By taking into account the distribution of the characteristi

By taking into account the distribution of the characteristic frequencies of a vibrating circular membrane and a string, can you justify why/why not a “drum could be less musical than a violin”?

Solution

A drum make a sound with a mix of frequencies that are not necessarily integer multiples of the lowest freqencies.

It can have several \"fundamental\" frequencies because the amplitudes in a mix that makes a particular drum sound do not necessarily neatly decrease with frequency.

A drum membrane vibrates in two dimensions, and it is typically circular. So vibration length along any path in 2D is not restricted to multiples of the shortest path, and paths of \"irrational\" length are introduced.

This is unlike instruments such as wind or string instruments (which we do find musical and are harmonic) where the vibrating element is one-dimensional and the resulting sound is a mix of a fundamental frequency with frequencies that are integer multiples of it (harmonics), with a decreasing amplitude as the multiplier increases.

So, a drum could be less musical than a violin.