Ron Nossaman wrote: > > > Yes and no. If their oscillation period is the same, one will lag, the > other will accelerate, and they will synchronize. In a system with no > damping in the shared flexible termination, they would oscillate back and > forth, but there's enough damping in the system as seen in the piano, that > they converge and stay there. Hmm... I am not sure just how much of a shared flexible termination the bridge represents here. At least in every textbook example in front of me the shared termination for two such oscillating systems is exactly that... the exact same spot. The most similar (visually) to this would be the hitch pin.. but that is a different matter entirely. The actual terminations of the two strings are separated by say 5 mm space, and do not share the same bridge pins at all. Slight variations in bridge of many sorts can influence the situation as well. I would tend to think that the bridge does not entirely conform to the shared flexible termination for coupled oscillating systems, though perhaps it nearly does so. Another point would be that the systems (the two / three string segments comprising a unison) themselves do not always behave identically as separate oscillators if left to themselves. Their behavior is inconsistent enough to cause phasing inconsistencies that would not be uncommon. Perhaps that partially explains why sometimes strings seem to quickly go into phase, and sometimes not, or for that matter appear to sometimes move in and out of phase ? The experiment you refer too was interesting though, and I would like to what would happen if one started methodically muting off different back scale segments to see how coincident partials as opposed to otherwise, effect your results. RicB
This PTG archive page provided courtesy of Moy Piano Service, LLC