Peter Phillips wrote:

> 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.

Let me respectfully disagree (but maybe I just didn't make clear the
level of discussion, which was "in principle/in theory", not "in
practice"):

Any paper roll can have a resolution down to the size of a "paper
atom".  There is e.g. no physical reason that prevents punching two
holes for two different notes so that the onset of the notes differs
one nanosecond.  Time resolution of a continuously moved paper roll
is analog.

> 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.

No.  You cannot set it to a resolution of [square root of 20000] ticks
per quarter, simply because this is not a rational number.

> ... You can have a higher MIDI resolution, but there's little point.

Of course I agree that, in practice, there is a useful upper limit on
time resolution.

> 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.

Of course it is :-)  But it's not binary.

> But it's still an on-off system ...

Well, no.  You cannot map 3 states to on-off: Either you need a
non-integral number of binary digits (or bits), which is physically
impossible to do, or you use 2 bits, but then you have an additional
4th state (i.e., you get redundancy).  Also aggregating many
base-3-states into a set of bits will always leave a little redundancy,
as a power of 3 is never equal to a power of 2.  So ternary is
fundamentally "non-on-off", or non-binary.

But I'll stop now with my esoteric considerations ...

Regards

Harald M. Mueller