I'm far from a musical expert, but I thought this was essentially how many instruments work: Each string/hole/whatever produces a different resonant frequency which is orthogonal from the others the instrument produces; therefore any combination of strings/holes/whatevers creates a sound that cannot be created by any other combination of strings/holes/whatevers.

Please, correct me if I'm wrong.

Edit (before someone nitpicks, I'll do it!): I'm aware interacting with instruments doesn't produce _only_ resonant frequencies; and that the off-resonance is what gives an instrument its characteristic sound, even when playing the same note as a different instrument.

That is exactly correct, for wind instruments at least: and in fact, some wind instruments have more than 10 holes or keys. But many combinations produce identical sounds, limiting the range of the instrument. The limiting factor on a wind instrument is the fact that it can only play a single note, (yes, with resonant frequencies, of course) and the length of the instrument, which determines the lowest note it can play.

Thanks for that. A little more to slow burn in my understanding of instruments before I eventually learn one!

The problem is the 88 keys don't just produce 88 notes. The combinations also produce unique sounds. Of course there aren't 88! factorial combinations in practice, but you couldn't get the necessary range from 8 keys.