Theme and variations

I recently promised some friends that I'd post the final project from the composition class I took last semester. I figured that my blog-following audience [as well as you lurkers; I know who (most of) you are. If you're going to read, you might as well leave a comment once in a while. Or, if the subject matter doesn't suit you, you can at least send a surrogate.] might be interested to see it, too.

But this... isn't that project. I'm actually quite proud of my work on the final project (a cello concerto), but I left a few things half-finished in order to meet the course deadlines. So, while I finish up the score for the cello concerto, allow me to offer this as a cop-out: my first composition project for the course, a theme and variations for piano.

The requirements were straightforward: one theme plus five "variations" on that theme, lasting in total approximately three minutes, containing at least one key change and one time signature change. I wrote each of the variations in a very different style, and since I believe that context always enhances the listening experience, let me drag you through a little bit of play-by-play analysis:

- Theme: It's... well, it's the theme, presented very simply in unremarkable four-part harmony. It's a little boring, even, but that's sort of the point, to take an ordinary theme on a wild ride through the variations. Plus, it's only thirty seconds; you can make it.

- Variation I: The first variation is a slow, brooding treatment of the theme. I like its atmosphere, but still the presentation is rather uncomplicated.

- Variation II: I lack the contrapuntal mettle to write a full-fledged fugue, but this variation is at least fugue-like. I love Bach's ability to weave passion and intensity into a tightly constructed musical mass; here is my effort at emulation.

- Variation III: Here I'm deliberately imitating the major-scale sappiness of Rachmaninoff. Although this variation was a good exercise in part-writing, it's a little too melodramatic for my tastes.

- Variation IV: I'm most proud of these last two variations, mostly because they exhibit qualities my of own compositional voice: asymmetrical time signatures, lots of dissonance, unapologetic parallel motion, and an emphasis on harmony over melody. And while the fast tempo forces this variation to be over too soon, it's far and away the best 20 seconds of the piece.

- Variation V: The final variation is an attempt to merge Sigur Ros-style ambience with an Eric Whiticare-style approach to harmony. (There's also a Sufjan Stevens reference; five points to the first person to correctly identify it!) I'm pretty happy with the result and its atmospheric minimalism. I won't pretend that there's some grand artistic meaning to my little school project, but I think this variation gives a fitting end to the piece: after folding, spindling, and torturing the theme, we pare it down to its essential elements and lay it to rest.

Below are links to the piece itself (.mp3) and the score (.pdf). Be forewarned: even though there have been great advances recently in electronic music, the mp3 file still came out of Finale's synthesizer. As far as synthesizers go, it's quite good, but don't expect it to sound like the real thing. And since I don't play the piano, a live recording isn't likely to be forthcoming anytime soon. Also: you may need to turn up the volume or use headphones. Finale is a little sissy about volume.

I know it isn't much, but it's something I created from scratch, and something I'm a little bit proud of. Please enjoy (please?):

Score (Finale)

(Sometime tomorrow I will upload the hand-written score, which will immediately make the whole thing at least 17% more bona fide. I'll also try to get Google player embedded into the post. I couldn't get it working, and I believe that blog jukeboxes are moderately evil, so we're stuck with this for now.)

Statuesque

If you follow the links embedded in my posts (and seriously, you really should; I spend considerable time hunting them down, and furthermore they are awesome), you know that I'm a fan of Bertrand Russell. Although he probably would have mostly thought of himself as a mathematician, he's better remembered now for his skeptical philosophy and quotable one-liners. Over the past several years, a few of his quotes have helped formalize my thoughts in a few areas I already felt strongly about: the value of questioning one's assumptions, the wisdom in acknowledging uncertainty, and the nobility of the scientific endeavor. He's also occasionally forced me to realize that sometimes I sympathize with the skeptic more readily than with the believer.

But as much as I like him, every so often he gets it terribly, terribly wrong. Consider the following:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty--a beauty cold and austere, like that of sculpture.

Sounds innocuous enough, maybe even something I'd support, given my overexuberance for mathematics. But no. As you might imagine, I take no issue with the idea that mathematics possesses truth and beauty--mathematics is all about the truth and beauty (although, if you want to be picky, we have to be careful about what we mean by mathematical truth. But I don't want to be picky.). Instead, my problem is with the "cold and austere" part. Maybe I misunderstand Mr. Russell, but I think he's missed the mark.

Here we go: it's become a cliche to characterize mathematics (and mathematicians) in simultanously dismissing and reverential terms. That is, it's terribly complicated and we could never understand it and it's SO amazing that someone could, in fact, understand it. But it's also so complicated and abstruse that it's entirely disconnected from our real life, so it's ultimately unimportant and irrelevant. By extension, we do the same thing to science in general: regard it as an impressively difficult, but impenetrably tedious task better left to someone else who happens to enjoy the pointlessness. (I could go on about how harmful this idea is, how it's perpetuated by our approach to math and science education, and what it says about us as a people, but I need to get back on point.)

"Cold and austere" only serves to reinforce this idea. It suggests that mathematics, science, and even logic in general are remote and lifeless and alien to everyday existence. That logical, mathematical thought is a robotic, passionless exercise that leads to a boring and unimportant answer. Even more, it misses so much of what logical thought actually is. Your friends, your parents, and even Yann Martel all want you to believe that logic happens in a sterile, Spockian vaccum of emotion and imagination. But they are all wrong. Logic is alive and hot with argument, struggle, and discovery. It requires (not merely permits) imagination, passion, and creativity. And its results have the power to fundamentally alter how we perceive our everyday reality. (I mean this: I dare any of you to learn calculus [or maybe learn about the Cantor set] without suffering an irreversible perceptual shift.)

To be fair, probably I've significantly exaggerated Russell's meaning. Indeed, he certainly knew something of the joys of mathematical exertion. But I still argue that his imagery isolates mathematics from reality, treating it as something to be curated and admired rather than experienced. Mathematics--and logic in general--is less like appreciating a classical statue and more like creating a Jackson Pollock: an effort to find truth and beauty out of instinct and intuition; an unpredictable, even violent process that forges order from the chaos of human thought.