Seasonal pitch change: was -- Long term pitch drop, was: Type O

[RicB]

Hi folks

I have a feeling that whats not being taken into account for is exactly 
what one can expect from a given vertical deflection change of the 
string at the bridge. It matters not whether this vertical deflection 
comes from the bridge swelling, or from a soundboard rising, or from any 
combination of these. 

The point is that given usual design string deflection numbers, usual 
string lengths and diameters, significant changes in frequency due to 
changes in vertical displacement carry too high a price in terms of 
change in downbearing to be realistic.  At least thats what it looks 
like to me.

Anyone interested is calculating change in frequency, downbearing, 
tensions etc for changes in vertical displacement can do so with 
reasonable accuracy using the attached formulas.  I worked out all this 
as a result of a correspondance with Alex Galembo a year or so back.  I 
needed a way of taking into consideration the elongation of the string 
due to changes in string deflection only before I could come in ballpark 
figures for changes in the other relevant parameters to work out this 
sheet the way I wanted to.   I've had it looked at by a few folks who've 
yet to punch any holes in the logic or calculations, tho I would be glad 
to learn of any error made here in either.

In anycase... if what I have here is correct or even reasonably so... 
then vertical string deflection as a significant cause of pitch change 
seems to carry to large a price in terms of change in downbearing 
force.  As the example shows, a change from 1 mm deflection to 2 mm 
causes downbearing for this single string unison to rise to 8 pounds.  
Figure that out over the entire piano.... If you on the other hand 
calculate withing reasonable downbearing force parameters... you end up 
with quite small changes in pitch.  Certainly much smaller then can 
account for the large pitch changes we see.

Cheers
RicB








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