More on Z-relations

I have analyzed all sets from 1 - 22tET for their Z-relations to look
for clustering (like I found with 22-tET)

First, below twelve, there are only two sets with Z-relations: 8-tET
has one Z-related pair in C(8,4)-reduced and 10-tET has three Z-
related pairs in C(10,5)-reduced (I wish I had a good name for this,
I am talking about the number of set types (combinatorical sets
reduced for mirror inverse and transposition).

Of note between 12 and 22 are:

14-tET: 7 (septachords) has 96, 6 has 12, 5 has 12. All pairs.
15-tET: 7 has 20, 6 has 50, 5 has 10. All pairs.
17-tET: 8 has 104, 7 has 48, 6 has 32. All pairs.
19-tET: 9 has 312, 8 has 180, 7 has 114 and 6 has 42. All pairs.

The even ones are more complicated and involve triples and quads.

14-tET: All are multiples of 12.
15-tET: All are multiples of 10.
17-tET: All are multiples of 8.
19-tET: All are multiples of 6.

Also, 20-tET: All its doubles are multiples of 8.
13-tET: Has a Z-related pair (in 4, counting as 2 sets) and 2 Z-
related pairs in 6 (counting as 4 sets).

12-tET: 6 has 30, (15 pairs), 5 has 6 (3 pairs) 4 has 2 (1 pair).
It's interesting to note that this matches C(10,5)-reduced with
3 pairs and C(8,4)-reduced with 1 pair.

I will update the files section with a nice spreadsheet.

So far, 22-tET is the only "nice" ET with Z-related triples (quads
and sextets)...

My goal is to find a set of formulas that calculates Z-relations for
any set size. Might not be possible, but I am hopeful. Usually Z-
relations can be found as transformations (like M5 symmetry) or
complementability (like the 15 complementary pairs in C(12,6)-reduced
(or should I say, set types?)

Paul Hj