I guess it's time to mention some of my own feelings about Duo-Art
expression adjustments.  Some of my points will agree with what others
have said, others may contradict.

1.  Monotonicity, or lack of glitches:  Everyone will agree with this,
but it's easy to overlook if you just use the test roll.  Looking for
the moment just at the movement output of the accordion stack, its
displacement versus the roll coding must be a steadily increasing
stairway, with no steps backwards!  Ideally it should be linear.

For example, numbering the steps 0 through 15, step 4 (just the 3rd
pneumatic) must be greater than step 3 (1st and 2nd pneumatics),
ideally by the step of the 1st pneumatic.  And Step 8 (just the 4th
pneumatic) must be greater than step 7 (1st, 2nd, and 3rd).  You
should set this up before even thinking about the stack, on the bench
if possible, feeding suction only to the expression 8-valve box.

There is nothing in the test roll to check that 4 is really louder
than 3, or 8 louder than 7.  Real music rolls will show it up.

2.  Curve.  Theoretically the plot of vacuum output versus roll code
should be exponential, meaning curving upwards.  Higher volume levels
should have more separation (in inches H2O) than lower levels.  In
practice, listening tests may show this is not needed, but it seems
clear that small differences at the high levels will not be audible,
as Craig mentions.

3.  But how to get a non-linear (curving upwards) plot from linear
accordions and linear springs?  The grand expression box contains a
"four bar function generator" linkage, which can produce a variety of
nonlinear curves, depending on how you set up adjustments before and
after it.

For any given zero level vacuum, you can then tighten up the nut where
the accordions pull down on their lever arm (which would increase that
vacuum), then back off the rotary adjustment screw that controls the
knife valve, to get the same zero intensity back.  But now those
nickel-plated linkages on the side of the box are in a different
position.  And the knife valve will now respond differently as the
accordions pull down in response to the roll codes.  So, depending on
the rest position of those linkages, you can probably get curves that
are concave upwards, linear, or concave downwards (no!).

This could explain why two people adjust their accordions the same,
use identical springs, set the same zero levels -- and get different
effects as the expression levels build up.  Whatever you think of my
other ideas, you should check the rest position of the linkages.
Especially if they're different on the Theme and Accomp sides, which
presumably you don't want!

4.  Energy storage versus regulator:  Craig mentions the importance of
judging loudness on chords, not single notes.  On single notes, or slow
trills, the D-A box is more or less a regulator.  But with big chords,
the Theme and Accomp expression pneumatics are more like energy storage
capacitors that discharge into the stack when the chord is struck.
With no stabilizing reservoir between them and the pump, what you hear
is what was stored in the pneumatic.

Here we can vindicate Craig's advocacy of a linear "curve."  The energy
delivered to a piano hammer goes up linearly with the vacuum in inches,
so long as the vacuum remains constant during the hammer stroke -- as
in a D-A playing a single note.

But the energy stored in the expression pneumatic goes up as the
*square* of the vacuum.  When that energy is dumped into a big chord,
the expression pneumatic collapses quite a bit, so the vacuum drops
while the hammers are going through their stroke, and the total energy
delivered is close to the square of the vacuum, meaning to the roll
code if the box has been adjusted linear.

Since a square function is very concave upwards, this helps a linearly
adjusted box approach the "ideal" exponential curve.  I put "idea" in
quotes since Craig and others have listened to a lot of Duo-Arts, and
what they year always trumps what scientists think.  But it would be
nice if science and observed reality can be made to agree :-)

I'd expect the spill valve also helps make the curve concave upwards.
Apparently setting it right is even more important than those side
linkages.

Mike Knudsen