Smith-Coleman/QUESTION

[A440A@AOL.COM]

Greetings, 
Jim writes:
>> >The effect of unisons changing as the 2nd and 3rd strings are pulled
>in  a a phenonemon which applies more to the 5th and 6th octaves than in
>the temperament octave according to measurements which I have taken. Even
>in that range, on some notes the change is almost negligible.
 
  Umm, me too.  I am guessing there are other things happening than the 
soundboard going down.  The following are just some points for consideration, 
add to it or prove me totally wrong here and I will thank you for it. (:)}}  
(I am aware that the various modes of transverse vibration don't model 
easily, and longitudinal vibrations are beyond this simple attempt to 
translate knowledge into tuning hammer behaviour.)    
     There is a "relative impedance" between strings.   The strings are 
coupled at the bridge, thus, they are entrained. When you have unlevel 
strings, the resulting difference in the strings' amplitudes  causes them to 
seek a common one, and they trade energy back and forth in an attempt to do 
this, going in and out of phase with one another while hunting a stable 
relationship. These changes in phase must be done by changing speeds, and we 
hear that as the out of phase "whine"  which is the hallmark of out of level 
strings.  
     Another factor is that the rigidity of the terminus affects the pitch of 
the string. ( I believe this is covered in Askenfelt's 'Five Lectures")  A 
flexible termination ( like a limber bridge) allows the string to behave as 
though its final termination is somewhat longer than the measured length.  An 
extremely rigid bridge forces the string to begin its vibration just short of 
the actual length, effectively causing the string to behave as though it is 
shorter. 
    Gabriel Weinriech has demostrated that the strings are linked and 
affective upon one another in the unison.   That the local rigidity of the 
bridge can be affected by the alignment of the unison's frequencies, 
stiffening  when they are180 degrees out, and allowing flexibility when 
synchronized.   
    Does it follow that tuning the strings of a unison changes the relative 
impedance(in the very localized area of the trichord) of the bridge as it 
progresses through the three strings?  Cobbling this all together, could the 
tuning of the three strings change the effective rigidity, and thus the 
effective lengths as one goes through them?    And that these changes must be 
aurally controlled?  I can believe it, but  I don't know.   
    I often am able to erase a falsebeat by placing one of the trichords 
strings in a place my machine would NEVER tell me to go.  And I get my 
cleanest, most sustaining unisons when I place one of the three strings by 
aural means along with the two others that stopped the lights on my SAT.  
Others? Thoughts? 
Regards, 
Ed