plate reaction was Re: Pitch Raising to A440.......Or Not?

[Ron Nossaman]

> A given string will not render past a front bridge pin until the tension 
>above the pin is equal to, or larger than, the tension of the speaking length 
>'plus' the friction gain at the pin 'and' across the bridge.  Additionally 
>the string will not render past the rearward bridge pin until the tension of 
>the speaking length is equal to, or larger than the sum of the friction gain 
>of front pin 'plus' bridge 'plus' friction gain of the rear pin.........(if 
>we add in aliquots then that friction gain would also have to be added to the 
>total)

Yep. This, of course, complicates the process of trying to figure out what
happens when, with only a measured speaking length pitch for data.


> Does the plate "flex" or "compress"...well yes without a doubt it does.... 
>to some extent......... the question is 'which way'? 
--------------------------------
>  For the sake of question No. 1 let's assume that the bridge/soundboard does 
>'not' flex....period.

I'd say that since the struts are above the string plane, they will bow up
in the middle - but that's not the flex that makes the pitch of tuned
strings drop as you raise pitch on the rest. The plate flexes in the
direction of string tension (in addition to any up, down, or rotational
flex - it gets shorter), and flexes more between the struts than at the
struts since the struts are trying to do their job of not allowing the
string tension to collapse the plate. I think Newton was talking about
doing a normal one pass pitch raise, measuring the resulting pitch of every
string, and plotting the results against what the pitch should be. The
graph will show least pitch drop at the struts, and the most half way
between. I haven't tried this myself, but I have no reason to doubt the
reports of those who have, and my math on soundboard deflection changes
don't account for anywhere near the drop we actually see in practice. Some
of this drop may be strings rendering through the bridge too, but that
should be a fairly uniform progression from one end of the scale to the
other, with no anomalies at the struts. There isn't much left besides plate
compression that will account for it.



> For question No. 2 we will add the 'flexibility' of the sounding board.
------------------------------------------
>......For the sake of the question let's suppose a 
>static temperature and also suppose that a soundboard rises just enough to 
>change speaking length tension but not enough to overcome "friction gain" at 
>the front bridge pin. In this situation the pitch of the speaking length will 
>rise, as will the pitch of the standing end of the string...except that 
>because of equal tension and differing speaking lengths the pitch of the 
>standing end will be proportionately higher than the speaking length...right?

Right.


> In this situation does the flexing/compressing of the plate follow the rise 
>of the soundboard or does the plate remain static and realtively unaffected 
>by this change?...............
>Ponder points only. :-)
>Jim Bryant (FL)

I'd say it doesn't follow the bridge up and down enough to be a factor. The
downbearing angles aren't extreme enough for that. However, since we're
talking about possibly 20 cent+ pitch changes from season to season, The
plate would almost certainly have to compress like it would with a pitch
raise with the high humidity cycle, and relax/rebound like it would with a
pitch lowering in the dry cycle. This is an interesting point I hadn't
considered. The plate is automatically partially compensating for humidity
induced pitch changes by being flexible! If it didn't flex under string
tension, the pitch swings would be dramatically worse within any given
humidity limits than they now are! Now this is cool. Good show.

Ok, here's one for you. I think I've demonstrated reasonably well that
humidity swings push strings up and down bridge pins. With a 20° pin angle
and 10° stagger, how much of the pitch increase with humidity increase is
from soundboard rise, and how much is from the fact that the string is
higher up the bridge pins and taking a longer path across the bridge
(stretching as necessary to do so)? 

I'm beginning to suspect that we went through a lot of years not knowing
squat about why and how pianos go out of tune.

Ron N