Partch and resolution

The current discussion of tonal drive and resolution in JI
seems to me to miss an elementary point stressed by Harry Partch
himself. JI increases the range of available consonance and dissonance
however C and D are defined, see Tenney's book _A History of
Consonance and Dissonance_.
Hence, in some contexts the dominant seventh chord should be
tuned 4:5:6:7 for maximum consonance, but in others one might wish to
use 20:25:30:36 (1/1 5/4 3/2 6/5) or even 36:45:54:64 (1/1 5/4 3/2 16/9).
One should read Chapter 11, "The Question of Resolution,"
in HP's _Genesis of a Music_, 2nd edition, pp 181-194. While HP
wrote everything in the key of G (392 hz), in part because of
material and technical limitations, in part for theoretical reasons
(monophony is the harmonic expansion of a single tone, the 1/1, see
the definition on page 71), he was very aware of resolution and
chordal motion and wrote some extremely dissonant, yet powerful
progressions. (Allen, do you still have your notes from his UCSD
class?).
Partch suggested several principles: Resolve voices by very
narrow intervals, avoid 11 O or U identities (11 th harmonic or
subharmonic of the tonic) in the bass, space the voices widely, and
mix harmonic and subharmonic (O and U) chords in progressions. One does
not have to use complete hexads (1 3 5 7 9 11 harmonics) and the remaining voices may be doubled as desired. Non-harmonic tones and tones outside
the conventional 43-tone scale may also be used (HP sometimes did this
on the canons and even changed reeds on the Chromelodea, i.e., 25/21
in Delusion.)

--John

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 11 Nov 1995 03:15 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id RAA18141; Fri, 10 Nov 1995 17:15:25 -0800
Date: Fri, 10 Nov 1995 17:15:25 -0800
Message-Id: <199511110113.RAA17982@eartha.mills.edu>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

Pardon my ignorance but what is meant by "LCM" and can someone explain
"minimum chords"?


thanx--

=========================================================================
| Allen Strange |
| http://cadre.sjsu.edu/music/strange.html |
|_______________________________________________________________________|
| Electro-Acoustic Music | International Computer Music Association |
| Studios | 2040 Polk St., Suite 330 |
| School of Music | San Francisco, CA 94109 |
| San Jose State University | Telephone + (408) 395-2538 |
| 1 Washington Square | Fax + (408) 395-2648 |
| San Jose, CA 95192-0095 | Email: icma@sjsuvm1.sjsu.edu |
| Telephone +(408) 924-4646 | |
| Fax +(408) 924-4773 | We hope to see you at the ICMC96 |
| | On the Edge in Hong Kong |
| | ICMC96@cs.ust.hk for info |
|=======================================================================

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 11 Nov 1995 23:38 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id NAA00386; Sat, 11 Nov 1995 13:37:59 -0800
Date: Sat, 11 Nov 1995 13:37:59 -0800
Message-Id: <951111213450_71670.2576_HHB6-4@CompuServe.COM>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

I believe that LCM is the usual mathematical abbreviation for "Least Common
Multiple". Marion and probably others use that as an indicator of the overall
harmonic complexity of a chord. The lower the LCM, the simpler the chord.

For example, the least common multiple of 4, 5, and 6 is 60. That's the
smallest number that is an even multiple of all three (4x15=5x12=6x10=60). So
that major triad voicing would be equally complex harmonically as a 10:12:15
minor triad (LCM is also 60), even though its numbers are somewhat higher on the
whole.

Some on the list have disputed whether LCM is the best measure of harmonic
complexity. Personally, it strikes me as a reasonable rule-of-thumb, although I
haven't personally compared it with other possibilities.


Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sun, 12 Nov 1995 06:00 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id UAA02660; Sat, 11 Nov 1995 20:00:29 -0800
Date: Sat, 11 Nov 1995 20:00:29 -0800
Message-Id: <199511120358.WAA19511@freenet3.carleton.ca>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu