Copied from Ganaram Inukshuk's template on 22 Oct 2024, the only change was changing an altered module.
Example of usage
12edo
These are 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
|
13edo
These are all moment of symmetry scales in 13edo.
Single-period MOS scales
Generators 7\13 and 6\13
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├──────┼─────┤
|
1L 1s
|
7, 6
|
7:6
|
| ├┼─────┼─────┤
|
2L 1s
|
6, 1
|
6:1
|
| ├┼┼────┼┼────┤
|
2L 3s
|
5, 1
|
5:1
|
| ├┼┼┼───┼┼┼───┤
|
2L 5s (antidiatonic)
|
4, 1
|
4:1
|
| ├┼┼┼┼──┼┼┼┼──┤
|
2L 7s (balzano)
|
3, 1
|
3:1
|
| ├┼┼┼┼┼─┼┼┼┼┼─┤
|
2L 9s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┤
|
13edo
|
1, 1
|
1:1
|
Generators 8\13 and 5\13
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├───────┼────┤
|
1L 1s
|
8, 5
|
8:5
|
| ├──┼────┼────┤
|
2L 1s
|
5, 3
|
5:3
|
| ├──┼──┼─┼──┼─┤
|
3L 2s
|
3, 2
|
3:2
|
| ├┼─┼┼─┼─┼┼─┼─┤
|
5L 3s (oneirotonic)
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┤
|
13edo
|
1, 1
|
1:1
|
Generators 9\13 and 4\13
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├────────┼───┤
|
1L 1s
|
9, 4
|
9:4
|
| ├────┼───┼───┤
|
1L 2s
|
5, 4
|
5:4
|
| ├┼───┼───┼───┤
|
3L 1s
|
4, 1
|
4:1
|
| ├┼┼──┼┼──┼┼──┤
|
3L 4s (mosh)
|
3, 1
|
3:1
|
| ├┼┼┼─┼┼┼─┼┼┼─┤
|
3L 7s (sephiroid)
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┤
|
13edo
|
1, 1
|
1:1
|
Generators 10\13 and 3\13
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├─────────┼──┤
|
1L 1s
|
10, 3
|
10:3
|
| ├──────┼──┼──┤
|
1L 2s
|
7, 3
|
7:3
|
| ├───┼──┼──┼──┤
|
1L 3s
|
4, 3
|
4:3
|
| ├┼──┼──┼──┼──┤
|
4L 1s
|
3, 1
|
3:1
|
| ├┼┼─┼┼─┼┼─┼┼─┤
|
4L 5s (gramitonic)
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┤
|
13edo
|
1, 1
|
1:1
|
Generators 11\13 and 2\13
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├──────────┼─┤
|
1L 1s
|
11, 2
|
11:2
|
| ├────────┼─┼─┤
|
1L 2s
|
9, 2
|
9:2
|
| ├──────┼─┼─┼─┤
|
1L 3s
|
7, 2
|
7:2
|
| ├────┼─┼─┼─┼─┤
|
1L 4s
|
5, 2
|
5:2
|
| ├──┼─┼─┼─┼─┼─┤
|
1L 5s (antimachinoid)
|
3, 2
|
3:2
|
| ├┼─┼─┼─┼─┼─┼─┤
|
6L 1s (archaeotonic)
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┤
|
13edo
|
1, 1
|
1:1
|
Generators 12\13 and 1\13
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├───────────┼┤
|
1L 1s
|
12, 1
|
12:1
|
| ├──────────┼┼┤
|
1L 2s
|
11, 1
|
11:1
|
| ├─────────┼┼┼┤
|
1L 3s
|
10, 1
|
10:1
|
| ├────────┼┼┼┼┤
|
1L 4s
|
9, 1
|
9:1
|
| ├───────┼┼┼┼┼┤
|
1L 5s (antimachinoid)
|
8, 1
|
8:1
|
| ├──────┼┼┼┼┼┼┤
|
1L 6s (onyx)
|
7, 1
|
7:1
|
| ├─────┼┼┼┼┼┼┼┤
|
1L 7s (antipine)
|
6, 1
|
6:1
|
| ├────┼┼┼┼┼┼┼┼┤
|
1L 8s (antisubneutralic)
|
5, 1
|
5:1
|
| ├───┼┼┼┼┼┼┼┼┼┤
|
1L 9s (antisinatonic)
|
4, 1
|
4:1
|
| ├──┼┼┼┼┼┼┼┼┼┼┤
|
1L 10s
|
3, 1
|
3:1
|
| ├─┼┼┼┼┼┼┼┼┼┼┼┤
|
1L 11s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┤
|
13edo
|
1, 1
|
1:1
|