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. . . More and more attempts
are being made to serialize
not only time-values but every type of relationship: dynamics, modes of
attack, tempos, proportions. Superficially, it might seem that the result
would be a completely saturated structure of analogies in many dimensions.
The crucial question remains: Do they coalesce in an aurally perceptible
unity? In an attempt to demonstrate that they do not, I pass over such
techniques as the serialization of dynamics and attacks—any application
of which can, I believe, be shown to be arbitrary—in order to concentrate
on the exemplary problem of the durational row, whether applied to simple
note-values or to longer sections.
The great stumbling-block in the way of the integration of a pitch-row with a durational one is that no common measure exists. There can be none even by analogy, since we perceive time and pitch in markedly different ways. We hear time-segments as durations, and we measure one against another, more or less proportionally. Pitches we hear as discrete points, ordered but not quantified. Numerical values assigned them by frequency are useful in physics but not in music; we simply do not hear tones in this way. Even if we accept some kind of proportional measure (such as Krenek’s based on the comparison of interval-sizes) as perceptible in the domain of pitch, we cannot compare it with durational measure without first transforming each into arithmetical terms. The connection between the two remains indirect and intellectual, not perceptual; it is based, not on mutual analogy, but on the relation of each dimension to an abstract third one. . There are other difficulties as well. How would one apply the fundamental operations of the serial system to the time-row? Retrogression is easy, but what of inversion and transposition? Babbitt’s suggestion that numerical complementation is analogous to inversion is brilliant, but as a practical technique it suffers from the kind of abstraction pointed out above. We do not actually hear complementation and inversion as similar operations; we come to this conclusion only after associating each with an arithmetical equivalent. But art is not a branch of mathematics, and quantities equal to the same quantity are not necessarily equal to each other. The same argument applies to the various analogies that have been suggested to effect temporal “transposition.” The trend towards abstraction is a dominant one today, and an unhealthy one for art. The devices criticized here, introduced in the hope of achieving a perfect unity within the twelve-tone system, have resulted in producing a unity, it is true—but outside the medium, in the realm of arithmetic. . . .
Edward T. Cone
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