Hexatonic MOS

Families of hexatonic MOS scales for all n-EDO tunings until 36EDO

Names for MOS families (according to the naming scheme):

1L 5s Happy hexatonic

2L 4s Rice hexatonic

3L 3s augmented

4L 2s bicycle

5L 1s Grumpy hexatomic

Additional constraints: L/s < 5, L/s > 7/6

n   MOS family         L  s
****************************
 7  Happy hexatonic     2  1
 8  Happy hexatonic     3  1
 8  Rice hexatonic      2  1
 9  Happy hexatonic     4  1
 9  augmented           2  1
10  Rice hexatonic      3  1
10  bicycle             2  1
11  Grumpy hexatonic    2  1
12  Rice hexatonic      4  1
12  augmented           3  1
13  Happy hexatonic     3  2
14  Happy hexatonic     4  2
14  Rice hexatonic      3  2
14  bicycle             3  1
15  Happy hexatonic     5  2
15  augmented           4  1
15  augmented           3  2
16  Happy hexatonic     6  2
16  Rice hexatonic      4  2
16  bicycle             3  2
16  Grumpy hexatonic    3  1
17  Happy hexatonic     7  2
17  Grumpy hexatonic    3  2
18  Happy hexatonic     8  2
18  Rice hexatonic      5  2
18  augmented           4  2
18  bicycle             4  1
19  Happy hexatonic     9  2
19  Happy hexatonic     4  3
20  Happy hexatonic     5  3
20  Rice hexatonic      6  2
20  Rice hexatonic      4  3
20  bicycle             4  2
21  Happy hexatonic     6  3
21  augmented           5  2
21  augemted            4  3
21  Grumpy hexatonic    4  1
22  Happy hexatonic     7  3
22  Rice hexatonic      7  2
22  Rice hexatonic      5  3
22  bicycle             4  3
22  Grumpy hexatonic    4  2
23  Happy hexatonic     8  3
23  Grumpy hexatonic    4  3
24  Happy hexatonic     9  3
24  Rice hexatonic      8  2
24  Rice hexatonic      6  2
24  augmented           6  2
24  augmented           5  3
24  bicycle             5  2
25  Happy hexatonic    10  3
25  Happy hexatonic     5  4
26  Happy hexatonic    11  3
26  Happy hexatonic     6  4
26  Rice hexatonic      9  2
26  Rice hexatonic      7  3
26  Rice hexatonic      5  4
26  bicycle             5  3
27  Happy hexatonic    12  3
27  Happy hexatonic     7  4
27  augmented           7  2
27  augmented           6  3
27  augmented           5  4
27  Grumpy hexatonic    5  2
28  Happy hexatonic    13  3
28  Happy hexatonic     8  4
28  Rice hexatonic      8  3
28  Rice hexatonic      6  4
28  bicycle             5  4
28  Grumpy hexatonic    5  3
29  Happy hexatonic    14  3
29  Happy hexatonic     9  4
29  Grumpy hexatonic    5  4
30  Happy hexatonic    10  4
30  Rice hexatonic      9  3
30  Rice hexatonic      7  4
30  augmented           8  2
30  augmented           7  3
30  augmented           6  4
30  bicycle             6  3
31  Happy hexatonic    11  4
31  Happy hexatonic     6  5
32  Happy hexatonic    12  4
32  Happy hexatonic     7  5
32  Rice hexatonic     10  3
32  Rice hexatonic      8  4
32  bicycle             6  4
32  bicycle             7  2
32  Grumpy hexatonic    6  2
33  Happy hexatonic    13  4
33  Happy hexatonic     8  5
33  augmented           9  2
33  augmented           8  3
33  augmented           7  4
33  augmented           6  5
33  Grumpy hexatonic    6  3
34  Happy hexatonic    14  4
34  Happy hexatonic     9  5
34  Rice hexatonic     11  3
34  Rice hexatonic      9  4
34  Rice hexatonic      7  5
34  bicycle             6  5
34  bicycle             7  3
34  Grumpy hexatonic    6  4
35  Happy hexatonic    15  4
35  Happy hexatonic    10  5
35  Grumpy hexatonic    6  5
36  Happy hexatonic    16  4
36  Happy hexatonic    11  5
36  Rice hexatonic     12  3
36  Rice hexatonic     10  4
36  Rice hexatonic      8  5
36  augmented           9  3
36  augmented           8  4
36  augmented           7  5
36  bicycle             7  4
36  bicycle             8  2
 
XXX
 
41  Happy hexatonic    16  5
41  Happy hexatonic    11  6