41

Here's a brief rundown of the scales of the 41-et.

34+7 6/41

Two triad systems should give us something good for triads, and they
do: [4 9 -15 10 -2] being the generators, suggesting that the 13-note
scale 1515151515155 has possibilities; there is also of course a 7-
note scale, with pattern 6666667. The 13-note scale gives us four
triads, as well as 11 and especially 13 harmonies.

31+10 4/41

This is the 41-et version of miracle, so it comes in for some stiff
competition from 31 and 72. Both 31 and 41 map 13 to -3 secors, and
if you aren't quite as picky as some about intonation it is a viable
alternative.

29+12 17/41

Two systems with good fifths give us a fifth system which is the 41-et
version of schismic, with primes mapped to [-1,8,14,18,-20,-7,3]. The
53-et gives it stiff competition. Graham also calls this Cassandra 2.

26+15 11/41

We have a prime mapping [-9,-10,3,-2,-16], so scales in this system
are interesting for exploring the higher prime limits. We have scales
3838388, 33533533535 and 333233323332332 of size 7,11, and 15, and
the 11-note scale already has quite a bit of harmony on offer.
Certainly one worth exploring!

22+19 13/41

This is good for triads, as we would expect, and is quite a nice
system, which Graham has dubbed "Magic". This and the previous
generator seem to be the most interesting ones for the 41-et, because
for both the 41-et seems to be the right way to make use of them. We
have generator map [5,1,12,-8] and scales 11 2 11 2 11 2 2,
9229229222, 7222722272222, and 5222252222522222, of sizes 7, 10, 13
and 16--of course 19 and 22 also if we want to go that high! The
7-note scale has two complete triads and a lot (of course) of major
thirds.

24+17 12/41

This has a map to primes of [2 -16 13 5 -1], and a neutral third
generator which we can consider to be 11/9 or 16/13. Graham seems to
like it, and it would be a good way to explore 11 and 13 if you are
prepared not to have much 5 or 7.