Seasonal pitch change:

[RicB]

Now this is an interesting thought. And better explains the left / right 
discrepancies in unions going out of tune then anything else I've 
pondered. Especially given the idea that this overall approximately 
equal change in length is the same for each string, yet different in 
terms of percentage of individual string overall lengths.

I've given this string riding up the bridge pin thing a bit of thought 
now, and see the string length change is largely concentrated at that 
length that covers the bridge surface itself.  I will have some more on 
that tommorrow. Probably a lengthy post with a good deal of math in 
it... but I think it points in a very interesting direcretion.

I ran through an example myself tonite with a simple 10 mm string length 
over the bridge surface, a 10 ¤ string path deflection, and 10 degree 
pin slants.  Not realistic in real life pianos... but adequate to check 
my math.  Looks like, assuming the pins can handle the increased 
pressure on them for the needed increase in the strings length over this 
span... that this is a very significant cause of pitch change.

Actaully... this is all quite fun.

Cheers
RicB

    It wouldn't help at all. When the humidity effect du jour
    changes all the string lengths in a unison by approximately
    the same amount, the shorter overall length string will still
    go out more than the longer because the change in length is a
    higher percentage of the overall length in the shorter string.
    Ron N