Fourier analysis indicates there is a huge space of timbre, but not necessarily a rich one. In my experience while timbres can be annoying, they aren't wrong like a an arbitrary harmonic progression is. Harmony being such a minefield is what makes its space so rich.
Ah, I see what you mean. I guess you can think of timbre as a mixture of dynamics and a very simplified version of harmony in which you can only have intervals of an octave.
you can have fifths and thirds too I think... you can pluck those harmonics on a single guitar string.
I don't know if any other intervals are possible as harmonics... perhaps the ratios for other intervals are too big to make it practical, they are too weak to sound
