Musical Symmetries and Emmy Loether
--Musical resonances with Noether's Theorem--
Emmy Noether's theorem was summaraized nicely by Natalie Angier in today's Science Times--
"What the revolutionary theorem says, in cartoon essence, is the following: Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see it’s angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move. "
--Science Times, Tuesday, March 27
I want to make one little musical connections with Noether's theorem. Noether could be Frank Brickle's secret muse, particularly with regard to Brickle's very unique approach to symmetries.
I discussed his approach here:
(Sorry to see some of the images are no longer showing up.)
I would like to mention that some very notable musical authorities assured me that we can't hear this way-- after a symmetry is instated, do we hear it carry on to infinity?. I have *learned* to hear this way in brickle's work, largely because his rhythmic framework for his use of symmetries rises to the challenge.
Notice how, in The Creation, "It shall be as I say", in stately eights and quarters is preceded by a sequence of 16ths that starts to suggest a dotted eighth pulse--
ta ta ta ta - ta ta ta ta - - | " It - - - shall - - be as - I - say" - - - |
The idea that pulse rates continue (even through silences) after they are set in motion is a notion with pretty wide currency. Conummating that rhythmic phenomenon with a Noether- inspired pitch conceit would be a wildly imaginative flight of fance.
Brickle assures me that Noether was not an influence on his approach to symmetries. Moreover, I remember how much Babbitt hated false analogies with math and science. Brickle upholds that tradition.