RE: 11-limit, 31 tones, 9 hexads within 2.7c of just (wa s: Strict JI considered undesirable)

OK, this 31-tone version looks like it might be a partial tempering of a 4-d
periodicity block. Let's see . . . Two of the unit vectors can be read off
the lattice (by looking at the instances of C, for example) as 224:225 and
384:385; in your first lattice the Ex/Gbb dichotomy suggests a ratio of
121:120; and since you don't have any commatic pairs it looks like 81:80
might be the last one. Factoring these ratios:

224:225 = [2^5*]3^(-2)*5^(-2)*7^1*11^0
384:385 = [2^7*]3^1*5^(-1)*7^(-1)*11^(-1)
120:121 = [2^3*]3^1*5^1*7^0*11^(-2)
80:81 = [2^4*]3^(-4)*5^1*7^0*11^0

So the Fokker matrix is

-2 -2 1 0
1 -1 -1 -1
1 1 0 -2
-4 1 0 0

and the determinant of that matrix is -31. Looks like a winner! So your
temperament distibutes the two smaller commas but not the two larger ones.
It is much like the diatonic scale in meantone, which can be seen as a
7-tone 2-d p.d. with unison vectors 81:80 and 25:24 where the smaller comma
is distributed but the larger comma is not, or my symmetrical decatonic
scale, which can be seen as a 10-tone 3-d p.d. with unison vectors 64:63,
50:49, and 49:48, where the two smaller commas are distributed but the
larger is not.

In your second lattice (where it appears you misspelled a few Fbbs as Fb)
the 224:225 and 384:385 unison vectors can still be found in the lattice.
The B#/Cb dichotomy suggests a 100:99 comma; the 121:120 is gone, while the
81:80 appears to remain a delimiting vector.

100:99 = [2^2*]3^(-2)*5^2*7^0*11^(-1)

F.M.:

-2 -2 1 0
1 -1 -1 -1
-2 2 0 -1
-4 1 0 0

Determinant: -19

So there are only 19 different notes in the corresponding p.d., though your
lattice still shows 31. That means this one is not equivalent to a tempered
periodicity block, or at least not one with these commas. I see -- what's
happening is that although you consider one B# to be inadmissable because
it's 100:99 from Cb, another B# 80:81 away from the inadmissable one is
right there in the lattice. So although you don't have any 100:99 pairs or
80:81 pairs, you must have 12 pairs separated by the product, 45:44 (=38.9
cents in JI). It is suggestive that for the second lattice you state: "It
may be useful when fewer than 31 tones are to be made available." Hmmm...