Using musical ear-training exercises, in conjunction with Lissajous figures, we will establish the simplest ratios for the frequencies of the major scale. We will call this scale the musician’s scale.

Then we will proceed to use strings and pipes to arrive at the harmonic series, which we will call the physicist’s scale. We will show how the I, V, and IV harmonies pervasive in Western music emerge naturally from our analyses with live piano performances in classical music and jazz.    American Association of Physics Teachers (AAPT) Plenary