Dear Nathaniel,

Thinking more about your very impressive essay,
I should point out that _your_ interpretation
of Apollonian as intellectual, which seems to me
eminently reasonable, is, however _not_ what
Nietzsche had in mind in that seminal essay about
the Birth of Tragedy.

Nietzsche envisioned the Apollonian mode as a dispassionate
sensual perception such as he thought was characteristic
of certain dreams or dreamlike states. I think what
Nietzsche had in mind was a sedate dispassionate apprehension
of beauty and order. e.g. the beginnings of the second movements
of both Beethoven's 5th and 7th symphonies. Both of these 
pieces beging in what I consider the Apollonian mood, but
unlike Mozart - who is often pure Apollo - Beethoven could
never escape Dionysus lurking in his gut.

In his Birth of Tragedy essay, Nietzsche was highly critical
of intellect and reason: indeed, when I reread the Birth of
Tragedy last month, it occurred to me that perhaps Nietzsche's
ultimate purpose was to malign Socrates, as the mind that
introduced reason (intellect) into Attic culture as its
guiding principle, and thereby made impossible tragedy such
as written by Aeschylus and Sophocles. For Nietzsche Attic
tragedy was unintellectual irrational uncritical. The consequence
of the introduction of reason into Attic culture so far as
Nietzsche was concerned, were the tragedies of Euripides, 
as argumentative word games, which Socratic irony had drained 
of all fateful passion and all passionate fate.

Another point that I consider important is that it didn't take
Adrian Leverkuehn or Arnold Schoenberg to arrange the marriage 
of mathematics and music. I know I've mentioned Hermann Hesse's
novel The Bead Game (Das Glasperlenspiel) which will fascinate
you when you read it, which describes a musical-mathematical
game, - the bead game - that encapsulates the essence of European
music. You should also review some of the theoretical compositions
of J.S. Bach, the Musical Offering, the Art of the Fugue, and the
Goldberg Variations, not to mention the preludes and fugues of his
Well-Tempered Clavier collection.  These are all works that are
constructed in the spirit of mathematics. Furthermore, Bach's
vocal works, the Passions and the Cantatas abound with verbal
and sometimes mathematical symbolism.  I suspect also, that there's
a lot of mathematics lurking in Scarlatti, Vivaldi, and other
composers of the Italian baroque, - but I don't really know.

I point this out because I think _you_ should understand it;
I doubt that any of your readers will be smart enough to know
the difference. I wouldn't bother making any changes in your
essay.

Yoyo (is that how you spell it?)