[Smt-talk] Fwd: Math-music structure of Plato's Dialogues

[matralab]

Hello smt-talkers

I sent the Kennedy link and parts of the smt discussion on Plato's Dialogues
to Sean Gurd, a colleague in the Classics dept at Concordia
who is currently researching ancient Greek music praxis
 - and below you can find his slightly mixed response.
He is ok with me sharing it with the list.

Best
Sandeep Bhagwati
Composer
Canada Research Chair Inter-X Art
Concordia University Montréal

---------- Forwarded message ----------
From: Sean Gurd <sgurd at alcor.concordia.ca>
Date: 2010/7/2
Subject: Re: [Smt-talk] Math-music structure of Plato's Dialogues
To: matralab <matralab at gmail.com>


Hi Sandeep!

Thanks for sending these along! This is interesting, though my initial
response is mixed (as I suspect will not be uncommon). And it is also
probably uninformed: I just read the Kennedy piece, which i didn't know, and
my musical remarks below may well be totally wrong.

I take it that his real interest is in the Pythagoreanism of Plato: this was
until very recently assumed to be a late interpretation hoisted on Plato by
the neo-platonist school, which got going no earlier than the 1st century CE
(Thrasyllus, Tiberius' astrologer, seems to be the important person here):
so close was neo-Platonism and the pythagorean interpretation that
neo-platonists are often called neo-pythagoreans as well. But it is now
clear that the evidence associating PLato and Pythagoras goes back much
earlier, to within perhaps a generation of Plato himself: Philip Sydney
Horky, in Oxford Studies in Ancient Philosophy 37 (2009): 47-103 is
interesting on this. So the idea that Plato was interested in and even
strongly influenced by Pythagorean thought -- which is in any case suggested
by the PLatonic texts themselves -- is alive and well.

But I'm really worried about two things, at least as they appear in the
Apeiron article.

(1) I'm not sure what the significance of stichometric analysis really is
here. William Johnson, who has done the standard study (Bookrolls and
Scribes in Oxyrhynchus, University of Toronto P. 2005), has shown that there
was no standard line-length in ancient book scrolls; indeed, while
individual professional scriptoria might have had standard formats, they did
not all have the same standard format, and I took away from Johnson's study
that the standard formats were not determined by letter-counts but by a
physical frame that scribes worked within. And different times saw different
book formats come into vogue. *And* not every book circulating in the
ancient world came from a professional scriptorium. People made copies for
themselves, in their own hands, and these copies -- which are common in the
papyri -- conform to no standard. So when Kennedy identifies a standard
line-length and then says it is 35 letters long, I think he is relying on
older, speculative scholarship that isn't supported by the evidence of the
papyri themselves. In any case, even if Plato himself arranged for his final
drafts to be written out in some standard line-length, this line length
would not have survived across many copies -- people didn't *reproduce
*stichometry
when they made copies, though they did keep track of it. So an absolute set
of proportions, e.g. making all his dialogues have lengths that were some
multiple of 12, would have been a very short-lived, even extremely private,
affair.

(Actually that doesn't totally rule out Kennedy's hypothesis. There is a
story preserved in Diogenes Laertius that you could go to the Academy and
see Plato's own manuscripts -- for a fee. So perhaps a "standard"
stichometry did exist, at least in one institutionally privileged copy.)

I'm also having a hard time envisaging Plato's working process -- he almost
certainly did not write in papyrus scrolls. Either he dictated -- most
likely, I would say -- or he wrote on wax tablets (cf. the story, found in
Dionysius of Halicarnassus, among others, of the tablet containing the first
sentence of the republic, which PLato had rewritten many times). In neither
of these cases is there a guarantee that any projected standard line-length
would or even could be preserved: tablets, especially, had totally different
dimensions. He might have counted individual letters, but this seems
unlikely for texts as long as the Republic (though writers like Perec did
it, so why not?). The *Laws*, Plato's last work, was unfinished at his death
and put together by a follower -- Philip of Opus -- and the sources suggest
that Philip found the text was written out on wax tablets. Did Philip follow
Pythagorean proportions and a platonically-determined standard line length
in making his edition?

On the other hand, does the standard line length even matter? Isn't the real
point proportionality, which can, on Kennedy's hypothesis, be expressed with
factors of 12? In that case any numerical metric would do -- in other words,
we could count letters, or any standard line length or any standard page or
column-size.

(The *Laws* raises another question. Kennedy presumably has more on this,
but at this point it looks like he is saying that there are "disharmonic"
moments, especially moments of disagreement, refutation, or dubious ethical
behaviour at passages in the dialogues that conform to the "disharmonious"
moments of his 12-note "scale" (on which, see below). I might be willing to
buy this for the dialogues which are energetically dramatic, like the *
Symposium* or the *Theatetus*, but it makes me wonder about the dialogues
that are essentially expository, like the *Laws*, or the *Statesman* or the
*Sophist*, where the dialogue form is really just a vehicle for a positive
and systematic exposition. I would want to see how hard Kennedy has to work
to get the relevant moments in those texts to reveal "disharmony.")

2. I don't understand the *musical* point of the number 12 (I understand, I
think, the mathematical point). The 12-tone scale was almost certainly an
innovation of Aristoxenus, working after Aristotle died, so much later than
Plato. And it was based (as ours is) on dividing the tone into two equal
parts -- two semitones. The octave could then be imagined as made out of 12
semitones. Pythagorean musicology flatly rejected this move, on mathematical
grounds: the ratio expressing a tone is 9:8: half of this, if I understand
the math (which I don't) would be an irrational number. Instead, the
Pythagoreans identified a series of different intervals smaller than the
tone, none of which are equal (and they vary, depending on the theorist),
and they based their analysis of the actave on the tetrachord, *not* these
microtonal intervals. An octave scale based on the tetrachord has 8
notes. At the very least, if Plato is a Pythagorean, then the division of
the octave into 12 should not be into 12 perfectly regular intervals (as it
is in the modern 12-tone scale), as Kennedy's stichometric analysis seems to
assume.

Thus my thoughts. ...

Sean
 --
Sean Alexander Gurd
Department of Classics, Modern Languages and Linguistics
Concordia University
1455 de Maisonneuve West Room H-663
Montréal, QC H3G 1M8
CANADA
-------------------------------
(514) 848 2424 x5473
------------------------------
sgurd at alcor.concordia.ca
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