operations over scales (J.Haluska)

Hi all,
Let the violinist John feel and play individually the Bach's Air ("On the
string G") in the Pythagorean Tuning. Let the violinist Jane feel and
play this Air individually in the 1/4-meantone tuning (why not?). We do
not doubt that the professional players John and Jane are able to play
this piece together with pleasure. The question is: IN WHICH TUNING?
More generally: clearly 6+2=8,6-2=4,6:2=3, 6x2=12, etc., where +,-,:,x
are operations over numbers 6 and 2.
CAN ANYBODY TELL ME SOMETHING OR GIVE A REFERENCE ABOUT OPERATIONS OVER
SCALES? They can be unary(one player), binary (duo), ..., n-ary (the
assembly play).
Regards,
Jan Haluska
High Tatra - Slovakia

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End of TUNING Digest 1457
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> I think its fair to say that there's a real "chicken and egg" problem
> with adaptive tunings. It's hard to compose or perform with adaptive
> tunings because there's no nice implementation - and there's no nice
> implementation because no-one is composing/performing that way.
>
> I went to Ensoniq and gave a presentation about various tuning
> issues, with a heavy emphasis on adaptive tunings, and they thought
> it was all very interesting, and thank you for coming. Given that their
> tuning expert (Steve Curtin) has moved on to other places, I don't
> they're a likely source for something like this at the current time
> (though I'd love to be proven wrong).
>
> All of my adative tuning work has been "off-line". I make a standard
> MIDI file, read it into my adaptive algorithm, wait a while, and then
> check out how it did. This is a very awkward way to work, and is
> essentially a kind of 'post-production' method as you describe. I
> think adaptive tunings will only be really useful when you can sit
> down and play as if it were a musical instrument. Such 'post-
> production' methods are fine for demonstrating the concepts, but not
> for exploring the technique fully.
>
> I'm currently attempting a 'real-time' version using Max, though its
> unclear at the present time how many simplifications are going to be
> needed before it will actually run in real time. Of course, this is for
> MIDI instruments only. A far more interesting thought is the idea of
> operating on acoustic sounds...
>
> Bill Sethares

I think Justonic's Pitch Palette is a good solution for adaptive tuning or
modulation in just intonation. Before this came along you needed a
synthesizer with a large number of tuning tables. This meant you needed a
Yamaha TX802, DX7IIFD or Kurzweil K2000/K2500, and a computer sequencer to
change the tuning tables.

John Loffink
jloffink@pdq.net