Cycles & symmetries

The idea of cycle, of return, of repetition, is omnipresent in music. Traditional constructions of melody or mode are based on returning to a fundamental note. A piece ending on a different note (or key) from where it began was considered unorthodox in Western music well into the 20th century. Works themselves, from the mass of Machaut and even earlier examples, were arranged as cycles from constituent elements. The sonata form remained a multi-movement "cycle" as such. Sound itself is built of repetition and return, the rise & fall of a membrane or back & forth of a string. Music is not only impossible without cycles, if it illuminates thought processes, then it continually reinforces our perception of cyclic phenomena. Ideas on cyclical reality are certainly prevalent, whether in Hindu cosmology or elsewhere, and one can in turn construct a basic dualism out of departure & return, a dualism sufficient to construct the manifest world in opposition. The yin-yang of Taoism likewise indicates a binary system which intermingles to form the shades of quality in the world.

To the Western mind, these constructions may not seem natural or logical, and one must question the extent to which music makes them seem natural in opposition to logic. However, this idea of opposition, of polarity, permeates logic itself. Binary logic is no more inevitable than human thought in general, and indeed it does not require extensive analysis of one's own life to discover statements which are really neither true nor false, or maybe both. Logic is itself a convenience, and not an a priori system to which others must conform. Indeed it is built on the convenience of reflection, of cyclic return, i.e. that if something is not-not-true it becomes fully true again in a very tight cycle. Formal logic also took a beating from Gödel. We can observe that things either change in one direction, i.e. they do not cycle, or that they come & go and are seen to cycle in at least some sense. This is as trite a statement as they come, much like the "the more things change, the more they stay the same" saw which stands in opposition to rallies for progress. Does music then blind us to progress? It is a wonderful question, one which draws out one's priorities as surely as any, and one to put aside for now.

Forming the idea of cycle, of pattern, from undifferentiated stimulus is also part of the act of perception. In some sense, everything is different, and there is never a return. The next time is the next time, as much for a season as for a musical key. We recognize the sameness, even the sameness of merely similar figures in variation forms, because that recognition enables perception. Variation forms, perhaps the most basic in music, at least in a general sense, are virtually didactic lessons on similarity appraisal, music as perceptual instruction: These are the same, so learn to hear them as the same. Rhythmic cycles assist in this task, and moreover order a sequence of sounds on more than the sequential level. Such structures and patterns can easily become more complicated than simply returning to a downbeat or a major key, and much of what modern music has done aims at pushing the envelope of structural perception, at least theoretically expanding our minds. (Whereas postmodern music is more about toying with those perceptions, tricking them, probing them from the far side.) Past discussions of mathematics & symmetries demonstrate just how far afield ideas on using patterns or cycles can lead. As alluded, under some constraints, apprehensible symmetry-breaking in the overtone series produced by a vibrating object can yield a mathematically precise determination of its shape. The power of symmetry & cycle can thus be observed even under the harshest light of modern logic.

Cycles affect music in more than form and construction. They also condition the backdrop of fashion against which both interpretation and composition must function. Although one might question the illusory nature of some cycles, cycles of fashion are confirmed phenomena. Changes in clothing styles are easily documented, and even observed as cyclical by the TV news. Styles of music seem to have their cycles as well, although since the era of historicism is still young, our evidence is relatively slim. Interest in medieval music seems to have peaked, at least for the time being, or at least interest in new recordings has. One can speculate that market saturation for CDs initiated this change, that now there are enough CDs, and in fact "new" releases this year seem to be mostly repackaged old releases (much like "classical" has become). It must be a cycle, I believe, because there are so many interpretive advances yet to appear. It will be as if the music is new again. Of course, we cannot continue such a renewal indefinitely, at least not without adopting personal counterfactual interpretive stances (something to which I do not object, but they are a different situation). That recorded examples are contracting just as interpretive discoveries are exploding and possibilities are expanding exponentially is perhaps coincidence, and perhaps not. Time will tell. There is no question but that the market for CDs has been radically altered, and some caution is understandable.

The idea of expansion & contraction, of death & rebirth, of Renaissance, is certainly not new. The suggestion that some cycles are positively correlated, while some cycles are negatively correlated and some simply move at different speeds, is not new either. Indeed one can posit a natural cycle to dominant worldviews (or paradigms), as one stays on top until it collapses, frequently in spectacular fashion, and music as art is negatively correlated with today's dominant views. That those views likewise cycle with compositional style itself is also plausible. Since today's emphasis on technology has yielded not time-saving and leisure, but rather even more hectic lives (rushing about in an effort to feel needed, one imagines), the simpler music of e.g. Glass or plainchant seems to be a natural complement. It is difficult to take such simplistic analysis too seriously, of course, as composers consciously play upon these ideas themselves in meta-fashion. Resulting layers of abstraction and meta-connection can only be positively correlated with the world of misdirected image. Unfortunately, simulated stimulus does not have a straightforward symmetric partner, not without raising the level of abstraction. Any cycle back to simplicity is therefore difficult to circumscribe, but almost necessarily involves ignorance as a cure for over-thinking.

Administrivia: Vacation time. Next column in four weeks.

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Todd M. McComb