Harald Mueller (MMD 030320) makes the valid point that binary could
also be called discrete.  This of course assumes that discrete can
refer to something with two discrete states, which for a piano roll
is either a hole, or no hole.  That's what digital is all about.

Binary is perhaps not the best term, as it refers to the mathematics
behind digital data, where 1's and 0's can represent a numerical value.
An example is the 16 levels of volume encoded by Duo-Art using four
lines of holes, where 4 to the power of 2 (binary) is 16.

However, I'm not sure about Harald's assertion regarding the timing
of the digital information on a piano roll.  He suggests that there
is a difference between MIDI data construction and the information
on a piano roll.  I can't agree.

An Ampico roll running at around Tempo 80 [8.0 feet per minute] has
a timing resolution of 20 milliseconds or so.  That is, the minimum
period between any two rows of holes is 20 milliseconds, quite a high
resolution.  A MIDI file can be set to have any resolution you want.
I use 384 ticks per quarter note, which at a tempo of 120 [beats per
minute] equates to 1.30 milliseconds resolution.

In other words, timing of the data is not unique to MIDI.  Digital
data is simply a way of storing information in a particular way.  It
therefore has to store every aspect of the information, which for piano
music must always be the three essentials of music: which note, when
it's played, and how loudly.

It's fortunate that our forebears discovered the virtues of digital
recordings, as today we can convert a piano roll into a MIDI file (or
other digital formats) and get pretty much an exact replica of the
original roll.  Because the MIDI data can have a higher resolution than
a piano roll, the timing of the notes will be within 1.25 milliseconds
of the original.  You can have a higher MIDI resolution, but there's
little point.

Harald asks a good question about using two levels of pins, or wider
holes, etc., to record a performance.  I'd suggest such a system, if it
exists, is still essentially digital, but with more digital variables.
E.g., a wider hole would trigger something, where a narrow hole would
trigger something else, and no hole would do something else yet again.
But it's still an on-off system, it's just encoded in a more complex
way.

There are many instances of encoding digital data with more than two
variables.  ADSL and ISDN are examples where all kinds of things go on
to get the data from A to B as quickly as possible.  But it's still
good ol' digital.

Peter Phillips
http://members.optushome.com.au/eleced/index.htm