How anomalous temperament intervals work

I mentioned the nice 9/7's which show up as alternatives to 5/4 when
using the Wilson fifth in a 12-note meantone temperament, and Margo has
discussed 14/11. Here's a brief rundown on how this relates to linear
temperament theory.

The standard septimal meantone maps 3/2 to one generator, 5/4 to 4, and
7/4 to 10. If we put such a thing on 12 notes, we hop backwards by 12
generators when we reach the wolf. We get the following:

(1) 3/2 --> 32/21

(2) 9/8 --> 8/7

(3) 5/3 --> 12/7

(4) 5/4 --> 9/7

(6) 7/5 --> 10/7

We've now come half-way round the cicle of fifths, and can stop. To
explain this table, the first number, in parenthesis, is both the
number of generators needed to reach the interval approximating the
second number, *and* the number of alternative versions of the
interval which "hop back" 12 generator steps. The fifth is reached in
on generator step, so there is one wolf fifth, which in septimal
meantone is an approximate 32/21. The major third is reached in four
generator steps, so there are four anomalous major thirds which are
9/7 in septimal meantone, and so forth.

Another example would be a "meanpop" tempering of 19 notes. "Meanpop"
is the 11-limit version of meantone which maps 11/8 to -13 generator
steps. A similar table for meanpop/19 would go

(1) 3/2 --> 22/15

(2) 9/8 --> 11/10

(3) 5/3 --> 33/20

(4) 5/4 --> 11/9

(6) 7/5 --> 11/8

(8) 14/9 --> 32/21

(9) 7/6 --> 8/7

We've now gone half-way round; we could continue as

(10) 7/4 --> 12/7

but this repeats (9). We might want to fill out the table completely
up to 9, however, as otherwise we miss things such as 21/20-->36/35
which may possibly be of interest.