Drifting Unisons

[Fred S. Sturm]

Ron,
	I agree we would have to account for the total "waste length" of every 
string (whether toward tuning pin or hitch pin), and their relative 
tensions, and the amount of friction involved, and bridge rise and roll, 
to come to a complete analysis. I have certainly considered all these 
factors in my musings while pitch raising/lowering for the ?thousandth 
time. 
	The puzzle for me is that uprights and grands both show the same 
tendency for the right string to move most, whether to a large or small 
degree. Hitch pin waste lengths vary, but typically not by much on any 
given piano. Tuning pin waste lengths vary pretty consistently, so that 
on all grands the right tuning pin's waste length is longest for the 
unison, while on an upright the right is shortest. So why isn't the 
pattern reversed for uprights? 

Fred

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

> * 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