Since 17 is a prime number, any interval can be repeatedly stacked to produce new intervals until all 17 tones are included. This page lists and visualizes the scales produced this way.
Diagram of mosses of 17edo
Mosses by generator pair
The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. A few notes:
- The table denotes each family using a rectangular horogram, starting with 1L 1s and adding notes until every note is added.
- For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
- TAMNAMS names are used wherever possible, except for scales with 4 or fewer notes and 1L ns scales for tidiness. Scales with at least four notes have clickable links to their corresponding mos page.
This page lists all moment of symmetry scales in 17edo.
Single-period MOS scales
Generators 9\17 and 8\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├────────┼───────┤
|
1L 1s
|
9, 8
|
9:8
|
| ├┼───────┼───────┤
|
2L 1s
|
8, 1
|
8:1
|
| ├┼┼──────┼┼──────┤
|
2L 3s
|
7, 1
|
7:1
|
| ├┼┼┼─────┼┼┼─────┤
|
2L 5s (antidiatonic)
|
6, 1
|
6:1
|
| ├┼┼┼┼────┼┼┼┼────┤
|
2L 7s (balzano)
|
5, 1
|
5:1
|
| ├┼┼┼┼┼───┼┼┼┼┼───┤
|
2L 9s
|
4, 1
|
4:1
|
| ├┼┼┼┼┼┼──┼┼┼┼┼┼──┤
|
2L 11s
|
3, 1
|
3:1
|
| ├┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┤
|
2L 13s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 10\17 and 7\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├─────────┼──────┤
|
1L 1s
|
10, 7
|
10:7
|
| ├──┼──────┼──────┤
|
2L 1s
|
7, 3
|
7:3
|
| ├──┼──┼───┼──┼───┤
|
2L 3s
|
4, 3
|
4:3
|
| ├──┼──┼──┼┼──┼──┼┤
|
5L 2s (diatonic)
|
3, 1
|
3:1
|
| ├─┼┼─┼┼─┼┼┼─┼┼─┼┼┤
|
5L 7s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 11\17 and 6\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├──────────┼─────┤
|
1L 1s
|
11, 6
|
11:6
|
| ├────┼─────┼─────┤
|
2L 1s
|
6, 5
|
6:5
|
| ├────┼────┼┼────┼┤
|
3L 2s
|
5, 1
|
5:1
|
| ├───┼┼───┼┼┼───┼┼┤
|
3L 5s (checkertonic)
|
4, 1
|
4:1
|
| ├──┼┼┼──┼┼┼┼──┼┼┼┤
|
3L 8s
|
3, 1
|
3:1
|
| ├─┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤
|
3L 11s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 12\17 and 5\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├───────────┼────┤
|
1L 1s
|
12, 5
|
12:5
|
| ├──────┼────┼────┤
|
1L 2s
|
7, 5
|
7:5
|
| ├─┼────┼────┼────┤
|
3L 1s
|
5, 2
|
5:2
|
| ├─┼─┼──┼─┼──┼─┼──┤
|
3L 4s (mosh)
|
3, 2
|
3:2
|
| ├─┼─┼─┼┼─┼─┼┼─┼─┼┤
|
7L 3s (dicoid)
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 13\17 and 4\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├────────────┼───┤
|
1L 1s
|
13, 4
|
13:4
|
| ├────────┼───┼───┤
|
1L 2s
|
9, 4
|
9:4
|
| ├────┼───┼───┼───┤
|
1L 3s
|
5, 4
|
5:4
|
| ├┼───┼───┼───┼───┤
|
4L 1s
|
4, 1
|
4:1
|
| ├┼┼──┼┼──┼┼──┼┼──┤
|
4L 5s (gramitonic)
|
3, 1
|
3:1
|
| ├┼┼┼─┼┼┼─┼┼┼─┼┼┼─┤
|
4L 9s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 14\17 and 3\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├─────────────┼──┤
|
1L 1s
|
14, 3
|
14:3
|
| ├──────────┼──┼──┤
|
1L 2s
|
11, 3
|
11:3
|
| ├───────┼──┼──┼──┤
|
1L 3s
|
8, 3
|
8:3
|
| ├────┼──┼──┼──┼──┤
|
1L 4s
|
5, 3
|
5:3
|
| ├─┼──┼──┼──┼──┼──┤
|
5L 1s (machinoid)
|
3, 2
|
3:2
|
| ├─┼─┼┼─┼┼─┼┼─┼┼─┼┤
|
6L 5s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 15\17 and 2\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├──────────────┼─┤
|
1L 1s
|
15, 2
|
15:2
|
| ├────────────┼─┼─┤
|
1L 2s
|
13, 2
|
13:2
|
| ├──────────┼─┼─┼─┤
|
1L 3s
|
11, 2
|
11:2
|
| ├────────┼─┼─┼─┼─┤
|
1L 4s
|
9, 2
|
9:2
|
| ├──────┼─┼─┼─┼─┼─┤
|
1L 5s (antimachinoid)
|
7, 2
|
7:2
|
| ├────┼─┼─┼─┼─┼─┼─┤
|
1L 6s (onyx)
|
5, 2
|
5:2
|
| ├──┼─┼─┼─┼─┼─┼─┼─┤
|
1L 7s (antipine)
|
3, 2
|
3:2
|
| ├┼─┼─┼─┼─┼─┼─┼─┼─┤
|
8L 1s (subneutralic)
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
Generators 16\17 and 1\17
| Step visualization
|
MOS (name)
|
Step sizes
|
Step ratio
|
| ├───────────────┼┤
|
1L 1s
|
16, 1
|
16:1
|
| ├──────────────┼┼┤
|
1L 2s
|
15, 1
|
15:1
|
| ├─────────────┼┼┼┤
|
1L 3s
|
14, 1
|
14:1
|
| ├────────────┼┼┼┼┤
|
1L 4s
|
13, 1
|
13:1
|
| ├───────────┼┼┼┼┼┤
|
1L 5s (antimachinoid)
|
12, 1
|
12:1
|
| ├──────────┼┼┼┼┼┼┤
|
1L 6s (onyx)
|
11, 1
|
11:1
|
| ├─────────┼┼┼┼┼┼┼┤
|
1L 7s (antipine)
|
10, 1
|
10:1
|
| ├────────┼┼┼┼┼┼┼┼┤
|
1L 8s (antisubneutralic)
|
9, 1
|
9:1
|
| ├───────┼┼┼┼┼┼┼┼┼┤
|
1L 9s (antisinatonic)
|
8, 1
|
8:1
|
| ├──────┼┼┼┼┼┼┼┼┼┼┤
|
1L 10s
|
7, 1
|
7:1
|
| ├─────┼┼┼┼┼┼┼┼┼┼┼┤
|
1L 11s
|
6, 1
|
6:1
|
| ├────┼┼┼┼┼┼┼┼┼┼┼┼┤
|
1L 12s
|
5, 1
|
5:1
|
| ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
1L 13s
|
4, 1
|
4:1
|
| ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
1L 14s
|
3, 1
|
3:1
|
| ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
1L 15s
|
2, 1
|
2:1
|
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤
|
17edo
|
1, 1
|
1:1
|
