Ragmonza 225/224 planar

When tuning 225/224-planar (which used to be called both Byzantine and
Pauline until people objected) there is no payoff in not having minor
thirds pure (the approximation to 7 involving 3 and 5 only in their
product of 15) and optimizing makes it pure. If we assume pure 6/5s
(and octaves, of course) we get a one-parameter family of
225/224-planar temperaments, rather as if it were a linear temperament.
If s is the amount by which the thirds and fifths are flat, we have

q3 = 3/s

q5 = 5/s

q7 = 225/(32 s^4)

for the size of the "3", "5", and "7". If s = 32805/32768 is exactly a
schisma, we get a 5-limit version of 225/224-planar

r3 = 32768/10935

r5 = 32768/6561

r7 = |55 -30 2>

r7 is shy of 7 by a comma which is ragisma/monzisma, which I guess we
may call the ragmonza of |-55 30 2 1>.

Another plausible 225/224 planar tuning sets the 7s to be pure, which
makes s = (225/224)^(1/4), a schisma of 1.928 versus one of 1.954. We
may also want to make 7/5 and 7/6 pure, which means
s = (225/224)^(1/3) and we flatten thirds and fifths by 2.571 cents.