Making Music with Math

John Kiltinen (Mathematics and Computer Science) recently combined his professional expertise in math with his avid personal interest in music. The project began shortly after Kiltinen wrote a book on permutation puzzles – challenges similar to a Rubik’s Cube that involve the scrambling and reordering of several pieces, but in numerical order.

He uses ‘80s-era puzzles such as Top Spin and the Hungarian Rings in his abstract algebra classes “to give students a concrete representation of how group theory provides the mathematical structure to understand and solve the puzzles.”

Kiltinen developed a CD-ROM of puzzle programs as a companion for the book. In the software (as pictured below in a captured image of an Oval Track puzzle), each move is accompanied by an audible tone.

“As you reach the final steps of solving a permutation puzzle, you have to repeatedly use moves known as commutators – the process of doing a first thing, then a second thing, then reversing the first and finally reversing the second,” he said. “This combination of moves produces a characteristic sequence of tones. I use the sounds as a feedback device in the software, but I got to thinking that they might also serve as a theme for an interesting musical composition.”

Kiltinen commissioned a piece from Peter Hamlin, a professor at St. Olaf College who has an interest in computers, electronics and mathematical applications in musical composition. The collaboration resulted in Commutator Music: Variations on a Theme of John Kiltinen. It was performed for the first time in January by a string quartet at a reception held during the Mathematical Association of America national conference in Phoenix.

The two men also spoke at a joint colloquium in March at St. Olaf, where the composition made its Midwest premiere. Kiltinen demonstrated his puzzle software and showed how the musical tones he inserted led to his idea for a composition that builds upon the motif. Hamlin discussed how he used commutators as a new device for composing music. He also demonstrated the Commutator Music Machine software he wrote in conjunction with the project.

Kiltinen has been interested in music since childhood. He participates in the Marquette Choral Society and previously commissioned pieces for orchestra, chorus and solo when the community first hosted the FinnFest USA celebration in 1996. While this is the first time Kiltinen has combined his two passions of math and music, he said the pairing makes perfect sense.

“Composers structure music,” he explained. “Any time you have structure, there is the potential to use math for study and analysis. It is more behind the scenes than on the surface, but math is closely intertwined with music.”