John Grant, thanks for your reply.  I think it was 30 years ago (!) I 
glued a nipple into a scrap DuoArt action pneumatic and performed some 
simple experiments.  I mounted the pneumatic so the moving board would 
push upward, just as in a piano, and I hung a string from it upon which 
I had a stack of steel washers and nuts.  There definitely was more 
force available to lift the weights when the pneumatic was open.

Let us define that 100% opening is when the pneumatic is completely 
open -- the cloth is stretched taut.  Assume that in the piano action 
stack the pneumatic motion occurs between the limits of 20% open 
(the note is held "on") and 80% open (note at rest).  When the note 
is played the hammer velocity results from the integral of the 
pneumatic force times the effective hammer mass, taken over the 
span of the motion of the pneumatic.

Now consider how lifting the hammer rest rail alters things.  The 
Soft Pedal moves the rest rail so that the hammer travel distance is 
reduced to one-half.  We assume that the travel of the key and action 
pneumatic is also halved, and therefore the pneumatic is working 
between 50% open (note at rest) and 20%.  The integrated force in this 
operating range is considerably less than half of normal, and the 
result is that the hammer velocity is much less than it would be if 
the force had remained constant.

You questioned, John, if halving the hammer blow distance predicts a 
3-decibel reduction in sound intensity.  You bet it does, and the 
equations are simple, so let's look at it.

Kinetic energy is proportional to velocity-squared, written V^2 on a 
typewriter. (The circumflex ^ says that the exponent follows.)  One 
of the definitions of decibels is that decibels (db) is ten times the 
logarithm of the energy, thus

         db = 10*log[V^2]

If you will hang a microphone near the soundboard of the piano and 
observe the sound intensity with an old-fashioned VU meter you can 
read the decibels sound energy.  (Use the meters on an old hi-fi
reel-to-reel tape recorder, John.  I bet you still have one _somewhere_
in your garage!)

Newton's Laws of Motion say that the kinetic energy of a mass (the 
hammer) is proportional to velocity-squared, and V^2=2as, where "a" 
is the acceleration and "s" is the distance traveled.  If the acceleration
is constant and the distance is halved then V^2 is halved, and 

         db = 10*log[0.5] = -3 db = 3 decibels reduction.

But the above assumes that the pneumatic force is constant, yielding 
constant acceleration.  In reality, because the pneumatic is operating 
in the "mostly closed" region, the acceleration term "a" is also 
reduced, and the result is that the Soft Pedal produces much more than 
3 db intensity reduction.

I'd like very much to read the articles in AMICA Bulletin that you 
mention.  Can someone help me obtain them?

-- Robbie Rhodes