magic chord

I was playing around with a harmonica sound on my Ensoniq VFX-SD tuned
as close as possible to JI (the scale being the JI version of the
pentachordal decatonic scale of my paper, hence 12 notes per octave with
two 50:49 "commas"). Playing the chord 1/1 5/4 3/2 7/4, and dropping the
3/2 down to 7/5, I didn't hear much of an increase in dissonance. After
some confusion, I realized that the only potentially dissonant interval
in this chord is the 28:25 (196 cents) between 5/4 and 7/5. Now the
Ensoniq's tuning tables allow cents values for each note, and I had
approximated the other intervals in such a way that the 28:25 was
nominally represented by 199 cents. Since the true tuning resolution of
the Ensoniq VFX-SD is 512 notes per octave, this interval was probably
represented by 85/512 octave, or 199.2 cents. This is only 4.7 cents off
a just 9/8, which explains the relative consonance of the chord. It is a
near miss to a saturated 9-limit chord. A true 28/25 would be 7.7 cents
off a just 9/8, which would be quite a bit more dissonant.

The difference between 28/25 and 9/8 is 225/224, a fundamental
comma-like interval in Fokker's writings. So the magic chord 1/1 5/4 7/5
7/4 will be possible in any temperament where the 225/224 vanishes. The
simplest ET that sounds like 9-limit JI is 41tET, and the 225/224 does
vanish in 41. The chord is 0 13 20 33 in 41. In 72tET, which sounds like
11-limit JI, the 225/224 also vanishes. The chord is 0 23 35 58 in 72.