source file: m1585.txt Date: Tue, 17 Nov 1998 17:07:43 -0500 Subject: meantone vs. just From: "Paul H. Erlich" Ken Overton's page _Distinctions Between Just-tuned Key Areas Within Musical Contexts_ (http://music.dartmouth.edu/~kov/lerdahl/tuningPaper.html) states: >Rasch's study (1985) of large sequences of simultaneous tones found that mistuning of >the intervals of the melody was more disturbing than mistuning of simultaneous >intervals. This suggests that listeners compare melodic intervals to an abstract interval >standard. This is a very interesting statement but unfortunately the Rasch paper does not appear in the list of references. Anyone know which study this refers to? Anyway, this (Rasch's conclusion) is a statement I've wanted to make for some time but I kept quiet because of an apparantly contradictory fact: the fact that much finer deviations are perceptible in the tuning of simultaneous tones (harmonic intervals) than in the tuning of successive tones (melodic intervals). However, these facts are not contradictory at all. What is more perceptible is not necessarily more disturbing. And I knew this, as a musician, but I just couldn't rationalize it because of the apparant contradiction. The upshot of this is that I unequivocally prefer meantone to standard just intonation for 5-limit diatonic music. The reason is that all the melodic intervals of a given type (using traditional musical nomenclature) are all the same size in a given meantone tuning (and quite close to the same size in a given key of a circulating temperament), so they can form an abstract interval standard in the mind of the listener. The worst harmonic error in a range of different meantones is under 6 cents. In just intonation, two different sizes exist for the unison, major second, minor third, and perfect fourth (and their inversions), and the differences are 21.5 cents. The point is that although a 6-cent harmonic error may be easier to hear than a 21.5-cent melodic error, the latter may in fact be more disturbing. A side note on Ken's page: The standard use of just intonation, as Doren's teacher pointed out, is to tune notes such as the second in the major scale according to their context. A looser interpretation of JI would allow the roots of the chords to come from, say, a meantone tuning, so long as the harmonic simultaneities were tuned exactly 4:5:6 (major) or 1/6:1/5:1/4 (minor). Chords like 27:32:40 (Ken's ii chord) would not normally occur in a just intonation performance of a common practice piece of music. Ken Overton's interpretation of just intonantion, which does not allow for variable pitches, allows "just" such sonorities, which is completely unprecedented and does not accord with any normal use of the term JI as far as I am aware. Ken, I've cc'd you so that you may respond to this discussion on the Alternative Tuning Mailing List. -Paul Erlich