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“Mathematical” was another
term that the “anti-formalists,”
together with their journalistic counterparts, invoked as a term of immediate,
automatic, and permanent derogation. Shostakovich, as a candidate for membership
in the Communist Party (at the age of 54) wrote that the twelve-tone system
was “based on mathematical calculation” and “destroyed
form,” reminding
one that the music, the same music, which was denounced by Stalinists
as “bourgeois modernism and formalism” was reviled by the
Nazis as “Bolshevist
modernism.” Strange that in the world of the self-proclaimed humanists,
a subject, mathematics, that is on the one hand viewed as representing
the most exalted and refined realm of human creative intellection is, on
the other hand, condemned as representing the unimaginative and mechanical.
Such simple mathematical structures as Fibonacci series and “golden
sections”
are approved instruments of “analysis” and, even,
composition, but imagined
mathematicization, particularly that associated with the number
“12” is
cause for alarm and accusations of obsession with numbers, not incidentally,
numbers employed precisely as they were in figured bass theory, only now
applied to the chromatic rather than the diatonic domain.
I have never been intrigued, even as a “thought experiment,” with the procedure or game of choosing a mathematical tautology (however interesting in itself) and then, by rules of correspondence with musical notation, producing a graphemic musical composition. Just as any musical composition can be represented (“analyzed”) by a time series, a polynomial, or even a Gödel number, so any musical composition can be so generated. This is a point which appears to have eluded even celebrated musicians. Pierre Boulez, only for example, has been reported as asserting that his “works are impossible to analyze because, within a given framework, the details follow one another as directed by the inspiration of creative fantasy.” Under a familiar truth-preserving transformation (modus tollens), the statement that “works are impossible to analyze if the details are directed by the inspiration of creative fantasy” is equivalent to “if the works are possible to analyze they are not directed by the inspiration of creative fantasy.” This produces a definition of the achievement of analysis which would please certain elements of musical society, but it does not, as Boulez does not, clarify what is meant by “analyzability,” since—as suggested above—there are not only universal “mathematical” analyses, but “chordal” analyses, etc., etc. The issue is rather that of “satisfactory” analyses, analyses of explanatory scope, in sum, the fundamental question of musical exegesis and understanding.
Milton Babbitt
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