In light of all the papers published so far, refuting Mr. Stephenson's
statement that valve gap in a player is unimportant, it would be redund-
ant for me to add yet another just to increase the majority.  However,
Mr.  Brougher's thoughtful submission, MMD 970227, concerning evenness of
loudness from bass to treble, tempts me to approach the matter of valve
gap from the point of view of control valve theory, which sometimes
appears to not be fully understood in the traditional player literature.

I believe that an analysis based on this will demonstrate that not
only that the flow restriction imposed by a correctly gapped valve is
essential for proper control of playing volume, but also that reasonable
equality of that gap among all the valves leads to the perceived equality
of loudness between bass and treble notes played at any given stack
vacuum level.

The basic principle governing this is the relationship between flow of
fluid through a restriction and the permanent change in the pressure in
the fluid flowing through it.  As flow through any restriction (the
slightly open valve, in this case) increases, the loss of pressure (or
vacuum) increases.  This is as inexorable as loss of voltage increases as
current increases through a resistor due to Ohm's law; except that for a
fluid, the loss of pressure (pressure drop) increases as the square of
flow increase.  Doubling the flow through any restriction robs the fluid
of four times as much pressure, for example.

Imagine a model consisting of a pneumatic closing under the influence of
a constant source of vacuum, connected by a tube with a flow restriction
such as a very large bleed in the tube.  There is a weight attached to
the pneumatic.  When the vacuum is first turned on, the pneumatic
immediately feels the full force of the vacuum across its surface, and
starts to close.  This force both lifts the weight and accelerates it.
As the speed of collapse increases, the flow of air from the pneumatic
increases.

But this increased flow causes some of the vacuum to be lost across the
restriction, leaving less force available to close the bellows.  Due to
the square-relationship, this loss of force rises abruptly, until a point
is soon reached where no more force is available to continue to accel-
erate the weight (mass).  Although the system continues to move towards
complete closure, it has reached "terminal velocity" and can no longer
speed up.

The only way that this terminal velocity can be increased is either by
opening up the restriction (the valve, for example), or by increasing the
vacuum at the source, allowing more 'room' for the flow, and the
resultant pressure drop, to increase before the system runs out of the
surplus force needed to accelerate the mass to a higher velocity.

Only the second method (source vacuum level change) is available to
either the Reproducing Piano system or to an interpretive pumper, to
control the terminal velocity of the hammer-action system, and thus to
control the loudness of any notes played.

Mr. Brougher proved that the static pressure available in any player
pneumatic, even at the lowest playing vacuum, is far too high to
theoretically play notes softly.  Only this dynamic behavior, involving
a self-compensating mechanism which controls the ultimate hammer head
velocity, can explain how a player can play very softly when the vacuum
level is properly controlled.

I suggest that the restriction of air flow from the pneumatic imposed
by a properly gapped valve, is not only unavoidable, but in fact is
essential for proper musical dynamic range, especially in moderato and
soft passages.

I further suggest that relative equality of these restrictions along the
length of the piano scale contributes to the evenness of loudness from
bass to treble.  This mechanism helps to explain how this effect seems
to be independent of the fact that most pneumatics are the same size
throughout the piano, in spite of the fact that the bass end hammer-
action system is heavier and has a far greater moment of inertia (the
requirement that it must absorb far more energy to reach the same hammer
velocity) than its fellows at the treble end.

It is a commonly held view that the piano is scaled such that equal
rotational velocity of the hammer head and shank, the only part of the
action who's stored energy is actually converted into sound, produces
equal perceived loudness all along the keyboard.  The increased mass,
therefore the increased stored energy requirement, of the bass hammer is
needed to compensate for the fact that a low note requires more sonic
energy to seem as loud as a high note; as well as to adjust for the
nonlinearities of scale (heavier strings) imposed by the practical limits
of piano construction.  The pianist strives *conciously* to alter the
loudness of play by adjusting the velocity with which the notes are
played, in a similar way all along the keyboard, and *unconciously*
compensates for the added force needed to achieve that velocity in the
bass end.

As an example of how this 'evening' occurs in a player piano; imagine
both a bass and a treble note being played simultaneously, at the same
stack vacuum level.  The light treble note accelerates quickly, soon
reaching the desired terminal velocity, well before the entire keystroke
is completed.  The bass note, being more massive, starts out slowly,
requiring lower flow and thereby leaving even more of the total pressure
available to start the system moving.

In due time, however, this system also accelerates to nearly the same
terminal velocity.  The acceleration may take a bit longer, and occupy
a larger portion of the keystroke prior to 'let-off', but the final
velocity of the hammerhead at equilibrium is about the same as for the
treble note, providing the pneumatic size (and thereby the relation of
air flow to action velocity), as well as the valve gap are fairly similar
for both notes.

Hickman's striving to achieve similarity of flow restriction for all the
valves in the Ampico-B, using the valve-seat press in conjunction with
a manometer to equalize pressure drop and thereby equalize flow capacity
for each valve manufactured, proves that this was a concern of a person
far more expert in these matters than any of us.

Richard Vance