Page:Works of Plato his first fifty-five dialogues (Taylor 1804) (Vol 2 of 5) (IA Vol2worksofplato00plat).pdf/453

 413

INTRODUCTION TO THU TIM^US.

exceeded by 12. And in the ſame manner we may proceed in all the follow¬ ing duple ratios, binding the duple by the fefquitertian and fefquialter, and connedling the two fefquitertians by a fefquioclave ratio.

We may run

through the triple proportions too in a fimiiar manner, excepting in the tone.

But becaufe fefquitertian ratios are not alone produced from two

tones, but from a femitone, and this a lefler, which is deficient from a full tone by certain fmall parts, hence Plato fays, that in the fefquitertian ratios a certain fmall portion remains 1. And thus much may fuffice for an epitome of the mode in which the duple and triple intervals are filled. But the words of Plato refpedfing thefe intervals plainly fhow, as Proclus well obferves, that he follows in this inftance the doflrine of the antient theologifts.

For they afifert, that in the artificer of the univerfe there are

feparating and connecting powers, and that through the former he feparates his government from that of his father Saturn, but through the latter applies the whole of his fabrication to his paternal unity ; and they call thefe opera¬ tions incifions and bonds.

Hence the demiurgus, dividing the effence of the

foul, according to thefe powers in demiurgic bounds, is laid to cut the parts from their totality, and again to bind the fame with certain bonds, which are pcro-rifTse, middles os mediums, and through which he connects that which is divided, in the fame manner as he divides, through fections, that which is united.

And as the firft numbers, 1, 2, 3, 4, 9, 8, 27, reprefented thofe

powers of the foul by which fhe abides in, proceeds from, and returns to, herfelf, and caufes the progreffion and converfion of the parts of the uni¬ verfe— fo, in thefe l'econd numbers, the fefquitertian, fefquialter, and other ratios conftitute the more particular ornament of the world ; and, while they fubfift as wholes themfelves, adorn the parts of its parts. I only add, that we mu ft not fuppofe thefe numbers of the foul to be a multitude of unities; but we muft conceive them to be vital felf-motive natures, which are indeed the images of intellectual numbers, but the exem¬ plars of luch as are apparent to the eye of fenfe.

In like manner, with

refpeCt to harmony, foul is neither harmony itl'elf, nor that which fubfifts in harmonized natures. For harmony itfelf is uniform, feparate, and exempt from the whole of things harmonized; but that which fubfifts in things har1 The proportion of 256 to 243 produces what is called in mufic

Mi/x./ia, lirnna,

or that which

remains. 3

l

2

monized