Professor's Music Research Takes a New Shape

Friday, May 23, 2008

From the Greek astronomer Pythagoras' theory of "the music of the spheres" to the concept of using colored lights to present songs to a deaf audience, the idea that we can "see" music or associate physical properties to it has been around for centuries. According to research supported by Saint Joseph's University mathematician Rachel Hall, Ph.D., that idea may not be far from the truth, and geometric delineation of music isn't as counterintuitive as some may think.

In a recent article in Science magazine, Hall expands on research by scientists from Florida State, Yale and Princeton universities that combines a large number of geometric theories that already exist and identifies techniques for exploring musical theory that had not previously been seen.

"[This new research] showed that even very basic musical relationships—the kind of thing one learns in an undergraduate music theory class—have complex mathematical implications," Hall said in an interview. "They used geometry to represent these relationships, and it turns out that the geometry is quite unusual. It's similar to some of the models physicists use."

In more simple terms, by mapping notes and chords to points in a geometrical space, researchers can better describe how composers combine melody and harmony to produce coherent music.

One of the most exciting outcomes from this research could be the development of new instruments, according to Hall. "This type of geometry actually appears in some instruments that have been around for a while," she said. "Studying the geometry could allow us to create new ones. For now, it will be extremely useful in teaching music theory and composition."

--Jeffrey Martin '04, '05 (M.A.)



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