THE GEOMETRY OF MUSIC

For years, string theorists have used music as a metaphor for fundamental particles, and now Tymoczko is usiing the mathematics of string theory to understand the fundamentals of music.

The math makes it easier to understand objectively what great musicians and composers do in their head. "When you sit down to interact with a piano, you're actually interacting with a non-Euclidean space, because there are many different ways you can play a C-major chord on a piano," Tymoczko said.

He said orbifolds capture the multidimensionality of music: how harmony interacts with counterpoint, how chords are connected with each other, even how notes are arranged "to minimize the amount of effort that musicians have to make when moving from chord to chord."

On Tymoczko's Web site, you can find additional resources, including his ChordGeometries software, a version of his Science paper and a series of four QuickTime video files that provide further audiovisual explanation. There's even a QuickTime depiction of the famous chords from Deep Purple's "Smoke on the Water."

url to the site

http://cosmiclog.msnbc.msn.com/archive/2006/07/07/950.aspx

This is important -- study Tymoczko's web site---SONGUL