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

Re:Actually

[Yetihehe]

Mathematical equations can be stochastic, they may have defined certain probabilities of happening. Stochastic L-Systems are good for demonstrating outcomes of some stochastic equations (I'm telling it after weekend with L-system parser for school project).

Re:Here comes the land rush

[radicalskeptic]

You can't copyright chord progressions, only melodies. Most famously, there have been dozens of jazz standards written that are based on the chord progression of Gershwin's "I've Got Rhythm". In fact, there's even a name for that form: "'Rhythm Changes".

Re:one suggestion..

[Anonymous Coward]

Have you considered getting a software sampler/synth/tracker, such as Cubase? Importing MIDI files into that gives you a pretty good visual representation of what they "look" like.

Boooring

[chord.wav]

I've never seen such a boring visual representation of music! While it may be accurate, even MS Media Player Visuals are better!

I was expecting to be blown up with something like this:
Flight 404 on Vimeo

How is this a surprise?

[the eric conspiracy]

Music and geometry have followed the same paths in western civilization since the days of Pythagoras.

MOD PARENT UP.

[Anne Honime]

http://aboutscotland.co.uk/harmony/prop.html

Re:but this goes for any stream of information

[nine-times]

At the very least, it would be foolish to take this as some kind of indication about the universe, i.e. this isn't an indication that string theory is correct, that the universe has more than 4 dimensions, or that music exists in "higher dimensions".

Being able to "represent" something in higher dimensional space just means it has more than 3 quantifiable features.

First Article on Music Theory they ever published?

[Vreejack]

This is emphatically NOT the first paper on music theory they have ever run. A cursory search turned up several other recent papers. I'm too busy reading Dmitri Tymoczko's report on "The Geometry of Musical Chords" to write any more ---Science 7 July 2006:
Vol. 313. no. 5783, pp. 72 - 74
DOI: 10.1126/science.1126287

Some Old, Some New

[DynaSoar]

The claim this is the first paper in Science regarding music theory is wrong. There have been others, including some on music theory and the physiological basis of music perception.

The use of the circle to described musical perceptions is not new. It's been used to describe among other things the "ascending/descending" illusion. However, the use of other topological/dimensional concepts is novel, and pretty damn awesome. I've studied musical perception and its physiology, and a circle is definitely insufficient. More dimensions are required, as the waveforms involved are never (as early as the ear, much less in neural processing) sine waves. A simple example is the fact that inclusion of noise improves reception. The ear itself introduces noise, quite possibly for this purpose. Another is the multimodal (ie. harmonics) nature of most musical instruments. For instance, look inside a piano. The "notes" have more than one string. Even a single string vibrates in a complex set of harmonic frequencies. Now consider that the complex harmonics alone can be used to recreate the missing fundamental (the "main") note in perception, and possibly even in the instrument. Many different multimodal waveforms can create the same result. That requires different approach paths to the solution, and that requires more dimensions.

Sadly, very few in the relevant psychological fields are prepared to understand and incorporate this theory into their work. I still can't find more than a handful that can understand nonlinear statistics above 2 dimensions, even though they often use them for such as fMRI (the vast majority team up with biophysicists who do understand it). When they do manage to grasp the concepts in TFA, or find enough people from a relevant field who do with whom they can work, the results will be damn interesting.