In a recent e-mail note, Robbie asked me to explain how I concluded that
the step advance of Ampico rolls corresponds to 356 steps per foot.
This note is in response to that request.

We have to make a clear distinction between the "intended" step advance
-- the value that the designers had in mind as the ideal target advance --
and the "experimental" step advance (the value found in practice).  The
former can be determined only by examining documents of the period.  The
latter is the value resulting from measurements which we can make today
on existing rolls or other artifacts dating from the period.

The relationship between these two is easy to understand.  The perforating
machinery was designed and built to achieve the intended step advance
within a given tolerance.  (Perhaps the step advance was variable, and was
adjusted from time to time by the operators.)  Thus, when a music roll was
perforated there was a degree of uncertainty in the perforating process
itself, since the machinery is not mathematically perfect.  In addition,
the paper was pulled through the perforator by grippers and may slip
slightly, either between the outer layers of paper and the grippers
themselves, or between adjacent layers of paper, or both.  Finally, the
paper dimensions may have changed over time from humidity or aging.

Thus, we cannot rely on measuring one or even a large quantity of existing
rolls to find the intended advance.  The only way to find the intended
value is by returning to the original documents.  Since the blueprints and
other related documentation for the perforators have apparently been lost,
we must turn to the test rolls.  In these rolls, as contrasted with rolls
containing musical material, the intent of the designers is made manifest.

We can find the step advance by examining a production roll and a master
roll, side by side.  The production test roll contains annotations printed
at the factory explaining the meaning of the marker events, and thus
serves as an official statement, authorized by the factory, of the
intended length.  The markers themselves are contained in the master
rolls, assigned to particular steps.  Since the step numbers in which the
markers occur are integers, they are not subject to the tolerances that
occur with other measurements.  (Of course, this is true only for
synchronous perforators; Ampico perforators are of this type.)

Consider Ampico Roll No. 61391, the "Inspector's Ampico Test Roll" issued
in December, 1922.  This is the only Ampico test roll whose use was
sanctioned by the factory throughout the 1920s, until Ampico Roll No.
70403 was issued in late 1929 for use with the New Ampico.  The Tempo test
in Ampico Roll No. 61391 is explained by a printed annotation on the
production roll itself, as follows:

 > Tempo lever at 60.  Single note and chord alternate at distance
 > of 6 inches.  Music [sheet] should travel from first chord to
 > last chord in 60 seconds.

Following this explanation are thirteen marker events: seven "chords" and
six "single notes" alternating along the length of the test.  It is clear
from the description that the overall length of the test is intended to be
exactly six feet, from the first chord to the last.

Turning next to the master roll, we find that the "chords" are in steps
2171, 2527, 2883, 3239, 3595, 3951, 4307.  The "single notes" reside in
steps 2349, 2705, 3061, 3417, 3773, 4129.  A few minutes with a calculator
(or old fashioned pencil and paper) shows that there are exactly 178 steps
from each chord to each single note and vice versa.  The entire test
occupies exactly 2136 steps.

We find the intended step advance by dividing the length of the Tempo test
in steps by the intended length of the test in feet.  Dividing 2136 by 6
yields 356 steps per foot.  There is no tolerance associated with the
value; instead, it is exact -- the value intended by the factory.

The only difficulty with this approach is gaining access to the material
required.  In the case of Ampico Roll No. 61391, I was able to locate
several copies of the production roll manufactured in the 1920s.  I
reconstructed the master roll from these production rolls by scanning the
rolls very accurately and using phase-lock-loop techniques to recover the
original step information.  The original master roll, wider than
production rolls and three times longer, and with sprocket holes along the
margins, still exists and is available for examination.  I invite all
interested parties to check my work by examining production rolls and the
factory (i.e. paper) master roll.

Knowing the step advance is critical to scanning and preserving Ampico
rolls.  We need to know the advance for two reasons: to recreate the
master roll from a production roll, and to perforate a new production roll
from the recreated master.  This process, when properly carried out,
yields enormous dividends in the form of exact copies of rolls of the
period, with all of the original webbing intact, each hole in its true
position.  Such new rolls are completely free of concerns regarding their
accuracy; they are the functional equivalent of rolls manufactured during
the 1920s.

With best regards,

Wayne Stahnke