The Geometry of Music

An anonymous reader notes a Time.com profile of Princeton University music theorist Dmitri Tymoczko, who has applied some string-theory math to the study of music and found that all possible chordal music can be represented in a higher-dimensional space. His research was published last year in Science — it was the first paper on music theory they ever ran. The paper and background material, including movies, can be viewed at Tymoczko's site.

Comments

Hmmmm.

[jd]

Neanderthals had flutes and discovered the octave. If we are to assume music is linked to string theory, then the problem of where they all went is solved! They were the aliens all the time! (Seriously, the paper is interesting, but you can always describe a simple system with a complex one. I'd want solid evidence that this is the reduced form.)

Re:Hmmmm.

[edittard]

Neanderthals had flutes and discovered the octave.

If you're referring to the bone fragment (singuilar) with holes in, it's by no means proven that it was a flute, or even that the holes were man made.

Re:Hmmmm.

[espiesior]

The wording is quite misleading. Tymoczko used "string theory" math... i.e. Geometric Topology (the article tries to play with "orbifolds" - fancy manifolds). Doesn't mean that string theory and music theory are intrinsically related in the physical world (which they are for the obvious OTHER reason), but rather, they can be expressed by the same monsters in the world of mathematics.

Related:

[Anonymous Coward]

http://en.wikipedia.org/wiki/Sacred_geometry

http://www.spiritofmaat.com/archive/jan4/williams.htm

but this goes for any stream of information

[jacquesm]

not to belittle the guys achievements, but isn't it so that any sequence of bits can be represented by any arbitrary higher dimensional space ?

The difficulty usually comes when trying to describe a higher dimensional space in a system with *less* dimensions, the other way around is trivial.

Re:but this goes for any stream of information

[Bjarke Roune]

It is often true that if you have some parametrized way for describing data, then you generally want as few parameters as possible. You definitely want fewer parameters than data points, so going to more parameters or dimensions is not an achievement, as you point out.

The article is light on mathematical details, but it seems that the achievement is that this space of points has been characterized in a useful way. The story is not that now it can be done with even more dimensions (which as you point out would be trivial). Rather, the story is that now this space of points has been characterized at all, and this description just so happened to require several or many dimensions.

Since this paper is the first ever on musical theory to be published in Science, which is a highly prestigious peer-reviewed journal, we can assume that the paper is saying something interesting within its field. Specifically, we can assume that this is not just a question of fitting some standard statistical model to some data points.

Does it work backwards too?

[josgeluk]

It would have been nice if the author had provided some examples of music that his model predicts. If I walk a circle in his four-dimensional space, what does it sound like?

Re:Actually

[baldass_newbie]

It's not the first time music has been represemted as mathematical equations

You're right. Plato did it in the Timaeus about 2500 years ago.
It's nice to see folks eschewing traditional Western culture and then 'discovering' things the same Western tradition developed over two millenia ago.

Sonny Bono owns you

[tepples]

This network, combined with various social and cultural studies, really provides a rich field of exploration (for example, the reason we concentrate on music by dead white europeans from 1700-1900 may include a cultural bias, not just technical). "White" and "Europeans" might come from cultural bias, but the "dead" part comes from copyright, specifically the U.S. term extensions of 1976 and 1998. It's much more expensive for schools to provide copies of "Rhapsody in Blue" or any more recent work, so schools just pretend Gershwin's compositions never happened.

Re:Watched the .movs

[Oktober Sunset]

but would running an episode of american idol through it give goatse?
If it did, It would be an improvement.

Melodies are just as finite

[tepples]

You can't copyright chord progressions only melodies. Even if this is true, melodies are just as finite.

Grr...

[ExecutorElassus]

I realize this is probably whiny of me, but it would have been nice if he hadn't built his entire freaking page as a Flash object. Since I run Firefox3 on 64bit Linux, the only way to see swf content is through an ugly hack that rarely works. This is one case where it does not: I just get a big white page. Is there another link to the article?
/rant

Pitch is Boring -- study rhythm

[kov]

Music theory is miles deep in frequency analysis, throw this one on that slag heap. I do congratulate him on proving that pitch is boring though: since his chordal (i.e., pitch-based) analysis manages to lump vastly different musics together, ironically he's shown that the vast majority of what makes them different from each other must be something else.