Partch Limit vs Prime Limit

I have always used the term "limit" as if it were really "prime
limit", and I think I am probably not the only person who sees
things this way. I find Partch's treatment of the subject to be
somewhat muddy. He definitely refers to a 9 limit, therefore, he
does not limit his limits to prime numbers.

I did a few minutes of research to find out what he really was
trying to say, and was referred to "identity" which was defined
in terms of "correlatives" and "pole of tonality", but I didn't
find a definition for "pole of tonality", or "correlatives".

I know that some of you out there probably have gone much deeper
into his work, and understand to some degree what he really may
have meant by all this, but I wonder at the utility of taking the
very simple concept of "prime limit" and confusing it with some
other, much more elaborate concept. Perhaps Partch's concept,
whatever it was, could have been better expressed in other terms
than "limit". My understanding is that the term was pretty well
defined to be something else when he did his work.

I find the concept of "prime limit" to be very useful, but I am
not convinced of the utility of Partch's concept of limit for my
view of diatonic harmony.

For me, the whole "lattice" approach is much less useful than
Aliquot Parts and Least Common Multiple for analyzing scales,
chords, and intervals.

Marion

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 28 Jun 1997 19:11 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA18913; Sat, 28 Jun 1997 19:11:45 +0200
Date: Sat, 28 Jun 1997 19:11:45 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA14412
Received: (qmail 4393 invoked from network); 28 Jun 1997 17:11:32 -0000
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 28 Jun 1997 17:11:32 -0000
Message-Id: <17181797810146@cybersim.com>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu