Saturday, July 13, 2013

Paying Attention

A friend asked me the other day why I had been spending so much time of late with the music and writings of some composers who were not exactly experimentalists, including names like Milton Babbitt, Seymour Shifrin, Nicolas Nabokov, William Denny, Ben Weber, and Roberto Gerhard.  Indeed, some of these were, as both composers and actors in the musical world, active opponents of the experimental.  The answer was that although each of these musicians did work that was distant from my own disciplines and tastes and, to my ears, moved mostly into musical-historical cul de sacs, they were working seriously and musically and my sense of ecology within the musical world was such that I couldn't ignore that seriousness and musicality, let it go to waste, let alone lose the opportunity to explore for myself some of the musical potential that might be left in those cul de sacs.  So, I have no apologies for spending time with a Gerhard Symphony that brilliantly incorporates electroacoustic sounds, or with Ben Weber's Symphony on Poems by William Blake, a beautiful piece with a striking orchestration idea (single winds, harp, piano, a tam tam, and the string section reduced to a single cello) and a completely intuitive tonal technique; it's well written for a good baritone voice, and doesn't seem to have received another performance since Stokowski recorded it.

One example: Almost in passing, while making a point about the rhythmic relationships implicit in an ordering of pitches in his essay on Twelve Tone Rhythmic Structure, Babbitt lists 11 possible relationships between two tones (in fact, if you allow for silence between separate appearances of the tone, there are 13:  given two points in time, duration ignored, two tones can start and stop together; with three points in time, A can follow B immediately or B can follow A, or A and B can begin and either A or B stops before the other, or A or B can begin alone and then be joined by and end with the other tone; with four points in time, A can play and stop with a pause before B plays, or vice versa, or A can play and B starts after and ends before A or vice versa, or A starts, then B starts, overlapping for a while until A stops, allowing B to extend past, or vice versa.)  Above and beyond the immediate context of Babbitt's essay, as far as I'm concerned, this is a basic, profound — and profoundly musical — observation.  These relationships are found in all polyphonic music and this description appealed to me, because, without durations, it had something of a topological flavor (as topological relationships are descrtibed without a precise (in terms of measurements or proportions) shape), and the idea of separating the relationships from a particular metric or set of durations strikes me as having considerable compositional potential.  And, naturally, I got to wondering what the situation would be for more than two tones which led me to consult with my long-term mathematical advisor.  It turns out to be a known mathematical problem (the number of different relationships between n numbers on a line), with a solution that, to me, suggests the rich musical potential of this way of think.  From 13 possible relationships for two tones, three tones jumps to 409, then to 23917 for four tones, and 2244361 for five (see: this and this); in musical terms, the variety of time relationships between tones increases significantly.  For two or three tones, we may well still have the ambition in a piece of music to exploit all of the possible time relationship, but using all of the relationships between four or more tones becomes all but unmanageable in a work of modest proportions.  Nevertheless, if exhaustion of the list is not a requirement, being able to list and access all of the potential relationships is something that strikes me as useful and I've since eagerly  used it in some pieces that have nothing obvious to do with my source. 

1 comment:

katkin said...

This tone relationships business is something I've been exploring lately. Peter Schat's The Tone Clock is an interesting treatise on the subject.