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

[Kyle adams]

Hello everyone,

I've been debating for the past couple days whether to post anything about this, for fear of betraying ignorance of Kennedy's theory, ancient Greek theory, or both; but I share some of Daniel Wolf's misgivings about Kennedy's work and would add a few of my own.

As I understand Kennedy's paper, his reasoning is thus:

1. Plato's written works tend to have numbers of lines that are evenly divisible by twelve.
2. Twelve is also a significant number in the music theory of classical antiquity.
3. If we therefore divide Plato's Dialogues into twelve equal parts, corresponding to the "scale of twelve notes produced by 
strings with lengths corresponding to the integers from one to twelve" (Kennedy's words), we can find significant events at each twelfth division of the text.
4. Moreover, since "notes which formed small whole number ratios with note twelve were consonant...More Consonant: 3, 4, 6, 8, 9," (also Kennedy's words) it can be demonstrated that textual passages at 3/12, 4/12, 6/12 etc. deal with harmonious or pleasing topics, while those at the other, more "dissonant" locations (e.g., 5/12) deal with topics like war or pain.
 
I trust Kennedy about point #1.
 
Point #2: it doesn't seem to me to follow logically that there is any relationship between the number twelve as divisions of Platonic texts and the number twelve in music theory. In fact, the only context in which I am familiar with 12 as a significant part of ancient theory is in the ratio 6:8:9:12, which Pythagoreans used to express the harmonic mean (6:8:12) and arithmetic mean (6:9:12) in order to accurately tune fourths and fifths within an octave. It seems like a rather large leap to assume that, beacuse the number twelve is significant in two different contexts, that these contexts are somehow related.
 
Point #3: I would reiterate Daniel Wolf's concern that there was, to my knowledge, no scale with twelve equal divisions of the octave in classical antiquity. In fact, as is well known, the inability to divide the whole tone into two equal parts was one of the cornerstones of ancient theory, at least until Aristoxenus, with theorists such as the author of the Euclidean Sectio Canonis going to great lengths to prove that the octave was not made up of six tones and that the tone was not made up of two semitones. This suggests that even if one wanted to divide Platonic writings into twelve parts, those parts should not be equally spaced--or, that if one finds significant events in Platonic texts at equal divisions of the twelfth, these decidedly do *not* have any musical significance. Furthermore, even if there had been a scale with twelve evenly-spaced pitches, it most certainly would not have been generated by strings with lengths corresponding to the
 integers from one to twelve. To give the most obvious example, a string with length 2 would sound an octave lower than a string with length 1.
 
Point #4: This is the point that I found the most confusing. Notes that form small whole number ratios with twelve may be consonant, but to the best of my knowledge, that concept does not appear anywhere in the music theory of classical antiquity. If Kennedy means that notes corresponding to the ratios 3/12, 4/12, etc. form consonant intervals, that is undoubtedly true (4:1, 3:1 etc. are all consonant ratios). But a series of such intervals would hardly fit within the framework of a single octave divided into twelve equal steps. Moreover, music theorists from classical antiquity would not have counted most of these among the primary consonances since they are not superparticular ratios (if I'm not mistaken, Ptolemy was the first to explicitly recognize octave equivalence). On the other hand, if Kennedy means that the scale steps at those numerical locations (the third step out of twelve, the fourth step out of twelve, etc.) corresponded to musical
 consonances, this contravenes most music theory from classical antiquity as well, in which both types of third were considered dissonant since they could not be expressed as superparticular ratios.
I apologize for the long posting, and would reiterate that I'm happy to be corrected about any misunderstandings here of either Kennedy's work or ancient Greek theory. But I feel that the theory as presented in Kennedy's paper is at best poorly worded, and at worst may represent a misreading of classical music theory.

Kyle Adams
Assistant Professor of Music Theory
Indiana University, Bloomington



________________________________
From: "Soderberg, Stephen" <ssod at loc.gov>
To: "Smt-talk at societymusictheory.org" <Smt-talk at societymusictheory.org>
Sent: Wed, June 30, 2010 8:09:04 AM
Subject: [Smt-talk] Math-music structure of Plato's Dialogues


Speaking of cross-discipline. . . 
 
I may be coming late to this, but I just learned of Dr. Jay Kennedy at University of Manchester who is publishing his  fascinating discovery relating Pythagorean math & music theory and stichometry to hidden formal & symbolic content in Plato's Dialogues:
 
http://personalpages.manchester.ac.uk/staff/jay.kennedy/
 
Any comments?
 
 
Stephen Soderberg
Senior Specialist
   for Contemporary Music
Music Division
Library of Congress


      
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