Fading families

As the 5-limit commas get more complex, the associated families fade
away--you get stuck with a single 7-limit version of the temperament,
with all the others ruled out in badness terms because if we have a
large nexial adjustment, it leads to large complexities. As the
complexity of the 5-limit comma gets even higher, this begans to work
the same way for higher limits also. To give an example of this, I
took a look at the atomic family, with starting point the atom of
Kirnberger. In the 5-limit, we have the absurdly precise (and quite
possibly theoretically useful) atomic temperament mapping [<12 19 28|,
<0 1 -7|], with period a semitone and generator a schisma. In the
7-limit, the only choice which makes much sense is 12&612, which
extends the mapping to [<12 19 28 34|, <0 1 -7 -16|], still very
accurate but not the crazed super-accuracy of the 5-limit, where we
have an rms error of 0.00012 cents, as opposed to 0.03484 cents in the
7-limit.

Also part of the pattern is that the way to get better badness numbers
is to subdivide the period, the octave, or both. For example, the
mapping [<24 37 63 68|, <0 5 -35 -3|], which does both, gets us down
to 0.00063 for an rms error.