Power of Mathematics Opens New Possibilities in Music

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Steve Koppes, University of Chicago writes, "Anthony Cheung’s formal mathematical training essentially ended with high school calculus. But as a musician and composer, he has explored mathematical phenomena in new ways, especially through their influence on harmony and timbre."

Composers found new ways of fusing the two musical qualities late last century, says Cheung, assistant professor in music. “Through technology and thinking about acoustics, we can change sounds on the computer in innumerable ways,” says Cheung, whose musical composition earned him a 2012 Rome Prize from the American Academy in Rome.

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The work of Cheung and others shows the power of mathematics to open new possibilities in music. Modern experiments with computer music are just the most recent example. According to musician-scholars like Eugenia Cheng, a visiting senior lecturer in mathematics and a concert pianist, the history and practice of music would have unfolded much differently without an appreciation of what unites music and math.

During the Baroque period, a mathematical breakthrough inspired one of Cheng’s favorite composers, Johann Sebastian Bach, to write The Well-Tempered Clavier (1722), his book of preludes and fugues in all 24 major and minor keys.

Expanding an audience for math
As an educator, Cheng is adept at relating just about anything to mathematics, including food. She developed a series of YouTube lectures on the mathematics of food, covering topics such as “The perfect puff pastry,” “The perfect Mobius bagel,” and “The perfect way to share a cake.” The series evolved into a book, How to Bake Pi, which will be published by Profile Books in March 2015. She also has brought mathematics to a wider audience through works such as the mathematics of cream tea, the mathematics of pizza, and mathematics and Lego. 

Mathematics of musical composition 
Cheung is a composer and musician who readily describes how an understanding of mathematics often can lead to a deeper appreciation of certain musical compositions.

In graduate school, Cheung studied with Tristan Murail, now a professor emeritus of music at Columbia University, who pioneered thoughts about how harmony and timbre could come together. Cheung cites Jonathan Harvey’s Mortuos Plango, Vivos Voco (1980), as a classic early example of doing this electronically. In this work, Harvey used spectral analysis and re-synthesis on a computer to morph the sounds of the tenor bell at Winchester Cathedral into the sound of a singing boy, his son.
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Source: The University of Chicago and The University of Chicago's Channel on (YouTube)