45/44 & 49/48

Here are 11-limit scales for which both 45/44 and 49/48 are chromas
(which entails that (45/44)/(49/48) = 540/539 is a comma.) They all
have the property that the scale degree is greater than the 7-limit
Graham complexity, and in five cases, for Wizard[28], Octoid[56],
Contraschismic[53], Dreielf[66] and Heptadec[9] it is greater than the
11-limit Graham complexity--these are presumably the really fun cases.

Wizard[28] [225/224, 385/384, 4000/3993]
[12, -2, 20, -6, -31, -2, -51, 52, -7, -86] [[2, 1, 5, 2, 8], [0, 6,
-1, 10, -3]]

bad 3830.785828 comp 107.1605720 rms 1.584514314
graham 26 scale size 28

Octoid[56] [540/539, 1375/1372, 4000/3993]
[24, 32, 40, 24, -5, -4, -45, 3, -55, -71] [[8, 13, 19, 23, 28], [0,
-3, -4, -5, -3]]

bad 4139.348941 comp 173.2618570 rms .7687062821
graham 40 scale size 56

Magic[19] [100/99, 225/224, 245/243]
[5, 1, 12, -8, -10, 5, -30, 25, -22, -64] [[1, 0, 2, -1, 6], [0, 5, 1,
12, -8]]

bad 4474.854491 comp 61.02789552 rms 4.730404304
graham 20 scale size 19

Catakleismic[38] [225/224, 385/384, 4375/4374]
[6, 5, 22, -21, -6, 18, -54, 37, -66, -135] [[1, 0, 1, -3, 9], [0, 6,
5, 22, -21]]

bad 4805.476809 comp 117.8180381 rms 1.697136764
graham 43 scale size 38

Meanpop[19] [81/80, 126/125, 385/384]
[1, 4, 10, -13, 4, 13, -24, 12, -44, -71] [[1, 2, 4, 7, -2], [0, -1,
-4, -10, 13]]

bad 5420.225566 comp 61.58085622 rms 5.644270538
graham 23 scale size 19

Schismatic[29] [225/224, 385/384, 2200/2187]
[1, -8, -14, 23, -15, -25, 33, -10, 81, 113] [[1, 2, -1, -3, 13], [0,
-1, 8, 14, -23]]

bad 5478.852555 comp 102.3231433 rms 2.447558936
graham 37 scale size 29

Contraschismic[53] [540/539, 1375/1372, 5120/5103]
[1, 33, 27, -18, 50, 40, -32, -30, -156, -144] [[1, 2, 16, 14, -4],
[0, -1, -33, -27, 18]]

bad 6259.259444 comp 177.5735716 rms 1.115729896
graham 51 scale size 53

Dreielf[66] [540/539, 1375/1372, 8019/8000]
[18, 39, 42, 9, 20, 16, -48, -12, -114, -120] [[3, 2, 1, 2, 9], [0, 6,
13, 14, 3]]

bad 6297.038152 comp 184.8474423 rms 1.049817759
graham 42 scale size 66

Heptadec[9] [36/35, 56/55, 77/75]
[5, 3, 7, 4, -7, -3, -11, 8, -1, -13] [[1, 1, 2, 2, 3], [0, 5, 3, 7, 4]]

bad 6400.766110 comp 32.19555159 rms 19.64440328
graham 7 scale size 9

Fourththirds[5] [16/15, 28/27, 77/75]
[1, -1, 3, -4, -4, 2, -10, 10, -6, -22] [[1, 2, 2, 4, 2], [0, -1, 1,
-3, 4]]

bad 6476.838089 comp 20.25383770 rms 43.03787612
graham 7 scale size 5

Pajarous[10] [50/49, 55/54, 64/63]
[2, -4, -4, 10, -11, -12, 9, 2, 37, 42] [[2, 3, 5, 6, 6], [0, 1, -2,
-2, 5]]

bad 6667.906202 comp 43.76707564 rms 12.26714784
graham 14 scale size 10

>Here are 11-limit scales for which both 45/44 and 49/48 are chromas

I guess what I just wrote on specmus is wrong. Can you show how
these two chroma arise?

>the scale degree is greater than the // Graham complexity

? The "scale degree"?

>Heptadec[9] [36/35, 56/55, 77/75]
>[5, 3, 7, 4, -7, -3, -11, 8, -1, -13] [[1, 1, 2, 2, 3], [0, 5, 3, 7, 4]]
>
>bad 6400.766110 comp 32.19555159 rms 19.64440328
>graham 7 scale size 9
>
>
>Fourththirds[5] [16/15, 28/27, 77/75]
>[1, -1, 3, -4, -4, 2, -10, 10, -6, -22] [[1, 2, 2, 4, 2], [0, -1, 1,
>-3, 4]]
>
>bad 6476.838089 comp 20.25383770 rms 43.03787612
>graham 7 scale size 5
>
>
>Pajarous[10] [50/49, 55/54, 64/63]
>[2, -4, -4, 10, -11, -12, 9, 2, 37, 42] [[2, 3, 5, 6, 6], [0, 1, -2,
>-2, 5]]
>
>bad 6667.906202 comp 43.76707564 rms 12.26714784
>graham 14 scale size 10

Say,

When you post lists of scales, could you post a template at the
top, so we know what all this notation is? I know it's pretty
standard every time, but still, for achives' sake.

-Carl