The Commentaries on the Timaeus of Plato — trans. Thomas Taylor

1 1 fumAiue is omitted in ibis place in I be original, but ought from tbc version of Thom.ru«, lobe ukcrltd.

1 Viz. a ibuig of tins kind is discrete quantity.

* For/ice in this place, read firra

* Slffna iv is omitted in the original.

IHIOK III.]

TIM.KUS OF PLATO.

consists of parts similar to itself, it will in no respect be separated from continuity and union. For if in bodies similars cohere with each other without a medium, how much more in an incorporeal nature must all the things that are as it were parts, lie united, and the whole he vanquished by unity, neither tin* parts being confused, through the position of the whole, nor the wholeness taken away through the separation of the parts? Yon may also assume from these things, that the soul aerording to all the parts of itself, is both impartible and partible. For if every part of it participates of all the middle genera, nothing m it can hr assumed w hi* h lines not eonsist ol these. The ancients also, looking to these tilings, concluded every where concernin'.; it, that all of it is being, life, and mfi llect, ami that whit h< ver you may assume of the three, you may infer that it contains the rrmninmi; two ; since all things in it proceed through all, the whole is one, the one of it is all perfect, and a part in it corresponds to the whole. But if each of the parts of it In ini; many, is a certain essence, as numerous as are the parts, so multitudinous also is the essence, in a similar manner also with respect to same¬ ness and difference, each of these in intellect indeed is one, and on this account it is impartible. For in intellect one tiling is not a part different from another. l*ut in the soul both these are divided according to rsseutial nundrer, and the parts of it are adapted to each other, causing it to Ik* one tiling from many, and a whole from parts.

For in intellect one tiling is not a part different from another. l*ut in the soul both these are divided according to rsseutial nundrer, and the parts of it are adapted to each other, causing it to Ik* one tiling from many, and a whole from parts.

Moreover, this also deserves to lie considered, that according to the generation of the elements, he [vegan as we have said, from essence; hut according to the composition of the whole, from difirrrucc; co-ndnpting tiie nature o (different, which is dillicult to he mingled with same, and mingling both with essence, llut according to the division of the whole into harmonic ratios, he began from same¬ ness. For he says’ that lie divided each part mingled from same, different, and < ssrnre. 1 or a coinnii neement from essence is entirely 1 adapted to the genera¬ tion of simple natures ; since essence is more simple than other things. 1 o the composition, however, of the whole, a commcneeuient from dilfercnce is adapted. For the generation of the whole from parts begins Imm things subordinate to the whole. And a enmnu neenunt from sameness is adapted to the hypostasis of harmony. For the Deinuirgus was willing th.it tins should terminate in tin* sameness and roinmiinion of the things that were divided. And, in short, he was willing that hurmonv should Is* etlcctive ol the sameness of the things harmonized.

These particulars, however, having been discussed by us as tar as we are able,

• For court here it is obviously ncccoary |o read

* Iustcad of rarrr birr, read

PROCLUS ON THE

[book 111.

C>C>

These particulars, however, having been discussed by us as tar as we are able,

• For court here it is obviously ncccoary |o read

* Iustcad of rarrr birr, read

PROCLUS ON THE

[book 111.

C>C>

it is necessary in the next place to premise those things which ought to l»e readily known hy us concerning numbers, and the harmonic ratios of the soul, in order that we may not attempt in vain the interpretation of what follows It is neces¬ sary then-fore to premise such things as are usually mentioned m harmonic dis¬ cussions, viz. what sound, inter*al, and system are, and that the Pythagoreans did not assume the symphonies in harmony from any thing else than numbers, and not from all these, but from multiples and super-particulars. 1 or they said that the diatessaron is in a sesipiitertian ratio ; hut the diapente in a sesquialter; and the diapason in a duple ratio. And again they said, that the diapason and -it the same time diapente is in a triple, lnit the disdiapason in a quadruple ratio. .For the diapason and at the same time diatessaron, did not appear to them to be symphonious, because it consists in a multiple soper-parlienl ratio, \ i/. in the ratio of It to 3. For b is a medium between the two, producing with the less numlx-r a duple, but with the greater, a su! isesqiiitcrtiau ratio. These tilings therefon*, must he premised, and also that the si-squioetave is m the ratio of a tone; that the sesipiitertian ratio consists of two tones and a leimma; and the sesquialter of lliree tones and a leimma. 1 lint we shall afterwards learn what the ratio of the leimm a is. Moreover, the Pythagoreans said, that there arcthree genera of harmonies, the diatonic, the enharmonic, and the chromatic. Likewise, that the diatonic consists of a semitone (hut this which I now call a semitone is not properly so, hut a leimma), and of a tone, and another tone. But the enharmonic consists of a diesis, another diesis, and a ililone. Ami the chro¬ matic of a semitone, another si untune, and a trisemitone. But diesis is as it were the fourth part of a tone, not hi ing in reality a fourth, as neither is a leimma accurately a semitone. These things, however, we shall demonstrate in what follows.

But a 4 there are three genera, each of which is a certain division of the tetraehord, Plato appears to ha* e used the diatonic genus alone. I’or he thinks lit to divide the seMjuitrrtian ratios, into sesquioctaves and leimmas, hut not into enharmonic dieses; since some of the ancients called a semitone diesis. Plato, likewise, seems to have assumed this genus, 1 mean the diatonic, as more grand, simple, and generous, than the other genera; though the enharmonic: appears to lie more adapted to erudition And if it he requisite to declare my own predic¬ tion on this subject, the enharmonic genus, presides over all tin- hie which is