Music with Math
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.
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.”
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.
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.”
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.
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.
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.
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