New mathematical technique turns Chopin into 3D shapes

A few weeks ago I had an exchange on Twitter with John Magee about music. He Tweeted “music is the least representative art. or is it? could it abstractly represent the noise of consciousness?”, which led us to talk about the relationship between music and math/geometry. I pointed out that when Howard Gardiner researched his theory of “multiple intelligences,” he so frequently found music and math paired up — i.e. somebody with facility in one invariably had facility in the other — that he considered making them a single intelligence: Two sides of the same coin, as it were.

(Other researchers have argued persuasively that this isn’t the case; when I profiled the neuroscientist and record-producer Daniel Levitin, he noted that people who have Williams syndrome often have fantastic musical abilities, even though their traditional IQ never rises above that of a small child — they almost never acquire any basic math at all. So the link between math and music can’t be that linear.)

Anyway, the Twitter exchange I had with Magee came back to me when I stumbled upon this: A bunch of music professors have invented a new way to visualize music — as points on different-dimensioned spaces. That picture above? It’s from this video, in which they represent the chord changes in Chopin’s E Minor Prelude as a set of dots moving around the periphery of circular “pitch class space”. Even trippier is this one, which maps the chord changes through a four-dimensional space.

The professors argue that their new representational system could produce some cool innovations:

“You could create new kinds of musical instruments or new kinds of toys,” he said. “You could create new kinds of visualization tools — imagine going to a classical music concert where the music was being translated visually. We could change the way we educate musicians. There are lots of practical consequences that could follow from these ideas.”

“But to me,” Tymoczko added, “the most satisfying aspect of this research is that we can now see that there is a logical structure linking many, many different musical concepts. To some extent, we can represent the history of music as a long process of exploring different symmetries and different geometries.”

I’m all in favor of new ways to let people visualize — and play around with — music. A lot of electronic music software embraces this sort of visual mess-around aesthetic — like the incredibly cool Nintendo DS game Electroplankton (which I wrote about for Wired News a while back), or even Korg’s Kaoss Pad, which, by letting you control two variables at once on an X-Y grid (like “resonance” and “frequency”, so that when you slide your finger around it creates a wah-pedal like effect) quite directly map musical/audio concepts into a spatial dimension.

I’ve often wondered whether someone could similarly use software to create a better way to teach the harmonica. A lot of the cool dynamics of harmonica playing are about embouchure — the different shapes you make with your lips, tongue, cheeks and jaw. The overall shape inside your mouth changes the resonance of the harmonica almost the way a particular X/Y position on a Kaoss Pad (using in “filtering” mode) changes the sound of in instrument passed through it. Drop your jaw and tongue down low and you “bend” a harmonica note downwards; push your finger on the Kaoss Pad up and to the left and you’ll filter the instrument so you only hear the very lowest frequencies.

The cool thing about a Kaoss Pad is that you can see the relationship between where you slide your finger and the attendant musical effect. But with harmonica, it’s really hard to visualize what’s happening inside the harmonica player’s mouth. “How to play the harmonica” guides tend to trip over themselves trying to explain precisely where the hell your tongue and cheeks and jaw and lips are supposed to be, and how relatively tense or loose they’re supposed to be, and how hard or soft you’re supposed to be blowing. I wonder if it’d be possible to create a sort of MRI-like visualization of what’s going on inside your mouth while playing the harmonica — as a visual aid? Or could you even create a virtual instrument that let you play a virtual harmonica using Kaoss-like controls?

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I'm Clive Thompson, the author of Smarter Than You Think: How Technology is Changing Our Minds for the Better (Penguin Press). You can order the book now at Amazon, Barnes and Noble, Powells, Indiebound, or through your local bookstore! I'm also a contributing writer for the New York Times Magazine and a columnist for Wired magazine. Email is here or ping me via the antiquated form of AOL IM (pomeranian99).

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