This note is intended primarily for Spencer Chase, but is presented
through the Digest for the benefit of other readers with an interest in
the subject.

Spencer, you have raised an interesting question that has never been
satisfactorily investigated or answered.  The punch advance (also
called step increment) of rolls made during the 1920s is a mystery to
all of us who have studied it.

The natural tendency is to assume that the punch advance is a "simple"
number.  We know that in every period designers seem to feel an almost
overwhelming pressure to build new instruments in such a way that the
target dimensions are "round" numbers, in the sense of being whole
increments of the smallest unit of measure commonly in use.  This is
not just a consequence of an exaggerated sense of orderliness; it is
also convenient at any time and place to use simple numbers that are
easily manipulated and measured in the workshop.  This tendency can
sometimes be used to reconstruct lost standards.  When measurements of
any device show its dimensions to be very close to a "round" number, it
is generally safe to assume that the whole number is the intended
dimension.

This sort of argument can be used as follows.  We find that for 88-note
rolls in general, and for QRS rolls of the early 1920s in particular,
the punch advance is very close to 240 punch steps per foot.  Such
rolls usually (but not always) have exactly 24 punch advances per beat;
this lends itself to subdivision into sixteenth notes, thirty-second
notes, and triplets, all without roundoff error.

Consider the timing that pertains at Tempo 100, corresponding  (by
definition) to a paper velocity of 10 feet per minute.  At 240 punch
steps per foot there are exactly 2400 punch steps per minute.  One beat
occupies 24 punch steps, so at Tempo 100 there are exactly 100 beats
per minute--the marking on Maelzel's Metronome for Tempo 100!
Similarly, Tempo 80 corresponds to M.M. = 80, and so forth.  It seems
(to me at least) that this argues strongly in favor of concluding that
the perforator designers chose 240 punch steps per foot as the target
punch advance, so that the "Tempo" marking on the roll matches the
musical tempo, as shown on the standard metronome.

Given this approach, we would expect that the punch advance of
reproducing piano rolls would similarly be an "even" number of punch
steps per foot.  It is therefore surprising to learn that it is not.
As you pointed out, the measured punch advance is usually close to a
"round" number, but not close enough to allow the discrepancy to be
attributed either to manufacturing tolerances or experimental error, or
to any combination of the two.

Moreover, there is solid evidence that "round" numbers are not the
intended values at all.  As an example of this, consider Ampico Roll
No. 61391.  This roll contains a Tempo Test in which chords have
apparently been manually inserted every 6 inches.  A reconstruction of
the master rolls shows that these chords do not appear every 180 punch
steps, as one would expect, given that the punch advance is nearly 360
punch steps per foot.  If memory serves, the timing chords are spaced
exactly 178 punch steps apart, uniformly from one to the next
throughout the timing test, yielding a punch advance of exactly 356
punch steps per foot.  We are extremely lucky that in this case we can
determine the punch advance exactly.

Similarly, late Welte-Mignon Licensee rolls exhibit a punch advance of
about 0.756 mm.  (Early rolls use a coarser advance.)  This is close to
400 punch steps per foot, but it is enough different (almost 1
percent), and so marvelously repeatable from roll to roll, that the
intended value is certainly different.  I have yet to determine what
that intended value is.

In your note, you mentioned that your immediate interest is in Duo-Art
rolls.  The punch advance of these rolls was changed sometime in the
mid 1920s.  Early rolls have an advance close to 256 punch steps per
foot (or 3/64 inch per step).  Late rolls have an advance almost
exactly 1-1/2 times this value, or 384 punch steps per foot.  I do not
know the exact numbers.  However, I have been able to locate, scan, and
reconstruct the master roll for the 1921 Duo-Art Test Roll.  (I
undertook this work at the suggestion of John Grant, who generously
provided an original roll from the period for the purpose.) My
recollection is that this test roll, like Ampico Roll 61391, provides
the exact value, competely without equivocation.  I am writing this
note from home, so I do not have the value at hand.

I hope this note has been useful.  It is my intent to encourage you and
others to study this problem.  I have great hopes that some day we will
have a complete knowledge of this and similar issues related to the
perforator technology of the 1920s.

With best regards,

Wayne Stahnke