This page lists all moment of symmetry scales in 12edo.
Single-period MOS scales
Generators 7\12 and 5\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├──────┼────┤
|
1L 1s
|
7, 5
|
7:5
|
├─┼────┼────┤
|
2L 1s
|
5, 2
|
5:2
|
├─┼─┼──┼─┼──┤
|
2L 3s
|
3, 2
|
3:2
|
├─┼─┼─┼┼─┼─┼┤
|
5L 2s (diatonic)
|
2, 1
|
2:1
|
├┼┼┼┼┼┼┼┼┼┼┼┤
|
12edo
|
1, 1
|
1:1
|
Generators 8\12 and 4\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├───────┼───┤
|
1L 1s
|
8, 4
|
2:1
|
├───┼───┼───┤
|
3edo
|
4, 4
|
1:1
|
Generators 9\12 and 3\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├────────┼──┤
|
1L 1s
|
9, 3
|
3:1
|
├─────┼──┼──┤
|
1L 2s
|
6, 3
|
2:1
|
├──┼──┼──┼──┤
|
4edo
|
3, 3
|
1:1
|
Generators 10\12 and 2\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├─────────┼─┤
|
1L 1s
|
10, 2
|
5:1
|
├───────┼─┼─┤
|
1L 2s
|
8, 2
|
4:1
|
├─────┼─┼─┼─┤
|
1L 3s
|
6, 2
|
3:1
|
├───┼─┼─┼─┼─┤
|
1L 4s
|
4, 2
|
2:1
|
├─┼─┼─┼─┼─┼─┤
|
6edo
|
2, 2
|
1:1
|
Generators 11\12 and 1\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├──────────┼┤
|
1L 1s
|
11, 1
|
11:1
|
├─────────┼┼┤
|
1L 2s
|
10, 1
|
10:1
|
├────────┼┼┼┤
|
1L 3s
|
9, 1
|
9:1
|
├───────┼┼┼┼┤
|
1L 4s
|
8, 1
|
8:1
|
├──────┼┼┼┼┼┤
|
1L 5s (antimachinoid)
|
7, 1
|
7:1
|
├─────┼┼┼┼┼┼┤
|
1L 6s (onyx)
|
6, 1
|
6:1
|
├────┼┼┼┼┼┼┼┤
|
1L 7s (antipine)
|
5, 1
|
5:1
|
├───┼┼┼┼┼┼┼┼┤
|
1L 8s (antisubneutralic)
|
4, 1
|
4:1
|
├──┼┼┼┼┼┼┼┼┼┤
|
1L 9s (antisinatonic)
|
3, 1
|
3:1
|
├─┼┼┼┼┼┼┼┼┼┼┤
|
1L 10s
|
2, 1
|
2:1
|
├┼┼┼┼┼┼┼┼┼┼┼┤
|
12edo
|
1, 1
|
1:1
|
Multi-period MOS scales
2 periods
Generators 4\12 and 2\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├───┼─┼───┼─┤
|
2L 2s
|
4, 2
|
2:1
|
├─┼─┼─┼─┼─┼─┤
|
6edo
|
2, 2
|
1:1
|
Generators 5\12 and 1\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├────┼┼────┼┤
|
2L 2s
|
5, 1
|
5:1
|
├───┼┼┼───┼┼┤
|
2L 4s (malic)
|
4, 1
|
4:1
|
├──┼┼┼┼──┼┼┼┤
|
2L 6s (subaric)
|
3, 1
|
3:1
|
├─┼┼┼┼┼─┼┼┼┼┤
|
2L 8s (jaric)
|
2, 1
|
2:1
|
├┼┼┼┼┼┼┼┼┼┼┼┤
|
12edo
|
1, 1
|
1:1
|
3 periods
Generators 3\12 and 1\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├──┼┼──┼┼──┼┤
|
3L 3s (triwood)
|
3, 1
|
3:1
|
├─┼┼┼─┼┼┼─┼┼┤
|
3L 6s (tcherepnin)
|
2, 1
|
2:1
|
├┼┼┼┼┼┼┼┼┼┼┼┤
|
12edo
|
1, 1
|
1:1
|
4 periods
Generators 2\12 and 1\12
Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
├─┼┼─┼┼─┼┼─┼┤
|
4L 4s (tetrawood)
|
2, 1
|
2:1
|
├┼┼┼┼┼┼┼┼┼┼┼┤
|
12edo
|
1, 1
|
1:1
|