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