MATH MUSIC

"Geometrical Music Theory," by Rachel Wells Hall. Science, 18 April 2008, pages 328-329.
"The shape of Beethoven's Ninth," by Davide Castelvecchi. ScienceNews, 24 May 2008, page 13.

Math in the Media

Recent research by Clifton Callendar, Ian Quinn, and Dmitri Tymoczko---all three of whom work in academic music departments---shows a novel way of using geometry to map out a musical score.

Using mathematics, and even geometry, to study music is not new, but the three authors present a way to look at each moment in time in a musical score, like a vertical snapshot of the written music, as a point in n-space, where n is the number of "voices," or instrumental parts, in the piece.

Callendar’s work also demonstrates how the mathematical concept of equivalence classes---a group of objects sharing a single property---can be applied to music.

According to the reviewer, the new research may lead to new methods for teaching and visualizing music.

(The research article, "Generalized Voice-Leading Spaces," starts on page 346 of the same issue.)
At left: Musical orbifold, ordered pairs of pitch classes, courtesy of Rachel Wells Hall.--- Lisa DeKeukelaere.