What is the relationship between music and math?

Music is richly mathematical, and an understanding of one subject can be a great help in understanding the other.

Geometry and angles

My masters thesis is devoted in part to a method for teaching math concepts using a drum machine organized on a radial grid. Placing rhythms on a circle gives a good multisensory window into ratios and angles.

Wave mechanics

The brain turns out to be adept at decomposing sinusoids into their component frequencies. We can’t necessarily consciously compare the partials of a sound, but we certainly do it unconsciously — that’s how we’re able to distinguish different timbres, and is probably the basis for our sense of consonance and dissonance. If two pitches share a lot of overtones, we tend to hear them as consonant, at least here in the western world. There’s a strong case to be made that overlapping overtone series is the basis of all of western music theory.

The concept of orbitals in quantum mechanics made zero sense to me until I finally found out that they’re just harmonics of the electron field’s vibrations. I wasn’t at all surprised to learn that Einstein conceptualized wave mechanics in musical terms as well.

Logarithms

Octave equivalency is really just your brain’s ability to detect frequencies related by powers of two. The relationship between absolute pitches and pitch classes is an excellent doorway into logarithms generally. You also need logarithms to understand decibels and loudness perception.

Symmetry

Music is really just a way of applying symmetry to events in time.  See this delightful paper by Vi Hart about symmetry and transformations in the musical plane.

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