Music And Math

Stupid Question ™
May 22, 2003
By John Ruch
© 2003

Q: I keep hearing that music has a lot of mathematical elements. What exactly about music is mathematical?
—Dawn Delfin


A: The succinct answer from Robert Peck, a music theory professor at Louisiana State University: “Music per se is not mathematical.”

Music-as-math is simply a metaphor that is only applicable under certain restricted definitions of “music” and “math.” It’s often invoked to “prove” the supposed intellectual superiority and/or utility of classical music.

Music, as a physical and technological phenomenon, is highly susceptible to mathematical analysis. In a common logical error, many people mistake the mathematics of the analysis for the music itself. As William Brooks of the University of York pointed out to me, music is no more (or less) mathematical than the phases of the Moon—another subject of much math analysis.

The analysis is real enough. Music is sound and can be measured and calculated as such. Every guitar is a lesson in wave harmonics and the ratio between a string’s length and its tone.

Almost all music “measures time,” as Brooks puts it, and this is often calculated mathematically, from time signatures on up. Intervals and pitch are now subjected to complex higher math such as number theory, group theory and topology, all to see how compositions work and to suggest new ways of writing.

But, as Edward Rothstein noted in his music/math book “Emblems of Mind,” attempts to reverse-engineer mathematical music (as by Bartok or the modern composer Milton Babbitt) are often not meaningful, musically speaking. The math tricks can be detected in the score, but not heard by the ear.

Musical physics are real. But the musical system of tones, scales, chords and so on used to organize sounds is a cultural choice, not a mathematical fact. The math analysis itself is often culturally determined. Math-heavy music theory only began about 50 years ago with the rise of computers.

When probed, the math/music metaphor usually proves thin and comes down to the platitude that both mathematicians and musicians are in search of Beauty and Truth. The metaphor has its roots in ancient Greece, where music and math were both considered ineffably True, and literally related to moral and spiritual states. Few people believe such a thing today, but the metaphor remains.

There are good reasons it remains powerful. Math and music are both mysterious and intangible, both real and unreal. It’s natural to feel like their mysterious powers might have a common source.

We may also process them neurologically in similar ways. People who have studied both subjects often remark that playing and calculating have the same “feel.”

There is also the oft-sensationalized “Mozart Effect” found in studies by California’s Musical Intelligence Neural Development (MIND) Institute that linked music to a boost in spatial/temporal thinking.

MIND noted that spatial/temporal thinking is “useful” in math, music and chess—and its results are often used to bolster the old math/music connection. Left unsaid is that spatial/temporal thinking is also useful in less intellectual pursuits such as sports, construction and truck-driving. So why don’t we spread the word that music is athletic?