Music by the Numbers
Some people seem to have perfect pitch but are equally proficient at high-level math. What’s the connection?
by Sherri Kimmel
June 29, 2010
Jeff Rodgers ’10 (right) and Michael Cameron (left) perform in April with the Dickinson Orchestra. “I shy away from saying that math skills automatically transfer to music,” says Rodgers, who plans to be a math or chemistry teacher and also work with a high-school music program. “You need to recognize how to use things to your advantage in the different media.”
Remember the Mozart effect? A couple decades ago soon-to-be parents found themselves spinning their radio dials far, far from the throat-straining vocals, crashing drums and guitars of Nirvana’s “Smells Like Teen Spirit” to the soothing string swoon of Beethoven’s Pastoral. The hope was that baby on board would emerge not only with a plump leg up on future music-appreciation classes but a more highly developed numbers sense. Woe to those babies weaned on the Beastie Boys.
But as Teresa Barber, associate professor of psychology, points out, the 1991 study that suggested exposure to classical music enhanced children’s ability at math and spatial reasoning has been discredited. “A few new follow-up studies showed maybe it isn’t music but general arousal” that accounts for the apparent connection, the neuroscientist says. “It seems to be consistent for short periods of time.” Mozart effect aside, the fact that some people seem equally able to sing with perfect pitch and puzzle out complex theorems is indisputable.
“Does it take a particular brain to come together to make that possible?” wonders Barber. Who knows? No scientific studies currently can answer the question of whether “music drives math or math drives music,” she says.
What is known is that plenty of Dickinson students, past and present, gracefully succeed in what seem two incongruent areas of studies. In fact, 45 years ago, Dickinson’s first music major also majored in math. That she has dual affinities for what appear to be disparate disciplines seems no accident, though the retired computer programmer can’t articulate the why and how.
“The way my brain works seems to work both for musical-type things and math and logic,” explains Carolyn Bryant ’66. “I’m highly intuitive, which seems backward for someone who does math and computer stuff. I approach everything, including the logic necessary to accomplish mathematically oriented tasks, through intuition. Somehow the music managed to help me with the discipline necessary to do the logic of math and computers. It’s all connected.”
During her career as a research scientist for the federal government, Bryant kept up her singing and playing (piano, clavichord and recorder). “Though math was my bread and butter, music was my real interest all along,” she concedes.
Now in retirement, Bryant’s only current use for a computer is to assist in her research for Grove’s Dictionary of American Music. “I’m the contributing editor in charge of articles on musical instruments.”
Laura Keller ’03, a former pianist who focused on performance at Dickinson, says her dual math/music major “was a great combination. It allowed me to do two different things for my college career. Math and music access different parts of your brain, and I loved the chance to do two totally different things.”
While music seems most closely aligned with the brain’s right hemisphere, the left seems more connected with mathematical functioning, according to Barber. “But you need both,” she says, citing people who suffer from amusia (an inability to comprehend or produce music), which does not derive strictly from one hemisphere or the other. As artistic planning coordinator for the Chamber Music Society of Lincoln Center, Keller, like Bryant, now works more with words than numbers—drawing heavily on both sides of her brain.
A Penchant for Precision
“Initially, I majored in math because I liked working with numbers and the sense of exactness,” Keller relates. “I also excelled in memorizing music and wanted to understand it inside and out. There is a connection there with editing and proofreading. You definitely need to be detail oriented for all three of these things.”
Though he’s a chemistry and math double major, Jeff Rodgers ’10 has spent as much time in the Weiss Center for the Arts as many music majors. This spring he seemed central to any campus activity requiring a skilled cellist, playing side-by-side with his teacher, Michael Cameron, at the Dickinson Orchestra concert and with organist Shirley King at the Collegium Concert.
Jeff has many gifts,” confirms Cameron, instructor in music. “Math and musicality are just two of them. Jeff has a very analytical mind. He can digest both things very well. It reminds me of that joke about Einstein, who was a good amateur musician. He was working with [pianist] Arthur Rubenstein. Rubenstein said, ‘For goodness’ sakes, professor, can’t you count to four?’
“Jeff doesn’t have that problem,” Cameron adds with a big smile. “He’s able to digest rhythms easily. He’s got that over Einstein.”
Keeping the Beat
“An analytical mind is helpful, especially with rhythm,” Rodgers confesses. To decipher rhythm, he says, one has to know how to measure time. But the ability to concentrate and endlessly practice also is key to success as a musician and a mathematician, Rodgers says.
“To be good at math you need to spend a lot of time with it,” confirms David Richeson, chair and associate professor of mathematics. “You need to do your homework problems over and over. They need to be so engrained that they [numbers patterns] come naturally to you. It’s the same with music. You don’t want to think what your fingers are doing. For both, the only way to get to that point is lots of practice.”
Writing in his book Musicophilia, Oliver Sacks delves into the meaning of practice. It “involves conscious application, monitoring what one is doing, bringing all one’s intelligence and sensibility and values to bear—even though what is so painfully and consciously acquired may then become automatic, coded in motor patterns at a subcortical level.”
Jennifer Blyth, a concert pianist and associate professor of music, also sees the connection between practice and success in both disciplines. “In piano, the hardest part is learning how to play all that stuff and keeping it in your head. Your performance comes out in memorization. It’s purely factual remembering.”
It All Adds Up
Mathematical and musical performance draw on the ability to visualize structure, memorization and the discipline to practice, practice, practice, says Blyth. In music-theory classes, the students who grasp numbers, ratios and proportions well are the ones who excel, she says.
“Kids who can do algebra and calculus out the wazoo do great in theory,” says Blyth, who loved chemistry and algebra during high school. “That’s the kind of brain I look for—that can analyze, that can intellectualize and not just rely on intuition. The math brain clearly comes out in theory class.”
Robert Pound, a composer who is chair and associate professor of music, agrees that students with mathematical ability tend to ace theory classes. But math also is useful for other areas of music, he contends.
“The more I’ve grown as a composer, the more I appreciate math. I make purposeful use of fractions in composing. Math is a means of understanding music.
“There always has been a link between math and music,” he points out, noting the Greek philosopher/ mathematician Pythagoras and his contribution to early music theory. “He tried to measure music in terms of numbers.”
Music of the Spheres
Richeson also invokes Pythagoras in his mathematics classes. “He thought the way to the divine was through mathematics and believed the ratios of whole numbers were very important to everything, including music.”
Pythagoras even believed that the planets and stars moved according to mathematical equations that corresponded to musical notes. Ludwig Wittgenstein, a later philosopher who also valued music, gave Principia Mathematica, a tome on the foundations of mathematics, his highest praise, claiming “it was like music.”
It’s helpful to have an open mind about the two disciplines and acknowledge the concrete and abstract qualities of both, says Jeff Rodgers, one who nimbly skips between math and music. “People might think math is ordered and music is expressive, but I can make examples for both. In music, the baroque period has a strict set of rules that everyone follows. Math is seen as being strict and ordered with integers, but you can describe structures in math that you can’t imagine, that are three-dimensional.”
Blyth, too, encourages the practice of boundary blurring. “I don’t believe in keeping humanities and science exclusive. Science is the search for truth, and high-end art does the same. We’re always in search of an answer.”
Carolyn Bryant Jennifer Blyth Robert Pound