yes, the only factor in sound production which governs the color or 'timbre' of a sound is the presense or absence of overtones and their relative strength or weakness in relation to the fundamental tone. Overtones give a sound its characteristic quality. So all instrumental sounds are combination sounds, consisting of a predominant tone and various overtones, harmonics or 'upper partials'.
So for example, they can vary from the simple mellow flute sound (a predominant tone with very few quiet harmonics) to the strident muted trumpet (with strong upper partials) or to the cymbal clash, with its harsh jangle of dissonant tones and overtones.
I hope this clarifies my question.. I'm not sure if there is a definite, or accepted way measure this... or, again, if there are any orchestration books that make any serious notes of it, because most of what I have read only briefly mentions such things.