Life of Pythagoras — Iamblichus, trans. Thomas Taylor (1818)

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 patellz 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 /ypate: 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, mete. 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

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semitone, a tone, and then a tone; and this is the diatessaron, being a system consisting of two tones, and of what is called asemitone. 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 diatesgaron; 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.

CHAP. XXVII.

Many also of the political actions of his followers are [deservedly] praised. For it is reported that the Crotonians being once impelled to make sumptuous funerals and interments, some one of them said to the people, that he had heard Pythagoras when he was

1 Tamblichus derived what he has said in this chapter about music, from Nicomachus.

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discoursing about divine natures observe, that the Olympian Gods attended to the dispositions of those that sacrificed, and not to the multitude of the sacrifices; but that, on the contrary, the terrestrial Gods, as being allotted the government of things less important, rejoiced in banquets and lamentations, and farther still, in continual libations, in delicacies, and in celebrating funerals with great expense.

Whence, on account of his wish to receive, Pluto is called Hades. He suffers, therefore, those that slenderly honor him to remain for a longer time in the upper world; but he always draws down some one of those who are disposed to spend profusely in funeral solemnities, in order that he may obtain the honors which take place in commemoration of the dead.

In consequence of this advice, the Crotonians that heard it were of opinion, that if they conducted themselves moderately in misfortunes, they would preserve their own salvation; but that if they were immoderate in their expenses, they would all of them die prematurely.

A certain person also having been made an arbitrator in an affair in which there was no witness, led each of the litigants to a certain monument, and said to one of them, the man who is buried in this monument was transcendently equitable; in consequence of which the other litigant prayed that the dead man might obtain much good; but the former said that the defunct was not at all better for the prayers of his opponent.

Pythagoras, therefore, condemned what the former litigant said, but asserted that he who praised the dead man for his worth, had done that which would be of no small importance in his claim to belief. At another time, in a cause of great moment, he decided that one of the two who had agreed to settle the affair by arbitration, should pay four talents, but that the other should receive two.

Afterwards, he condemned the defendant to pay three talents; and thus he appeared to have given a talent to each of them. Two persons also had fraudulently