Only one player action, to my knowledge, was built a little differently
than all the rest in regard to its pneumatic sizes.  Duo-Art used three
different size pneumatics (and sometimes four) in their large pianos,
like Steinway and early Weber players.

Most rebuilders, including myself, assumed that the reason for this
graduation of sizes (the largest pneumatics being in the bass) was
probably due to the weight of the piano action in the bass versus the
treble.  We knew that while the performers hand is able to make up a
difference unconsciously, the pneumatic cannot.  Therefore, the pneu-
matic, if marginal, should be made larger to accommodate the heavier
action parts and heavier key weight.

Of course larger pneumatics have greater power, but when fed by the same
valve, lift commensurably slower at the same time.  Duo-Art used identi-
cal valves, all gapped identically, all fed by the same supply, and all
having exactly the same size pouch and bleed.  So although their largest
pneumatic is 25% larger than their smallest, it is also slower to close
-- a fact of life.  At high vacuum, no difference can be heard, but at
close to zero intensity, the larger pneumatic will play a long, heavy
string faintly softer than a smaller one would play it, irrespective of
the weight of the action (which has already been accounted for by the
manufacturer).

A fine piano has already been dynamically voiced in its design to play as
equally loud from bass to treble as it is possible to make it, given an
equal force strike at any given key.  But it is the nature of the human
ear to combine both the loudness of a string tone with the duration of
the note and hear the integrated effect of intonation as "volume."
Duo-Art engineers knew of this effect and for that reason decided to
compensate for it by sizing the pneumatics accordingly.  You might call
it, "Gilding the Lily."

Years ago, I was led to this new conclusion by a scientific paper reprint
explaining why Aeolian built their stacks this way.  Before that, I had
always assumed that larger pneumatics were needed to lift heavier
hammers.  I was wrong.  Since then, I have mislaid that tract, but I
think the physical principles speak loudly enough for themselves without
the need for this reprint.

For those who like facts and figures:

The lowest intensity in a Duo-Art is about 5" of vacuum pressure which
equates to about .18 lbs/in sq.  The smallest pneumatic measures 1-3/8" X
4", or 5.5 sq. in area.  At its center, the force of the pneumatic is 1
lb. at the very lowest zero intensity, so at its open end, its force is 8
oz, or 1/2 lb.  That is so many times more force than one needs to
operate any key on any piano, that force becomes a mute point.  That
equates to about a factor of ten times more power than required to move
the key.  So you can see that if the smallest pneumatic at the very
lowest intensity exerts a half-pound of force, the larger one exerts 5/8
lb.  Clearly not even a marginal factor for a pneumatically powered stack
when considering that piano keys are weighted to begin actuation from 30
to 65 grams!  Obviously then, there was another reason, other than "raw
power."

In any mechanical device, you cannot get out more than you put in.  That
means, if the mass times velocity of a hammer translates logarithmically
to loudness, then loudness is certainly a function of velocity.  The
velocity of a hammer is a factor of the moment of force at the key!
The momentive force at the key (in a frictionless system) equals the
momentive force at the hammer.  So given an equal force on a low bass
note and a high treble note, the instant velocity of the hammer at the
string becomes a function of the hammer's mass.  Simply put, if f=ma,
and you keep f constant as you change m, acceleration must change
proportionally.  The product will be a constant.

What this proves absolutely, is that an equal _force_ at a key does not
create an equal hammer _velocity_ at the string.  It varies proportion-
ally with the mass of the hammer.

Now some might say, "There you go -- that proves that larger hammers must
travel slower with equal key force, so we need more key force for bass
hammers."  But that won't help you, since we've already shown that we
have ten times more power in reserve than needed, just like the human
finger.  The hammer weight is overcome by finger momentum -- force times
velocity.  As soon as you exceed the weight of the hammer, it moves.  So
now we see why an artist presses the key for a soft note more slowly than
he does a loud note.  It is the velocity of the key which actually
translates into loud and soft, once the power capacity has been exceeded
beyond anything the key would ever need.  (Like lifting a clod with a
bulldozer.  Does the clod slow down the bucket?  Well yes, theoretically,
but not so you could ever notice.)

The perceived volume of long strings over very short ones at lowest
levels of playing is not a shortcoming of a piano.  It is a characteris-
tic of the human ear.  Were a key-strike gauge to play a very low tone
and a very high one at the same time at lowest intensity, you would not
hear the high tone very well, since the low tone would cover up the high
one.  So you can see from this physical fact that you do not want to make
the low tone louder!  If you wish to compensate for the ear, you will have
to slow down the bass key strike a little to make them sound more equal.

The final blow to my once closely-held erroneous belief about graduated
pneumatics was the fact that the second-generation reproducers, such as
the new Steinway Duo-Arts and Ampico B's, didn't use graduated pneumatics
in their latest stacks.  Why?  It wasn't necessary.  It was an attempt to
compensate for an effect, not a shortcoming.  It was not a mechanical
error, but a human trait of hearing, which the ear expected to
experience, anyway.

Orchestrion design uses the same principle.  If you wish to beat a drum
more loudly, use a smaller pneumatic.  If you wish to time a reaction, so
that one pneumatic always closes before the other, make the pneumatics
different sizes.  It is a tried and true pneumatic principle and it
always works.

Craig Brougher