Turning math into music

Standing in his office beside a white board scrawled with equations, Sean Hardesty lifted a violin to his shoulder and played the opening of the Sibelius Violin Concerto.

His instrument has an angular, asymmetrical body painted black and red and was built of balsa wood and carbon-fiber laminates by a boat designer in Maine. Its sound in his Duncan Hall office with the door closed is piercing and precise.

“This is an experimental violin,” said Hardesty, a postdoctoral research fellow and lecturer in computational and applied mathematics (CAAM). “It’s a work in progress, not a finished product. I think it sounds pretty good.”

Hardesty distills sound to its mathematical essentials; he is working to design violins by applying the tools of optimization to shell structure acoustics.

“Sean is working at the intersection of mathematics, music and materials,” said Matthias Heinkenschloss, professor and chair of CAAM, and Hardesty’s former Ph.D. thesis adviser. “Specifically, he is developing mathematical and computational tools to model and ultimately design violin.”

For Hardesty, the well-documented relations between music and mathematics have been a living fact since childhood. His family was casually musical. “My mother put a violin in my hands when I was 2 or 3 years old,” said Hardesty, who began taking lessons at age 5 and continued through high school, when he began thinking about the physics of musical instruments.

“I realized in college that I was more interested in violin physics than in quantum physics,” he said.

SEAN HARDESTY

Hardesty went on to earn his B.S. in physics from the California Institute of Technology in 2004 and his master’s degree and Ph.D. in computational and applied mathematics in 2006 and 2010, respectively, from Rice. From 2007 to 2009, Hardesty played viola with the Doctors’ Orchestra of Houston, and until 2011, he served as the group’s principal violist.

For a decade he has been a regular participant in the acoustics workshops sponsored by the Violin Society of America (VSA) and has built a violin top using a mathematical model he devised and state-of-the-art 3-D printing technology. During a recent VSA gathering at Oberlin College in Ohio, Hardesty played a Stradivarius, often judged the instrument’s sonic ideal.

He noted that the Stradivarius violin known as “The Hammer,” which sold at auction for $3.54 million in 2006, was built in 1707, the year Swiss mathematician Leonhard Euler was born. “You could easily be tempted to believe that violin making is one of those rare fields of human endeavor that has become drastically worse over the last 300 years. But this view undervalues the best contemporary traditional makers and leaves nothing for the future,” he said.

Hardesty, like other avant-garde violin designers and builders, intends to challenge the supremacy of the “Strad” and other traditionally designed instruments. “With the violin, there isn’t a best sound. It depends entirely on the taste and skill of the player,” he said.

Key to the sounds produced by a violin is the resonating top or soundboard, which turns the energy of the vibrated strings into the instrument’s distinctive voice. Hardesty’s task is to turn a player’s subjective reactions to that sound into the mathematical essentials that produced it.

“Every instrument is different,” said Hardesty, who would like to customize instruments to the precise tastes of their owners. “You always get something and then you lose something. Most professional players end up making tradeoffs, one quality for another.”

At the opposite end of the skill spectrum, Hardesty also foresees designing and manufacturing inexpensive but comparably sophisticated violins for students just beginning their studies.

“I would really like to make it possible for more people to play the violin, and to play it well and produce a good sound,” he said. “I know how much pleasure I’ve derived from making music and listening to it all my life.”

— Patrick Kurp is a science writer in the George R. Brown School of Engineering.