Drifting Unisons

[Ron Nossaman]

Hi Fred, I doubt that this will answer anything well enough to clear this
up, but here are a few observations.

>  There is a consistent difference between left and right 
>strings, sometimes as much as 20 cents in mid to upper treble (Yamaha. 
>Steinway as much as 10 cents) after a change of 40 to 60 percent (over 
>the summer, with next to no use or tuning). Talk about wild unisons!


>	I thought the general wisdom about this being a result of relative 
>lengths of "waste lengths" (capo or agraffe to tuning pin) explained 
>this, until I noted there was little or no such effect between adjacent 
>unisons on a Steinway B (with the offset unison pattern in the 
>plate/block: greater difference in waste length between adjacent unisons 
>than between strings within any unison). 
>	I have no explanation, but simply want to confirm that this is a 
>commonly observed phenomenon (or at least it happens here in New 
>Mexico). My best guess is that it has something to do with bridge roll 
>combined with notching, more for lack of any other explanation than 
>because it actually seems plausible. 

* Let's consider what we are looking at. There is more involved than just
the strings from the bridge to the tuning pins. You need to consider the
entire string length from the hitch to the tuning pin. When the bridge
rises and lowers with the soundboard, the strings render over the rear
aliquot, the V bar, the front counter bearing bar(s), and, unless the total
length of string segments behind the bridge equals those in front of the
bridge, the strings will render through the bridge pins to some degree. The
bridge is the high friction point, so it takes bigger tension changes to
move a string across it. In general, the longer the total string length is,
the less the tension change with bridge rise or fall (not roll). The left
string of the unison has the shortest length from the bridge to the tuning
pin, but not necessarily from the tuning pin to the hitch. This will change
from unison to unison depending on the distance from the bridge pins to the
hitch for any string. If the total back scale is significantly shorter than
the total front scale, here's what should happen when the soundboard and
bridge rises with humidity increase: The tensions in the back scale will
increase as a faster rate, and peak at higher values than the tensions in
the front scale segments. If the difference in tension is enough to
overcome the friction at the bridge, the string will render across the
bridge toward the hitch pin, further raising the tension in the front scale
as the back scale tension decreases. The pitch rise of the speaking segment
in this instance will end up being sharper than that of a string segment of
a neighboring unison who's tuning pin is closer to the capo than this one is. 

Just like everything else in a piano, you have to take fourteen different
things into account to make any sense of what you're looking at. After you
factor in the string segment lengths, proportions of front segments
relative to rear segments, vertical bridge movements, and friction, it
begins to make some sense. The biggest problem as I see it is that we can't
really know what the tension is in any given section at any given time (or
can we?). If we could measure segment tensions we could see exactly what's
happening.


Ron N