Grid Music

Music is too easily reduced to positive space: music is stuff, arranged in a particular order, with particular relationships. But so much of music's effect is in its negative space -- syncopation's invisible beats, the implied harmony in a solo line, the remembered head behind a jazz solo, sonata form or Bob Dylan (or where I'm from, Townes Van Zandt), abstract and looming.

The grid, as a feature in negative musical space, is endemic to our tradition. It is traditional notation's first axiom -- to map pitch on one axis, rhythm on another, with regular intervals and a 'snap to' default gives us enormous leverage to understand and organize, just as perspective revolutionized painting, and the Cartesian plane revolutionized, by way of mathematics, most everything we do. It's all one idea.

It makes me uncomfortable, though, when I'm writing music without a pulse. It feels unethical, somehow, to start the page "quarter equals sixty" and then fill it with ties, fives, threes, grace notes, dotted, shifted, irregular everythings. And it comes out sounding stiff -- I can hear the grid in there, despite what I've done to hide it. I've posed this question of conscience to my teachers, and I've often gotten some variation of Stockhausen's response -- I'm thinking of the story where Stockhausen is shouting at Morton Feldman that he "cannot live in the sky:" a sound either lands (while pounding time on the table) "here, here, or here." I disagree. Who the hell are you? Where did you come from? And why are you pounding the table through my piece?

I'm not arguing that it's a prison. That's an old saw -- most every composition teacher I've had has told me, at one time or another, to scoot this over an eighth, tie it over the barline, and hip people everywhere groan about obvious beats. And there's plenty of unabashedly gridded music that's fantastic too.

But the grid -- the idea of the grid -- has changed. The parade of ideas that gave it to us has moved on, and we should pause to consider the consequences.

Traditional notation locks us into a Euclidean geometry in that it is based on an immobile, transcendent frame of reference (give me a place to stand and I will count to four). To describe any form, you need to embed it in a larger box with fixed values (pure invention) and plot it according to correspondences between the two. Eventually, this method proved unsatisfactory to mathematicians who, like me, probably felt a little guilty about depending so heavily on something so arbitrary. We were all eventually liberated from that box by Gauss and then Riemann, who invented a way to describe forms without it. As I understand it, they used a continuum of differential equations to describe change from one point to another as the form is traversed. Bingo -- we can exhaustively define anything by relating all of its points to one another -- no grid.

[Almost a century later Schoenberg introduces his method of composing with "all twelve notes related only to one another." I'll have to think about it for a while, before I get too excited, but what an analogy! Only his grid wasn't the grid, it was tonality. Taken together these describe a kind of liberation strategy.]

Then, working out Riemann, Einstein: matter curves space. IF you were to draw a grid, its lines could not be perfectly straight. They cannot be indifferent to what they traverse. Motion too, will warp even the emptiness around it.

While I don't think we are required by Progress to imitate science, I do find it beautiful that ideas transcend discipline, and I think connections like these are worth pursuing. It's not clear how to begin applying this to music. I suppose one route is Riemann's escape -- find a way to describe the shape and placement of sounds through self-reference. Goodbye notation as we know it. Another approach would grant a grid but allow it to be warped by the music embedded in it, just as it shapes that music. It would require a new musical math, a counterpoint of space.

Counterpoint already does all this, just on a different scale. In counterpoint, every change shapes the environment that shaped it -- general relativity. Events don't warp the pitch/rhythm grid, but they do warp the grid that describes each line's possible paths. It's a nonlinear dynamical system, de Landa would say, and, as such, is an organically generative machine (like CI). I want to apply the same to the physics of music. (See Sower) An explosion in the brass? How could the winds not be shaken from their tune?