Useful Symmetry

Symmetry in music is most interesting, I suspect, when it allows us to focus on the given asymmetries in our perception.  Time — for our purposes here, at least — can't go backward and our sense of pitch is radically asymmetrical.  Cage once quipped, in a bit of self-criticism of an early palindromic work that it suffered from its symmetry and that, for him, "symmetry indicates the absence of an idea."  And he was certainly right, in the sense that just writing out a palindrome or pitch-symmetric passage was, at its worst, just an automatism (and one quite typical of student composers venturing into the serial), generating more volume out of the source material, but the stuff generated was not necessarily going to be interesting, let alone musically useful.  But that's the worst case and, in the better and best cases, in which the composer is using symmetries — whether notational, or exact (as is possible with electronic media) — in ways that allow the material to articulate or bring out or even make vivid the real asymmetries, as in Feldman's use of rhythmic and metrical "crippled symmetries" — borrowing from the rug makers' trade the use of slight variations in repeated and mirrored patterns — or even in that sometimes classy, sometimes cheesy emblem of early live electronic music, ring modulation.