Seasonal pitch change:

[Jason Kanter]

So has anyone measured plate expansion and contraction with temperature
changes? Wouldn't that be the most likely suspect given this newfound
innocence of the soundboard?

Jason

On 3/7/07, RicB <ricb at pianostemmer.no> wrote:
>
> 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
>
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-- 
=cell 425 830 1561=
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