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

• After Xti/j/zarti 111 tlie original, it is necessary to su|>|dv from tlie version of riioma-us, the word* to Xe i' ik Tfutuv rdiur k«i Xti/iftfiTB i I relcr llie reader slio is desirous of thoroughly understand¬ ing what is here, and fat (her on, said, to in> Theoretic Arithmetic.

HOOK III,]

TIM.tlS* OF PLATO.

p. 57

divisible about bodies, 1 just as llie diatonic presides over the rational lie Hence the enharmonic genus, is adapted to instruct and discipline llie «iiv isihb life, lint the cliromatic genus presides orer tin corporeal idea itself. Helici: it is e/l'emuiate and ignoble. The enharmonic genus therefore is deseneiilv tbs iplinativc, • Hence, Socrates in the lb public thinks lit to mention it particularly, in w hat he says about harmony. And Timauis knowing this, anil having beard Socrates asserting these things on the preceding day, at the same time constitutes the essence oi the soul through the diatonic, and not through the enharmonic genus; the latter, as we have said, being adapted to erudition. Tor on tln> account, the ancients called the leadt i s [or preceptors] of these diseiphm s Ilarmnnici |or skilh d in music]. Aristoxenus therefore, in the first hook of his Harmnnir Klemeuts, says, it happened that those wen: truly called Hannonici, who formerly employed themselves in what pertains to music. Tor bring solely engaged in bannonv they neglected every other pursuit. In which Aristoxenus also asserts what is wonderful, vi/. that the ancients had no knowledge of the diatonic diagram. Tor lie thus writes: “ As an indication of the truth of this, their diagram alone exhibits enharmonic systems, but no one ever saw a diatonic or chromatic dia¬ gram delineated by them." It is worthy of admiration, however, that lie should assert these things, since Plato exhibits a diagram according to the diatonic genus, and also Timauis himself. Perhaps therefore what Adrastus says is true, who derides Aristoxenus as a man of not very elegant manners,* but studious of appearing to say something new.

Perhaps therefore what Adrastus says is true, who derides Aristoxenus as a man of not very elegant manners,* but studious of appearing to say something new.

Plato, therefore, in the diatonic genus, makes a division of letrachords, and proceeds not only as far as to the diapason, hut also as far as to a quadruple diapason and diapente, adding likewise a tone. Or according to Severiis, Plato did not produce the tetrachords without a tone, but ended m a leimrna, and not in a tone. If, however, some one should doubt, how Plato produced the diagram to such an extent, let him attend to the words of Adrastus. Tor he says that Aristoxenus, extended the magnitude of hw multiform diagram, as tar as to the diapason and diatessaron, and the symphony of these, in consequence of prefer¬ ring the information of the ears to the derision of intellect. Hut the more modem musicians extended the diagram a-* far as to the fifteenth mode, vi/. to the thrice diapason and tone, in so doing looking solely to our utility, and thinking that those who contend in singing could not exceed this, nor their auditors judge clearly beyond

1 Instead of rou wrpi tom irw/i im firpiarcut m this place, il is neeewary lo read rqi *-«p« rmi empimw • * For m *«£k>« here, it u requisite from llie version of Thomarus, to read ro hm. Plat.

VOL. II.

II

p. 68

PKOCLUS ON Tin:

[BOOK III.

it. Plato, however, looking to nature, constitutes the soul from all these, in order that it might proceed as far as to solid tuuuliers, as it ought to preside over bodies. For the progression a> far as to the quadruple diapason and diapeiite, necessarily follows the seven terms [or hounding number*]. llut tliis is evident from tlie greatest term liciug twenty s* veil. And thus much in answer to the doubt.

For the progression a> far as to the quadruple diapason and diapeiite, necessarily follows the seven terms [or hounding number*]. llut tliis is evident from tlie greatest term liciug twenty s* veil. And thus much in answer to the doubt.

In short, then are these three things into which the consideration of harmony inav be divided. One of these is the « \posilion ot the seven parts. The second is the insertion of tin* two media. I'he third is the div ision of the sesipiitertian and sesquialter ratios, into sesquimtaves and leimnias. Hence some, a** Ad rust us, are acciistomed to make three triangles, and in one of them, v\ hit h is the least, to describe the seven parts, making the summit ot the triangle to be one of die parts, and distributing the other six about tins. In one ot the sides also, they describe I lie whole duple order, hut in th< other, the wind triple order. Murcov* r, in the other triangle, which is greater, ami contains the former, they increased the immhers, and attain in a similar manner in** ited two nu-dia, arranging the duple separate from the triple numbers ; and placing one of the parts at the summit. But in the third triangle, which comprelicnds liotli tin* others, tiny described after the same maim* r the whole di r, r rmi. Olliers attain, adopting a description in tlie form of the I* tier X, arrange the numbers successively, as m the s* etion of a rule, according to three centers, assuming the first, second, and third immhers, as we aFo shall do. I his method likewise is adopted by Porphyry and Severus. And such are the particulars which ought to In premised, ami also licit Plato divides this h ail into three parts, in the lii"t ot the three, discussing the seven parts, in which there are three duple, and three triple intervals, according to the geometrical middle, i c. according to the same ratios. But in the serum! part, he discusses the iiiseition of the other two media, viz. the harmonic and arith¬ metic, into each interval ot the duple and triple numbers. \nd m the third part, he considers the division of the sesipiitertiau and sesipiialter ratios, into scsijuioetaves and leimnias, and as far as to these • Mends the discussion ot the parts of the soul.

It is necessary however to he well acquainted with such things as are said about the three media, and to know tin ir dilh-rcnccs, ami what the methods are through which they are discovered. The arithmetical medium, therefore, is that in which the middle t* rin exreeds and is e\e* eded by an equal 1 quantity, as tuav In* seen in all the numbers that are in a consequent order, conformably to the definition of Timams himself. But tlie harmonic medium is that in which the

* \ocv is omillttl in the original.

BOOK III.]

TIM /HUS OF PLATO.