Limit to music

A friend said to me is there a limit to the amount of music that can be made? Well fundamentally it depends on what he means by music because you could change one note and it'd be different. So lets concentrate on melodies. Is there a finite number of melodies?

Very recently a result was proved about drums(or rather, a connected bounded circular region in R^3 with smooth boundary)

If two drums produced the same sounds(in terms of eigentheory), then they would have the same heat diffusion rate.
Hence since there are uncountably many possible diffusion rates, they are uncountably many possible sounds and hence uncountable amount of music possible.