A table of 7-limit MOS

Here are 7-limit r2 temperaments which have a MOS less than 40 in
size, and greater than or equal to their 7-limit Graham complexity in
size. I've also filtered them by requiring the TOP error to be less
than 2, and TOP-Graham logflat badness less than 300. The idea for
doing this came from considering Joe Pehrson's problem of finding a
low-error MOS of size around 19. As you can see, there are many
possibilities, some of which have been discussed, and many of which
have not. I also note that I'd missed Myna as one solution of the
low-error 19-note MOS question, because of the high irregularity of
the resulting MOS, and had discounted hemiwuerschmidt because it
didn't really work up very many complete chords at just 19 (25 would
be better.)

ennealimmal <<18 27 18 1 -22 -34||

complexity 27 error 0.036 bad 26.5 MOS 27, 36

hemiwuerschmidt <<16 2 5 -34 -37 6||

complexity 16 error 0.308 bad 78.8 MOS 19, 25, 31, 37

grendel <<23 -1 13 -55 -44 53||

complexity 24 error 0.328 bad 189.2 MOS 25, 28, 31

unidec <<12 22 -4 7 -40 -71||

complexity 26 error 0.421 bad 284.9 MOS 33

tritikleismic <<18 15 -6 -18 -60 -56||

complexity 24 error 0.449 bad 258.4 MOS 29

hemithirds <<15 -2 -5 -38 -50 6||

complexity 20 error 0.480 bad 191.9 MOS 25, 31

catakleismic <<6 5 22 -6 18 37||

complexity 22 error 0.536 bad 259.6 MOS 34

hemikleismic <<12 10 -9 -12 -48 -49||

complexity 21 error 0.589 bad 259.6 MOS 23, 38

semisept <<17 6 15 -30 -24 18||

complexity 17 error 0.612 bad 179.4 MOS 18, 31

miracle <<6 -7 -2 -25 -20 15||

complexity 13 error 0.631 bad 106.6 MOS 21, 31

rodan <<3 17 -1 20 -10 -50||

complexity 18 error 0.895 bad 289.9 MOS 21, 26, 31, 36

garibaldi <<1 -8 -14 -15 -10 -25||

complexity 15 error 0.913 bad 205.4 MOS 17, 29

quartonic <<11 18 5 3 -23 -39||

complexity 18 error 0.917 bad 297.0 MOS 26, 27

orwell <<7 -3 8 -21 -7 27||

complexity 13 error 0.946 bad 114.5 MOS 13, 22, 31

septimin <<11 -6 10 -35 -15 40||

complexity 17 error 0.950 bad 274.7 MOS 23, 32

tritonic <<5 -11 -12 -29 -33 3||

complexity 17 error 1.02 bad 295.7 MOS 17, 19, 21, 23, 25, 27, 29, 31

valentine <<9 5 -3 -13 -30 -21||

complexity 12 error 1.05 bad 151.2 MOS 15, 16, 31

myna <<10 9 7 -9 -17 -9||

complexity 10 error 1.17 bad 117.2 MOS 11, 15, 19, 23, 27, 31

magic <<5 1 12 -10 5 25||

complexity 12 error 1.28 bad 183.8 MOS 13, 16, 19, 22

superkleismic <<9 10 -3 -5 -30 -35||

complexity 13 error 1.37 bad 231.9 MOS 15, 26

sensi <<7 9 13 -2 1 5||

complexity 13 error 1.61 bad 272.2 MOS 19, 27

meantone <<1 4 10 4 13 12||

complexity 10 error 1.70 bad 169.9 MOS 12, 19, 31

mothra (exact TOP error tie with meantone) <<3 12 -1 12 -10 -36||

complexity 13 error 1.70 bad 287.0 MOS 16, 21, 26, 31

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

Thanks, Gene, for revisiting this problem... I'll puzzle over this
when
I get a chance...

JP