Julian Dyer's comments a few days ago on MMD got me to thinking a bit
on the accuracy of copying paper rolls.  Specifically, he said that
"[copies] were always 'synchronous' -- cut in a punch-advance-punch
manner.  New rolls to date have pretty well all been non-synchronous
copies..."

Punches are always synchronous to some clock.  The problem is that
different clock rates and advance intervals may not match the original.
Mechanically advanced punches thus must often be re-geared to match the
original stepping as close as possible.  Due to dimensional changes in
the original over time and humidity, it may be impractical to recreate
the stepping exactly using gearing.  So we end up with the occasional
relative timing error in punch nibbles.

What accuracy is required to make the copies sound "right"?  This is
different from the question of how accurately the original should be
captured.  The following is oriented towards the piano, but applies as
well to other reproducing media.

The human senses are differential in response.  That is to say, they are
most sensitive to rate of change.  A fast change is perceived as stronger
than a slow change of equal magnitude.  As well, in the world of hearing,
quite small time intervals can be perceived.  Some studies show that
intervals in the order of 10's of microseconds can affect perception.
Other studies have shown that the average person can detect timing
between two notes in the order of 10 milliseconds, and some can hear
5 milliseconds.

The smallest punch nibble I've seen is about 0.015", and today's
perforators are doing more like 0.040" per nibble.  If I've done the math
right, at a roll speed of 80 and a punch advance of 0.015" the time
interval between nibbles is about 9 milliseconds, and 25 milliseconds for
0.040" per nibble.  So a one nibble error is significant for closely
related notes.  For instance, a slightly advanced note, if "corrected"
to align with its associated notes, would lose its enhanced sound.  And
normally a pianist would not play a chord with one note offset by 25
milliseconds.

Based on the above, here are a few observations:

1.  A misalignment of notes will cause one to be perceived as louder
or softer.

2.  A misalignment of notes will cause a muddying of the music.
(Obvious, of course.)

3.  The beginning of the note is the most important event.  Punch size
per se doesn't matter much.

4.  The shorter the note, the more important the ending time.  Here
punch size does matter.

5.  Relative timing is more important than absolute timing.

So back to the question:  What accuracy (resolution) is required to sound
"right"?  I suspect that even the best regulated pneumatic players don't
approach an evenness of 5-milliseconds in start time over the range of
notes and intensities, and the ending times are even worse, due to
variability in bleeds, cloth stiffness, etc.  However, a 25-millisecond
error, or one nibble at 0.040" step will make an audible difference.
Buried in the music, a single 9-millisecond error, or one nibble at
0.015" step would probably not be noticeable, but a lot of 9-millisecond
errors would be.  My opinion is that 5-milliseconds at the copy would be
"good enough".

Of course this raises other questions about how one reads the original
with this accuracy, as well as punching the copies.  As I've said before,
the line-scan camera is my choice for reading, as it can resolve as fine
as required.  For copying I think a stepper drive with 0.001" per step is
a possible answer.  The advance could then be in multiples of 0.001",
which would be satisfactory, and not difficult to implement.

Julian is right that currently we are not producing archival quality
copies.  Whether they are musically good enough is a matter of opinion
and the alignment of various parts of the reading/copying process.
It's a bit like high end audio -- a lesser system may not be perfect,
but it can be enjoyable.

I enjoy listening to my home system, but I can still occasionally get
goose bumps hearing something on my car radio.  This is not to say that
we shouldn't improve our current technology.  We can and should do so.

Comments?

Bob Billings