RE: 41-TET and those difficult synths

Thanks Carter for describing a useful technique which at least wasn't
obvious for me.

> (It occurs to me that some just scales. e.g. tetrachordal types, might
> have internal congruences and repetitions that could exploit such fixed
> channel offsets. These would, though, require tedious calculation on a
> case-by-case basis. It would be an interesting exercise to determine
> if the Partch scale is sufficiently self-similar to use this technique.)

The answer is yes. One can easily determine this with Scala. Do
load partch_43
show transpose
It shows how many notes are different for each transposition. Look at
the second amount which shows how many are different regardless of
degree order. If we take Brian's upper limit of 17 notes per channel
then we are looking for a transposition with about 43-17& notes
different. Candidates are 7 and 12 with 25 and 14 with 27. Let's take
7 (10/9). Then we do
copy 0 1
key 7
intersect 1
show/line
and we get this scale
81/80 21/20 16/15 11/10 9/8 6/5 9/7 4/3 27/20 7/5 3/2 8/5 18/11 27/16 12/7
16/9 9/5 2/1
Midi channel 1 then gets a pitch bend of 10/9 182.4 cents.
With some more manipulation we determine which pitches still have to
be done:
33/32 12/11 8/7 14/11 21/16 11/8 16/11 32/21 11/7 7/4 11/6 64/33
That's only twelve, with one note per channel there would be enough
channels left. Some can be grouped together like the ones with 11 in
the numerator, another group with 11 in the denominator, etc. But how
to get a minimum amount of channels in general could indeed be
somewhat tedious. If you settle for a smaller range than that of the
piano it can be less.

Manuel Op de Coul coul@ezh.nl

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Date: Fri, 20 Dec 1996 07:02:13 -0800
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