His paper has been published in Science, the first music theory article ever published in that journal. We've known about the close relationship of music to math for centuries, what makes Tymoczko's theory significant?
"Composers have been exploring the geometrical structure of these maps since the beginning of Western music without really knowing what they were doing," Said Tymoczko. "If someone you a map, 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 musical pathmaking and realize that there are some very simple principles that describe the process."
One thing I find fascinating about Tymoczko's work is that it is less interested in "explaining" music than it is in mapping how music in various styles moves through his "orbifold space." Any definition of music thattreats it as a steady state phenomenon is doomed to incompleteness.
Go to Tymoczko's website for more.
Special bonus for John Marks: "Smoke on the Water" as an orbiform map.