Seasonal pitch change:

[RicB]

Hi List

I see I sent the wrong post, a copy of one earlier sent. Please excuse. 
What I meant to write was the following.


I've been running some numbers and thinking a bit about this traditional 
idea that vertical deflection of the strings is the main cause of pitch 
change and thought some of you might find this interesting.

Given the following string lengths, all with identical back lengths 
(50mm), and lengths from front termination to tuning pins (200mm) (to 
make the example simple) and assuming a 1 mm string deflection as the 
starting point for all strings (also for simplicity) and calculating for 
a roughly 50 cent pitch rise we get:

A string length of :

1400 mm needs 6 mm additional deflection which results in about 22 lbs 
of downbearing.
1000 mm needs 5 mm additional deflection -->19 lbs downbearing
800 mm needs 4,5 mm additional deflection --> 18lbs downbearing
500 mm needs 3,5 mm additional deflection --> 15 lbs downbearing
250 mm needs 2,5 mm additional deflection --> 13 lbs downbearing.
100 mm needs 1,75 mm additional deflection --> 13 lbs downbearing
50 mm needs 1,2 mm additional deflection --> 13 lbs downbearing.

As you can see neither the amount of deflection needed to exact the 
actual 50 pitch rise to begin with, nor the resulting downbearing 
figures are within reason... which leaves one no choice but to admit 
that something else is primarily responsible for seasonal pitch change.

Its also good to note that if we are starting with a 1 mm deflection to 
begin with.. which btw yeilds reasonable enough string deflection 
angles, then the absolute most downward pitch change possible is when 
the panel flattens out and bearing becomes 0.  In this case the same 
string lengths yeild :

1400 mm length --> -1 cent
1000 mm length --> -1,4 cent
800 mm length --> -1,7 cent
500 mm length --> -2,4 cent
250 mm length --> -4 cent
100 mm length --> -7 cent
50 mm length --> -10 cent

These examples are simply illustrative of the kinds of things that 
actually has to happen if the soundboard rise and fall is to account for 
most of the pitch change.  I apply all the resulting change on the 
speaking length itself and do not account for any friction.  This is a 
best case scenario. In reality the string will disperse some of any 
change in tension caused by a change in vertical deflection... lessening 
the frequency change and resulting downbearing... but necessitating even 
more vertical change for any give change in pitch.

I can not help but conclude... looking closer at the consequences.... 
that vertical rise and fall of the soundboard simply doesnt have much to 
do with the seasonal pitch change at all. 

Tension change, and hence pitch change can come from an altering of the 
relative positions of end points to each other... i.e. hitch pin and 
tuning pin.  Pitch change can also happen without tension change if the 
speaking length is somehow altered.  Seems to me that ruling out 
vertical deflection... one has to look to these to general conditions 
for the explaination.

Cheers
RicB