Tone group relative epimorphic scales

By "tone group" I mean a regular temperament equipped with a
particular tuning, see

http://66.98.148.43/~xenharmo/regular.html

I've mentioned a few times that the definition of epimorphic scales
generalizes to tone groups; p-limit JI, after all, is a tone group. A
tone group can be defined as a finitely generated subgroup of the
additive reals, or equivalently of the multiplicative positive reals.

Epimorphic scales for r2 temperaments include MOS/DE, and are very
close to the "modmos" scales I've discussed before. For an r3
temperament, they sometimes are pretty close to being 5-limit scales.
For instance, the 7-limit can be expressed in terms of [2,3,5,7], but
equally well in terms of [2,3,5,225/224]; if we invert the matrix of
monzos we get a matrix with columns
[<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|, <0 0 0 -1|]. The first three define
the mapping of the 7-limit to the generators of tempered 2,3,5 for
marvel tempering. If we choose the tuning where 2,3,5 are pure, we get
the 5-limit (and not very terrific, but certainly usable, 7s.) In
practical situations, if we have an epimorphic scale in this tuning,
it will stay epimorphic if we retune to 1/4 kleismic, 72-edo, etc.

This approach won't always work. For 2401/2400, we need something like
[2,49/40,10/7,2401/2400] to represent the 7-limit, and the group
generated by {2,49/40,10/7}, is not a p-limit group, but is {2,5,7}.
We could, therefore, look at epimorphic scales in terms of just the
primes 2, 5 and 7, and those for practical purposes could be taken as
epimorphic breed temperament scales. Inverting the monzo matrix of
[2,5,7,2401/2400] gives us
[<1 -5 0 0|, <0 -2 1 0|, <0 4 0 1|, <0 -1 0 0|], which allows us to
translate the 7-limit to breed-tempered 2,5, and 7. 5-limit scales
which temper well via marvel tend to be spread along the secor axis,
and similarly here we would look along the 49/40, neutral third, axis.
Perhaps a look at {2,5,7} diamonds tempered by breed would be interesting.