(31) "On a seven-stringed lyre we shall sing new hymns," writes a poet of note, teaching us that the ancient lyre was seven-toned. The organs of the senses situated on our face are also seven - two eyes, two passages of hearing, two nostrils, and the seventh the mouth. And that the changes in the periods of life take place by sevens, the Elegies of Solan teach thus: "The child, while still an infant, in seven years, Produces and puts forth its fence of teeth; And when God seven years more completes, He shows of puberty's approach the signs; And in the third, the beard on growing cheek With down o'erspreads the bloom of changing skin; And in the fourth septenniad, at his best In strength, of manliness he shows the signs; And in the fifth, of marriage, now mature, And of posterity, the man bethinks; Nor does he yet desire vain works to see.

(10) Further, as an example of music, let us adduce David, playing at once and prophesying, melodiously praising God. Now the Enarmonic s suits best the Dorian harmony, and the Diatonic the Phrygian, as Aristoxenus says. The harmony, therefore, of the Barbarian psaltery, which exhibited gravity of strain, being the most ancient, most certainly became a model for Terpander, for the Dorian harmony, who sings the praise of Zeus thus: "O Zeus, of all things the Beginning, Rule, of, all; O Zeus, I send thee this beginning of hymns."

(2) Employing this method, therefore, as a basis, and as it were an infallible rule, he afterwards extended the experiment to various instruments; viz. to the pulsation of patellæ or pans, to pipes and reeds, to monochords, triangles, and the like. And in all these he found an immutable concord with the ratio of numbers. But he denominated the sound which participates of the number 6 hypate : that which participates of the number 8 and is sesquitertian, mese ; that which participates of the number 9, but is more acute by a tone than mese, he called paramese , and epogdous ; but that which participates of the dodecad, nete . Having also filled up the middle spaces with analogous sounds according to the diatonic genus, he formed an octochord from symphonious numbers, viz. from the double, the sesquialter, the sesquitertian, and from the difference of these, the epogdous.

And thus he discovered the [harmonic] progression, which tends by a certain physical necessity from the most grave [i. e. flat] to the most acute sound, according to this diatonic genus. For from the diatonic, he rendered the chromatic and enharmonic genus perspicuous, as we shall some time or other show when we treat of music. This diatonic genus, however, appears to have such physical gradations and progressions as the following; viz. a semitone, a tone, and then a tone; and this is the diatessaron, being a system consisting of two tones, and of what is called a semitone. Afterwards, another tone being assumed, viz. the one which is intermediate, the diapente is produced, which is a system consisting of three tones and a semitone.

In the next place to this is the system of a semitone, a tone, and a tone, forming another diatessaron, i. e. another sesquitertian ratio. So that in the more ancient heptachord indeed, all the sounds, from the most grave, which are with respect to each other fourths, produce every where with each other the symphony diatessaron; the semitone receiving by transition, the first, middle, and third place, according to the tetrachord. In the Pythagoric octachord, however, which by conjunction is a system of the tetrachord and pentachord, but if disjoined is a system of two tetrachords separated from each other, the progression is from the most grave sound. Hence all the sounds that are by their distance from each other fifths, produce with each other the symphony diapente; the semitone successively proceeding into four places, viz. the first, second, third, and fourth. After this manner, therefore, it is said that music was discovered by Pythagoras. And having reduced it to a system, he delivered it to his disciples as subservient to every thing that is most beautiful.

(11) The lyre, according to its primary signification, may by the psalmist be used figuratively for the Lord; according to its secondary, for those who continually strike the chords of their souls under the direction of the Choir-master, the Lord. And if the people saved be called the lyre, it will be understood to be in consequence of their giving glory musically, through the inspiration of the Word and the knowledge of God, being struck by the Word so as to produce faith. You may take music in another way, as the ecclesiastical symphony at once of the law and the prophets, and the apostles along with the Gospel, and the harmony which obtained in each prophet, in the transitions of the persons.

(1) Since, however, we are narrating the wisdom employed by Pythagoras in instructing his disciples, it will not be unappropriate to relate that which is proximate in a following order to this, viz. how he invented the harmonic science, and harmonic ratios. But for this purpose we must begin a little higher. Intently considering once, and reasoning with himself, whether it would be possible to devise a certain instrumental assistance to the hearing, which should be firm and unerring, such as the sight obtains through the compass and the rule, or, by Jupiter, through a dioptric instrument; or such as the touch obtains through the balance, or the contrivance of measures;—thus considering, as he was walking near a brazier’s shop, he heard from a certain divine casualty the hammers beating out a piece of iron on an anvil, and producing sounds that accorded with each other, one combination only excepted.

But he recognized in those sounds, the diapason, the diapente, and the diatessaron, harmony. He saw, however, that the sound which was between the diatessaron and the diapente was itself by itself dissonant, yet, nevertheless, gave completion to that which was the greater sound among them. Being delighted, therefore, to find that the thing which he was anxious to discover had succeeded to his wishes by divine assistance, he went into the brazier’s shop, and found by various experiments, that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the figure of the hammers, nor from the transposition of the iron which was beaten. When, therefore, he had accurately examined the weights and the equal counterpoise of the hammers, he returned home, and fixed one stake diagonally to the walls, lest if there were many, a certain difference should arise from this circumstance, or in short, lest the peculiar nature of each of the stakes should cause a suspicion of mutation.

Afterwards, from this stake he suspended four chords consisting of the same materials, and of the same magnitude and thickness, and likewise equally twisted. To the extremity of each chord also he tied a weight. And when he had so contrived, that the chords were perfectly equal to each other in length, he afterwards alternately struck two chords at once, and found the before-mentioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, produced, when compared with that which was stretched by the smallest, the symphony diapason. But the former of these weights was twelve pounds, and the latter six. And, therefore, being in a duple ratio, it exhibited the consonance diapason; which the weights themselves rendered apparent.

But again, he found that the chord from which the greatest weight was suspended compared with that from which the weight next to the smallest depended, and which weight was eight pounds, produced the symphony diapente. Hence he discovered that this symphony is in a sesquialter ratio, in which ratio also the weights were to each other. And he found that the chord which was stretched by the greatest weight, produced, when compared with that which was next to it in weight, and was nine pounds, the symphony diatessaron, analogously to the weights. This ratio, therefore, he discovered to be sesquitertian; but that of the chord from which a weight of nine pounds was suspended, to the chord which had the smallest weight [or six pounds,] to be sesquialter.

For 9 is to 6 in a sesquialter ratio. In like manner, the chord next to that from which the smallest weight depended, was to that which had the smallest weight, in a sesquitertian ratio, [for it was the ratio of 8 to 6,] but to the chord which had the greatest weight, in a sesquialter ratio [for such is the ratio of 12 to 8.] Hence, that which is between the diapente and the diatessaron, and by which the diapente exceeds the diatessaron, is proved to be in an epogdoan ratio, or that of 9 to 8. But either way it may be proved that the diapason is a system consisting of the diapente in conjunction with the diatessaron, just as the duple ratio consists of the sesquialter and sesquitertian, as for instance, 12, 8, and 6; or conversely, of the diatessaron and the diapente, as in the duple ratio of the sesquitertian and sesquialter ratios, as for instance 12, 9, and 6.

After this manner, therefore, and in this order, having conformed both his hand and his hearing to the suspended weights, and having established according to them the ratio of the habitudes, he transferred by an easy artifice the common suspension of the chords from the diagonal stake to the limen of the instrument, which he called chordotonon . But he produced by the aid of pegs a tension of the chords analogous to that effected by the weights.

(1) Conceiving, however, that the first attention which should be paid to men, is that which takes place through the senses; as when some one perceives beautiful figures and forms, or hears beautiful rythms and melodies, he established that to be the first erudition which subsists through music, and also through certain melodies and rythms, from which the remedies of human manners and passions are obtained, together with those harmonies of the powers of the soul which it possessed from the first. He likewise devised medicines calculated to repress and expel the diseases both of bodies and souls. And by Jupiter that which deserves to be mentioned above all these particulars is this, that he arranged and adapted for his disciples what are called apparatus and contrectations, divinely contriving mixtures of certain diatonic, chromatic, and euharmonic melodies, through which he easily transferred and circularly led the passions of the soul into a contrary direction, when they had recently and in an irrational and clandestine manner been formed; such as sorrow, rage, and pity, absurd emulation and fear, all-various desires, angers, and appetites, pride, supineness, and vehemence.

For he corrected each of these by the rule of virtue, attempering them through appropriate melodies, as through certain salutary medicines. In the evening, likewise, when his disciples were retiring to sleep, he liberated them by these means from diurnal perturbations and tumults, and purified their intellective power from the influxive and effluxive waves of a corporeal nature; rendered their sleep quiet, and their dreams pleasing and prophetic. But when they again rose from their bed, he freed them from nocturnal heaviness, relaxation and torpor, through certain peculiar songs and modulations, produced either by simply striking the lyre, or employing the voice. Pythagoras, however, did not procure for himself a thing of this kind through instruments or the voice, but employing a certain ineffable divinity, and which it is difficult to apprehend, he extended his ears, and fixed his intellect in the sublime symphonies of the world, he alone hearing and understanding, as it appears, the universal harmony and consonance of the spheres, and the stars that are moved through them, and which produce a fuller and more intense melody than any thing effected by mortal sounds.

This melody also was the result of dissimilar and variously differing sounds, celerities, magnitudes, and intervals, arranged with reference to each other in a certain most musical ratio, and thus producing a most gentle, and at the same time variously beautiful motion and convolution. Being therefore irrigated as it were with this melody, having the reason of his intellect well arranged through it, and as I may say, exercised, he determined to exhibit certain images of these things to his disciples as much as possible, especially producing an imitation of them through instruments, and through the mere voice alone. For he conceived that by him alone, of all the inhabitants of the earth, the mundane sounds were understood and heard, and this from a natural fountain itself and root.

He therefore thought himself worthy to be taught, and to learn something about the celestial orbs, and to be assimilated to them by desire and imitation, as being the only one on the earth adapted to this by the conformation of his body, through the dæmoniacal power that inspired him. But he apprehended that other men ought to be satisfied in looking to him, and the gifts he possessed, and in being benefited and corrected through images and examples, in consequence of their inability to comprehend truly the first and genuine archetypes of things. Just, indeed, as to those who are incapable of looking intently at the sun, through the transcendent splendor of his rays, we contrive to exhibit the eclipses of that luminary, either in the profundity of still water, or through melted pitch, or through some darkly-splendid mirror; sparing the imbecility of their eyes, and devising a method of representing a certain repercussive light, though less intense than its archetype, to those who are delighted with a thing of this kind. Empedocles also appears to have obscurely signified this about Pythagoras, and the illustrious and divinely-gifted conformation of his body above that of other men, when he says:

(28) And now the whole world of creatures born alive, and things that grow, revolves in sevens. The first-born princes of the angels, who have the greatest power, are seven. The mathematicians also say that the planets, which perform their course around the earth, are seven; by which the Chaldeans think that all which concerns mortal life is effected through sympathy, in consequence of which they also undertake to tell things respecting the future.

(399) under the circumstances, and acquiescing in the event. These two harmonies I ask you to leave; the strain of necessity and the strain of freedom, the strain of the unfortunate and the strain of the fortunate, the strain of courage, and the strain of temperance; these, I say, leave. And these, he replied, are the Dorian and Phrygian harmonies of which I was just now speaking. Then, I said, if these and these only are to be used in our songs and melodies, we shall not want multiplicity of notes or a panharmonic scale? I suppose not. Then we shall not maintain the artificers of lyres with three corners and complex scales, or the makers of any other many-stringed curiously-harmonised instruments? Certainly not. But what do you say to flute-makers and flute-players? Would you admit them into our State when you reflect that in this composite use of harmony the flute is worse than all the stringed instruments put together; even the panharmonic music is only an imitation of the flute? Clearly not. There remain then only the lyre and the harp for use in the city, and the shepherds may have a pipe in the country. That is surely the conclusion to be drawn from the argument. The preferring of Apollo and his instruments to Marsyas and his instruments is not at all strange, I said. Not at all, he replied. And so, by the dog of Egypt, we have been unconsciously purging the State, which not long ago we termed luxurious. And we have done wisely, he replied. Then let us now finish the purgation, I said. Next in order to harmonies, rhythms will naturally follow, and they should be subject to the same rules, for we ought not to seek out complex systems of metre, or metres of every kind, but rather to discover what rhythms are the expressions of

(4) From two letters, or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty; from seven, five thousand and forty; and from thence their numbers increase in a manner beyond counting; and are incomprehensible. These seven are Planets of the Universe, the Sun, Venus, Mercury, Moon, Saturn, Jupiter, and Mars; the seven days are the days of creation; and these an the seven gateways of a man, two eyes, two ears, two nostrils and a mouth, through which he perceives by his senses.

(617) coloured by the reflected light of the seventh; the second and fifth [Saturn and Mercury] are in colour like one another, and yellower than the preceding; the third [Venus] has the whitest light; the fourth [Mars] is reddish; the sixth [Jupiter] is in whiteness second. Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other, and of these the swiftest is the eighth; next in swiftness are the seventh, sixth, and fifth, which move together; third in swiftness appeared to move according to the law of this reversed motion the fourth; the third appeared fourth and the second fifth. The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne: these are the Fates, daughters of Necessity, who are clothed in white robes and have chaplets upon their heads, Lachesis and Clotho and Atropos, who accompany with their voices the harmony of the sirens—Lachesis singing of the past, Clotho of the present, Atropos of the future; Clotho from time to time assisting with a touch of her right hand the revolution of the outer circle of the whorl or spindle, and Atropos with her left hand touching and guiding the inner ones, and Lachesis laying

(531) their ears before their understanding. You mean, I said, those gentlemen who tease and torture the strings and rack them on the pegs of the instrument: I might carry on the metaphor and speak after their manner of the blows which the plectrum gives, and make accusations against the strings, both of backwardness and forwardness to sound; but this would be tedious, and therefore I will only say that these are not the men, and that I am referring to the Pythagoreans, of whom I was just now proposing to enquire about harmony. For they too are in error, like the astronomers; they investigate the numbers of the harmonies which are heard, but they never attain to problems—that is to say, they never reach the natural harmonies of number, or reflect why some numbers are harmonious and others not. That, he said, is a thing of more than mortal knowledge. A thing, I replied, which I would rather call useful; that is, if sought after with a view to the beautiful and good; but if pursued in any other spirit, useless. Very true, he said. Now, when all these studies reach the point of inter-communion and connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects; otherwise there is no profit in them. I suspect so; but you are speaking, Socrates, of a vast work. What do you mean? I said; the prelude or what? Do you not know that all this is but the prelude to the actual strain which we have to learn? For you surely would not