothing less.

Teacher: And do you not grant that these same ears are an animated member?

Student: I grant it.

Teacher: Since, then, that which in this member is like air is moved when the air is struck, do we think that the soul, which before this sound was quickening the body of the ears in silence by a vital motion, can either cease from the work of moving what it animates, or move the air of its ear, stirred from without, in the same way as it moved it before that sound glided in?

Student: It does not seem so, except otherwise.

Teacher: This moving otherwise, then—must it not be admitted to be acting, not undergoing?

Student: It is so.

Teacher: So not absurdly do we believe that the soul's own motions, or actions, or activities—or by whatever other name they can more conveniently be signified—do not lie hidden from it when it feels.

6. 5. 12. But these activities are applied either to preceding passions of bodies—as they are when those passions of the light interrupt the form of our eyes, or sound flows into the ears, or exhalations into the nostrils, flavors to the palate, and any solid and bulky things are set against the rest of the body from without, or something migrates or passes from place to place in the body itself, or the whole body itself is moved by its own or another's weight: these are the activities which the soul applies to preceding passions of the body, which delight it when it associates with them and offend it when it resists. But when it undergoes something from these its own activities, it undergoes it from itself, not from the body—though plainly when it accommodates itself to the body; and therefore it is less in itself, because the body is always less than itself.

6. 5. 13. Turned, then, from its Lord to its servant, it necessarily fails; turned likewise from its servant to its Lord, it necessarily advances, and grants to that same servant a most easy life, and therefore one not laborious and busy, to which, because of the highest quiet, no attention is bent aside—such as is that affection of the body which is called health: for it has need of no attention of ours, not because the soul then does nothing in the body, but because it does nothing more easily. For in all our works we work the more attentively the more difficultly. But this health will then be most firm and most certain when this body has been restored, at its own fixed time and order, to its former stability; which resurrection of it, before it is most fully understood, is healthfully believed. For the soul ought both to be ruled by a superior and to rule an inferior. That superior is God alone, that inferior the body alone, if you regard the whole and entire soul. So, as it cannot be entire without its Lord, so it cannot excel without its servant. But as its Lord is more than it, so its servant is less. So, intent on its Lord, it understands his eternal things, and is the more; and the servant too is the more, in its own kind, through it. But, the Lord being neglected, intent on the servant by the carnal desire by which it is led, it feels its own motions which it presents to it, and is the less; yet not so much less as the servant itself, even when it is most fully in its own nature. But by this fault of the mistress it is much less than it was, when, before the fault, it was more.

6. 5. 14. Therefore it now lords it over what is mortal and frail with great difficulty and attention. Hence error befalls it, so that it esteems the pleasure of the body, because the material yields to its attention, more than health itself, which has need of no attention. And no wonder that it is entangled in hardships, preferring care to security. But for the soul turning itself to its Lord, a greater care arises, lest it be turned away; until the onrush of carnal businesses, unbridled by long habit and thrusting itself into its conversion with tumultuous recollections, settles down: thus, its own motions by which it was carried out into external things being calmed, it keeps within a free leisure, which is signified by the sabbath; and so it knows that God alone is its Lord, whom alone it serves with the highest freedom. But it does not extinguish those carnal motions when it pleases, as it puts them forth when it pleases. For the penalty of sin is not in its power as sin is. For the soul itself is a great thing, and does not remain fit by itself to suppress its own wanton motions. For it is stronger when it sins, and after the sin, made weaker by the divine law, is less able to take away what it has done. Wretched man that I am! who will deliver me from the body of this death? The grace of God through Jesus Christ our Lord. (Rom 7:24–25) The motion of the soul, then, keeping its own onrush, and not yet extinguished, is said to be in the memory; and when the mind is intent on something else, the former motion is as though not present in the mind, and truly becomes less, unless, before it perishes, it is renewed by a certain nearness of like things.

6. 5. 15. Student: You seem to me to speak plausibly, and I would not dare to resist.

Teacher: Since, then, feeling itself is to move the body against that motion which has been made in it, do you not judge that we therefore do not feel when bones and nails and hair are cut—not because these things do not live at all in us (for otherwise they would not be held together or nourished or grow, or even show their power in begetting offspring), but because they are penetrated by air, that mobile element, too little freely for so swift a motion to be made there by the soul as is that against which it is made when feeling is said to occur? Since some such life is understood to be in trees and the other plants, it is in no way fitting to prefer it not only to our own life, which even excels by reason, but not even to that of the beasts. For it is one thing to feel nothing by the highest dullness, another by the highest health of body. For in the one the instruments are lacking, which might be moved against the passions of the body; in the other, the passions themselves.

Student: I approve and agree.

6. 6. 16. Teacher: Return, then, with me to our purpose, and answer about those three kinds of numbers—one of which is in the memory, another in feeling, another in the sound—which seems to you to excel.

Student: I set the sound after those two which are in the soul and live in a way; but which of these two I should judge the more excellent I am uncertain—unless perhaps, since we had said that those in action are to be preferred to those in the memory for no other reason than that the former are making and the latter made by them, by the same reasoning these too, which are in the soul while we hear, ought to be preferred to those that are made by them in the memory, as indeed seemed to me a little while ago.

Teacher: I do not think your answer absurd; but since it has been argued that these numbers which are in feeling too are activities of the soul, how do you distinguish them from those that we notice to be in act, even when in silence the soul, not recollecting, does something rhythmical through spans of time? Is it that the latter belong to the soul moving itself toward its body, but these, in hearing, to the soul moving itself against the passions of its body?

Student: I accept that difference.

Teacher: And do you think one should abide by the view that those toward the body are judged more excellent than those against the passions of the body?

Student: Those that are in silence seem to me freer than those that are put forth not only toward the body but also against the passions of the body.

Teacher: I see five kinds of numbers distinguished by us and ordered by certain grades of merit; on which, if you please, let us impose fitting terms, lest in the rest of the discussion we be forced to use more words than things.

Student: I agree indeed.

Teacher: Let the first, then, be called judging (iudiciales), the second advancing (progressores), the third encountering (occursores), the fourth recalling (recordabiles), the fifth sounding (sonantes).

Student: I have it, and I will use these names gladly.

6. 7. 17. Teacher: Attend, then, in turn, and tell me which of these seem to you immortal, or whether you judge that all fail and fall in their own times.

Student: The judging numbers alone I think immortal; the rest I see either pass away as they come about, or are erased from the memory by forgetting.

Teacher: Are you as certain of the immortality of these as of the perishing of the rest, or must one inquire more carefully whether these are truly immortal?

Student: Let us inquire indeed.

Teacher: Tell me, then: when I pronounce a verse somewhat more shortly or more drawn out, while I keep the law of time-units by which feet agree at single to double, do I offend the judgment of your sense by any deception?

Student: Not at all.

Teacher: And that sound which is uttered with shorter and, as it were, more fleeting syllables—can it take up more time than it sounds?

Student: How can it?

Teacher: If, then, those judging numbers were held by the bond of time within as great a span as these sounding ones are arranged in, could they aspire to the judgment of those sounding ones that are poured forth a little more drawn out by the same iambic law?

Student: In no way.

Teacher: So it appears that these, which preside over judging, are not held by the delay of time-units.

Student: It appears so entirely.

6. 7. 18. Teacher: You assent rightly. But if they were held by none, however much more drawn out I uttered iambic sounds at lawful intervals, they would nonetheless be applied to judging; but as it is, if I gave one syllable in as much delay as (not to say much) three paces of a walker are made, and another in double, and so arranged iambs so long, that law of single and double would nonetheless be kept; yet we could not apply that natural judgment to approving these measures. Or does it not seem so to you?

Student: I cannot deny that it seems so: for in my view, at least, the matter is in the open.

Teacher: So these judging numbers too are held by certain bounds of temporal spans, which they cannot exceed in judging, and whatever exceeds these spans they do not reach to judge; and so, if they are held, how they are immortal I do not see.

Student: Nor do I see what to answer. But although I now presume less about their immortality, I yet do not understand by what means they are convicted of being mortal. For it can happen that whatever spans they can judge, they always can, since I cannot say, as of the rest, either that they can be abolished by forgetting, or that they exist or are extended only so long and so far as the sound is driven and the encountering numbers are extended, or so long as the numbers we called advancing are produced or drawn out; for both of these pass away with the very time of their activity. But these judging numbers—whether they are in the soul I do not know, but in the very nature of man at least they remain, to judge about what is offered, although they vary from a fixed brevity up to a fixed length, approving the rhythmical in these and condemning the disturbed.

6. 7. 19. Teacher: At least you grant this: that some men are offended more quickly by limping numbers, others more slowly, and that most judge them faulty only by comparison with whole ones, when they have heard both the harmonious and the unharmonious.

Student: I grant it.

Teacher: Whence, in the end, do you think this difference arises, except either from nature, or from exercise, or from both?

Student: So I judge.

Teacher: I ask, then, whether someone can at some time judge and approve more drawn-out intervals which another cannot.

Student: I believe it can be.

Teacher: And he who cannot, if he exercises himself fittingly and is not too slow, will he not be able to?

Student: He will indeed.

Teacher: Can these advance so far in judging more drawn-out things that they can grasp, by that judicial sense, the double and single spans of hours, or days, or even months and years—when they are at least interrupted by sleep—and approve them, as it were like those iambs, by the nods of motion?

Student: They cannot.

Teacher: Why can they not, except that to each living thing, in its own kind, by the proportion of the universe, a sense of places and times has been granted; so that, as its body, by the proportion of the universal body of which it is a part, is just so great, and its age, by the proportion of the whole age of which it is a part, is just so long, so its sense agrees with its action, which it does by the proportion of the universal motion of which it is a part? Having all things thus, this world is great—which is often named in the divine Scriptures by the name of heaven and earth—of which, if all the parts be diminished by proportion, it is just so great; and if increased by proportion, it is nonetheless just so great: because nothing in the spans of places and times is great by itself, but in relation to something shorter; and nothing again in these is short by itself, but in relation to something greater. Therefore, if to human nature, for the actions of carnal life, such a sense has been granted that it cannot judge greater spans of time than the intervals belonging to the use of such a life demand—since the nature of such a man is mortal, I think such a sense too mortal. For not without reason is habit called, as it were, a second and, as it were, an added nature. And we see that certain senses, as it were new, in judging corporeal things of every kind, are affected by habit, and decay by another habit.

6. 8. 20. But however these judging numbers stand, they certainly excel in this: that we doubt, or investigate with difficulty, whether they are mortal. But about the other four kinds there is no question that they are mortal; of which, even though they do not grasp certain ones, because these are stretched beyond their own rights, they yet claim the kinds themselves for their own examination. For those advancing numbers too, when they seek some rhythmical activity in the body, are regulated by the hidden nod of these judging ones. For that we—whether walking are restrained from uneven steps, or striking from uneven intervals of blows, or eating or drinking from uneven motions of the jaws, or scratching from uneven strokes of the nails; and, not to run through many other activities, that we, in any attentive doing of something through the members of the body, are checked and held back from uneven motions, and a certain equality is silently commanded—this very thing is some judging power, I know not what, which intimates God the Founder of the living being: whom it surely befits to believe the author of all agreement and concord.

6. 8. 21. And those encountering numbers, which surely are produced not by their own nod but for the passions of the body, are offered for judging and judged by these judging ones just so far as the memory can guard their intervals. For this number, which consists of intervals of time, unless we are helped in it by memory, can in no way be judged by us. For however short a syllable, since it both begins and ends, its beginning sounds at one time and its end at another. So it too is stretched over some interval, however small, of time, and from its beginning, through its middle, stretches to its end. So reason finds that local as well as temporal spans admit infinite division; and therefore the end of no syllable is heard together with its beginning. And so, in hearing even the shortest syllable, unless memory helps us, so that at the moment of time when now not the beginning but the end of the syllable sounds, that motion remains in the mind which was made when the beginning itself sounded, we cannot say that we have heard anything. Hence is that which often, occupied by another thought, we seem not to ourselves to have heard those speaking before us: not because the soul does not then produce those encountering numbers, since without doubt the sound reaches the ears, and it cannot cease in the passion of its body, nor can it but be moved otherwise than if that passion did not occur; but because, by the intention upon something else, the onrush of the motion is presently extinguished, which, if it remained, would surely remain in the memory, so that we both found and felt that we had heard. And if the slower mind follows less, about one short syllable, what reason finds, about two at least no one doubts that no soul can hear them together. For the second does not sound unless the first has ceased; but what cannot sound together, how can it be heard together? As, then, the diffusion of rays helps us to grasp the spans of places—rays that flash out from the little pupils into open spaces, and so belong to our body that, although in things set far off which we see, they are quickened by our soul; as, then, we are helped by their outpouring to grasp the spans of places, so memory, which is as it were the light of temporal spans, grasps just so much of those same spans as it can in its own kind, in a way, be thrust out. But when a sound, distinguished by no joints, strikes the ears longer, and at last, joined from some end, another is uttered in double, or even in just so great a span, then, by the attention upon the perpetually succeeding sound, that motion of the mind which was made by the attention as it passed to the past and elapsed sound is repressed—that is, does not so remain in the memory. Therefore those judging numbers, which cannot judge numbers set in intervals of time (except the advancing ones, by which they also regulate the advance itself) unless memory, as a handmaid, offers them—are they not themselves to be reckoned as stretched through a fixed span of time? But it matters in what spans of time either it slips from us, or we remember, what they judge. Since not even in the very forms of bodies that pertain to the eyes can we judge round or square, or any other solid and determinate things, and feel them at all, unless we turn them before our eyes; but when one part is looked at, if what was looked at in another part has slipped away, the intention of the one judging is altogether frustrated, because this too is done in some delay of time, for whose variation it is needful that memory keep watch.

6. 8. 22. But that we judge the recalling numbers by these judging ones, the memory itself offering them, is much more evident. For if the encountering ones are judged just so far as they are offered by it, much more those to which we are called back by recollection, as if laid up after other intentions, are found to live in the memory itself. For what else do we do when we call ourselves back into memory, than in a way seek what we have laid up? But there recurs into the thought, on the occasion of like things, a motion of the mind not extinguished, and this is what is called recollection. So we produce numbers, whether in thought alone or also in the motion of the members, which we have already at some time produced. But we know that they have not come, but returned, into the thought, because, when they were committed to memory, they were repeated with difficulty, and we needed some prompting to follow; and when this difficulty is removed, when they offer themselves suitably to the will, consequently in their times and order—so easily that those which have clung more strongly are now performed as if by their own nod, even while we are thinking of something else—we surely do not feel them to be new. There is also another thing whence, I think, we feel that a present motion of the mind has already at some time existed, which is to recognize, when we compare, by a certain inner light, the recent motions of that action in which we are when we recollect (which are surely more lively) with the recalling numbers, now more settled: and such acknowledgment is recognition and recollection. So the recalling numbers too are judged by these judging ones, never alone, but with the active, or the encountering, or both joined, which bring them as it were out of their hiding places into the open, and which, as if restored when they were already being abolished, are recalled again. So, since the encountering numbers are judged just so far as memory has brought them to the ones judging, the recalling numbers too, which are in the memory, can in turn be judged when the encountering ones present them: with this difference, that, that the encountering ones may be judged, memory offers, as it were, the fresh traces of those fleeing; but the recalling ones, when we judge them by hearing, their same traces, as it were, grow green again as the encountering ones pass by. And now, indeed, what need is there to speak of the sounding numbers, since they are judged among the encountering ones, if they are heard? But if they sound where they are not heard, who doubts that they cannot be judged by us? Of course, as in sounds through the instrument of the ears, so in dances and the other visible motions, as concerns the temporal numbers, by the same memory helping we judge by these same judging numbers.

6. 9. 23. Student: The force and power of these judging numbers moves me greatly: for they themselves seem to me to be those to which the ministries of all the senses are referred. And so whether anything more excellent than these can be found among numbers, I do not know.

Teacher: Nothing is lost by our inquiring more carefully. For either we will find higher ones in the human soul, or we will affirm that these are the highest in it, if indeed it has become clear that none are more excellent in it. For it is one thing not to be, another not to be able to be found, whether by any man or by us. But I think that when that verse proposed by us is sung, Deus creator omnium, we both hear it by those encountering numbers, and recognize it by the recalling ones, and pronounce it by the advancing ones, and are delighted by these judging ones, and estimate it by some others I know not, and, about that delight—which is, as it were, the verdict of these judging numbers—pass another, more certain verdict according to these more hidden ones. Or does it seem to you one and the same thing to be delighted by sense and to estimate by reason?

Student: I admit they are diverse. But first I am moved by the very term: why should not those rather be called judging in which reason resides, than those in which delight resides? Then I fear that this estimation of reason may be nothing else than a certain more careful judgment of those numbers about themselves: so that there are not some numbers in delight, others in reason, but one and the same now judge about the things done in the body, when memory offers them, as was shown above; now about themselves, more removed from the body and more sincerely.

6. 9. 24. Teacher: About the terms, busy yourself not at all; the thing is in our power, for they are imposed by agreement, not by nature. But that you judge them the same, and that this force does not admit these as two kinds of numbers, this, unless I am mistaken, carries you away: that the same soul produces both. But you need to notice that in the advancing numbers too the same soul moves the body, or is moved toward the body; and in the encountering ones this same soul goes to meet its passions; and in the recalling ones this very soul, until they in a way subside, fluctuates, as it were, with those motions. So we, in numbering and distinguishing these kinds, are discerning the motions and affections of one nature, that is, of the soul. Therefore, just as it is one thing to be moved toward what the body undergoes, which happens in feeling; another to move oneself toward the body, which happens in working; another to retain what has been made in the soul from these motions, which is to remember; so it is one thing to assent to or refuse these motions, whether when they are first put forth or when they are roused again by recollection (which happens in the delight at the agreement, and offense at the absurdity, of such motions or affections); and another to estimate whether these rightly or otherwise delight, which happens by reasoning: we must necessarily admit that these are two kinds, as those are three. And if it rightly seemed to us that, unless the very sense of delight were imbued with certain numbers, it could in no way assent to equal intervals and reject disturbed ones, it can rightly seem too that reason, which is set over this delight, can in no way, without certain more lively numbers, judge about the numbers it has below it. And if these things are true, it appears that five kinds of numbers have been found in the soul; to which, when you have added those corporeal ones which we called sounding, you will recognize six kinds of numbers set out and ordered. Now then, if you please, let those that had crept up on us to obtain the primacy be named sensual, and let the name of judging, since it is more honorable, be taken by those that have been found more excellent; although I think the name of the sounding ones too should be changed, since, if they are called corporeal, they will more clearly signify those too that are in dance, and in the rest of visible motion. If, however, you approve what has been said.

Student: I approve indeed: for these things seem to me both true and manifest. I gladly accept too the correction of these terms.

6. 10. 25. Teacher: Come, now look at the force and power of reason, as far as we can look at it from its works. For it itself—to say chiefly what pertains to the undertaking of this work—first considered what good measuring itself is, and saw that it lies in a certain free motion, turned toward the end of its own beauty. Then it saw that in the motions of bodies one thing is what varies by the shortness and length of time, insofar as it is more or less lasting, another by the striking of local spaces, in certain degrees of swiftness and slowness; and, this division being made, that which lay in the delay of time, by moderate intervals accommodated to human sense, made various numbers articulately, and pursued their kinds and order up to the measures of verses. Finally it attended to what the soul, whose head it itself was, did in regulating, working, feeling, and retaining these; and it separated all these animate numbers from the corporeal; and it recognized that it could itself neither notice, nor distinguish, nor rightly number all these without certain numbers of its own, and it preferred these, by a certain judicial estimation, to the rest of a lower order.

6. 10. 26. And now, with that delight of its own which weighs the moments of time and presents its nods for regulating such numbers, it acts thus: what is it that we love in sensible rhythm? Is it anything but a certain equality and equally measured intervals? Or would that pyrrhic foot, or spondee, or anapest, or dactyl, or proceleusmatic, or dispondee delight us otherwise than because it compares its part to the other part by an equal division? And what beauty do the iamb, trochee, tribrach have, except that they divide their larger part equally into just so many parts by their smaller? And further, the feet of six time-units—do they sound more pleasantly and festively from any other source than that they are divided by either law: namely either into two equal parts holding three time-units each, or into one single part of equal time-units and another double—that is, so that the larger has the smaller twice, and in that way is divided equally by it, the two time-units measuring out and cutting the four time-units into two each? What of those feet of five and seven time-units? Whence are they more fit for prose, which they seem to be than for verses, except that their smaller part does not divide the larger into equal parts? And yet these very ones, whence are they admitted, in the order of their kind, to temporal rhythm, except because both in five time-units the smaller part has just so many little parts as the larger three, and in seven the smaller just so many as the larger four? So in all feet no smallest part marked by some joint of division is without the rest agreeing with it in as great an equality as they can.

6. 10. 27. Come, in joined feet—whether this joining is stretched in free perpetuity, as in rhythms; or recalled from some fixed end, as in meters; or even distributed into two members agreeing with each other by some law, as in verses—by what, in the end, is foot friendly to foot, except by equality? Whence the middle syllable of the molossus and the ionics, which is long, can be distributed into two equal moments, not by section but by the very nod of the one pronouncing and beating, so that the whole foot agrees even to three time-units each when it is joined to others that are divided in the same way; why, except by the right of equality holding sway—namely that it is equal to its sides, which are of two time-units each, since it too is of two time-units? Why can the same not be done in the amphibrach, when it is joined to others of four time-units, except because there so great an equality is not found, the middle being double, the sides single? Why, in the intervals of silences, is the sense offended by no deception, except because what is owed is paid to that same right of equality, if not in sound, yet in span of time? Why, a silence following, is even a short syllable taken for a long—not by institution, but by that very natural judgment which presides over the ears—except because in a longer span of time we are forbidden, by that same law of equality, to compress the sound into narrow bounds? And so, to draw out a syllable beyond two time-units, so that what can be filled by silence is filled by sound too, the nature of hearing and of being silent admits; but that a syllable should take up less than two time-units, while a span remains for silent nods, is a certain deception of equality, because there cannot be equality in less than two. But now, in that very equality of members by which those periods are varied which the Greeks call so, and verses are figured, how is one led back more secretly to the same equality, except that in a period the shorter member agrees with the larger by equal feet to the beat, and in a verse, by a more hidden consideration of numbers, those unequal members that are joined are found to have the force of equality?

6. 10. 28. Reason, then, inquires, and questions the carnal delight of the soul—which claimed the judging part for itself, when the equality of number in temporal spans charms it—whether two short syllables, whichever it hears, are truly equal; or whether it can happen that one of them is uttered more drawn out, not up to the measure of a long syllable, but below it by however little, by which yet it exceeds its fellow. Can it be denied that this can happen, when this delight does not perceive it, and rejoices in unequal things as if equal? Than which error and inequality what is more base? Whence we are admonished to turn delight away from those things that imitate equality, and whether they fulfill it we cannot grasp; nay, that they do not fulfill it we perhaps grasp; and yet, insofar as they imitate it, that they are beautiful in their own kind and in their own order, we cannot deny.

6. 11. 29. Let us not, then, envy things lower than we are, and let us so order ourselves, by the help of God our Lord, among those things that are below us and those that are above us, that we be not offended by the lower, but delighted only by the higher. For delight is, as it were, the weight of the soul. Delight, then, orders the soul. For where your treasure is, there will your heart be also (Matt 6:21): where the delight, there the treasure; but where the heart, there blessedness or misery. But what are the higher things, except those in which the highest, unshaken, unchangeable, eternal equality abides? Where there is no time, because there is no changeableness; and whence times are fashioned and ordered and regulated, imitating eternity, while the turning of the heaven returns to the same point, and recalls the heavenly bodies to the same point, and, by days and months and years and lustra, and the other circlings of the stars, obeys the laws of equality and unity and ordering. So earthly things, subjected to the heavenly, associate the circlings of their own times, by a rhythmical succession, as it were to the song of the universe.

6. 11. 30. Among these things many seem to us disordered and disturbed, because we have been sewn to their order according to our deserts, not knowing what beautiful thing the divine providence works concerning us. Since if anyone, for example, were set like a statue in some one corner of a most spacious and most beautiful building, he could not perceive the beauty of that structure of which he himself would be a part. Nor can a soldier in the line behold the order of the whole army. And in any poem, if the syllables lived and felt for as long a span as they sound, that rhythm and the beauty of the woven work would in no way please them, which they could not behold and approve as a whole, since it would be fashioned and completed out of those very single ones passing away. So God ordered the sinning man as base, not basely. For he was made base by his will, losing the whole which, obeying God's precepts, he possessed, and he was ordered in a part, so that he who would not act by the law might be acted upon by the law. But whatever is done lawfully is surely done justly; and whatever is done justly is surely not done basely: because even in our bad works God's works are good. For a man, insofar as he is a man, is some good; but adultery, insofar as it is adultery, is a bad work: yet often a man is born of adultery—from a bad work of man, that is, a good work of God.

6. 11. 31. Therefore, to bring ourselves back to the purpose for which these things have been said, these numbers of reason excel in beauty; and if we were wholly cut off from them, when we incline toward the body, they would not regulate the sensual advancing numbers; which in turn, in moving bodies, produce the sensible beauties of times; and so the encountering numbers too are fashioned, meeting the sounding ones; all of which the same soul, receiving their onrushes, in a way multiplies in itself, and makes recalling; which power of it is called memory, a certain great help in the most busy acts of this life.

6. 11. 32. This memory, then—whatever it holds of the motions of the mind that have been produced against the passions of the body—is called in Greek by a name for which I do not find what I would rather call it in Latin; to hold these for known and for perceived is the opinionative life, set at the very entrance of error. But when these motions meet one another, and seethe, as it were, with diverse and conflicting blasts of intention, they bring forth other motions from others—now not those that are held, impressed from the senses by the encounters of the body's passions, but yet like them, as it were images of images, which it has pleased to call "phantasms." For I think of my father, whom I often saw, in one way, of my grandfather, whom I never saw, in another. The first of these is a phantasy, the other a phantasm. The one I find in the memory, the other in that motion of the mind which has arisen from those things the memory holds. But how these arise is hard both to find and to explain. Yet I judge that, if I had never seen human bodies, I could in no way figure them by thinking in a visible appearance. But what I make from what I have seen, I make by memory; and yet it is one thing to find a phantasy in the memory, another to make a phantasm from the memory. All which the power of the soul can do. But to hold even true phantasms for known is the highest error. Although there is in each kind that which we not absurdly say we know—that is, that we have felt such things, or that we imagine such things. That I had a father and a grandfather, in fine, I can say without rashness; but that they are the ones whom my mind holds in a phantasy or in a phantasm, I would most madly say. But some follow their phantasms so headlong that there is no other material of all false opinions than to hold for known the phantasies or phantasms which are known through the senses. Therefore let us resist these most of all, nor so accommodate our mind to them that, while our thought is in them, we judge that we discern them by the understanding.

6. 11. 33. But why, if numbers of this kind that come about in the soul given over to temporal things have a beauty of their own kind, although they keep producing it by passing away, should the divine providence envy this beauty, which is formed from our penal mortality, which we have deserved by the most just law of God—in which, however, he has not so deserted us that we cannot run back, and, by his mercy stretching out a hand, be called back from the delight of the carnal senses? For such delight fixes firmly in the memory what it draws from the slippery senses. But this habit of the soul, made with the flesh, is named in the divine Scriptures, because of the carnal affection, "flesh." This struggles against the mind, when that apostolic word can now be said: With the mind I serve the law of God, but with the flesh the law of sin. (Rom 7:25) But, the mind being suspended in spiritual things and there fixed and remaining, the onrush of this habit too is broken, and, gradually repressed, is extinguished. For it was greater when we followed it; yet not wholly none, but certainly less, when we curb it; and so, by certain returns from every wanton motion, in which is the soul's defect of essence, delight being restored to the numbers of reason, our whole life is turned toward God, giving to the body the numbers of health, not receiving gladness thence; which will come to pass when the outer man is corrupted and changed for the better.

6. 12. 34. Student: There, I think, is what is more excellent than bodies; but whether in the soul itself, or even above the soul, I do not know.

6. 12. 35. Teacher: If, then, we ask whether that rhythmic or metrical art, which those who make verses use, has any pure numbers according to which they fashion verses?

Student: I can think nothing else.

Teacher: Whatever these numbers are, do they seem to you to pass away with the verses, or to remain?

Student: To remain indeed.

Teacher: We must agree, then, that some passing numbers are fashioned from some remaining ones?

Student: Reason compels me to agree.

Teacher: And this art—do you think it anything other than a certain affection of the craftsman's mind?

Student: So I believe.

Teacher: Do you believe this affection is also in one who is unskilled in this art?

Student: In no way.

Teacher: And in one who has forgotten it?

Student: Not in him either, because he too is unskilled, even if he was skilled at some time.

Teacher: And if someone reminds him by questioning—do you think those numbers migrate back to him from the very one who questions, or that he moves himself inwardly, within his own mind, toward something whence what he had lost may be repaid to him?

Student: I think he does it within himself.

Teacher: And do you judge that he is reminded by questioning even which syllable is to be shortened, or which lengthened, if it has utterly slipped away—since, by the ancient agreement and custom of men, a smaller delay has been given to some syllables, a greater to others? For surely, if it were fixed and stable by nature or by discipline, learned men of a more recent time would not have lengthened some that the ancients shortened, or shortened some that they lengthened.

Student: I think this too is possible, since however much anything slips away, it can return into the memory by a reminding question.

Teacher: It would be a wonder if you supposed that, with anyone questioning, you could recollect what you dined on a year ago.

Student: I admit I cannot; nor do I now think that he can be reminded by questioning about syllables whose spans he has utterly forgotten.

Teacher: Why so, except because in this name which is "Italia" the first syllable was shortened according to the will of certain men, and now is lengthened according to the will of others? But that one and two are not three, and that two does not answer to one in double, no one of the dead has been able, no one of the living is able, no one of those to come will be able, to make.

Student: Nothing is more manifest.

Teacher: What, then, if in that way in which we inquired most plainly about one and two, all the other things that pertain to those numbers were asked also of him who is unskilled not by forgetting, but because he never learned? Do you not judge that he can likewise come to know this art, the syllables excepted?

Student: Who would doubt it?

Teacher: Toward what, then, do you think this man too will move himself, so that these numbers may be impressed on his mind and make that affection which is called art? Or will that questioner at least give them to him?

Student: In that way I judge that this man too acts within himself, so that he understands and answers that the things asked are true.

6. 12. 36. Teacher: Come, now tell me whether these numbers, about which it is thus inquired, seem to you changeable.

Student: In no way.

Teacher: So you do not deny that they are eternal.

Student: On the contrary, I admit it.

Teacher: And will not that fear be present, lest some inequality in them deceive us?

Student: Nothing makes me more secure than the equality of these.

Teacher: Whence, then, must we believe that what is eternal and unchangeable is granted to the soul, except by the one eternal and unchangeable God?

Student: I do not see what else ought to be believed.

Teacher: And is not this manifest: that he who, with another questioning, moves himself within toward God, so that he may understand the unchangeable truth, cannot—unless he holds that same motion of his by memory—be recalled to behold that truth, with no one admonishing from without?

Student: It is manifest.

6. 13. 37. Teacher: I ask, then, whither this man departs from the contemplation of things of this kind, so that it is necessary for him to be recalled to it by memory. Or is the mind, intent perhaps on something else, to be thought to need such a return?

Student: So I judge.

Teacher: Let us see, if you please, what so great a thing that is toward which it can be intent, so as to be turned away from the contemplation of the unchangeable and highest equality. For beyond three kinds I see nothing more. For the mind, when it is turned away from here, is intent either on something equal and on another of the same kind, or on something higher, or on something lower.

Student: We must inquire about the other two; for what is higher than the eternal equality I do not see.

Teacher: Do you see, I beg, what could be equal to it, that yet would be another?

Student: Not even that do I see.

Teacher: It remains, then, that we inquire what is lower. But does not the soul itself occur to you first, which surely confesses that equality to be unchangeable, but acknowledges that it itself is changed by this very thing, that now it beholds this, now something else; and in this way, pursuing one thing and another, produces the variety of time, which in eternal and unchangeable things is none?

Student: I agree.

Teacher: This affection, then, of the soul, or motion, by which it understands that eternal things are, and that temporal things are lower than these, even in itself; and knows that these higher things are to be sought rather than those lower ones—does it not seem to you prudence?

Student: It seems nothing else.

6. 13. 38. Teacher: And this—do you think it is to be considered any less, that it is not yet in the soul to cling to eternal things at the same time, although it is already in it to know that it must cling to these?

Student: On the contrary, I ask most of all that we consider this, and I desire to know whence it comes about.

Teacher: You will easily see it, if you notice to what things we are accustomed to direct the mind most, and to show great care; for those, I think, are the ones we love much. Or do you think otherwise?

Student: No others indeed.

Teacher: Tell me, I beg you, can we love anything but the beautiful? For although some seem to love the unshapely—those whom the Greeks commonly call lovers of the ugly—yet it matters how much less beautiful they are than those that please more people. For it is manifest that no one loves those things whose foulness offends the sense.

Student: It is as you say.

Teacher: These beautiful things, then, please by number, in which we have already shown that equality is sought. For this is found not only in that beauty which belongs to the ears and is in the motion of bodies, but also in the very visible forms, in which beauty is now more usually spoken of. Or do you judge it anything other than rhythmical equality, when two members, equal to equal, answer in pairs—but those that are single hold the middle place, so that toward them equal intervals are kept on each side?

Student: I think not otherwise.

Teacher: And in the very visible light, which holds the primacy of all colors—for color too delights us in the forms of bodies—what else, then, do we seek in light and colors, except what agrees with our eyes? For we turn away from too great a brilliance, and we are unwilling to look at things too dark, just as in sounds too we shrink from things sounding too loud, and do not love things as it were whispering. Which is not in the intervals of time, but in the sound itself, which is, as it were, the light of such numbers, to which silence is contrary as darkness is to colors. In these, then, when we seek the agreeable according to the measure of our nature, and reject the disagreeable—which we yet perceive to be agreeable to other animals—do we not here too rejoice by a certain right of equality, when we recognize, by more hidden ways, that equals have been assigned to equals? This may be noticed in odors and flavors, and in the sense of touch, which it would be long to pursue more thoroughly, but most easy to test: for there is none of these sensible things that does not please us by equality or likeness. But where there is equality or likeness, there is rhythm; for nothing is so equal or so like as one and one. Unless you have something against this.

Student: I agree entirely.

6. 13. 39. Teacher: And did not that earlier discussion persuade us that the soul does these things in bodies, and does not undergo them from bodies?

Student: It did persuade us indeed.

Teacher: The love, then, of acting against the succeeding passions of its body turns the soul away from the contemplation of eternal things, the care of sensible pleasure calling off its intention: and this it does by the encountering numbers. The love of working upon bodies turns it away too, and makes it restless: and this it does by the advancing numbers. Phantasies and phantasms turn it away: and these it does by the recalling numbers. Finally, the love of the most empty knowledge of such things turns it away: and this it does by the sensual numbers, in which there are, as it were, certain rules of the art rejoicing in imitation; and from these is born curiosity, by the very name of care hostile to security, and, by its emptiness, having no command of truth.

6. 13. 40. But the general love of action, which turns away from the true, proceeds from pride, by which fault the soul preferred to imitate God rather than to serve God. And so it is rightly written in the holy books: The beginning of man's pride is to depart from God (Sir 10:12); and Pride is the beginning of all sin. (Sir 10:13) But what pride is could not be better shown than in what was said there: Why is earth and ashes proud, since in his life he has cast away his inmost parts? (See Sir 10:9–10) For since the soul through itself is nothing—for otherwise it would not be changeable, and would not suffer defect from its essence—since, then, it is itself through itself nothing, but whatever being it has is from God, then, remaining in its own order, it is quickened in mind and conscience by the presence of God himself. And so it has this good as its inmost good. Therefore to swell with pride is for it to advance into the outermost things, and, so to speak, to become empty, which is to be less and less. But to advance into the outermost things—what else is it than to cast away the inmost things, that is, to put God far from oneself, not by a span of places, but by an affection of mind?

6. 13. 41. But this is an appetite of the soul: to have other souls under itself—not of cattle, which is granted by divine right, but rational ones, that is, its neighbors, and its fellows and companions under the same law. Upon these the proud soul desires to work, and this action seems the more excellent than that upon bodies, by as much as every soul is better than every body. But to work upon rational souls, not through the body but through itself, God alone can do. Yet by the condition of sinners it comes about that souls are permitted to do something upon souls, moving them by signifying through their respective bodies, whether by natural signs, such as the face or a nod, or by agreed ones, such as words. For both those commanding and those persuading act by signs, and whatever else there is besides command and persuasion, by which souls do something upon souls or with souls. But it has rightly followed that those which by pride desired to excel the rest neither command their own parts and bodies without difficulty and pains, being partly foolish in themselves, partly weighed down by mortal members. And so by these numbers and motions too, by which souls act upon souls, by seeking honors and praises they are turned away from the perception of that pure and sincere truth. For God alone honors, making blessed in secret, before himself, the soul that lives justly and piously.

6. 13. 42. Student: There is nothing I would dare to object.

6. 14. 43. Teacher: What, then, remains? Is it that, since we have considered, as well as we could, the defilement and the weighing-down of the soul, we see what action is divinely commanded to it, by which, purified and unburdened, it may fly back to rest, and enter into the joy of its Lord?

Student: Let it be so.

Teacher: Why do you think I ought to say more about this, when the divine Scriptures, endowed with so many volumes and with so great authority and holiness, do nothing else with us than that we love God our Lord with our whole heart, with our whole soul, and with our whole mind, and love our neighbor as ourselves? (See Matt 22:37–39) If, then, we refer all those motions and numbers of human action to this end, we will without doubt be cleansed. Or do you think otherwise?

Student: Nothing else indeed. But as brief as this is to hear, so hard and arduous it is to do.

6. 14. 44. Teacher: What, then, is easy? To love colors, and voices, and cakes, and roses, and bodies softly smooth? Is it easy for the soul to love these, in which it seeks nothing but equality and likeness, and, considering a little more carefully, scarcely recognizes their farthest shadow and trace; and is it hard to love God, in whom, thinking of him as far as it can—still wounded and soiled—it suspects nothing unequal, nothing unlike itself, nothing shut off by places, nothing varied by time? Or does it delight to pile up masses of buildings, and to be stretched out in works of this kind—in which, if numbers please (for I find nothing else), what equal and like is named in them that the principle of the discipline does not mock? And if this is so, why does it slip down from that most true citadel of equality to these things, and by its own ruins erect earthly machines? This was not promised by him who knows not how to deceive. For my yoke, he says, is light. (See Matt 11:30) The love of this world is more laborious. For what the soul seeks in it—constancy, that is, and eternity—it does not find: since the lowest beauty is completed by the passing-away of things, and what in it imitates constancy is passed through it from the highest God by the soul: since a form changeable only by time is prior to one changeable both by time and by places. So, as it has been commanded to souls by the Lord what they should love, so through the apostle John what they should not love. Do not love the world, he says, for all that is in the world is the desire of the flesh, and the desire of the eyes, and the ambition of the age. (See 1 John 2:15–16)

6. 14. 45. Student: You proclaim a certain great man, and truly most humane.

6. 14. 46. Teacher: It is not, then, the numbers that are below reason and are beautiful in their own kind, but the love of the lower beauty, that defiles the soul: which, while it loves in that beauty not only equality—of which enough has been said for the work undertaken—but also order, has itself lost its own order; yet it has not gone beyond the order of things, since it is there, and is so, where to be, and in what way to be such, is most fully ordered. For it is one thing to keep order, another to be kept by order. The soul keeps order, loving with its whole self what is above it, that is, God, and its fellow souls as itself. For by this power of love it orders the lower things, and is not soiled by the lower things. But what soils it is not evil, because the body too is a creation of God, and is adorned by its own appearance, however lowest, but is despised before the dignity of the soul; just as the dignity of gold is soiled even by mixture with the most purified silver. Therefore whatever numbers have been made even from our penal mortality, let us not reject them from the fashioning of the divine providence, since they are beautiful in their own kind. Nor let us love them, as if by enjoying such things we were made blessed. For from these, since they are temporal, as from a plank in the waves, neither casting them away as burdensome, nor embracing them as if firmly grounded, but using them well, we shall be free of them. But from the love of neighbor, as great as is commanded, a most sure step is made for us, that we may cling to God, and not only be held by his ordering, but also keep our own order unshaken and sure.

6. 14. 47. Or does the soul perhaps not love order, those sensual numbers too bearing witness? Whence, then, is the first foot a pyrrhic, the second an iamb, the third a trochee, and so on the rest? But you may rightly say that this followed reason rather than sense. What, then—is not this to be granted to the sensual numbers: that, when, for example, eight long syllables take up as much time as sixteen shorts, yet in the same span the shorts rather expect to be mixed with longs? And when reason judges about this sense, and it is reported to it that proceleusmatic feet are equal to spondee feet, it finds that nothing else holds force here than the power of ordering, because neither are long syllables long except by comparison with shorts, nor again are shorts short except by comparison with longs; and therefore an iambic verse, however drawn out it is pronounced, the rule of single and double not being lost, does not lose its name; but that verse which consists of pyrrhic feet, the delay of pronouncing being added little by little, suddenly becomes spondaic, if you consult not grammar but music. But if it is dactylic or anapestic, since the longs are perceived by comparison with the shorts mixed in, it keeps its own name in whatever delay it is pronounced. Why are additions of half-feet not to be kept by the same law at the head as at the end, nor all to be applied, although they are fitted to the same beat? Why the setting sometimes of two shorts rather than of one long at the end? Are they not regulated by the very sense? Nor in these is the number of equality found, to which nothing is lost, whether it be this or another, but the bond of order. It would be long to run through the rest pertaining to the same force in the numbers of time. But surely the very sense too spurns visible forms, either bent contrary to what is becoming, or with the head downward, and the like, in which not inequality—the equality of the parts remaining—but perversity is disapproved. Finally, in all our senses and works, when we reconcile to our appetite, by certain steps, things mostly unusual and on that account unpleasant, and accept them first tolerably, then gladly—do we not weave the pleasure by order, and, unless the first are joined harmoniously to the middle, and the middle to the last, shrink from it?

6. 14. 48. Therefore let us place our joys neither in carnal pleasure, nor in the honors and praises of men, nor in the probing of those things that touch the body from without, having within us God, where all that we love is fixed and unchangeable. So it comes about both that, when these temporal things are present, we are nevertheless not entangled in them, and that, without the sense of pain, those that are outside the body may be absent; and the body itself may be taken away with no sense of pain, or none grievous, and be given back, to be reformed to its own nature, by death. For the attention of the soul to a part of the body draws together restless businesses, and, the universal law being neglected, there is a love of some private work—which yet cannot itself be estranged from the universe that God rules. And so he is subjected to the laws who does not love the laws.

6. 15. 49. But if, when for the most part we are thinking most attentively about incorporeal things that hold themselves always in the same way, whatever temporal numbers we happen at that time to produce in any motion of the body—an easy and most usual one indeed, whether walking or singing psalms—pass by while we are wholly unaware of them, although without our producing them they would be none; if, finally, even in our own empty phantasms, when we are occupied, these likewise pass by while we produce and yet do not perceive them: how much more, and how much more constantly, when this corruptible shall have put on incorruption, and this mortal shall have put on immortality (1 Cor 15:53)—that is, to say this very thing more plainly, when God shall have given life to our mortal bodies, as the Apostle says, because of his Spirit that dwells in us (See Rom 8:11)—how much more, then, shall we, intent upon the one God and the clearly seen truth, as has been said, face to face (1 Cor 13:12), perceive with no restlessness the numbers by which we move bodies, and shall rejoice? Unless perhaps it is to be believed that the soul, while it can rejoice over those things that are good through it, cannot rejoice over those from which it itself is good.

6. 15. 50. Student: I acknowledge and understand.

Teacher: What further? When the soul advances on this road, already foretasting and almost grasping eternal joys, does the loss of temporal things, or any death, frighten one now able to say to his lower companions: It is good for me to be dissolved and to be with Christ; but to remain in the flesh is necessary for your sake (See Phil 1:23–24)?

Student: So I judge.

Teacher: But this affection of his, by which it dreads no adversities or death—what else is it to be called than fortitude?

Student: This too I acknowledge.

Teacher: And that very ordering of it, by which it serves none but the one God, seeks to be made equal to none but the purest souls, seeks to lord it over none but the bestial and corporeal nature—what virtue, in the end, does it seem to you to be?

Student: Who would not understand that this is justice?

Teacher: You understand rightly.

6. 16. 51. Student: I do not see, when the adversities against which it struggles have passed away, how either prudence can be there, which chooses what to follow only amid adversities; or temperance, which turns love away only from adversities; or fortitude, which endures only adversities; or justice, which seeks to be made equal to the most blessed souls, and to lord it over a lower nature, only amid adversities—that is, not yet having attained the very thing it seeks.

6. 16. 52. Teacher: Your answer is not altogether absurd; and that this has seemed so to certain learned men I do not deny. But I, consulting the books which no authority surpasses, find it thus said: Taste and see that the Lord is sweet. (Ps 34:8 (33:9)) Which the apostle Peter too interposed thus: If indeed you have tasted that the Lord is sweet. (See 1 Pet 2:3) This, I judge, is what takes place in those virtues which, by the very conversion, purify the soul. For the love of temporal things would not be conquered, except by some sweetness of eternal things. But when one has come to that which is sung, The sons of men will hope under the covering of your wings; they will be inebriated by the abundance of your house, and you will give them to drink of the torrent of your pleasure; for with you is the fountain of life (See Ps 36:7–9 (35:8–10)), he no longer says that the Lord will be sweet to the taste; but you see what inundation and affluence of the eternal fountain is proclaimed; which a certain inebriation also follows: by which name there seems to me to be wonderfully signified that forgetfulness of worldly vanities and phantasms. He then weaves the rest, and says, In your light we shall see light. Stretch forth your mercy to those who know you. (See Ps 36:9–10 (35:10–11)) "In light"—to be taken, namely, in Christ, who is the Wisdom of God, and is so often called light. Where, then, it is said we shall see, and to those who know you, it cannot be denied that prudence will be there. Or can the true good of the soul be seen and known where there is no prudence?

Student: Now I understand.

6. 16. 53. Teacher: And can the upright in heart be without justice?

Student: I recognize that by this name justice is more often signified.

Teacher: What else, then, does the same prophet admonish consequently, when he sings: And your justice to those who are upright in heart (See Ps 36:10 (35:11))?

Student: It is manifest.

Teacher: Come on, recall, if you please, that we treated enough above how by pride the soul slips down to certain actions of its own power, and, the universal law being neglected, falls into the doing of certain private things—which is called departing from God.

Student: I remember indeed.

Teacher: When, then, it acts so that this no longer delights it at any time, does it not seem to you to fix its love in God, and to live most temperately and most chastely and most securely, free of all defilement?

Student: It seems so indeed.

Teacher: See also how the prophet adds this too, saying: Let not the foot of pride come to me. (See Ps 36:11 (35:12)) For by calling it a "foot" he signifies that very departure or fall, from which the soul, by being temperate, clinging to God, lives forever.

Student: I accept and follow.

6. 16. 54. Teacher: Fortitude, then, remains. But as temperance avails against the fall that is in free will, so fortitude avails against force, by which one can even be compelled, if he is less strong, to those things by which he may be overturned and lie most wretched. But this force is fittingly wont to be signified in the Scriptures by the name of "hand." And who, indeed, but sinners try to bring this force to bear? When, then, by this very thing the soul is fortified and guarded by the firmament of God, so that this can in no way befall it from anywhere, it bears a certain stable and, so to speak, impassible power, which—unless something displeases you—is rightly named fortitude; and I judge it is so called when there is added: And let not the hand of sinners move me. (See Ps 36:11 (35:12))

6. 16. 55. Student: On the contrary, I do not see how it could be otherwise most perfect and most blessed.

Teacher: This contemplation, then, sanctification, impassibility, and ordering of it, either are those four perfect and consummated virtues; or—lest we labor in vain about names when the things agree—in place of these virtues, which the soul uses while set amid labors, certain such powers are to be hoped for it in the eternal life.

6. 17. 56. Let us only remember—what pertains most to the present discussion undertaken—that it comes about through the providence of God, by which he created and rules all things, that even the sinful and wretched soul is acted by numbers, and produces numbers, down to the lowest corruption of the flesh: which numbers can certainly be less and less beautiful, but cannot be wholly without beauty. But God, supremely good and supremely just, envies no beauty, which is fashioned whether by the damnation, or the regression, or the perseverance of the soul. Now number both begins from one, and is beautiful by equality and likeness, and is coupled by order. Therefore whoever admits that there is no nature which, in order to be whatever it is, does not seek unity, and try to be like itself as far as it can, and hold its own order, whether in places or in times, or by a certain balance in some body, its own welfare—he must admit that, from one principle, through a form equal and like to it, by the riches of his goodness, by which the One and the One-from-One are joined to each other in a love most dear, so to speak, all things have been made and founded, whatsoever they are, insofar as they are.

6. 17. 57. Therefore that verse proposed by us, Deus creator omnium, is most pleasing not only to the ears by its rhythmical sound, but much more to the soul by the soundness and truth of its meaning. Unless perhaps the slowness moves you—to speak more mildly—of those who deny that anything can be made from nothing, when almighty God is said to have done this. Or can a craftsman, by the rational numbers that are in his art, produce the sensual numbers that are in his practice, and, by the sensual numbers, those advancing ones by which he moves his members in working, to which now intervals of time belong, and by these again can visible forms, rhythmical in intervals of place, be fashioned from wood—and yet can the nature of things, serving the nods of God, not make the wood itself from earth and the other elements; and could those very elements not be made from nothing? Nay, even the local numbers of a tree must necessarily be preceded by temporal numbers. For there is no kind of plant which does not, by fixed measures of time proper to its own seed, both take root, and germinate, and shoot forth into the air, and unfold its leaves, and grow strong, and bear back, by the most hidden numbers of either the fruit or of the wood itself, the power of seed again: how much more the bodies of animals, in which the intervals of the members offer a rhythmical equality much more to the sight? Or can these things be made from the elements, and the elements themselves could not be made from nothing? As if, indeed, there were anything in them cheaper and more abject than earth is. Which first has the general appearance of a body, in which a certain unity and number and order is shown to be. For from some indivisible point any particle of it, however small, must be stretched out into length, take on a third dimension, breadth, and a fourth, height, by which a body is filled. Whence, then, this manner of progression from the first up to the fourth? Whence too the equality of parts, which is found in length and breadth and height? Whence a certain co-rationality (for so I have preferred to call analogy), so that the ratio which length has to the indivisible point, the same breadth has to length, and height to breadth? Whence, I ask, do these things come, except from that highest and eternal sovereignty of numbers and of likeness and equality and order? And yet, if you take these away from earth, it will be nothing. Therefore almighty God made earth, and earth was made from nothing.

6. 17. 58. What further? That very appearance by which earth is distinguished from the other elements—does it not both display some one thing, in the measure it has received, and is no part of it unlike the whole, and, by the connection and concord of those same parts, hold, in its own kind, the lowest and most healthful seat? Over which is poured out the nature of the waters, itself too striving toward unity, more beautiful and more transparent because of the greater likeness of its parts, and keeping the place of its order and welfare. What shall I say of the nature of air, striving toward unity by a much easier embrace, and as much more beautiful than the waters as they are than the lands, and so much higher toward welfare? What of the supreme circuit of heaven, by which the whole universe of visible bodies is bounded, and the highest appearance in this kind, and the most healthful excellence of place? All these things, surely, which we number by the ministry of the carnal sense, and whatsoever are in them, can neither receive nor have the local numbers which seem to be in some fixed state, unless there precede the inmost and silent temporal numbers which are in motion. These same, agile in the intervals of times, a vital motion precedes and regulates, serving the Lord of all things, having not the temporal intervals of its numbers set in order, but a power supplying times; above which the rational and intellectual numbers of the blessed and holy souls transmit the very law of God—without which a leaf does not fall from a tree, and by whom our hairs are numbered (See Matt 10:29–30)—receiving it with no nature set between, all the way down to earthly and infernal rights.

6. 17. 59. These things, so far as I could and as I could, I, so little, have considered with you about so great matters. But if any read this our discussion committed to writing, let them know that these things have been written for those far weaker than are those who, following the authority of the two Testaments, venerate and worship the consubstantial and unchangeable Trinity of the one highest God—from whom are all things, through whom are all things, in whom are all things (See Rom 11:36)—by believing, hoping, and loving it. For these are purified not by glittering human reasonings, but by the strongest and most flaming fire of love. But we, while we do not think that those should be neglected whom heretics deceive by a deceitful promise of reason and knowledge, walk more slowly, by the consideration of the very roads, than holy men who do not deign to attend to them, since they fly over them. Which yet we would not dare to do, did we not see that many pious sons of the catholic Church, our best mother—who in childhood studies had attained as much faculty of speaking and discussing as is enough—had done the same, by the same necessity of refuting heretics.