meantone vs. just

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