Seiji Iigaya
8th Grade, Tenafly Middle School
Tenafly, NJ
Modeling Violin Expression: Timbral Dynamics at the Instability Boundary
Seijiís violin teacher wanted him to play with more expression, and Seiji wanted to know which sound was most expressive. He modeled a violin string, and measured variations in bow speed and pressure. He found that expressivity of sound was highest right before the sound waveform became unstable.
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Project Background
Seiji plays the violin and has been trying to play with more expression. “I have been getting better at it, but I still don’t quite understand how exactly it’s done,” Seiji says. Expressivity, after all, is subjective. The key might be in the stability of the sound, a combination of the bow’s speed and the pressure on the string. Seiji suspected the most expressive playing would be close to unstable. He decided to develop a mathematical model to find out which pressure and speed produced the most expressive sound.
Tactics and Results
Using the programming language Python, Seiji simulated a violin string. He divided it into 100 potential points of interaction between the bow and string. He then calculated a range of bow speeds and bow pressures. Each combination would produce a slightly different sound waveform, and he could calculate the expressivity and instability index of each one, based on the desirable solo tone of a violin, which is brilliant and has a lot of sound spectrum variation. Seiji’s expressivity index measured the variability of the sound waveforms, while the instability index measured how much the waveforms overlapped. He found that expressivity was highest at the moment right before the waveform became unstable, and that there is a small zone in pressure and speed where the sound is most expressive before it becomes unstable.
Beyond the Project
Seiji of course plays the violin. “It allows me to express myself in a quiet space,” he says. Over the last two summers, he’s also been playing Japanese chess, or shogi, in Japan. “It’s similar to playing the violin. I get to express myself. But there is also an opponent,” he says. He also enjoys contributing to citizen science on Zooniverse, an online citizen science platform, where he has worked on a project that asks visitors to the site to classify images to help scientists do research on asteroids. Seiji would like to become an astrophysicist.
