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Making 'beautiful music' with mathematics

By Amy Gage
February 29, 2004

Composing a piece of music can be like solving a puzzle -- getting on paper the sound you hear in your head -- and mathematicians would certainly say there is poetry or artistry in their profession.

How else are the two disciplines intertwined? A professor of math and a professor of music will demonstrate on Tuesday, March 2, at 1:30 p.m. in the Science Center, room 182, by showing how "commutators" can solve puzzles and compose music. The music performance will be held in the Science Center lobby at 2:30 p.m.

A commutator is, at its most abstract, a group element of the form ABA^(1)B^(-1). Less formally, you start by doing a first thing and then a second thing, and follow this by reversing the first thing and then reversing the second thing.

John Kiltinen, a professor of mathematics at Northern Michigan University, will describe how commutators are fundamental to solving permutation puzzles. He will demonstrate his puzzle software and show how adding musical sounds to the puzzles as a feedback device leads to the idea of commutators in music.

Peter Hamlin, an associate professor of music and theory composition at St. Olaf College, will then discuss using commutators as a new device for composing music, and demonstrate his Commutator Music Machine software.

The presentation will end -- unusually, for a mathematics talk -- with the Minnesota premiere performance by the string quartet Mathemusica of an original composition by Hamlin. The work is built on a commutator motif from one of Kiltinen's puzzles.

Kiltinen has taught mathematics at Northern Michigan University for more than 30 years. He has served in many capacities in the Mathematical Association of America, including a three-year stint as governor. His book, Oval Track and Other Permutation Puzzles, which comes with a CD-ROM of puzzle programs, was published by the MAA in 2003.

Hamlin has taught composition, music theory and electronic music at St. Olaf since 1992. He received his doctorate from the Eastman School of Music, where he studied with Joseph Schwantner and Samuel Adler. He has a longtime interest in computers, electronics and mathematical applications in musical composition.

For more information, contact Hamlin at 507-646-3189

Contact David Gonnerman at 507-786-3315 or gonnermd@stolaf.edu.