Z-relations in 22-et by subset

Just a quick explanation of the file I just posted. (22tETZrels.xls)
That pattern I have found is that ALL Z-relations in 22-et
are multiples of five, (usually 10), not only for all the Z-relations
in a subset (like C(22,11)-types), but for each type of Z-relation
in a subset (doubles, triples, quads, sextuples). So I think there is
meaning to classifying musical sets by their interval vectors.

Quick definition: Z-related sets are when 2 or more set types share
the same interval vector - which is a count of all the intervals in a
set - for example in 22 et, it would be the intervals from 1 to 11,
since 12 through 21 are just inversions. Thanks to Jon Wild for
supplying the raw data on interval vectors!

There is also the issue of hendecachords in 22-et: complementary sets
can be Z-related. I know how many there are, but it gets more
complicated because these complementary z-related pairs can also
share the same interval vector with another singleton, pair etc.

So, starting with the number of set types (this is when the sets are
reduced for transposition and mirror-inverse) I have classified by
singletons, doubles, triples etc. within each subset class. The
first column is the number of sets before you reduce for Z-relation
the second column is dividing by 2,3,4 etc. which gives you the
number of interval vectors. (reducing for z-relation). The last
column gives the differences. Totals for each column are given.

22-et is kind of special because it has this pattern of using
multiples of five in its Z-related doubles, triples, etc. In fact,
every one is a multiple of ten EXCEPT doubles in hexachords and
doubles in hendecachords of 22-et.

I know this isn't exactly "tuning" but someday I hope to tie this
into the mathematics of tuning!

Thoughts anyone?

Paul Hj