Correlation of Partch Limit with LCM

Since Paul E finds Partch's limit to be superior to LCM as a
predictor of consonance, I have again made an attempt to find a
definition of this concept in his book without much success.

Having made at least some effort to wade through Partch's polemic
pronouncements, I feel I might be entitled to ask a question:
Would it be fair to say that the Partch's limit for a given ratio
is derived by enforcing octave equivalence and then taking the
largest odd number.

Assuming that might be true, the Partch limit of 3:4:5 would be
taken by octave inverting it to 4:5:6 and then calling the limit
5?

Is a given Partch musical space defined by just one limit, or are
more required?

I would like to determine this exactly, so I can determine the
degree of correlation between LCM and the Partch Limit.

Marion

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 12 Jul 1997 09:04 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA23102; Sat, 12 Jul 1997 09:05:10 +0200
Date: Sat, 12 Jul 1997 09:05:10 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA23148
Received: (qmail 1869 invoked from network); 12 Jul 1997 07:04:41 -0000
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 12 Jul 1997 07:04:41 -0000
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

On Sat, 12 Jul 1997, Charles Lucy wrote:
> All this chat about meantone tuning is very interesting, yet it
> would seem very difficult to affirm the details of which tunings
> were used on keyboard instruments, as the tuning is perishable.

Haven't you been listening? Daniel has several times mentioned the fact
that many of the organs available to Mozart were in meantone. Organs
hold their tuning splendidly.

> Does anyone have access to physical fretted instruments from the
> periods in question, so that fret, nut and bridge distances may
> be measured?

Meanwhile, fretted instruments have used ET almost exclusively
throughout their history, because of the difficulty of frets needing to
be in different places from one string to the next.

--pH http://library.wustl.edu/~manynote <*>
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 12 Jul 1997 17:35 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA23361; Sat, 12 Jul 1997 17:35:47 +0200
Date: Sat, 12 Jul 1997 17:35:47 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA22873
Received: (qmail 19837 invoked from network); 12 Jul 1997 15:35:43 -0000
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 12 Jul 1997 15:35:43 -0000
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

On Sat, 12 Jul 1997, Charles Lucy wrote:
> All this chat about meantone tuning is very interesting, yet it
> would seem very difficult to affirm the details of which tunings
> were used on keyboard instruments, as the tuning is perishable.
> Does anyone have access to physical fretted instruments from the
> periods in question, so that fret, nut and bridge distances may
> be measured?

Of course, the other instrument that if fairly stable in tuning is the
organ. If pipes are 'dead-cut' to 'correct'length,(which was not uncommon
in earlier times, and not uncommon now amongst better builders) then it is
possilbe to get a fair idea of the builders ideas about tuning. In fact,
a lot of the info about tuning does come from organs, especially organs in
poor areas, where the resources were not available to 'up-date' the organ
to the latest fancy.

Joe Downing,
in Syracuse

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sun, 13 Jul 1997 14:04 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05968; Sun, 13 Jul 1997 14:05:03 +0200
Date: Sun, 13 Jul 1997 14:05:03 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA05808
Received: (qmail 8669 invoked from network); 13 Jul 1997 12:04:49 -0000
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 13 Jul 1997 12:04:49 -0000
Message-Id: <33C725C5.2800@erols.com>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu