On System and State

I recently got into a bit of a fix trying to explain my piece Decoherence (n) for n orchestras of n players. I fear that my explanation may have led some to conclude, reasonably, that the title was a misprint for Incoherence.

A day or two later, while listening to some great pieces by Gordon Mumma, it occurred to me that in most of Mumma's works various sorts of symmetries play an important role -- in time (palindromes) or in pitch or in the physical space of either the performing space or of electronic circuitry -- but at any given moment the symmetry may actually be represented by its absence, in that a local asymmetry may be a place holder for or within a global symmetry, even if that global symmetry is never actually expressed in the music, pregnantly remaining only a potential. And that situation, the representation of a simple, perfect form by its absence (Feldman's phrase "crippled symmetry" is spot on; I've written here before about the musical uses of pseudo-repetition) seems to me to be a fair description of the greater part of a great deal of music, my Decoherence (n) included.

In Decoherence (n), I tried out, impressionistically, superficially and shamelessly stealing a term from physics with complete disregard for its precise meaning in that discipline, an alternative metaphor for the ensemble process musicians associate with the term counterpoint. Instead of the traditional metaphor of "this against that", I wanted to think instead in terms of lines or surfaces that cohere, sharing aspects of identity when not playing in unison, and then have the capacity to separate in identity, to decohere, and sometimes even have the potential to recohere, to return to identity with one or more of the other ensemble members. Such a program is at least implied by the traditional rules for counterpoint, in that one pays attention to various degrees of similitude between voices and then, according to these degrees, restricts repetitions, to insure that voices are sufficiently different. Thus direct repetitions of perfect consonances are avoided as they lead to melodies that are inadequately differentiated while limited numbers of inperfect consonances in succession are permitted. In my piece, I had the idea that one might then hear the piece as exhibiting various degrees of distance between that of an ideal state, an ensemble unison, and a total lack of cohesion among all of the ensemble's lines, with recoherence serving as an important structural control, bringing things back into recognizable order in the complete ensemble as well as among various sub-groupings with the square number configuration of the ensembles is designed to aid in this. (To be fair to my little piece, Decoherence (3) never strays particularly far into decoherence; it's actually a cheerful little serenade and wasn't altogether inappropriate for a April 1st afternoon.)

In some cases, it might be useful to think of pieces of music as little machines executing ensembles of simple processes. In Decoherence (3) , I happen to have used the nine ways of varying a musical motive* that I learned from Lou Harrison who, himself, learned these from Adolph Weiss, a student of Schoenberg. But the processes can even be simpler: prolonging a sound, through sustain or through repetition, simple alterations or variations, for example through accumulated errors in repetition. And processes are often made to respond to controls, regulating the relationship between any local moment in a work of music, the state, and the global identity of the system, for example, the return to unison in my piece, or the default symmetry found in Mumma's works, or the classical technique of the elimination of accumulated errors or variations.

John Cage, when asked about his early Sonata for solo clarinet, a work written as a perfect palindrome, he quipped self-critically that "symmetry indicates the absence of an idea". But isn't it more to the point that an ideal state -- a drone, a unison, or a symmetrical configuration -- is, even in its absence, a fertile point of departure and reference, indeed, not an idea in itself but a productive source of ideas?
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* for those of you who don't have your copy of Lou Harrison's Music Primer in hand, these are: "1) changing the intervals or notes & holding the rhythms, 2) changing the rhythm & using the same tones or intervals, 3) simultaneous combination of both these methods, 4) inversion, 5) elongation, 6) contraction, 7) elision (of one or more notes), 8) interpolation (of one or more notes), 9) the crab form (motus cancrizans, repeating the motive backwards)."