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Volume 22, Number 9 — September 2014

James Warden's thoughts on Math and Music

James Warden
James Warden

By Leslie Grace | A! Magazine for the Arts | February 27, 2013

James Warden is a retired physics professor, who taught at Emory & Henry College for more than 20 years. He began writing songs about 10 years ago as a hobby. One of his songs was played on "Car Talk" and others can be heard on WEHC-FM. He plays the piano and guitar.

"Humans are hard-wired to recognize visual and aural patterns. Any pattern has a mathematical basis and can be either analyzed or simply appreciated according to one's purpose in recognizing it. The scientist in me would find it difficult to imagine a reality where mathematics does not provide the underlying structure.

"The Western "equally tempered' scale is based upon a logarithmic order of pitches (or frequencies). Additionally, the vibrations of a string or air column include many harmonics that give the particular instrument its tonal quality. You can use a mathematical technique called Fourier analysis to identify the harmonics and build a synthesizer that mimics the original instrument. Finally, the mathematical "circle of fifths' illustrates the relationship of different musical intervals.

"Patterns and repetition are important elements to both mathematics and music and creativity is important in both.

"I suspect that many people remember only their grade school mathematics, which required memorizing tables or formulas. Creating useful mathematical models for a physical or biological system, or coming up with new approaches to prove a theorem, require a significant amount of creativity, analogous to finding a new theme for a symphony.

"I lament that less than half of my college students have ever studied music. I believe that studying a musical instrument can help one appreciate music listening and can provide stress relief from other pursuits. In informal conversations with students, I know that serious mathematics students often have a musical background as well. One science teacher in my summer course who plays guitar was amazed and pleased to find out how to calculate fret positions on the guitar neck. So these little bits of insight surface occasionally.

"Learning more about the relationship between music and mathematics is more of an enhancement than a need to know. Exploring the connection can expand a curious person's appreciation and enjoyment of both areas."

>> THERE'S MORE: The Mozart Effect.


Topics: Music