This is fantastic! Bessel functions != music.
Originally shared by Larry Phillips
Why drums do not sound musical
The animation shows the first two vibration modes of a drum head. The net motion is the sum of these motions (plus still higher order modes). The frequency of the second mode is 2.3 times that of the first.
By contrast, when a string vibrates, each mode’s frequency is a multiple of the lowest order mode. To the human ear, the resulting tone has a pleasing, “musical” sound. The frequencies of the drum’s sound are not multiples of each other.
Mathematically, the difference is due to the fact that string vibration modes are made up of sine waves, which are periodic. The drum vibration is based on Bessel functions, which are not periodic.