Often, abstract ideas can be more easily understood when translated into visual terms. Either through teaching duties, or through ordinary curiosity, I often put together visualizations of one sort or another. Here are a few of them. For now the focus is on sound-related visualizations, mainly because they are of use in my acoustics course, but in time I'll develop a broader family of them.

Just intonation

An audio-visual demonstration of just intonation of the musical interval of a perfect fifth, and the imperfect approximation allowed by the twelve-tone equal-tempered scale. I expect to update this visualization soon to add fourths, thirds, and sixths.

Transharmonic glissandi

Spectrographic exploration of harmonicity (a tool that our brains use to associate pitches to complex waveforms) being slowly broken and restored.


Fourier synthesis of a sawtooth wave, modulated by formant resonances such as those in the vocal cavity that give rise to the perception of vowel sounds.

Resonances of an ideal rope

An ideal rope is fixed at one end, and swung at the other, at an adjustable frequency. The resulting standing waves have maximum amplitude for certain resonant frequencies and weaker amplitude for others.

MTW-style Inner Products

A graphical representation of the inner product of a vector and a one-form.