I was looking into why my attempt to find an analog to Miracle with

2401/2400 a comma and with a generator between 50/49 and 49/48 didn't

work, and found out something fascinating--such a thing is

algebraically impossible. However, we can find an analogue of sorts.

For a 7-limit wedgie to have 2401/2400 as a comma, it must be of the

form [4b - 2a, a, b, -4c - 5a, -2c - 5b, c] with a, b, c relatively

prime. This tells us, for instance, that a fifth always requires an

even number of generator steps to be represented, and so a fifth can

never be a generator for such a temperament. If we look at the number

of generator steps needed for 49/48 (or equivalently, 50/49), which

is the first component of the wedge of the above wedgie with the

Monzo representation of 49/48, we get that it is 2a-2b, so we can't

have what I was looking for, which is that this be 1. However, we

*can* get something with two generator steps, with a wedgie

[2n, n+2, n+1, -5n - 4c - 10, -5n - 2c - 5, c]. Such a temperament

will have a generator of 7/5; of course (7/5)^2 = 49/25 = 2 (49/50)

and so this has the required two-step relationship to 50/49 (and so

49/48.)

If we look for wedgies of low badness in this form, we find them for

n = -48, -15, -13 and most especially, n = 20. This gives us a good

microtemperament, which is the closest thing available as an analogue

to Miracle unless you are willing to count things like Ennealimmal,

with non-octave periods. The wedgie is

[40, 22, 21, -58, -79, -13], the mapping

[[1, 21, 13, 13], [0, -40, -22, -21]], 83/171 is a poptimal

generator, and it can be described as 68&171 in terms of standard

vals. The TM basis is [2401/2400, 48828125/48771072].