Humidity Change and Unisons

[Ron Nossaman]

>Think of the plate as a lever. a very small change in angle at the point of
>contact with the rim makes a large difference in pitch at the string. Any
>easy experiment (or mistake LOL) that many of us made when we were starting
>out was to do a pitch correction and then tighten the plate.

Hi Don,
That's not the angle, but rather the height of the plate relative to the
bridge. Think of the plate and accompanying string plane as, well gee -
look at that - a *plane*. When the plane of the plate changes relative to
the bridge top, or vice versa, the already tuned piano goes out of tune. 



>As for bridge *twist* affecting smearing of unisons the treble side string
>is the shortest tail length so *if* (and goodness knows I don't know the
>answer) there is a counter clockwise *twist* then the bridge pins would
>cause a greater pitch change on the shorter string. 

Ok, I see your point. Since it takes (temperature considerations aside) a
change in length to produce a change in tension, calculate the total
possible height differences within, say, 2 millimeter total vertical bridge
rise, on a 100 millimeter radius of "roll" on either side of a hitch pin.
With a big hummer hitch pin of say, five millimeters, you'd have, what, 0.1
millimeter, or 0.004" total vertical difference. Say you have a back
bearing on the bridge of  2 millimeters in a 100 millimeter back scale
length. That will change the string length sqrt((2.0004*2.0004)+(100*100))
- sqrt((2*2)+(100*100)) = 100.020006 - 100.019998 =0.000008mm, or
0.00000031496" length change. That 2 mm bridge rise, correspondingly, would
directly change the length sqrt((4*4)+(100*100)) = 100.079968 - 100.019998
= 0.05997mm, or 0.00236". That's a difference of 7496.25 to one for bridge
height. How fine do you want to split hairs?



>Could you Ron make a list (or add to) in point form of the various factors
>that *may* be changing as humidity rises.
>


Modification: "changing" <> "important" <> "noticeably affecting pitch" 

Points regarding expected resulting pitch change.

(1) soundboard *curl*
(1) bridge *roll*
(1) bridge *twist* (if there is any)
(3) rim and frame shape change causing plate distortion:
(1) plate angle
(3) plate position
(3) nose bolt rise    - interesting notion - possibly (6)
(7496.25) soundboard rise
(9000) bridge length change low tenor
(3) bridge length change, everywhere else
(1000) bridge height change
(2) casters
(412) rumor and/or tuner error 


These figures are my own quick personal guestimates, currently unqualified
by measurement, argument, accepted dogma, or repeated browbeating. They are
subject to continual revision, pending better answers than what got them
there in the first place.

Now, back to the issue at hand. Have you sat down yet and worked out what
happens to the tensions in the different sections, taking into account
section lengths (elasticity), and friction at the bearing points? That and
soundboard rise and fall alone should account for the unison smearing
you're measuring without having to invoke tiny little smoke producing
demons at the far ranges of probability. Just a passing thought.

Ron N