250047/250000

This is (2401/2400)/(4375/4374), so it's an ennealimmal comma. In
monzo form, it is |-4 6 -6 3>, so up to octave equivalence it is a
cube. If we take 5/4 and sharpen it by 126/125 to 63/50, we get
something very close to 2^(1/3); in fact 400.10848 cents. Three of
these are sharper than an octave by 250047/250000.

Equivalence by this comma allows us to express the entire seven limit
by three layers of the five limit lattice. The element c = 63/25 is a
torsion element so far as octave equivalence goes; c^3=1. The
generators of the temperament are 63/50, 3 and 5, which under octave
equivalence becomes c, 3, and 5, with c^3=1. We can reduce the seven
limit to a form where the exponent of 7 is -1, 0 or 1, and we can
reduce the octave-equivalent lattice similarly, leading to the
three-layer picture of the seven-limit. We do this simply by
multiplying any 7-limit rational number q by whatever power of
250047/250000 makes the exponent of 7 in the range -1 to +1. This we
may do by taking the exponent of 7, dividing it by 3, and rounding to
the nearest integer, using that as the power to raise 250047/250000
by. Given any 5-limit scale, we can multiply it by 7 and 1/7, reducing
to the octave, and get another scale three times as large; tempering
these by 250047/250000 might lead to some interesting 7-limit scales.