Stretch Vs.Temperament, (was Beat Rates)

[Richard Brekne]

Ron Nossaman wrote:
> 
> >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.
> 
> Nothing is ever entirely anything, and if it has to be to be valid, then
> nothing is ever valid. I'm so glad we could clear this up so quickly and
> cleanly and get it out of the way. Thank you.

Exactly, and THAT is why the question IS whether or not the
piano bridge represents enough of a shared and damped
flexible termination to justify the claim of inevitable
synchronization of the two string segments oscillations and
thereby serve as a way of refuting arguments presented in
the Five Lectures by Weinreich, amoung others, to the
contrary. And the secondary question remains whether the
strings oscillate in a consistant enough fashion to begin
with. Enough deviation from the ideals and we have what many
claim to observe... non synchronous oscillation. Certainly
not entirely all the time...perhaps not even entirely most
of the time, but enough of the observable circumstances to
give credence to their claims.

> 
> >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 ?
> 
> I don't partially think they sometimes seem to go in and out of phase
> unless they are mostly not in tune in the first place, or there's a false beat.

I see. So what are we saying here ? That when the strings
behave as tho they were ideal oscillating systems sharing
and ideal damped and shared flexible termination they behave
as such ? With all the falsness in the average good quality
piano, it would seem to me like we are bound to accept a
good deal of exception to the synchronous "rule". 

> 
> >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
> 
> Nothing's stopping you, either now or the last time we discussed this.

I have experiments of my own going. Just thought I would
throw out a friendly spirited idea. No offence meant.

> 
> Ron N

Cheers !

RicB