Word: tymoczko
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...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...
...Tymoczko's website music.princeton.edu/~dmitri) 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...
...discovery is useful for at least a couple of reasons, says Tymoczko. "One is that composers have been exploring the geometrical structure of these maps since the beginning of Western music without really knowing what they were doing." It's as though you figured out your way around a city like Boston, for example, without realizing that some of your routes intersect. "If someone then showed you a map," he says, "you might say, 'Wow, I didn't realize the Safeway was close to the disco.' We can now go back and look at hundreds of years of this intuitive...
That's likely to help both scholars and teachers, he argues. By showing how compositions of various styles move through his orbifold spaces, says Tymoczko, you can see how different styles of Western music relate to each other and evolve. Tymoczko's maps can also be an aid to composers, says Cohn. Most have a favorite corner in orbifold space, a set of related chord types that they tend to explore over and over in different ways. Venturing into a different part of space can be tough; you have to learn your way around a whole new auditory neighborhood...
That doesn't mean you can program a computer with Tymoczko's orbifold maps and have it spit out beautiful compositions. "I don't want to sell these maps as the royal road to composition," he warns. "They don't substitute for the hard work of learning how to move notes around." But they can help show when a new idea is promising and when it will probably lead to a dead end. "They might make an O.K. composer good," says Tymoczko, "but they won't make a good composer great...