Seasonal pitch change:

[David Love]

The changes aren't just deflection changes.  Expansion and contraction of
the case contributes some too.  

David Love
davidlovepianos at comcast.net 
www.davidlovepianos.com

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of RicB
Sent: Saturday, March 10, 2007 3:41 PM
To: pianotech at ptg.org
Subject: Seasonal pitch change:

Hi John

Its true that the lower breaking % will cause a greater change in pitch 
for any deflection induced change in overall string length.  But this 
still doesnt account for anywhere near enough as far as I can see.  Take 
the following example string.

1400 mm long. 1.2 mm Ø,  back length of 100 mm and front termination to 
pin of 200 mm with 132 lbs of undeflected tension.  That puts us at 21 
pitch.  A very long and very low tension string ... yes ?   Assume a 0.5 
mm upwards deflection by the bridge... yeilding a 0.31 ¤ string bearing 
angle as a starting point. That brings tension up to 132.04 lbs, a pitch 
rise of 0.267 cents and a 0.0013 mm increase in overall string length.  
Now... if the board manages to push upwards at that point say 0.5 mm 
more you come up to 0053 mm  in overall string length increase from the 
undeflected length, rises to string tension 132.16 lbs and a pitch rises 
to 1.068 cents over the undeflected pitch.   Now on top of that lets say 
the bridge swells such that the string climbs up the pin 0.2 mm as has 
been tossed around.  This yeilds an increase of 0.025 mm in string 
length assuming a 20 mm wide bridge, 10 degree offset angle and 20 
degree bridge pin angle.  Such an increase in string length by 
deflection will result in the tension rising to 132,9 lbs and a total 
combined pitch change of around 5.9 cents over the undeflected pitch, or 
about 5.6 cents over the nominally deflected string (0.5 mm). 

So, considering both these factors, a board rise of 0.5 mm, and a string 
climb up the bridge pin by 0.2 mm... we still dont see more then a 5.6 
cent change in pitch for this very long very low tension string. 

Its significant... but not enough.  Noteworthy is that a 60 mm string, 
0.825 mm Ø, same back and front lengths at 160 lbs undeflected, a 
starting string deflection of 1 mm, similiar 0.5 mm soundboard rise and 
0.2 mm string climb up the pin will expericence a combined pitch change 
of about 21 cents over the undeflected pitch, and around 17 cents over 
the design spec deflection of 1 mm.

Seems to me that none of this can explain the pitch change patterns we 
see, excepting the left / right bit with unisons. Something else has to 
play a major part. As you, I am also tempted to think about the break in 
string tension at the doglegs, and endpoints. 

Cheers
RicB


    Could it be because that's where the strings end? You have an abrupt
    loss of
    downward force on the bridge/soundboard, plus (if I understand what
    the Rons
    and Del are saying), those strings tend to have less tension due to poor
    scale design. I think Ron N was saying some days ago that his
    redesigns are
    not nearly as susceptible to pitch change as the original scale was.

    The strings adjacent the plate struts are more prone to change during
    tuning. Gotta be something to do with the lack of tension on those
    portions
    of the bridge at the ends of a section of strings.

    JF