Vance, Good point. Overtones are a bitch. And very uncooperative given that they aren't in equal temperament, or even the same going up or down. There is only one really fixed relationship the octave is the first overtone and the dominant one, and is double the frequency of the tonic. The fifth, then the next octave, then slip in the third, but by now the integer relationships are slipping a bit.
Harmonic resonance is another bitch. Yet it is that that differentiates the instruments. It is best described in the woodwinds and brasses, the characteristic tone comes to a great extent from the particular part of the overtone series that is emphasized, and sometimes that is one that isn't in the equal tempered scale. I'll not go into it, all the music graduates on this list know it, but simply stated the goal of the modern instrument is compromise. Comprimise between the physics of the actual overtone sequence and our perceived scale. The strings don't know that compromise and may vibrate sympathetically according to the laws of nature. We'll not avoid it until we can convince nature that four perfect fifths should equal two octaves. I don't expect to be able to do that. Until then we either compromise or play the violin. Best, Jon
