In the Music Animation Machine’s bar-graph display, different intervals between pitches are shown as a distance. This means that an octave (two notes twelve half-steps apart) looks about the same as a minor ninth (two notes thirteen half-steps apart). And yet, these two intervals sound very different; what accounts for this difference?
A big part of it has to do with the interaction of the harmonics of the notes. To explore this, I wrote a program that shows the harmonics of two notes, and lets you change the interval between them, so that you can hear what happens as the harmonics interact :