[CAUT] pre-stretching new string?

[Richard Brekne]

I agree that the numbers do not support the idea of rise and fall of 
soundboards accounting for more then a basically negligible amount of 
pitch change. Not only does the vertical displacement necessary for such 
a change need to be very much larger then we could possibly observe in 
real pianos... but even moderate vertical displacement changes are 
accompanied by changes in downbearing to large for the piano to handle.

The idea of bridge surface swelling and forcing the strings up the pins 
and thereby increasing this segments length by virtue of the increase in 
offset angle the string takes through the pin is interesting... but I 
would like to point out that if this is to account for pitch changes... 
then there are two things that simply must be admited.

First.. one must admit that strings can indeed climb up bridge pins.  
Secondly one is forced to admit then that there would be a very uniform 
graduated affect in pitch change directly related to the overall length 
of the string.  Basically this means that any change in the effective 
height of the bridge surface that is within reason will have virtually 
no effect on long strings and the shorter strings would be very much 
effected. 

On top of this you still have the problem presented by the increased 
downbearing that accompanies any given increase in vertical deflection. 
It matters not whether this deflection comes from a rise in the 
soundboard or a swelling of the bridge cap.  You simply cannot expect 
the soundboard assembly as a whole to support more then very very 
moderate levels of string deflection.

I posted the math needed to do figure this... math approved in personal 
correspondance with Dr. Alexander Galembo and myself.. so there should 
be no reason to question it.  And it is not just simple trig... one has 
to take into account the change in tension that occurs for a given 
change in deflection all else being equal... and to do that you need to 
know how to work in the strings elongation into the thing..  you need to 
work Hook's law into the thing.. according to this the change in tension 
will be equal to  Youngs Modulus X the cross section of the wire X the 
change in the strings length / the origional length.

The <<simple>> trig will only get you the change in length... nothing more.

Cheers
RicB