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

[Daniel Wolf]

The handful of passages found in Platonic dialogues dealing directly with  
musical practice are well-known, if often unfortunately translated (i.e.  
"flute" for aulos, and the near random use of "mode" or "scale") .  In  
none of these, however, is the musical content described in terms of the  
numbers one would find in a classical treatise on music or harmonics (the  
theory of ratios and proportions, related, in part, to musical practice  
via the comparison of monochord distances).   In his "The Pythagorean  
Plato" and other texts, Ernest McClain proposed that groups of numbers  
found in several dialogs, used principally in the descriptions of various  
political systems, might be related to harmonics.  The various political  
systems, in McClain's analysis, are thus comparable in terms of complexity  
and unwieldiness of the tonal systems described. This is naturally highly  
conjectural, and McClain's works grew progressively more speculative, but  
when, for example, a specific number like 729 (3^6) is used prominently by  
Plato, one does have to wonder if the musical-harmonic relevance of the  
number (3^6, reduced by 4 octaves is an augmented fourth) is being played  
upon by the author.   In the present example, Kennedy proposes that the  
composition of the dialogues themselves corresponds to an harmonic  
system.  That the dialogues are tightly structured, as drama, is  
well-known.   That the manuscripts of the dialogues were written down on  
standardized paper formats with fixed line lengths and counts was also,  
more or less, well-known, and Kennedy's work in solidifying this data  
appears very useful.  That the dramatic structure corresponds to a  
rational division of the lines, however, seems to be a new proposal and  
that this division corresponds to a rational (and thus, non-equal) 12-tone  
division of the octave is also new and, to my mind, highly speculative.  
Like McClain, Kennedy centers his theory on a 12-tone division, which I  
find difficult to support from that which we know of either 5th and 4th c.  
B.C. musical practice or the theory of harmonics, with its greater focus  
on tetrachords and ethnic modes.   That reiterated rational fifths and  
fourths do not return to a unison or octave would have been well-known,  
but not necessarily a fact with much practical musical relevance in the  
classical period.   The notion that a dialogue, with a dramatic form,  
would be broken up dramatically into parts corresponding to the simplest  
rational intervals does not strike me as particularly surprising — many  
writers (not least US undergrads writing term papers or blue book exams  
with fixed word counts)  look at the rough proportions of their texts and  
pay attention to how much space is left to be filled and how to fill it  
best, frequently landing, intuitively on similar ratios — so it remains  
for Kennedy to provide some convincing evidence for the necessity of an  
octave-based musical/harmonic interpretation.

Dr. Daniel Wolf
composer
Frankfurt