Defenition of JI

>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


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