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The preoccupation with ordering in the post-Schoenbergian
evolution of serial composition has been, to my mind, a preoccupation with
what is ultimately a secondary and superficial aspect of Schoenberg’s
twelve-tone
“method.” Arbitrary and artificial constraints imposed by the
ordering
principle have been countered by the imposition of other arbitrary and
artificial extensions of the same principle. By applying various arithmetical
procedures to the order and pitch-class numbers of the notes, an endless
“variety” of set transformations beyond those conceived by
Schoenberg may
be derived. The notion of ordering has been extended to rhythm and dynamics,
and even to other “parameters,” as a way of arriving at a
“total” or “integral”
serialism. This necessitated the invention of bizarre and arbitrary precompositional
constructs such as durational scales of twelve note-values and intensity
scales of twelve dynamic levels. As John Backus concludes in his remarks
on Boulez’s Structures [in
Perspectives of New Music]: “What
results can only be described as composition by numerology. The possibilities
are endless; a computer could be programmed to put down notes according
to this prescription and in a very short time could turn out enough music
to require years for its performance. By using different numerical
rules—using a knight’s move, for example, rather than the
bishop’s move along
the diagonals—music for centuries to come could be produced.”
As the
inventor of the “Digionic Synthesizer” puts it: “With
serial music we can
take thirteen tones, plug them into this, and you get 4000 permutations
immediately. Why should a composer waste his time making permutations?”
And is it really not self-evident that there is no analogy between our
perception of pitch intervals and dynamic intervals? What is the octave
of a mezzo forte? Is it not self-evident that between our tolerance
of deviations from the ratio of 2:1 in pitch octaves and in Stockhausen’s
“duration octaves” there is no relation whatever? What is the
pitch-succession
equivalent of an accelerando? Such extensions of Schoenberg’s
twelve-tone
system have more relevance to the invention of cryptographic codes than
to musical composition.
It is hardly surprising that “composition by numerology” should have found its analog, in much of what passes for contemporary music theory today, in analysis by numerology. “Pitch classes are equated with pitch-class numbers, intervals with interval numbers, and ostensible observations about musical relations turn out to be trivial observations about the collection of integers, modulo 12.” Questions of spacing, doubling, and voice-leading are entirely eliminated, and what are put forth as statements about notes are in effect statements about subsets of unassigned numbers. . . .
George Perle
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