Wednesday, August 20, 2008

Temporary Notes (6)

One of the first tricks many of us tried in an electronic music studio was recording something — preferably with a text — then reversing it, learning to perform the retrograde version, recording that, and finally reversing the retrograde recording so that you end up with something that has a clear resemblance to the original (forward) recording, but remade into something strange and disorienting. This is a species of variation made from accumulated errors in the transmission of information, but the errors here have a special character due to the fact that our perception of sounds is largely non-symmetrical with regard to time. (The same technique is used by some filmmakers, including Lynch and Scorsese, to disconcerting effect).

John Cage, in describing his own early Sonata for solo clarinet, a piece based on strict palindromes in both pitch and rhythm, criticized his own use of symmetry in the work as "indicat(ing) the absence of an idea". Indeed the presence of a symmetrical rhythm can often lead to precisely the same sort of leveling recently discussed on this page.

Messiaen's term for palindromic sequences of rhythmic values (which, to be honest, has always struck me as an awkward formulation) was non-retrogradable rhythm. What does a non-retrogradable rhythm accomplish? Either it is a instance with no real musical value, a transformation of a sequence of musical events with a net change of zero, i.e. an identity operation, within the rhythmic domain, or it is a transformation that somehow depends upon our non-symmetrical perception of time. If we have a sequence of eighth-quarter-quarter-eighth, in real performance, each note value is going to be quite distinct as each note is heard in a unique context, but taking it as a retrograde implies an erasure of any such distinction. To recover the distinction, the symmetry thus has to be violated in some way.

Morton Feldman, in his extraordinary essay (and in a series of works beginning a piece of the same title), Crippled Symmetry, calls attention to simple but rich techniques in which a symmetrical pattern is broken, for example by using a pitch sequence which is non-symmetrical to "color" (to use the medieval term) a symmetrical rhythm. Why are such techniques so effective? Or: What, precisely, is the utility of a symmetry if it is projected on a musical surface by materials that contradict that symmetry?


A technique I have used several times, based upon a sequence of perfect card shuffles, includes a palindromic aspect, but rather than introducing the symmetry directly it is, instead, embedded in the shuffling process. Let's say we have a deck of eight cards, numbered 1 through 8. The deck at the beginning is ordered

1 2 3 4 5 6 7 8

To make a perfect shuffle, you have to cut the deck exactly in half, 1 2 3 4 & 5 6 7 8, and then shuffle the two halves back together perfectly:

5 1 6 2 7 3 8 4

Again, cut the deck in half and shuffle:

7 5 3 1 8 6 4 2


8 7 6 5 4 3 2 1

There's the retrograde! Again

4 8 3 7 2 6 1 5


2 4 6 8 1 3 5 7

And back again to the beginning:

1 2 3 4 5 6 7 8

Now with a small deck, the process is brief and rather transparent, but with ever larger decks, the process gets more interesting, and as it goes through each shuffle, the original sequence — in my usage, it's usually a tune of some sort — is, in effect, comb filtered and laid over itself so that one hears a shadow of the original melody which has been halved in two different ways — split down the middle and slowed to half the tempo.

1 comment:

Samuel Vriezen said...

That's a clever card trick. I like it.

When Dante Boon (who at the time was going by the name of Dante Oei) & I were working on our CD of Tom Johnson's Symmetries, we often marvelled at how in many of those pieces, the way back feels very different in musical effect from the first half. The effect is very particular to those pieces: we were playing several other compositions that involved symmetry which could be much more 'level'. It's probably due to the fact that the processes in Tom's music are so clearly directional and develop to something, like with the subset of pieces that I think of as 'diamonds' which grow a complex polyphonic web out of a central E and go back to the E again, generally within half a minute or so; when processes as cognitively transparent as those are inverted, it's so clearly the other way.