What Music and String Theory Have in Common

Here's an excerpt from a fascinating article that's going to be in tomorrow's TIME.

When you first hear them, a Gregorian chant, a Debussy prelude and a John Coltrane improvisation might seem to have almost nothing in common--except that they all include chord progressions and something you could plausibly call a melody. But music theorists have long known that there's something else that ties these disparate musical forms together. The composers of these and virtually every other style of Western music over the past millennium tend to draw from a tiny fraction of the set of all possible chords. And their chord progressions tend to be efficient, changing as few notes, by as little as possible, from one chord to the next.

Exactly how one style relates to another, however, has remained a mystery--except over one brief stretch of musical history. That, says Princeton University composer Dmitri Tymoczko, "is why, no matter where you go to school, you learn almost exclusively about classical music from about 1700 to 1900. It's kind of ridiculous."

But Tymoczko may have changed all that. Borrowing some of the mathematics that string theorists invented to plumb the secrets of the physical universe, he has found a way to represent the universe of all possible musical chords in graphic form. "He's not the first to try," says Yale music theorist Richard Cohn. "But he's the first to come up with a compelling answer."

Tymoczko's answer, which led last summer to the first paper on music theory ever published in the journal Science, is that the cosmos of chords consists of weird, multidimensional spaces, known as orbifolds, that turn back on themselves with a twist, like the Möbius strips math teachers love to trot out to prove to students that a two-dimensional figure can have only one side. Indeed, the simplest chords, which consist of just two notes, live on an actual Möbius strip. Three-note chords reside in spaces that look like prisms--except that opposing faces connect to each other. And more complex chords inhabit spaces that are as hard to visualize as the multidimensional universes of string theory.

But if you go to Tymoczko's website you can see exactly what he's getting at by looking at movies he has created to represent tunes by Chopin and, of all things, Deep Purple. In both cases, as the music progresses, one chord after another lights up in patterns that occupy a surprisingly small stretch of musical real estate. According to Tymoczko, most pieces of chord-based music tend to do the same, although they may live in a different part of the orbifold space. Indeed, any conceivable chord lies somewhere in that space, although most of them would sound screechingly harsh to human ears.

Comments

[Edward G. Nilges]

Fascinating stuff, Gina. However, it may rest on a preconceived notion of what is pleasant-to-hear. It may not take into account the evolution, or possibly devolution, of hearing and listening, something with an historical basis.

Usually, when these mathematicians get started, you encounter a wall of resentment when you mention 12 tone composition.

Thanks for the link, I will check it out.

[Edward G. Nilges]

Wow, fascinating stuff...in a sense. Wow, Philistinism on drugs...in another.

I mean: you have just enough time to cathect to the Chopin and figure out that you are initially in a tone space from which Chopin, in the Romantic register, seeks exit, when the minimovie ends ... and one "has" in my case to go out for one's ten mile run.

[One chooses, I know.]

It's basically the aesthetic of Disney's 1939 Fantasia, in which real musicians are downsized into alienated orchestra members under a god-conductor (Stokowski) in such a way that scientists and mathematicians take over musical interpretation.

Watch in the original Fantasia how the actual members of the orchestra, people who've studied for years, are patronized as people who, as soon as they have a break, would rather play jazz...as if the entire "classical music" enterprise is just a joke, one of Eulenspiegel's merry pranks.

It was in the same era that Aaron Copland noticed that ordinary members of symphony orchestras never seemed to be interested in music, never carried to work any other scores but the one that was to be played.

I think the problem is that classical music requires an immense amount of discipline unless one's Glenn Gould, a charming fellow who had so much hand that he could afford to not self-brutalize. Independent of the classical music establishment, most performers perform internally repressive stunts so often that they end up with unacknowledged rage and a union contract.

Watch how Steve Martin and Bette Midler patronize classical musicians and musicianship in Fantasia 2000, brutally. For the same reason my iPod makes symphonic movements into "songs", the orchestra becomes the boys in the band, nothing more.

The task of interpretation is picked up by scientists and mathematicians.

I am very conflicted, in other words, about Tymoczko's website. It reveals even as the primitive oscilloscope displays (built by those Hewlett and Packard boys in Palo Alto) revealed something in the 1939 Fantasia.

But by putting it under control, it simultaneously forbids us to go any further.

My head in other words hurts.

But thanks for expanding my universe.

[Edward G. Nilges]

Hmm, my mistake. Dmitri Tymoczko is primarily a musician, not a mathematician. However, I don't think this changes my questions as to "scientism" in the arts, the inability to listen without a sort of scientific crutch.

Sorry about the confusion and thanks again for the link to his work which is interesting *malgre lui*.

[Basslogic]

I think music is a language we still don't understand.We can express feelings and emotions in musical scale tones.It's sort of like a 12 cord alphabet if you will.Only it's relative to the real truth of our existance. In a world where native language lacks the tools needed to communicate on a universal scale.Music can acomplish just that on a level not possible in taditional spoken langauge methods currently in use today.They say music is the universal language. I say music is a multidimension language, a window to a 4TH dimension which
we can't see yet we can sense and feel thru the magic of vibrations that link us to another world of reality !!

[Dexter Mahadeo]

Ever seen the connection between Tracey Chapman's song "Change" and John message in Matthew Chp 3 v 2 (yeah the Bible)