Interesting article

[Richard Brekne]

> >Now to the other subject of single strings exhibiting a difference of pitch
> >from three strings which are tuned identically. In my studies, I found
> >that this difference exhibits itself more in the 5th and early 6th
> >octave on the piano and not as much elsewhere. I have not found 1 and 2
> >cent variances as some have claimed. What are your findings? I find
> >greater differences between the pitches of the prompt sound and the
> >later decay sound (the TuneLab shows this quite clearly). It is easy to
> >confuse these two sources.
> >
> >Jim Coleman, Sr.
>

One thing to keep in mind in all this speculation is that there are a few
details that are known about coupled strings. We know that two strings which
vibrate in a theoretically assymetrical mode will have a canceling effect
regarding the force exerted by either on the bridge. This would result in an
infinitly rigid bridge response which in turn will result in very long and even
decay. Since one string vibrating by itself is neccessarilly more symetric then
two strings very close to one another on the bridge and vibrating at the same
frequency (or very nearly so) it is to be expected that a single string will
have a much quicker decay rate then two such coupled strings. Now this is
relative to sound level but this may also influence this buisness about
frequencies lowering slightly in coupled strings. There is an impedance variance
in the bridge as seen from each individual change from a non coupled to a
coupled situation. The so called killer octave is also the area of the piano
with the least degree of sustain if I understand things correctly, so we may
actually be dealing with an area in the scale that for some reason has the least
amount of coupling affect. (as seen from how coupling affects sustain and sound
level)  Increased coupling results in greater sustain and more even decay, and
perhaps less variance in frequency throughout the decay.

If this is so then the only questions would be why this is the case, and what to
do about it. It might be interesting to play around with both increasing and
decreasing the coupling capacity of unisions in this area and see what happens
in each different case.

musing a bit on Sunday afternoon... grin.. Its been a beautiful springy day in
Bergen.

--
Richard Brekne
Associate PTG, N.P.T.F.
Bergen, Norway