Monday, June 12, 2006

In the garden of secret theories

I entertain a suspicion that most musicians have -- at least within the privacy of our ateliers, rumpus rooms, redoubts and cloister cells -- rather idiosyncratic ways of thinking about what we do when we make music. With time and experience, you come to certain understandings with the muse: the terms and metaphors you use to describe music, its parts and its attributes, the habitual networks of associations with which you tie those parts and attributes together, and the external sentiments we attach to both parts and their connections.

On the one hand, this is simply the personalization of the theory that we have received through institutions and teachers, but I think that it is both more and less than that. Personalizing puts weights and values on systems and structures that come to us from "official" music theory with a certain degree of value neutrality. But a personal, private, theory is under no obligation to be either complete or internally consistant, demands that are reasonably made of public theories. (Personal theories are not validated by the truth or logical consistancy of the theory, but by the character of the works and performances they help bring into being.) And personal theories can make connections among repertoire that represent the individual's experience and taste, and that repertoire has no need to be understood as coherent in any terms other than the individual's experience and taste.

The metaphor can come from anyplace. I was told once that the composer Robert Erickson described tonal functions in terms of a baseball diamond. I could well imagine other sporting metaphors (cricket, mumblety-peg, poker, and thoroughbred racing are my preferences) or handwork or programming or even a culinary tact. Algorithms have considerable currency, and an individual algorithm has metaphoric character: given the difficulty (indeed, impossibility) of finding the shortest algorithm required to produce a given work of music, any given algorithm is going to have something arbitrary and tentative about it. (For what it's worth, I used to think about the relationship between algorithmic discipline and impromptu handwork in my own music in terms of tending header on a wheat harvester. (1)

I have a couple of theoretic notions that I keep coming back to in my work, and I like to think that I am able to keep them rich by avoiding or postponing the expression of these notions in formal terms. Perhaps at risk of public doubt of my complete sanity, I'll mention a few of these. One is the notion of a field, a space in which musical materials are assembled.(2) The space could be organized along some strict metric -- pitch height or class, a tuning lattice, a row box, or a Partchian diamond or one of Erv Wilson's Combination-Product Sets -- or it could be filled in some random way, a one dimensional list, or one of Cage's multi-dimensional charts (as in the Concerto for Prepared Piano and Chamber Orchestra or the Music of Changes), or the pools of material found in some of Christian Wolff's "cuing" pieces. I often think of my scores as paths across such fields. These paths might be random, or weighted, or patterned, or could be forced to follow a kind of gravity. (For example, if you think of the primary, root position, triads in common practice tonality as positions in a series of fifths IV -- I -- V, common practice allows any move to the right, but only moves of one step to the left). Another notion dear to me is that of spacing -- how pitches are assembled vertically. I pay close attention to gaps and densities in the spacing, and often times the choice of a new pitch will come more immediately to me from spatial rather that functional harmonic considerations. I've come to recognize three basic spacing structures: one in which intervals get smaller as frequency increases, in this resembling a harmonic series, I call "harmonic", another when intervals get smaller as frequency descends, I call "subharmonic", and a third, in which intervals are more or less equally distributed, I call "neutral" or "equal". (It's not neccesary that these relationships be precisely harmonic, equal/neutral, or subharmonic, juat the rough characterization suffices). As this is purely a private theory, I'm not going to formalize it, but I do believe that on the basis of a spacing model, you could construct a reasonbly complete description of species counterpoint, tonal harmony (major/minor, consonant/dissonant) or even orchestration (clear/muddy, thin/dense etc.).

(1) Yes, it is often a good thing that private theories stay private.
(2)In my catalog, there are a number of pieces which come directly out of this : Field Study, Crossing The Field, Fieldwork (String Quartet II.), Afar Afield, Farther Afield, The Art of Fielding. Aside from sharing the notion of the field as a point of departure, these works have little in common.

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