Learsfool,
The basic difference in timbre between a flute and a violin, to use your example, is that one is made of metal and one is made of wood, not to mention the fact that their sounds are created in a completely different manner as well. This is obviously the largest factor in the difference in timbre. Without going into the science of it, waves produced by a string behave very differently from waves produced by a tube. A tube with one end closed behaves differently than one open at both ends, and conical and cylindrical tubes behave differently as well. Side holes in the tubes have their effects as well, of course. Not to mention different types of wood or metal alloys used in the instrument's construction, which have very great effect on the timbre.
I think that in order for our understandings to converge, what is needed is a description of the differences in spectra that RESULT from the differences you are describing. Although I'm not sure that any of us can provide that without further research. I may try to do some research on that if I get a chance tonight or tomorrow.
If a violin and a flute were to play notes having the same fundamental frequency, the same volume, and the same duration, and if their respective notes as captured by a microphone were fed into a spectrum analyzer (a device which shows the frequency components of a signal, and the amplitudes of each of those components), what would the differences be between the two spectra, that account for their very different sounds? That is the key question, as I see it.
Electronic distortion cannot introduce or create new harmonics, it can only distort those already present.
Although it may not have been your intention, this statement would seem to imply that a distortion component at a given frequency would not be added by the system were it not for the presence in the original sound of a harmonic at that same frequency. Which is not the case, as I and Kijanki (whose post I am in full agreement with) indicated.
Although some of these various timbres are more acoustically complex than others, the overtone series for all of them is always the same - it doesn't matter what instrument is creating it.
Their frequencies are always the same, for a given fundamental frequency. But the amplitudes of each overtone in the series will be very different for different instruments.
The flute happens to be one of the purest instrumental timbres.
Yes, which I think corresponds to its notes having less harmonic content than in the case of most other instruments. I.e., its notes come closer to being a pure sine wave than those produced by other instruments (although of course they are still considerably different than a pure sine wave). Which I think is a basic reason that a flute, when not well recorded and reproduced, can often tend to be "hard" sounding.
Another word on the audibility of these harmonics....
To clarify, I certainly do not assert that individual harmonics are readily perceivable. What I believe is that differences in harmonic structure (the amplitudes of the harmonics, relative to the amplitudes of other harmonics and to the amplitude of the fundamental) are the primary determinant of timbre and tone. Therefore when we perceive differences in timbre and tone, we are perceiving the EFFECTS of differing harmonic structures.
Best regards,
-- Al