A Square Peg in a Round Hole?
By Bill Koenigsberg

The idiomatic expression that is the title of this article dates back
to at least the 1800s.  It was used to metaphorically portray that
something or someone was not well suited to a situation or did not fit
in effectively.

For the pneumatic application under consideration here, it is suggested
that the Aeolian 'knife valve' and the associated round air-flow port
used in many 'early' (1914-1920) Duo-Art expression boxes did not
control vacuum levels as well as those made after about 1920-1923.  The
initial title for this article was more specific, but less colorful,
i.e., 'On the Aeolian Duo-Art Knife Valve'.

The thinking behind the above assertion is based on the fact that the
Aeolian Corporation in the United States changed the shape of their
knife-valve air flow port from circular to racetrack shape (oblong),
probably starting in the time frame 1920-1923.

Why did Aeolian do that?  It is not clear if Aeolian did the same thing
with their British-made Duo-Art instruments.  Today, one could utilize
computational fluid dynamics (CFD) and computer-based simulation to
analyze the knife-valve performance differences between the two shapes.

However, there may be a simpler approach, the essence of which is
described below.  The story that follows may be viewed as an attempt
to explain why certain engineering changes were implemented.  This
effort is an example of industrial archaeology, supported by Holmesian
detective work and some reasonable conjectures.

To begin, an equation characterizing the impedance to air flow through
the circular knife-valve port in a vacuum regulator was derived.  It
reflected geometric blockage of the effective pneumatic passageway
(relative to the total cross-sectional area of the unobstructed round
opening of the airflow port) that the straight knife assembly produced
as a function of the transverse position of the blade of the knife.

Graphical analysis of the 'occluding geometry' equation clearly shows
that the blocked area of the circular port is not proportionally
(linearly) related to the lateral traverse of the straight knife
blade across the round portal.  This lack of proportionality is
mathematically described as a strongly nonlinear relationship.  The
physical implication is that this particular knife-valve port design
can adversely affect vacuum regulator function under certain
circumstances.

This result means that the 'gain' (instantaneous spatial slope of the
'geometric blocking' relation cited above) of the nonlinear control
device (the knife-valve assembly) can and will vary as the knife moves
about the circular opening of the port.

Such variation will be dependent on the Duo-Art intensity level coding
(Theme and Accompaniment) as well as the pneumatic load imposed on the
corresponding vacuum regulator by the number of notes being played at
a given moment in time.  From a linear control systems point of view,
preventing the 'gain' from changing over different operational
conditions is a desirable objective.

Ideally, the value of the gain associated with the controlling knife
valve should be independent of other circumstances and variables, i.e.,
constant.  If the gain is not constant, performance of some control
systems can be erratic, sometimes unpredictable, and may preclude
repeatability.  For the 'early' Duo-Art knife valve, the calculated
'gain' is near zero at initial valve closure, maximum at the midpoint
of valve closure, and again near zero when the knife approaches full
closure.

The calculated gain curve of the early Duo-Art vacuum regulator is
symmetric about the midpoint of the traverse of the knife across the
round port (typically 1-inch in diameter).  During operation, when
a Duo-Art piano roll is being played, the 'cutting edge' of the knife
blade in each vacuum regulator will be located quite near the full
closure position (known as the operating point) of each knife-valve
assembly.

The above 'near full closure' observation reflects a balance among the
strength of the regulator spring, the area of the movable board of the
bellows, and the capability of the vacuum pump.  (If bellows pneumatic
cloth were optically transparent, it would be easy to make this 'near
full closure' visual observation.) Because the operating point of
a given vacuum regulator (with round port hole) is usually near
a condition of full valve closure, the 'gain' of the knife valve can
be distressingly low.  (Low gain can cause slow response of the vacuum
regulator).

Without resorting to the use of equations, the qualitative behavior
of the early Aeolian knife valve (with the circular air flow port) is
described here in more detail.  Ideally, such a control valve should
block off the passage of the air flow by the same amount for each fixed
incremental advance of the knife portion of the valve assembly.  For
convenience, we refer to this characteristic as 'uniformity of valve
closure'.  This idealized behavior is consistent with the cumulative
incremental motion advance of the four collapsible chambers of the
corresponding 'accordion pneumatic' assemblies.

If hoses were rectangular (or square) in cross-section, using
a straight knife blade to control air flow through a rectangular
cross-section valve would make good sense.  This follows because the
rectangular cross-section geometry of the valve can intrinsically
satisfy the uniformity of valve closure mentioned above.  For this
configuration, it is understood that the cutting edge of the knife
blade must be parallel to either side of the rectangle.  But most
hoses, and certainly those utilized in automatic musical instruments,
are round in cross-section.

What is important here is the rectangular shape of the flow-through
passageway of the knife-valve assembly inside the structure of the
vacuum regulator.  It would be acceptable, if not preferred, to connect
round cross-section hoses to the input and output of such a rectangular
geometry valve.  This follows because the uniformity of valve closure
would be governed and preserved by the rectangular geometry of the
valve itself.  With the uniformity of valve closure established, the
gain of such a knife-valve assembly would be constant.

Noncircular cross-section hoses, i.e., with polygonal corners, could be
made.  However, they would be more costly to manufacture, and could not
be bent as easily without kinking, compared to hoses with round cross
section.  This contrasting geometric comparison is the basis for the
title of this article - a square peg in a round hole.

So let us look at the early (pre-1920ish) Aeolian knife-valve assembly.
When the straight knife just begins to intersect (overlap) the circular
port a given amount, it 'blocks' only a very small section (in the form
of a segment of a circle) of the round hole.  As the knife advances
transversely a little bit further (by the same amount), the blocked
area becomes larger.

The degree to which the blocked cross-sectional area becomes larger
is not linearly proportional to the lateral advance of the knife (up to
the middle of the round port).  As the knife advances still further,
the blocked area continues to increase, but at a reduced rate.  When
the knife approaches the end of its travel (corresponding to full valve
closure), the relative increase of the blocked area is again very
small.

For the round Aeolian knife-valve port, this mathematically-derived
determination suggests that each of the two early Duo-Art regulators
(theme and accompaniment) of the expression box will exhibit certain
functional difficulties.  For example, at low vacuum levels, the
probability of soft sounding notes 'dropping out' can increase
substantially.

For Duo-Art enthusiasts, the dropping-out of soft-playing notes is
a well-known problem.  This occurs, in part, because the 'gain'
associated with the pneumatic blockage characteristic is quite small
when low vacuum levels are present inside the regulator.  The gain is
small because the 'Operating point' of the regulator occurs at almost
full closure of the knife valve.  The low-gain condition increases the
time that the regulator takes to reach its intended (roll designated)
vacuum level.

Incidentally, when the regulator vacuum level is low, the associated
pneumatic bellows is nearly in a wide open position.  When the bellows
is configured nearly wide open, some of the pneumatically-developed
forces (generated by lateral pressure on the collapsing pneumatic
rubber cloth) on the movable board are relatively large and behave in
a decidedly nonlinear manner.  This further complicates the motional
behavior of the regulator assembly, potentially increasing the
probability that soft-playing notes can be dropped.  Aeolian used
several different approaches to address this problem, sometimes
artificially increasing the regulator vacuum level (by activating an
associated accordion chamber) when soft notes were involved.

When high vacuum levels are called for, the corresponding regulator
can also behave in a sluggish manner (because of low gain).  Remember
that during operation, when a Duo-Art roll is being played, the
'cutting edge' of the knife blade in each vacuum regulator will be
located quite near the full closure position of each knife-valve
assembly.  As mentioned earlier, that 'Operating point' corresponds to
a low gain position.

Here the term sluggish refers to the extra time that the vacuum
regulator must take to reach its roll-assigned value.  This high-vacuum
characteristic may have contributed to Aeolian's motivation to
incorporate its so-called 'crash valve' in the Duo-Art expression box.
This may have been done to compensate for the relatively slow regulator
response associated with the knife valve proper when high vacuum levels
are called for.

It is understood that the expression coding of the Duo-Art piano roll
'sets up' the intended vacuum level before the note (notes) to be
played is called for.  Therefore, it would seem that the speed of
response of the vacuum regulator should not matter, so long as the
required vacuum level is established ahead of time.

However, depending on the expression coding present on the piano roll,
the two vacuum regulators (theme and accompaniment) of the Duo-Art
expression box can interact with each other.  For example, this can
occur by having one regulator put an 'extra' vacuum demand on the pump.
This means that the vacuum level in the theme regulator can affect the
vacuum in the accompaniment regulator.  The consequent cross-coupling
of vacuum levels makes it very challenging for the Duo-Art roll editor
to assign the correct theme and accompaniment coding to produce the
desired musical results.

In all likelihood, the coding process must have been iterative in
nature.  That is, after a first pass was completed, a second would
be required, then a third, and so on.  This refinement process was
probably terminated when the roll editor and/or roll artist was
satisfied with the playback performance.  If such refinement was
terminated prematurely, this could easily result in a playback
performance that might be considered by some listeners to be musically
unsatisfactory.

A consequence of the circular contour of the knife-valve air-flow port
is that the required speed of response (of the theme and accompaniment
vacuum regulators) may have become a more significant issue than
originally expected.  That is, an intended vacuum level might not have
been attained by the time that specific notes were called for.  What
could the Aeolian Corporation do to address this troublesome situation?

It would appear that the so-called racetrack knife-valve port (two
straight-aways and two semicircular end pieces) replaced the circular
air flow port in the expression regulators by Aeolian around 1923.
Prior to this time, coding of the early Duo-Art piano rolls must have
been a real headache for the D-A roll editors.  Coding for Duo-Art
rolls may have gotten 'easier' after the racetrack knife-valve port was
introduced.  Frank Milne certainly figured out how to encode D-A rolls
very well; his rolls today are highly sought after.  It is to Aeolian's
credit that their Duo-Art roll editors appeared to have improved their
musical reproduction skills over the years.

Because of its almost-rectangular shape, the racetrack-shape design
for the air-flow port gave rise to a nearly constant 'gain' over the
complete range of motion (fully open position to fully closed position)
of the knife valve.  Interestingly, Aeolian subsequently replaced
the racetrack-port design with a then completely new vacuum-control
structure in the theme and accompaniment regulators.  The new design,
described below, reflected the clear objective of implementing a pure
rectangular shape for the air flow port in the theme and accompaniment
regulators.

After 1927 or so (precise date is not known), Aeolian incorporated a
miniature, spring-loaded, rolling-pin window shade (of leather) furling
and unfurling over a tiny metal sidewalk-grate (think NYC) in their
'fan-accordion' Duo-Art expression box system.  These fan-accordion
systems continued to be manufactured until at least 1936 (Steinway
Model S 285081 is an example of that).  Unfortunately, because of the
Great Depression, relatively few of these fan-accordion instruments
were made.  Most, if not all, of the high-end Aeolian Concertola pianos
(Steinway and Weber, maybe others) incorporated the fan-accordion
Duo-Art expression system.  When properly restored, the performance of
a fan-accordion system is exemplary.

In the fan-accordion system the port (over which the leather window
shade rolled) was clearly rectangular in shape.  The 'gain' of this
valve implementation was now constant over the entire range of motion
of the rolling-pin leather.  The rolling-pin design might be considered
the Aeolian 'equivalent' of the curtain valve used in the crescendo
box of the Ampico B pump (and also the Ampico B pedal regulator).  The
Ampico B curtain valve is known for its simplicity of construction and
rapidity of motion.

Although it may not be obvious at first, the Ampico A vacuum regulator
valve intrinsically 'incorporates' a rectangular shape for its pressure
(vacuum) control function.  This can be visualized by considering
a long flat rectangle of paper and wrapping it circumferentially (end
to end, the long way around) into a simple sliced section of a circular
cross-section hollow tube.  As the 'piston' in the Ampico A pneumatic
valve moves axially in its cylindrical space, the effective
circumferential area through which air can flow changes in direct
proportion to the piston's longitudinal motion.

Consequently, the 'gain' associated with the Ampico A 'knife valve'
(perhaps it should be called a piston valve) is automatically constant.
Is it possible that Charles F. Stoddard, the inventor of the Ampico A
reproducing mechanism, did not realize that his 'piston' valve design
was inherently linear to begin with?

At present, please consider the thoughts expressed above as
conjectural.  But isn't it curious that early Duo-Art rolls (not all
of them) do not seem to play back particularly well (my experience),
and that D-A rolls made after about 1923 sound somewhat better?

There may also be a chronological correlation between early D-A rolls
that display red ink on their roll identification labels, and later
D-A rolls (made after about 1923?) which display black ink.  This
correlation may explain why that print-color change was incorporated
at that time in Aeolian's piano roll manufacturing process, i.e., to
distinguish the early rolls from the later ones.

If this is true, it may be that D-A piano rolls with red-print should
be played on a Duo-Art made before 1923 or so.  Correspondingly,
black-print D-A piano rolls might sound better if played on a Duo-Art
piano made after 1923.  It may also be that different D-A test rolls
were introduced (at least three of them?) to take into account the
respective 'hardware modifications' that were made to the Duo-Art
playback system during the formative years 1914-1923.

Although some of the concepts introduced above are conjectural, they
can serve to stimulate additional research into the evolutionary
development of the Aeolian Duo-Art expression box.  Presumably, the
Aeolian Duo-Art knife valve with circular port was incorporated into
the earliest (circa 1914 -1915) Duo-Art expression boxes.  This thought
is supported by some early Aeolian documentation, viz., Duo-Art Tubing
and Schematic Chart (circa 1913-1918), which clearly depicts all the
relevant knife-valve air-flow ports as circular.  This includes the
knife valve in the air motor governor.  Reprints of the above document
were formerly available from Player Piano Company, Wichita, KS.

It is historically ironic that the shape of the spill valve port (not
within a vacuum regulator structure) in a pre-1920, likely about 1918,
Duo-Art expression box is precisely in the form of an oblong racetrack.
Therefore, it would seem that Aeolian knew early on about the racetrack
shape, but did not appreciate, at that time, its potential benefits
within the theme and accompaniment vacuum regulators.

For some reason, Aeolian did not use the racetrack-shape port in
vacuum regulators until about 1923.  Had they utilized it earlier in
the expression box regulators, it could have contributed significantly
to simplifying improvements in the Duo-Art roll coding process.  One
can only wonder about (and lament) all those Duo-Art piano rolls that
were issued between 1914 (year of introduction of pianos equipped with
the D-A mechanism) and 1923.  What took so long?

Credit is accorded to several individuals whose contributions aided
in the research effort outlined above.  Thanks are extended to Kirk
Russell, who provided close-up photos and detailed measurements of the
interior of a pre-1920 D-A expression box.  Thanks to Louis Gentile,
who had a pre-1920 D-A expression box for sale, which I purchased.
Thanks to Allen Koenigsberg, who suggested the catchy title of this
esoteric article.  Thanks to David Saul, who added the question mark
at the end of the title.  Thanks to Herbert Lindahl, who shared many
of his Duo-Art experiences with me.  Thanks to Geoffrey Kaiser, who
generously answered questions by email regarding Aeolian history and
relevant Duo-Art technology.

Bill Koenigsberg
Concord, Massachusetts
billkberg@comcast.net.geentroep [delete ".geentroep" to reply]