Totals for 31-tET subsets

Here are my totals for subsets in 31-tET. This does not include
reduction for Z-relations. That is in my Files section...

First, full count for Subsets 0-15:

1
1
15
145
1015
5481
23751
84825
254475
650325
1430715
2731365
4552275
6653325
8554275
9694845

Next, reduced for mirror-image, again, for 0-15

1
1
15
80
560
2793
12103
42640
127920
325845
716859
1367184
2278640
3329165
4280355
4850640

Of course, 16-31 are the same as 0-15 backwards.

Since 31 is prime, there are no other group-theoretical symmetries to
consider. Since it is odd, there are no complement-sets to consider
(other than 15 and 16, 14 and 17 etc). I guess that leaves only
C31 and D31 then!

Now let's consider the 7-limit. The largest set factors into
3^2 * 5 * 17 * 19 * 23 * 29, which is nothing special, just
factors in the binomial Binom(31,15)/31. Reduced for mirror image
we get 4850640, 2^4 * 3^2 * 5 * 6737, not pretty, symmetrical
sets are are 6435, 3^2 * 5 * 11 * 13. A little better.

But that has nothing to do with the 7-limit lattice, hexanies,
or 7LTD. 23751 and 12103 are all the possibilities for hexachords.
These would have representatives in both the stellated hexany
and 7LTD, as with 12tET. It would be fun to map out all the hexanies
and tetrads in 31t-ET and see which sets they correspond to. Tetrads
would be boring, you would only get 1 utonal and 1 otonal.

How many notes would be canvassed in 31 by each (SH and 7LTD), and
what sets could you make from them, and how would that relate
set totals?

Another task is applying group-theoretical operations independent
of an ET, on these lattices, although I think one's choices would
be limited.

Paul Hj