Photo: Lynne Harty
You don’t have to understand math in order to make great music, but it helps. Music is intrinsically mathematical, and the two disciplines have a symbiotic relationship. Pitch, frequency, ratios, intervals, chords, proportion, balance—it can all be understood mathematically. Many math departments of big-name universities boast accomplished musicians.
At Harvard University, for example, Grammy-nominated composer-pianist Vijay Iyer (pronounced “VID-jay EYE-yer”), one of today’s most celebrated jazz musicians and a 2013 MacArthur Fellow, makes a point of teaching the math behind the music. It doesn’t hurt that Iyer earned his own undergraduate degree in math and physics and his interdisciplinary Ph.D. in cognitive science. When he breaks music down mathematically in the classroom, he said, “it’s a revelation” for his students.
The Beat Goes On
“You can count beats, divide a rhythm cycle into subdivisions, then combine them into different patterns,” Iyer said. “Suppose I have a cycle that has 28 beats; I can divide it into four sevens, or 10 plus 10 plus 8, and that’s two very different ways to divide the same span of time. When you do that, it feels different.”
Feeling the music—which derives largely from rhythm—is what’s critical to Iyer. He loves to play with distinctive rhythms that cause people to sway, bob their heads, dance, or simply move in different ways. Organizing musical rhythm, he feels, equals organizing human motion.
“The structure of our ears and anatomy, the movement of limbs and fingers, the way we breathe and speak … all of them are the source of music.”
“Music has to come into the world somehow; it isn’t simply an intellectual abstraction,” he says. “It’s a body process; it involves us physically doing stuff. The structure of our ears and anatomy, the movement of limbs and fingers, the way we breathe and speak with the lungs and the mouth, the way we walk—all of them are the source of music.”
Basic Math, Complicated Rhythms
In his article, “Strength in Numbers: On Mathematics and Musical Rhythm” (featured in The Best Writing on Mathematics 2010), Iyer wrote that the mathematical ideas he works with are “easy enough for a twelve-year-old to understand, but they help me find sounds and rhythms that I might never have made otherwise.”
“Iyer hypothesizes where a musical structure might lead, then experiments and explores ... It’s a dance of sorts, an ever-developing relationship between the cerebral and the physical.”
He’s particularly keen on using Fibonacci numbers to structure his initial compositions, then seeing where the music takes him and his fellow musicians. Applying the tools of scientific research to the understanding of what music is and does, Iyer hypothesizes where a musical structure might lead, then experiments and explores, seeing how a note or phrase takes shape through live improvisation. It’s a dance of sorts, an ever-developing relationship between the cerebral and the physical.
Vijay Iyer Trio: Break Stuff (Album EPK)
Boosting Kids Math Learning
Iyer’s unique experimentation with music benefits more than Harvard students and audiophiles. He’s also a contributor to the Thelonious Monk Institute of Jazz “Math, Science & Music” initiative, which helps students gain STEM skills and learn to think creatively. Elementary school students who study the Institute’s “Mathematical Foundations of Indian Rhythm” curriculum, which Iyer oversaw, learn to visualize rhythms using arithmetic, fractions, ratios, geometry, algebra, permutations and combinations.
Iyer hopes his work with the Institute helps boost kids’ math learning as well as their musical understanding.
“There’s research about how doing music at an early age prepares you for math. Pitches and note names and chords. Abstractions that have an order to them. Group theory, etcetera," he said. "The fact that I played music from an early age probably prepared me for mathematical abstraction."
Keeping Faith in the Future
Based on his years of experience on both sides of the lectern, Iyer has recommendations for children and their teachers.
“I know a lot of people who think they weren’t good at math in school who now work for Google or in STEM fields.”
“Anything you have the opportunity to study, you want to be patient and take your time. I was a late bloomer as far as music goes. I didn’t know I would be good enough to have a life in music; all I cared about is that it was meaningful to me. I had to take my time, and still have to, to deal with its intricacies and subtleties.
“So, the main lesson is: patience and faith. Things will make sense in the long run. You may think you have to learn things on a timeline, because that’s what you do in school, but I know a lot of people who think they weren’t good at math in school who now work for Google or in STEM fields,” he said.
“It’s also important for educators to give students time, and as much individual attention as possible, to help them realize their potential. Often you don’t know what that potential is early on. Not everything is obvious at that young age about what a child can become. You have to give them time and space to develop.”
Vijay Iyer Trio: NPR Music Tiny Desk Concert