source file: mills2.txt Date: Sun, 12 Nov 1995 08:54:37 -0800 Subject: Defenition of JI From: jinetwk@hopf.dnai.com (Just Intonation Network) >The Early Music list has just been informed, with the Harvard >Dictionary of music as authority, that Just Tuning is "any >tuning that incorporates five or more acoustically pure types >of intervals within the octave." That means, of course, that >Pythagorean and 1/4-comma meantone, and, for that matter, most >early temperaments, are Just Tunings! Somehow, I don't think >that is the definition that JI advocates use today. The definition of JI that I use (and one that is pretty common, if not universal, among JI users, at least in the U.S.), is essentially that of Partch: Just Intonation is any tuning in which all of the intervals can be expressed as integer ratios, *with a strongly implied preference for the smallest numbers that are compatible with a given aesthetic purpose.* Just Intonation systems are commonly further qualified by the prime factors by which they are generated, e.g., five-limit JI, seven-limit JI, 3 x 7, JI, etc. Pythagorean is a form of JI (three-limit), but not a good system for triadic harmony, i.e., it does not use "the smallest numbers that are compatible with _that_ aesthetic purpose." 1/4-comma meantone is definitely NOT a variety of JI, even though it includes just (5:4) major thirds, because it also includes irrational intervals derived from the square root of 5. The same goes for most of the historical temperaments. Further, the "any tuning that incorporates five or more acoustically pure types of intervals within the octave" definition implies a twelve-tone fixed scale, and most people working with JI today don't restrict themselves to 12-tone fixed scales, or in many cases, to any fixed scale whatever. --DBD ========================================================================== David B. Doty jinetwk@dnai.com Just Intonation Network http://www.dnai.com/~jinetwk Phone:(415) 824-5325 535 Stevenson Street FAX: (415) 864-8726 San Francisco, CA 94103 Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 12 Nov 1995 20:47 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA08225; Sun, 12 Nov 1995 10:47:16 -0800 Date: Sun, 12 Nov 1995 10:47:16 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu