source file: m1413.txt
Date: Tue, 12 May 1998 09:23:38 -0500 (CDT)

Subject: Re:  TUNING digest 1404

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Mon, 11 May 1998, Bill Alves wrote:
> >                                       To me, the essential things are
> >    that there are 12 pitch/interval classes and no wolves; if those two
> >    conditions are met (that pretty much describes the circulating
> >    temperaments that were used increasingly throughout the Baroque) I'd
> >    be willing to call it some form of 12TET.
[snip]
> 
> So, if your point is that a composer will write the same music whether the
> temperament is 12TET or 12TET-like, I would have to add the above criterion
> (symmetrical distribution of dissonance) to your two conditions on the
> definition of 12TET-like.

No, that's not quite my point.  My point is that unequal circulating
temperaments, even with key color, are so close to 12TET compared to
other stuff that I consider them still part of the whole process of
exploring the possibilities of the number 12.  If you think of a tree
diagram:

-+-Just Intonation
 |
 +-Open (meantone) temperaments
 |
 +-Closed (circulating) temperaments
   |
   +-with 12 pitch classes
   | |
   | +-unequal with key color
   | |
   | +-Unequal with little or no key color
   | |
   | +-absolutely equal
   |
   +-with 19 pitch classes
   |
   +-with 31 pitch classes
   |
   etcetera . . .

I don't consider meantone very 12-ish because the wolves make some
intervals and triads unusable, so instead of 12 usable triads there are
really only 8 (okay, 24 and 16, but you know what I mean)--and even if
you add more notes you still can't make the enharmonic modulations,
because the circle doesn't close.

Paul Erlich has mentioned that he's been messing with a
"well-temperament" variation in his 22TET work, but I doubt he considers
it significantly de-22-ated. (-ized?)

This is _really_ splitting hairs.  Agree or disagree as you will.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Churchill? Can he run a hundred balls?"
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