CHAP. XXVI.
‘Since, however, we are narrating the wisdom em-
ployed by Pythagoras in instructing his disciples, it will
not be unappropriate to relate that which is proximate
1 Odyss. lib. 4.
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 con-
sidering once, and reasoning with himself, whether it
would be possible to devise a certain instrumental
assistance to the hearing, which should be firm and un-
erring, such as the sight obtains through the compass
and the rule, or, by Jupiter, through a dioptric instru-
ment; or such as the touch obtains through the
balance, or the contrivance of measures;—thus con-
sidering, as he was walking near a brazier’s shop, he
heard from a certain divine casualty the hammers beat-
ing 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, tnat 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. Bein
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. After-
wards, from this stake he suspended four chords con-
sisting of the same materials, and of the same magnitude
and thickness, and likewise equally twisted. To the
extremity of each chord also te tied a weight. And
when he had so contrived, that the chords were per- fectly equal to each other in length, he afterwards alternately struck two chords at once, and found the beforementioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, pro- duced, 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 g 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 ses- quitertian 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.
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 pulsa-
tion of patellz or pans, to pipes and reeds, to mono-
chords, 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 parti-
cipates 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 octo-
chord from symphonious numbers, viz. from the
double, the sesquialter, the sesquitertian, and from the
difference of these, the epogdous. And thus he dis-
covered 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 chro-
matic 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 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 receiv-
ing by transition, the first, middle, and third place,
according to the tetrachord. In the Pythagoric octa-
chord, 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.
discoursing about divine natures observe, that the Olympian Gods attended to the dispositions of those that sacrificed, and not to the multitude of the sacri- fices; 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 Cro- tonians 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
deposited a garment with a woman who belonged to
a court of justice, and told her she was not to give it
to either of them unless both were present. Some time
after, for the purpose of circumvention, one of them
received the common deposit, and said that it was with
the consent of the other. But the other, who had not
been present [when the garment was returned], acted
the part of a sycophant, and related the compact that
was made at the beginning, to the magistrates. A
certain Pythagorean, however, taking up the affair
said, that the woman had acted conformably to the
compact, as both parties had been present. Two
other persons also appeared to have a strong friend-
ship for each other, but had fallen into a silent sus-
icion through a flatterer of one of them, who told
im that his wife had been corrupted by the other.
It so happened, however, that a Pythagorean came into
a brazier’s shop, where he who conceived himself to be
injured, was showing to the artist a sword which he
had given him to sharpen, and was indignant with him
because it was not sufficiently sharp. The Pythagorean,
therefore, suspecting that the sword was intended to
be used against him who was accused of adultery, said,
This sword is sharper than all things except calumny.
This being said, caused the man to consider with him-
self [what it was he intended to do], and not rashly to
sin against his friend who was within, and who had
been previously called [by him in order that he might
kill him]. A zone also that had golden ornaments
having fallen [at the feet] of a certain stranger in the
temple of Esculapius, and the laws forbidding any one
to take up that which had fallen on the ground, a
Pythagorean advised the stranger, who was indignant
at this prohibition, to take away the golden ornaments
which had not fallen to the ground, but to leave the
zone, because this was on the ground. That
1 The first part of this sentence in the original is févov twos éx BeBAykoros ev’ AckAnmeiw Zovyv xpvoiov éxoveay, and in translating