Robphy said mentioned the boundary conditions of a string and a drum, citing the boundary conditions of these things as a reason why spherical instruments aren't as common. You subsequently endorsed his comment. If boundary conditions are the important factor, why is a sphere any less useful...
Surely predictable/manipulatable harmonics depend upon symmetry - hence why pretty much all resonant instruments exhibit it. It just seems to me that a perfectly-symmetrical shape is the perfect candidate for an instrument dependent upon harmonic properties. As for boundary conditions, I'm sure...
When it comes to waves, spherical harmonics are, like, da bomb. I'm no expert - probably obvious from the question - but it seem to me that an instrument which maximises the utilisation of harmonics/resonances would be spherical.
And yet, I can think of no spherical instruments - the most...