Her book on Plato
So she says since 729 is three to the sixth power it represents the tripartite soul.
The late Ernest McClain might elucidate this:
But the actual mathematics that occurs in the dialogues is very frequently ignored by commentators. (One stark example of this is found in the 1947 translation of the Republic by F.M. Cornford, in which Cornford permitted himself to omit entirely Plato’s “extremely obscure” account (at 8.546b) of the so-called ruling or nuptial number, and also to “simplify” the text (at 9.587b) concerning the number of the Tyrant.
The Tyrant is held, in the Republic, to be exactly 729 times less fortunate than the good ruler. Not “about 700,” not 730.O.K. (I quote my correspondence with Professor McClain in my 2012 pdf) so then we get this pdf.
And so the 3 to the sixth power actually refers to six cycles of Perfect Fifths, since 3 is the Perfect Fifth, thereby creating the Tritone.Musicologist Ernest G. McClain states thst “The number 2 is 'female' in the sense that it creates the ... create 'cycles of barrenness', in Socrates' metaphor, for multiplication and division by 2 can never introduce .... quality of the tritone (the ratio 36 = 729, a cycle of six perfect fifths above the fundamental), the worst possible ...drawastraightlineandfollowit.com/Sound_v2011_F_R9.pdf