Near-linear 7-limit temperaments

I've already mentioned that beta (the 5120/5103) temperament, tuned to
the (1,1) list of beat ratios, is very nearly hemififths. Here (n,m)
means (b5,b7) where 5+b5*x is the approximate 5, 7+b7*x is the
approximate 7, when 3+x is the approximiate 3. Other examples of this
kind for other beat ratio lists can be given. One thing which can be
done with these is to temper a Fokker block using the commas of a
temperament for its construction, or some other detempering of a MOS
of the temperament. Tempering this with a tuning of the temperament
leads to a MOS. Tempering it with a (n,m) tuning of a rank three
temperament leads to a near-MOS; that is, a variant, slightly
irregular MOS with some synched septimal chords.

Examples of such near-linear temperaments are the (0,1) tuning of
81/80 planar, the (0,0) tuning of 81/80 planar, and the (2,2) tuning
of marvel. The (0,1) tuning has 1/4 comma fifths, pure major thirds,
and an approximate 7/4 which is a root of
16*s^4-64*s^3+96*s^2-64*s+11=0. It shrinks 126/125 to 0.74 cents, and
sends 225/224 to -0.74 cents. Hence, it works as an irregular meantone
tuning. The (0,1) tuning has a 1/4 comma fifth, and pure 5s and 7s. It
is very nearly a semififths tuning, where by "semififths" (not
hemififths) I mean another neutral third temperament with comma basis
81/80 and 6144/61225. This tuning shrinks 6144/6125 to a tiny -0.0145
cents. The (2,2) marvel tuning, which has an approximate 3 given by
the positive real root of 4*a^4-4*a^3+a^2-64*a-32=0, shrinks 1029/1024
and 2401/2400 to 2/3 of a cent, and can therefore be used as a miracle
tuning.