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Mathematical Models, Computational Techniques, and Music

Music technology is already well on the way to future applications, like a "musical Google" in which the user can retrieve music files from the Internet simply by humming a melody or providing an audio sample.

As the demand grows, so does the complexity of the software to generate, manipulate, process, store and retrieve digitally encoded music.

Operations research offers much to music computing researchers such as pianist/engineer Elaine Chew, a 2007-08 Radcliffe Institute Fellow and associate professor in the Daniel J. Epstein Department of Industrial and Systems Engineering and the Ming Hsieh Department of Electrical Engineering at the University of Southern California.

In her paper Math & Music: The Perfect Match, Chew described the advantages of an operations research approach to solving computational problems in music composition, analysis and performance.

Operations researchers use mathematics and computing tools to model complex problems in fields ranging from advertising to zoology in order to find optimal or feasible solutions. To model, study and assist humans in what they do in analyzing, composing, and performing music is a natural next step, Chew said.

"The field of music and computing has experienced unprecedented growth in recent years, spurred on by the pervasiveness of computing and widespread access to digital music information," Chew said. "Mathematical representations of music allow music knowledge to be encoded in computer-friendly terms, so that music computing researchers can design software to help us process and understand complex and vast amounts of music information."

Chew cited two music technologies already on the market: Shazam and Pandora.

Shazam allows users to retrieve details of a music recording based on an audio example that is dialed-in over the phone. Pandora will suggest new songs based on the user's current favorites. Interactive music games, in which a user might take on the persona of a rock star, are a perennial favorite.

Beyond the market-driven motivations for music and computing, mathematical and computational tools applied to music can help researchers discover important knowledge about human culture and creativity, including insights into how composers and performers experiment with, and decide on, new ideas. These scientific processes and discoveries are expected to impact fields such as musicology and neuroscience.

The article presented resources for learning more about this emerging field of mathematics and computation in music, including venues where music computing researchers convene and publish.

The article also cited open courseware and selected examples in automated music analysis, music composition and improvisation, and expressive performance, based on research projects at the USC Viterbi School of Engineering's Music Computation and Cognition Laboratory as well as related work.

A computational scientist on leave from USC, Chew designs mathematical models and computational techniques to analyze music and its performance. As a pianist, she performs a wide range of contemporary, eclectic music.

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