Stretch Vs.Temperament, (was Beat Rates)

[Richard Brekne]

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