The sound of a kettledrum is unmusical. Why?
Dear student,
In drums, a circular membrane stretched over a hoop, when you solve its equation of motion, the resulting natural frequencies do not yield pretty integral ratios. The natural frequencies are the roots of Bessel Functions, which have a ratio like 1 : 1.59 : 2.14 : 2.40... This doesn't add up too beautifully and the resulting waveform is nothing but a haphazard function having no distinct pitch to it, nor any pattern.
Regards
In drums, a circular membrane stretched over a hoop, when you solve its equation of motion, the resulting natural frequencies do not yield pretty integral ratios. The natural frequencies are the roots of Bessel Functions, which have a ratio like 1 : 1.59 : 2.14 : 2.40... This doesn't add up too beautifully and the resulting waveform is nothing but a haphazard function having no distinct pitch to it, nor any pattern.
Regards