JI vs. equal temp.

Many of the JI enthusiasts neglect to mention that the language of
Common Practice (i.e., Western c. 1600-1900 plus Tin Pan Alley, etc.)
music requires the vanishing of the syntonic comma. Some form of
temperament (not necessarily equal despite Neil's claim, but any regular
or irregular meantone temperament) is therefore required for
performances of this music. If one wishes all the chords to be perfectly
pure, and one does not make constant slight adjustments to the pitch
level of common tones, one will find the pitch of the music wandering,
usually descending by several commas. But that does not mean JI music
cannot support chord changes. From the latest issue of The Microtome, an
interview with Ben Johnston:

"I asked myself, suppose in writing some of the really very intense slow
movements that he did, Beethoven had not had the tempered scale to work
with, but had instead just intonation, what might that music have been?
Then I tried to write that piece, as an exercise for myself. It's
actually part of a piece--I liked it well enough that I put it into a
piece. But at first of course it's just to find out. The richness is one
thing, the flexibility is another. The typical Beethoven progression,
for example will cause you to drop by a microtonal amount every time the
progression repeats itself. What I did was to work it out that the pitch
would drop, gradually, until the whole thing drops almost a half step,
and then I force it to come back up by working out progressions that
would make it do that. That is, of course, quite different from what
Beethoven was dealing with. He would have had to deal with that had he
been actually using just intonation with the kind of interests that he
had."

For guitarists, the set of pitches that Ben Johnston needed for this
example is quite forbidding, as is any interval less than a comma near
the middle of the fretboard. Equal temperaments make sense for guitar
music because only then is the same set of pitches available on all
strings, and because styles that make use of bending come to grief when
one encounters a dog-legged fret. Of course, a fretless guitar
alleviates all these problems, but even so one still has to contend with
the error of one syntonic comma in tuning the open strings of a guitar
to something resembling standard tuning. This will be a problem in any
tuning that is not a meantone tuning (12-, 19-, and 31-equal are
meantone tunings that happen to be finite). Neil H. has stated that the
interval between the G and B strings on his 34-tone guitar is one degree
of the tuning larger that the "best" major third, and Jon Catler's D and
G strings are one syntonic comma farther apart than a just perfect
fourth. My 22-tone guitar also has two adjacent strings separated by a
major third augmented by one degree; although this interval is only 1
cent off a just 9:7, it is too low (approx. Eb-G below middle C) to
sound consonant by itself.


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