Wizard and 72-et

I've been discussing "poptimal" generators for temperaments on the tuning-math list. A "poptimal" generator can lay claim to being absolutely and ideally perfect as a generator for a given temperament, which makes the question of which ets for a given temperament give us such a generator of some interest.

For 72-et, it seems, sadly, that it is *not* poptimal for Miracle in either its 7 or 11 limit incarnation. It *is* poptimal for Kleismic, but so is 53. However, it does have at least one linear temperament for its very own--the system of two chains of major thirds a half-octave apart I've dubbed "Wizard" (to compare with "Magic".)

Wizard has wedgie [12, -2, 20, 52, 2, -31] and mapping to primes

[[2, 7, 4, 12], [0, -6, 1, -10]]

It has a kernel given by the commas 225/224 and 118098/117649, where the second comma tells us that (9/7)^5 ~ 7/2. It has as 22-note MOS
4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3
which one might compare to Blackjack, though Wizard is hardly in the same league in terms of efficiency. However, its generators of
[1/2, 23/72] *are* poptimal, and the 72-et seems to own this one free and clear, so fans of 72 might take note.