List of MOS scales in edos 5 to 30

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This page lists every MOS scale to occur in each EDO from 5 to 30.

5edo

These are all moment of symmetry scales in 5edo.
Single-period MOS scales

Generators 3\5 and 2\5
Step visualization MOS (name) Step sizes Step ratio
├──┼─┤ 1L 1s 3, 2 3:2
├┼─┼─┤ 2L 1s 2, 1 2:1
├┼┼┼┼┤ 5edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 4\5 and 1\5 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───┼┤ | 1L 1s | 4, 1 | 4:1 |- | ├──┼┼┤ | 1L 2s | 3, 1 | 3:1 |- | ├─┼┼┼┤ | 1L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┤ | 5edo | 1, 1 | 1:1 |}

6edo

These are all moment of symmetry scales in 6edo.
Single-period MOS scales

Generators 4\6 and 2\6
Step visualization MOS (name) Step sizes Step ratio
├───┼─┤ 1L 1s 4, 2 2:1
├─┼─┼─┤ 3edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\6 and 1\6 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼┤ | 1L 1s | 5, 1 | 5:1 |- | ├───┼┼┤ | 1L 2s | 4, 1 | 4:1 |- | ├──┼┼┼┤ | 1L 3s | 3, 1 | 3:1 |- | ├─┼┼┼┼┤ | 1L 4s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┤ | 6edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 2\6 and 1\6
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┤ 2L 2s 2, 1 2:1
├┼┼┼┼┼┤ 6edo 1, 1 1:1

7edo

These are all moment of symmetry scales in 7edo.
Single-period MOS scales

Generators 4\7 and 3\7
Step visualization MOS (name) Step sizes Step ratio
├───┼──┤ 1L 1s 4, 3 4:3
├┼──┼──┤ 2L 1s 3, 1 3:1
├┼┼─┼┼─┤ 2L 3s 2, 1 2:1
├┼┼┼┼┼┼┤ 7edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\7 and 2\7 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼─┤ | 1L 1s | 5, 2 | 5:2 |- | ├──┼─┼─┤ | 1L 2s | 3, 2 | 3:2 |- | ├┼─┼─┼─┤ | 3L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┤ | 7edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 6\7 and 1\7 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼┤ | 1L 1s | 6, 1 | 6:1 |- | ├────┼┼┤ | 1L 2s | 5, 1 | 5:1 |- | ├───┼┼┼┤ | 1L 3s | 4, 1 | 4:1 |- | ├──┼┼┼┼┤ | 1L 4s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┤ | 7edo | 1, 1 | 1:1 |}

8edo

These are all moment of symmetry scales in 8edo.
Single-period MOS scales

Generators 5\8 and 3\8
Step visualization MOS (name) Step sizes Step ratio
├────┼──┤ 1L 1s 5, 3 5:3
├─┼──┼──┤ 2L 1s 3, 2 3:2
├─┼─┼┼─┼┤ 3L 2s 2, 1 2:1
├┼┼┼┼┼┼┼┤ 8edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 6\8 and 2\8 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼─┤ | 1L 1s | 6, 2 | 3:1 |- | ├───┼─┼─┤ | 1L 2s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┤ | 4edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 7\8 and 1\8 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼┤ | 1L 1s | 7, 1 | 7:1 |- | ├─────┼┼┤ | 1L 2s | 6, 1 | 6:1 |- | ├────┼┼┼┤ | 1L 3s | 5, 1 | 5:1 |- | ├───┼┼┼┼┤ | 1L 4s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┤ | 1L 6s (onyx) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┤ | 8edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 3\8 and 1\8
Step visualization MOS (name) Step sizes Step ratio
├──┼┼──┼┤ 2L 2s 3, 1 3:1
├─┼┼┼─┼┼┤ 2L 4s (malic) 2, 1 2:1
├┼┼┼┼┼┼┼┤ 8edo 1, 1 1:1

9edo

These are all moment of symmetry scales in 9edo.
Single-period MOS scales

Generators 5\9 and 4\9
Step visualization MOS (name) Step sizes Step ratio
├────┼───┤ 1L 1s 5, 4 5:4
├┼───┼───┤ 2L 1s 4, 1 4:1
├┼┼──┼┼──┤ 2L 3s 3, 1 3:1
├┼┼┼─┼┼┼─┤ 2L 5s (antidiatonic) 2, 1 2:1
├┼┼┼┼┼┼┼┼┤ 9edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 6\9 and 3\9 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼──┤ | 1L 1s | 6, 3 | 2:1 |- | ├──┼──┼──┤ | 3edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 7\9 and 2\9 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼─┤ | 1L 1s | 7, 2 | 7:2 |- | ├────┼─┼─┤ | 1L 2s | 5, 2 | 5:2 |- | ├──┼─┼─┼─┤ | 1L 3s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┤ | 4L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┤ | 9edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\9 and 1\9 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼┤ | 1L 1s | 8, 1 | 8:1 |- | ├──────┼┼┤ | 1L 2s | 7, 1 | 7:1 |- | ├─────┼┼┼┤ | 1L 3s | 6, 1 | 6:1 |- | ├────┼┼┼┼┤ | 1L 4s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┤ | 1L 6s (onyx) | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┤ | 9edo | 1, 1 | 1:1 |}
Multi-period MOS scales
3 periods

Generators 2\9 and 1\9
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┤ 3L 3s (triwood) 2, 1 2:1
├┼┼┼┼┼┼┼┼┤ 9edo 1, 1 1:1

10edo

These are all moment of symmetry scales in 10edo.
Single-period MOS scales

Generators 6\10 and 4\10
Step visualization MOS (name) Step sizes Step ratio
├─────┼───┤ 1L 1s 6, 4 3:2
├─┼───┼───┤ 2L 1s 4, 2 2:1
├─┼─┼─┼─┼─┤ 5edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 7\10 and 3\10 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼──┤ | 1L 1s | 7, 3 | 7:3 |- | ├───┼──┼──┤ | 1L 2s | 4, 3 | 4:3 |- | ├┼──┼──┼──┤ | 3L 1s | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┤ | 3L 4s (mosh) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┤ | 10edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\10 and 2\10 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼─┤ | 1L 1s | 8, 2 | 4:1 |- | ├─────┼─┼─┤ | 1L 2s | 6, 2 | 3:1 |- | ├───┼─┼─┼─┤ | 1L 3s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┤ | 5edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\10 and 1\10 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼┤ | 1L 1s | 9, 1 | 9:1 |- | ├───────┼┼┤ | 1L 2s | 8, 1 | 8:1 |- | ├──────┼┼┼┤ | 1L 3s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┤ | 1L 4s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┤ | 1L 6s (onyx) | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┤ | 10edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 3\10 and 2\10
Step visualization MOS (name) Step sizes Step ratio
├──┼─┼──┼─┤ 2L 2s 3, 2 3:2
├┼─┼─┼┼─┼─┤ 4L 2s (citric) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┤ 10edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 4\10 and 1\10 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───┼┼───┼┤ | 2L 2s | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┤ | 2L 4s (malic) | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┤ | 2L 6s (subaric) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┤ | 10edo | 1, 1 | 1:1 |}

11edo

These are all moment of symmetry scales in 11edo.
Single-period MOS scales

Generators 6\11 and 5\11
Step visualization MOS (name) Step sizes Step ratio
├─────┼────┤ 1L 1s 6, 5 6:5
├┼────┼────┤ 2L 1s 5, 1 5:1
├┼┼───┼┼───┤ 2L 3s 4, 1 4:1
├┼┼┼──┼┼┼──┤ 2L 5s (antidiatonic) 3, 1 3:1
├┼┼┼┼─┼┼┼┼─┤ 2L 7s (balzano) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┤ 11edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 7\11 and 4\11 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼───┤ | 1L 1s | 7, 4 | 7:4 |- | ├──┼───┼───┤ | 2L 1s | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┤ | 3L 2s | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┤ | 3L 5s (checkertonic) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┤ | 11edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\11 and 3\11 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼──┤ | 1L 1s | 8, 3 | 8:3 |- | ├────┼──┼──┤ | 1L 2s | 5, 3 | 5:3 |- | ├─┼──┼──┼──┤ | 3L 1s | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┤ | 4L 3s (smitonic) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┤ | 11edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\11 and 2\11 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼─┤ | 1L 1s | 9, 2 | 9:2 |- | ├──────┼─┼─┤ | 1L 2s | 7, 2 | 7:2 |- | ├────┼─┼─┼─┤ | 1L 3s | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┤ | 1L 4s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┤ | 5L 1s (machinoid) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┤ | 11edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\11 and 1\11 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼┤ | 1L 1s | 10, 1 | 10:1 |- | ├────────┼┼┤ | 1L 2s | 9, 1 | 9:1 |- | ├───────┼┼┼┤ | 1L 3s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┤ | 1L 4s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┤ | 11edo | 1, 1 | 1:1 |}

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

{| class="wikitable center-all"

|+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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

{| class="wikitable center-all"

|+ style="font-size: 105%;" | 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

{| class="wikitable center-all"

|+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}

14edo

These are all moment of symmetry scales in 14edo.
Single-period MOS scales

Generators 8\14 and 6\14
Step visualization MOS (name) Step sizes Step ratio
├───────┼─────┤ 1L 1s 8, 6 4:3
├─┼─────┼─────┤ 2L 1s 6, 2 3:1
├─┼─┼───┼─┼───┤ 2L 3s 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┤ 7edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 9\14 and 5\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼────┤ | 1L 1s | 9, 5 | 9:5 |- | ├───┼────┼────┤ | 2L 1s | 5, 4 | 5:4 |- | ├───┼───┼┼───┼┤ | 3L 2s | 4, 1 | 4:1 |- | ├──┼┼──┼┼┼──┼┼┤ | 3L 5s (checkertonic) | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼┼─┼┼┼┤ | 3L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 14edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\14 and 4\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼───┤ | 1L 1s | 10, 4 | 5:2 |- | ├─────┼───┼───┤ | 1L 2s | 6, 4 | 3:2 |- | ├─┼───┼───┼───┤ | 3L 1s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┤ | 7edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\14 and 3\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼──┤ | 1L 1s | 11, 3 | 11:3 |- | ├───────┼──┼──┤ | 1L 2s | 8, 3 | 8:3 |- | ├────┼──┼──┼──┤ | 1L 3s | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼──┤ | 4L 1s | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼┤ | 5L 4s (semiquartal) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 14edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\14 and 2\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼─┤ | 1L 1s | 12, 2 | 6:1 |- | ├─────────┼─┼─┤ | 1L 2s | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┤ | 1L 3s | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┤ | 1L 4s | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┤ | 7edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\14 and 1\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼┤ | 1L 1s | 13, 1 | 13:1 |- | ├───────────┼┼┤ | 1L 2s | 12, 1 | 12:1 |- | ├──────────┼┼┼┤ | 1L 3s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┤ | 1L 4s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 14edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 4\14 and 3\14
Step visualization MOS (name) Step sizes Step ratio
├───┼──┼───┼──┤ 2L 2s 4, 3 4:3
├┼──┼──┼┼──┼──┤ 4L 2s (citric) 3, 1 3:1
├┼┼─┼┼─┼┼┼─┼┼─┤ 4L 6s (lime) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 14edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\14 and 2\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼─┼────┼─┤ | 2L 2s | 5, 2 | 5:2 |- | ├──┼─┼─┼──┼─┼─┤ | 2L 4s (malic) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼┼─┼─┼─┤ | 6L 2s (ekic) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 14edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 6\14 and 1\14 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼┼─────┼┤ | 2L 2s | 6, 1 | 6:1 |- | ├────┼┼┼────┼┼┤ | 2L 4s (malic) | 5, 1 | 5:1 |- | ├───┼┼┼┼───┼┼┼┤ | 2L 6s (subaric) | 4, 1 | 4:1 |- | ├──┼┼┼┼┼──┼┼┼┼┤ | 2L 8s (jaric) | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼─┼┼┼┼┼┤ | 2L 10s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 14edo | 1, 1 | 1:1 |}

15edo

These are all moment of symmetry scales in 15edo.
Single-period MOS scales

Generators 8\15 and 7\15
Step visualization MOS (name) Step sizes Step ratio
├───────┼──────┤ 1L 1s 8, 7 8:7
├┼──────┼──────┤ 2L 1s 7, 1 7:1
├┼┼─────┼┼─────┤ 2L 3s 6, 1 6:1
├┼┼┼────┼┼┼────┤ 2L 5s (antidiatonic) 5, 1 5:1
├┼┼┼┼───┼┼┼┼───┤ 2L 7s (balzano) 4, 1 4:1
├┼┼┼┼┼──┼┼┼┼┼──┤ 2L 9s 3, 1 3:1
├┼┼┼┼┼┼─┼┼┼┼┼┼─┤ 2L 11s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 15edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 9\15 and 6\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼─────┤ | 1L 1s | 9, 6 | 3:2 |- | ├──┼─────┼─────┤ | 2L 1s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┤ | 5edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\15 and 5\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼────┤ | 1L 1s | 10, 5 | 2:1 |- | ├────┼────┼────┤ | 3edo | 5, 5 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\15 and 4\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼───┤ | 1L 1s | 11, 4 | 11:4 |- | ├──────┼───┼───┤ | 1L 2s | 7, 4 | 7:4 |- | ├──┼───┼───┼───┤ | 3L 1s | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┼──┼┤ | 4L 3s (smitonic) | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┼─┼┼┤ | 4L 7s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 15edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\15 and 3\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼──┤ | 1L 1s | 12, 3 | 4:1 |- | ├────────┼──┼──┤ | 1L 2s | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┤ | 1L 3s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┤ | 5edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\15 and 2\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼─┤ | 1L 1s | 13, 2 | 13:2 |- | ├──────────┼─┼─┤ | 1L 2s | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┤ | 1L 3s | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┤ | 1L 4s | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┤ | 7L 1s (pine) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 15edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\15 and 1\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼┤ | 1L 1s | 14, 1 | 14:1 |- | ├────────────┼┼┤ | 1L 2s | 13, 1 | 13:1 |- | ├───────────┼┼┼┤ | 1L 3s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┤ | 1L 4s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 15edo | 1, 1 | 1:1 |}
Multi-period MOS scales
3 periods

Generators 3\15 and 2\15
Step visualization MOS (name) Step sizes Step ratio
├──┼─┼──┼─┼──┼─┤ 3L 3s (triwood) 3, 2 3:2
├┼─┼─┼┼─┼─┼┼─┼─┤ 6L 3s (hyrulic) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 15edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 4\15 and 1\15 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───┼┼───┼┼───┼┤ | 3L 3s (triwood) | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼──┼┼┤ | 3L 6s (tcherepnin) | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 3L 9s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 15edo | 1, 1 | 1:1 |}
5 periods

Generators 2\15 and 1\15
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┼─┼┼─┼┤ 5L 5s (pentawood) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 15edo 1, 1 1:1

16edo

These are all moment of symmetry scales in 16edo.
Single-period MOS scales

Generators 9\16 and 7\16
Step visualization MOS (name) Step sizes Step ratio
├────────┼──────┤ 1L 1s 9, 7 9:7
├─┼──────┼──────┤ 2L 1s 7, 2 7:2
├─┼─┼────┼─┼────┤ 2L 3s 5, 2 5:2
├─┼─┼─┼──┼─┼─┼──┤ 2L 5s (antidiatonic) 3, 2 3:2
├─┼─┼─┼─┼┼─┼─┼─┼┤ 7L 2s (armotonic) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 16edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 10\16 and 6\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼─────┤ | 1L 1s | 10, 6 | 5:3 |- | ├───┼─────┼─────┤ | 2L 1s | 6, 4 | 3:2 |- | ├───┼───┼─┼───┼─┤ | 3L 2s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┤ | 8edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\16 and 5\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼────┤ | 1L 1s | 11, 5 | 11:5 |- | ├─────┼────┼────┤ | 1L 2s | 6, 5 | 6:5 |- | ├┼────┼────┼────┤ | 3L 1s | 5, 1 | 5:1 |- | ├┼┼───┼┼───┼┼───┤ | 3L 4s (mosh) | 4, 1 | 4:1 |- | ├┼┼┼──┼┼┼──┼┼┼──┤ | 3L 7s (sephiroid) | 3, 1 | 3:1 |- | ├┼┼┼┼─┼┼┼┼─┼┼┼┼─┤ | 3L 10s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 16edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\16 and 4\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼───┤ | 1L 1s | 12, 4 | 3:1 |- | ├───────┼───┼───┤ | 1L 2s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┤ | 4edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\16 and 3\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼──┤ | 1L 1s | 13, 3 | 13:3 |- | ├─────────┼──┼──┤ | 1L 2s | 10, 3 | 10:3 |- | ├──────┼──┼──┼──┤ | 1L 3s | 7, 3 | 7:3 |- | ├───┼──┼──┼──┼──┤ | 1L 4s | 4, 3 | 4:3 |- | ├┼──┼──┼──┼──┼──┤ | 5L 1s (machinoid) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼─┼┼─┤ | 5L 6s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 16edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\16 and 2\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼─┤ | 1L 1s | 14, 2 | 7:1 |- | ├───────────┼─┼─┤ | 1L 2s | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┤ | 1L 3s | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┤ | 1L 4s | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┤ | 8edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\16 and 1\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼┤ | 1L 1s | 15, 1 | 15:1 |- | ├─────────────┼┼┤ | 1L 2s | 14, 1 | 14:1 |- | ├────────────┼┼┼┤ | 1L 3s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┤ | 1L 4s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 16edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 5\16 and 3\16
Step visualization MOS (name) Step sizes Step ratio
├────┼──┼────┼──┤ 2L 2s 5, 3 5:3
├─┼──┼──┼─┼──┼──┤ 4L 2s (citric) 3, 2 3:2
├─┼─┼┼─┼┼─┼─┼┼─┼┤ 6L 4s (lemon) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 16edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 6\16 and 2\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼─┼─────┼─┤ | 2L 2s | 6, 2 | 3:1 |- | ├───┼─┼─┼───┼─┼─┤ | 2L 4s (malic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┤ | 8edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 7\16 and 1\16 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼┼──────┼┤ | 2L 2s | 7, 1 | 7:1 |- | ├─────┼┼┼─────┼┼┤ | 2L 4s (malic) | 6, 1 | 6:1 |- | ├────┼┼┼┼────┼┼┼┤ | 2L 6s (subaric) | 5, 1 | 5:1 |- | ├───┼┼┼┼┼───┼┼┼┼┤ | 2L 8s (jaric) | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼──┼┼┼┼┼┤ | 2L 10s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼─┼┼┼┼┼┼┤ | 2L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 16edo | 1, 1 | 1:1 |}
4 periods

Generators 3\16 and 1\16
Step visualization MOS (name) Step sizes Step ratio
├──┼┼──┼┼──┼┼──┼┤ 4L 4s (tetrawood) 3, 1 3:1
├─┼┼┼─┼┼┼─┼┼┼─┼┼┤ 4L 8s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 16edo 1, 1 1:1

17edo

These are 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

{| class="wikitable center-all"

|+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | 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 |}

18edo

These are all moment of symmetry scales in 18edo.
Single-period MOS scales

Generators 10\18 and 8\18
Step visualization MOS (name) Step sizes Step ratio
├─────────┼───────┤ 1L 1s 10, 8 5:4
├─┼───────┼───────┤ 2L 1s 8, 2 4:1
├─┼─┼─────┼─┼─────┤ 2L 3s 6, 2 3:1
├─┼─┼─┼───┼─┼─┼───┤ 2L 5s (antidiatonic) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┤ 9edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 11\18 and 7\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼──────┤ | 1L 1s | 11, 7 | 11:7 |- | ├───┼──────┼──────┤ | 2L 1s | 7, 4 | 7:4 |- | ├───┼───┼──┼───┼──┤ | 3L 2s | 4, 3 | 4:3 |- | ├┼──┼┼──┼──┼┼──┼──┤ | 5L 3s (oneirotonic) | 3, 1 | 3:1 |- | ├┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┤ | 5L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 18edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\18 and 6\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼─────┤ | 1L 1s | 12, 6 | 2:1 |- | ├─────┼─────┼─────┤ | 3edo | 6, 6 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\18 and 5\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼────┤ | 1L 1s | 13, 5 | 13:5 |- | ├───────┼────┼────┤ | 1L 2s | 8, 5 | 8:5 |- | ├──┼────┼────┼────┤ | 3L 1s | 5, 3 | 5:3 |- | ├──┼──┼─┼──┼─┼──┼─┤ | 4L 3s (smitonic) | 3, 2 | 3:2 |- | ├┼─┼┼─┼─┼┼─┼─┼┼─┼─┤ | 7L 4s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 18edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\18 and 4\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼───┤ | 1L 1s | 14, 4 | 7:2 |- | ├─────────┼───┼───┤ | 1L 2s | 10, 4 | 5:2 |- | ├─────┼───┼───┼───┤ | 1L 3s | 6, 4 | 3:2 |- | ├─┼───┼───┼───┼───┤ | 4L 1s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 9edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\18 and 3\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼──┤ | 1L 1s | 15, 3 | 5:1 |- | ├───────────┼──┼──┤ | 1L 2s | 12, 3 | 4:1 |- | ├────────┼──┼──┼──┤ | 1L 3s | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┼──┤ | 1L 4s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┤ | 6edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\18 and 2\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼─┤ | 1L 1s | 16, 2 | 8:1 |- | ├─────────────┼─┼─┤ | 1L 2s | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┤ | 1L 3s | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┤ | 1L 4s | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 9edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\18 and 1\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼┤ | 1L 1s | 17, 1 | 17:1 |- | ├───────────────┼┼┤ | 1L 2s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┤ | 1L 3s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┤ | 1L 4s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 18edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 5\18 and 4\18
Step visualization MOS (name) Step sizes Step ratio
├────┼───┼────┼───┤ 2L 2s 5, 4 5:4
├┼───┼───┼┼───┼───┤ 4L 2s (citric) 4, 1 4:1
├┼┼──┼┼──┼┼┼──┼┼──┤ 4L 6s (lime) 3, 1 3:1
├┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┤ 4L 10s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 18edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 6\18 and 3\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼──┼─────┼──┤ | 2L 2s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┤ | 6edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 7\18 and 2\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼─┼──────┼─┤ | 2L 2s | 7, 2 | 7:2 |- | ├────┼─┼─┼────┼─┼─┤ | 2L 4s (malic) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼──┼─┼─┼─┤ | 2L 6s (subaric) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼┼─┼─┼─┼─┤ | 8L 2s (taric) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 18edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\18 and 1\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼┼───────┼┤ | 2L 2s | 8, 1 | 8:1 |- | ├──────┼┼┼──────┼┼┤ | 2L 4s (malic) | 7, 1 | 7:1 |- | ├─────┼┼┼┼─────┼┼┼┤ | 2L 6s (subaric) | 6, 1 | 6:1 |- | ├────┼┼┼┼┼────┼┼┼┼┤ | 2L 8s (jaric) | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼───┼┼┼┼┼┤ | 2L 10s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼──┼┼┼┼┼┼┤ | 2L 12s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┤ | 2L 14s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 18edo | 1, 1 | 1:1 |}
3 periods

Generators 4\18 and 2\18
Step visualization MOS (name) Step sizes Step ratio
├───┼─┼───┼─┼───┼─┤ 3L 3s (triwood) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┤ 9edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\18 and 1\18 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼┼────┼┼────┼┤ | 3L 3s (triwood) | 5, 1 | 5:1 |- | ├───┼┼┼───┼┼┼───┼┼┤ | 3L 6s (tcherepnin) | 4, 1 | 4:1 |- | ├──┼┼┼┼──┼┼┼┼──┼┼┼┤ | 3L 9s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ | 3L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 18edo | 1, 1 | 1:1 |}
6 periods

Generators 2\18 and 1\18
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ 6L 6s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 18edo 1, 1 1:1

19edo

These are all moment of symmetry scales in 19edo.
Single-period MOS scales

Generators 10\19 and 9\19
Step visualization MOS (name) Step sizes Step ratio
├─────────┼────────┤ 1L 1s 10, 9 10:9
├┼────────┼────────┤ 2L 1s 9, 1 9:1
├┼┼───────┼┼───────┤ 2L 3s 8, 1 8:1
├┼┼┼──────┼┼┼──────┤ 2L 5s (antidiatonic) 7, 1 7:1
├┼┼┼┼─────┼┼┼┼─────┤ 2L 7s (balzano) 6, 1 6:1
├┼┼┼┼┼────┼┼┼┼┼────┤ 2L 9s 5, 1 5:1
├┼┼┼┼┼┼───┼┼┼┼┼┼───┤ 2L 11s 4, 1 4:1
├┼┼┼┼┼┼┼──┼┼┼┼┼┼┼──┤ 2L 13s 3, 1 3:1
├┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼─┤ 2L 15s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 19edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 11\19 and 8\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼───────┤ | 1L 1s | 11, 8 | 11:8 |- | ├──┼───────┼───────┤ | 2L 1s | 8, 3 | 8:3 |- | ├──┼──┼────┼──┼────┤ | 2L 3s | 5, 3 | 5:3 |- | ├──┼──┼──┼─┼──┼──┼─┤ | 5L 2s (diatonic) | 3, 2 | 3:2 |- | ├┼─┼┼─┼┼─┼─┼┼─┼┼─┼─┤ | 7L 5s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\19 and 7\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼──────┤ | 1L 1s | 12, 7 | 12:7 |- | ├────┼──────┼──────┤ | 2L 1s | 7, 5 | 7:5 |- | ├────┼────┼─┼────┼─┤ | 3L 2s | 5, 2 | 5:2 |- | ├──┼─┼──┼─┼─┼──┼─┼─┤ | 3L 5s (checkertonic) | 3, 2 | 3:2 |- | ├┼─┼─┼┼─┼─┼─┼┼─┼─┼─┤ | 8L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\19 and 6\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼─────┤ | 1L 1s | 13, 6 | 13:6 |- | ├──────┼─────┼─────┤ | 1L 2s | 7, 6 | 7:6 |- | ├┼─────┼─────┼─────┤ | 3L 1s | 6, 1 | 6:1 |- | ├┼┼────┼┼────┼┼────┤ | 3L 4s (mosh) | 5, 1 | 5:1 |- | ├┼┼┼───┼┼┼───┼┼┼───┤ | 3L 7s (sephiroid) | 4, 1 | 4:1 |- | ├┼┼┼┼──┼┼┼┼──┼┼┼┼──┤ | 3L 10s | 3, 1 | 3:1 |- | ├┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┤ | 3L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\19 and 5\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼────┤ | 1L 1s | 14, 5 | 14:5 |- | ├────────┼────┼────┤ | 1L 2s | 9, 5 | 9:5 |- | ├───┼────┼────┼────┤ | 3L 1s | 5, 4 | 5:4 |- | ├───┼───┼┼───┼┼───┼┤ | 4L 3s (smitonic) | 4, 1 | 4:1 |- | ├──┼┼──┼┼┼──┼┼┼──┼┼┤ | 4L 7s | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 4L 11s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\19 and 4\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼───┤ | 1L 1s | 15, 4 | 15:4 |- | ├──────────┼───┼───┤ | 1L 2s | 11, 4 | 11:4 |- | ├──────┼───┼───┼───┤ | 1L 3s | 7, 4 | 7:4 |- | ├──┼───┼───┼───┼───┤ | 4L 1s | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┼──┼┼──┼┤ | 5L 4s (semiquartal) | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ | 5L 9s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\19 and 3\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼──┤ | 1L 1s | 16, 3 | 16:3 |- | ├────────────┼──┼──┤ | 1L 2s | 13, 3 | 13:3 |- | ├─────────┼──┼──┼──┤ | 1L 3s | 10, 3 | 10:3 |- | ├──────┼──┼──┼──┼──┤ | 1L 4s | 7, 3 | 7:3 |- | ├───┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼──┼──┼──┤ | 6L 1s (archaeotonic) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┤ | 6L 7s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\19 and 2\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼─┤ | 1L 1s | 17, 2 | 17:2 |- | ├──────────────┼─┼─┤ | 1L 2s | 15, 2 | 15:2 |- | ├────────────┼─┼─┼─┤ | 1L 3s | 13, 2 | 13:2 |- | ├──────────┼─┼─┼─┼─┤ | 1L 4s | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 9L 1s (sinatonic) | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\19 and 1\19 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼┤ | 1L 1s | 18, 1 | 18:1 |- | ├────────────────┼┼┤ | 1L 2s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┤ | 1L 3s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┤ | 1L 4s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 19edo | 1, 1 | 1:1 |}

20edo

These are all moment of symmetry scales in 20edo.
Single-period MOS scales

Generators 11\20 and 9\20
Step visualization MOS (name) Step sizes Step ratio
├──────────┼────────┤ 1L 1s 11, 9 11:9
├─┼────────┼────────┤ 2L 1s 9, 2 9:2
├─┼─┼──────┼─┼──────┤ 2L 3s 7, 2 7:2
├─┼─┼─┼────┼─┼─┼────┤ 2L 5s (antidiatonic) 5, 2 5:2
├─┼─┼─┼─┼──┼─┼─┼─┼──┤ 2L 7s (balzano) 3, 2 3:2
├─┼─┼─┼─┼─┼┼─┼─┼─┼─┼┤ 9L 2s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 20edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 12\20 and 8\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼───────┤ | 1L 1s | 12, 8 | 3:2 |- | ├───┼───────┼───────┤ | 2L 1s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┤ | 5edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\20 and 7\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼──────┤ | 1L 1s | 13, 7 | 13:7 |- | ├─────┼──────┼──────┤ | 2L 1s | 7, 6 | 7:6 |- | ├─────┼─────┼┼─────┼┤ | 3L 2s | 6, 1 | 6:1 |- | ├────┼┼────┼┼┼────┼┼┤ | 3L 5s (checkertonic) | 5, 1 | 5:1 |- | ├───┼┼┼───┼┼┼┼───┼┼┼┤ | 3L 8s | 4, 1 | 4:1 |- | ├──┼┼┼┼──┼┼┼┼┼──┼┼┼┼┤ | 3L 11s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┤ | 3L 14s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 20edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\20 and 6\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼─────┤ | 1L 1s | 14, 6 | 7:3 |- | ├───────┼─────┼─────┤ | 1L 2s | 8, 6 | 4:3 |- | ├─┼─────┼─────┼─────┤ | 3L 1s | 6, 2 | 3:1 |- | ├─┼─┼───┼─┼───┼─┼───┤ | 3L 4s (mosh) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 10edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\20 and 5\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼────┤ | 1L 1s | 15, 5 | 3:1 |- | ├─────────┼────┼────┤ | 1L 2s | 10, 5 | 2:1 |- | ├────┼────┼────┼────┤ | 4edo | 5, 5 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\20 and 4\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼───┤ | 1L 1s | 16, 4 | 4:1 |- | ├───────────┼───┼───┤ | 1L 2s | 12, 4 | 3:1 |- | ├───────┼───┼───┼───┤ | 1L 3s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┤ | 5edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\20 and 3\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼──┤ | 1L 1s | 17, 3 | 17:3 |- | ├─────────────┼──┼──┤ | 1L 2s | 14, 3 | 14:3 |- | ├──────────┼──┼──┼──┤ | 1L 3s | 11, 3 | 11:3 |- | ├───────┼──┼──┼──┼──┤ | 1L 4s | 8, 3 | 8:3 |- | ├────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼──┼──┼──┤ | 6L 1s (archaeotonic) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ | 7L 6s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 20edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\20 and 2\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼─┤ | 1L 1s | 18, 2 | 9:1 |- | ├───────────────┼─┼─┤ | 1L 2s | 16, 2 | 8:1 |- | ├─────────────┼─┼─┼─┤ | 1L 3s | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┼─┤ | 1L 4s | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 10edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\20 and 1\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼┤ | 1L 1s | 19, 1 | 19:1 |- | ├─────────────────┼┼┤ | 1L 2s | 18, 1 | 18:1 |- | ├────────────────┼┼┼┤ | 1L 3s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┤ | 1L 4s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 20edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 6\20 and 4\20
Step visualization MOS (name) Step sizes Step ratio
├─────┼───┼─────┼───┤ 2L 2s 6, 4 3:2
├─┼───┼───┼─┼───┼───┤ 4L 2s (citric) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 10edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 7\20 and 3\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼──┼──────┼──┤ | 2L 2s | 7, 3 | 7:3 |- | ├───┼──┼──┼───┼──┼──┤ | 2L 4s (malic) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼┼──┼──┼──┤ | 6L 2s (ekic) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┤ | 6L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 20edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\20 and 2\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼─┼───────┼─┤ | 2L 2s | 8, 2 | 4:1 |- | ├─────┼─┼─┼─────┼─┼─┤ | 2L 4s (malic) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼───┼─┼─┼─┤ | 2L 6s (subaric) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 10edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\20 and 1\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼┼────────┼┤ | 2L 2s | 9, 1 | 9:1 |- | ├───────┼┼┼───────┼┼┤ | 2L 4s (malic) | 8, 1 | 8:1 |- | ├──────┼┼┼┼──────┼┼┼┤ | 2L 6s (subaric) | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼─────┼┼┼┼┤ | 2L 8s (jaric) | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼────┼┼┼┼┼┤ | 2L 10s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼───┼┼┼┼┼┼┤ | 2L 12s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┤ | 2L 14s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┤ | 2L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 20edo | 1, 1 | 1:1 |}
4 periods

Generators 3\20 and 2\20
Step visualization MOS (name) Step sizes Step ratio
├──┼─┼──┼─┼──┼─┼──┼─┤ 4L 4s (tetrawood) 3, 2 3:2
├┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┤ 8L 4s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 20edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 4\20 and 1\20 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───┼┼───┼┼───┼┼───┼┤ | 4L 4s (tetrawood) | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼──┼┼┼──┼┼┤ | 4L 8s | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 4L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 20edo | 1, 1 | 1:1 |}
5 periods

Generators 3\20 and 1\20
Step visualization MOS (name) Step sizes Step ratio
├──┼┼──┼┼──┼┼──┼┼──┼┤ 5L 5s (pentawood) 3, 1 3:1
├─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ 5L 10s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 20edo 1, 1 1:1

21edo

These are all moment of symmetry scales in 21edo.
Single-period MOS scales

Generators 11\21 and 10\21
Step visualization MOS (name) Step sizes Step ratio
├──────────┼─────────┤ 1L 1s 11, 10 11:10
├┼─────────┼─────────┤ 2L 1s 10, 1 10:1
├┼┼────────┼┼────────┤ 2L 3s 9, 1 9:1
├┼┼┼───────┼┼┼───────┤ 2L 5s (antidiatonic) 8, 1 8:1
├┼┼┼┼──────┼┼┼┼──────┤ 2L 7s (balzano) 7, 1 7:1
├┼┼┼┼┼─────┼┼┼┼┼─────┤ 2L 9s 6, 1 6:1
├┼┼┼┼┼┼────┼┼┼┼┼┼────┤ 2L 11s 5, 1 5:1
├┼┼┼┼┼┼┼───┼┼┼┼┼┼┼───┤ 2L 13s 4, 1 4:1
├┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼──┤ 2L 15s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼─┤ 2L 17s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 21edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 12\21 and 9\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼────────┤ | 1L 1s | 12, 9 | 4:3 |- | ├──┼────────┼────────┤ | 2L 1s | 9, 3 | 3:1 |- | ├──┼──┼─────┼──┼─────┤ | 2L 3s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┤ | 7edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\21 and 8\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼───────┤ | 1L 1s | 13, 8 | 13:8 |- | ├────┼───────┼───────┤ | 2L 1s | 8, 5 | 8:5 |- | ├────┼────┼──┼────┼──┤ | 3L 2s | 5, 3 | 5:3 |- | ├─┼──┼─┼──┼──┼─┼──┼──┤ | 5L 3s (oneirotonic) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼┤ | 8L 5s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\21 and 7\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼──────┤ | 1L 1s | 14, 7 | 2:1 |- | ├──────┼──────┼──────┤ | 3edo | 7, 7 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\21 and 6\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼─────┤ | 1L 1s | 15, 6 | 5:2 |- | ├────────┼─────┼─────┤ | 1L 2s | 9, 6 | 3:2 |- | ├──┼─────┼─────┼─────┤ | 3L 1s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┤ | 7edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\21 and 5\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼────┤ | 1L 1s | 16, 5 | 16:5 |- | ├──────────┼────┼────┤ | 1L 2s | 11, 5 | 11:5 |- | ├─────┼────┼────┼────┤ | 1L 3s | 6, 5 | 6:5 |- | ├┼────┼────┼────┼────┤ | 4L 1s | 5, 1 | 5:1 |- | ├┼┼───┼┼───┼┼───┼┼───┤ | 4L 5s (gramitonic) | 4, 1 | 4:1 |- | ├┼┼┼──┼┼┼──┼┼┼──┼┼┼──┤ | 4L 9s | 3, 1 | 3:1 |- | ├┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┤ | 4L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\21 and 4\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼───┤ | 1L 1s | 17, 4 | 17:4 |- | ├────────────┼───┼───┤ | 1L 2s | 13, 4 | 13:4 |- | ├────────┼───┼───┼───┤ | 1L 3s | 9, 4 | 9:4 |- | ├────┼───┼───┼───┼───┤ | 1L 4s | 5, 4 | 5:4 |- | ├┼───┼───┼───┼───┼───┤ | 5L 1s (machinoid) | 4, 1 | 4:1 |- | ├┼┼──┼┼──┼┼──┼┼──┼┼──┤ | 5L 6s | 3, 1 | 3:1 |- | ├┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┤ | 5L 11s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\21 and 3\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼──┤ | 1L 1s | 18, 3 | 6:1 |- | ├──────────────┼──┼──┤ | 1L 2s | 15, 3 | 5:1 |- | ├───────────┼──┼──┼──┤ | 1L 3s | 12, 3 | 4:1 |- | ├────────┼──┼──┼──┼──┤ | 1L 4s | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┤ | 7edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\21 and 2\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼─┤ | 1L 1s | 19, 2 | 19:2 |- | ├────────────────┼─┼─┤ | 1L 2s | 17, 2 | 17:2 |- | ├──────────────┼─┼─┼─┤ | 1L 3s | 15, 2 | 15:2 |- | ├────────────┼─┼─┼─┼─┤ | 1L 4s | 13, 2 | 13:2 |- | ├──────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 10L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\21 and 1\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼┤ | 1L 1s | 20, 1 | 20:1 |- | ├──────────────────┼┼┤ | 1L 2s | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┤ | 1L 3s | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┤ | 1L 4s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}
Multi-period MOS scales
3 periods

Generators 4\21 and 3\21
Step visualization MOS (name) Step sizes Step ratio
├───┼──┼───┼──┼───┼──┤ 3L 3s (triwood) 4, 3 4:3
├┼──┼──┼┼──┼──┼┼──┼──┤ 6L 3s (hyrulic) 3, 1 3:1
├┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┤ 6L 9s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 21edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\21 and 2\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼─┼────┼─┼────┼─┤ | 3L 3s (triwood) | 5, 2 | 5:2 |- | ├──┼─┼─┼──┼─┼─┼──┼─┼─┤ | 3L 6s (tcherepnin) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┤ | 9L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 6\21 and 1\21 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼┼─────┼┼─────┼┤ | 3L 3s (triwood) | 6, 1 | 6:1 |- | ├────┼┼┼────┼┼┼────┼┼┤ | 3L 6s (tcherepnin) | 5, 1 | 5:1 |- | ├───┼┼┼┼───┼┼┼┼───┼┼┼┤ | 3L 9s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┤ | 3L 12s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┤ | 3L 15s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 21edo | 1, 1 | 1:1 |}
7 periods

Generators 2\21 and 1\21
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ 7L 7s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 21edo 1, 1 1:1

22edo

These are all moment of symmetry scales in 22edo.
Single-period MOS scales

Generators 12\22 and 10\22
Step visualization MOS (name) Step sizes Step ratio
├───────────┼─────────┤ 1L 1s 12, 10 6:5
├─┼─────────┼─────────┤ 2L 1s 10, 2 5:1
├─┼─┼───────┼─┼───────┤ 2L 3s 8, 2 4:1
├─┼─┼─┼─────┼─┼─┼─────┤ 2L 5s (antidiatonic) 6, 2 3:1
├─┼─┼─┼─┼───┼─┼─┼─┼───┤ 2L 7s (balzano) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 11edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 13\22 and 9\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼────────┤ | 1L 1s | 13, 9 | 13:9 |- | ├───┼────────┼────────┤ | 2L 1s | 9, 4 | 9:4 |- | ├───┼───┼────┼───┼────┤ | 2L 3s | 5, 4 | 5:4 |- | ├───┼───┼───┼┼───┼───┼┤ | 5L 2s (diatonic) | 4, 1 | 4:1 |- | ├──┼┼──┼┼──┼┼┼──┼┼──┼┼┤ | 5L 7s | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┼┼┼┤ | 5L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\22 and 8\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼───────┤ | 1L 1s | 14, 8 | 7:4 |- | ├─────┼───────┼───────┤ | 2L 1s | 8, 6 | 4:3 |- | ├─────┼─────┼─┼─────┼─┤ | 3L 2s | 6, 2 | 3:1 |- | ├───┼─┼───┼─┼─┼───┼─┼─┤ | 3L 5s (checkertonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 11edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\22 and 7\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼──────┤ | 1L 1s | 15, 7 | 15:7 |- | ├───────┼──────┼──────┤ | 1L 2s | 8, 7 | 8:7 |- | ├┼──────┼──────┼──────┤ | 3L 1s | 7, 1 | 7:1 |- | ├┼┼─────┼┼─────┼┼─────┤ | 3L 4s (mosh) | 6, 1 | 6:1 |- | ├┼┼┼────┼┼┼────┼┼┼────┤ | 3L 7s (sephiroid) | 5, 1 | 5:1 |- | ├┼┼┼┼───┼┼┼┼───┼┼┼┼───┤ | 3L 10s | 4, 1 | 4:1 |- | ├┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┼──┤ | 3L 13s | 3, 1 | 3:1 |- | ├┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┼─┤ | 3L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\22 and 6\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼─────┤ | 1L 1s | 16, 6 | 8:3 |- | ├─────────┼─────┼─────┤ | 1L 2s | 10, 6 | 5:3 |- | ├───┼─────┼─────┼─────┤ | 3L 1s | 6, 4 | 3:2 |- | ├───┼───┼─┼───┼─┼───┼─┤ | 4L 3s (smitonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 11edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\22 and 5\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼────┤ | 1L 1s | 17, 5 | 17:5 |- | ├───────────┼────┼────┤ | 1L 2s | 12, 5 | 12:5 |- | ├──────┼────┼────┼────┤ | 1L 3s | 7, 5 | 7:5 |- | ├─┼────┼────┼────┼────┤ | 4L 1s | 5, 2 | 5:2 |- | ├─┼─┼──┼─┼──┼─┼──┼─┼──┤ | 4L 5s (gramitonic) | 3, 2 | 3:2 |- | ├─┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┤ | 9L 4s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\22 and 4\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼───┤ | 1L 1s | 18, 4 | 9:2 |- | ├─────────────┼───┼───┤ | 1L 2s | 14, 4 | 7:2 |- | ├─────────┼───┼───┼───┤ | 1L 3s | 10, 4 | 5:2 |- | ├─────┼───┼───┼───┼───┤ | 1L 4s | 6, 4 | 3:2 |- | ├─┼───┼───┼───┼───┼───┤ | 5L 1s (machinoid) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 11edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\22 and 3\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼──┤ | 1L 1s | 19, 3 | 19:3 |- | ├───────────────┼──┼──┤ | 1L 2s | 16, 3 | 16:3 |- | ├────────────┼──┼──┼──┤ | 1L 3s | 13, 3 | 13:3 |- | ├─────────┼──┼──┼──┼──┤ | 1L 4s | 10, 3 | 10:3 |- | ├──────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 7, 3 | 7:3 |- | ├───┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼──┼──┼──┼──┤ | 7L 1s (pine) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┤ | 7L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\22 and 2\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼─┤ | 1L 1s | 20, 2 | 10:1 |- | ├─────────────────┼─┼─┤ | 1L 2s | 18, 2 | 9:1 |- | ├───────────────┼─┼─┼─┤ | 1L 3s | 16, 2 | 8:1 |- | ├─────────────┼─┼─┼─┼─┤ | 1L 4s | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 11edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\22 and 1\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼┤ | 1L 1s | 21, 1 | 21:1 |- | ├───────────────────┼┼┤ | 1L 2s | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┤ | 1L 3s | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┤ | 1L 4s | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 6\22 and 5\22
Step visualization MOS (name) Step sizes Step ratio
├─────┼────┼─────┼────┤ 2L 2s 6, 5 6:5
├┼────┼────┼┼────┼────┤ 4L 2s (citric) 5, 1 5:1
├┼┼───┼┼───┼┼┼───┼┼───┤ 4L 6s (lime) 4, 1 4:1
├┼┼┼──┼┼┼──┼┼┼┼──┼┼┼──┤ 4L 10s 3, 1 3:1
├┼┼┼┼─┼┼┼┼─┼┼┼┼┼─┼┼┼┼─┤ 4L 14s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 22edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 7\22 and 4\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼───┼──────┼───┤ | 2L 2s | 7, 4 | 7:4 |- | ├──┼───┼───┼──┼───┼───┤ | 4L 2s (citric) | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┼──┼──┼┼──┼┤ | 6L 4s (lemon) | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┼─┼┼─┼┼┼─┼┼┤ | 6L 10s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\22 and 3\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼──┼───────┼──┤ | 2L 2s | 8, 3 | 8:3 |- | ├────┼──┼──┼────┼──┼──┤ | 2L 4s (malic) | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼─┼──┼──┼──┤ | 6L 2s (ekic) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼─┼┼─┼┼─┼┤ | 8L 6s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\22 and 2\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼─┼────────┼─┤ | 2L 2s | 9, 2 | 9:2 |- | ├──────┼─┼─┼──────┼─┼─┤ | 2L 4s (malic) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼────┼─┼─┼─┤ | 2L 6s (subaric) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼──┼─┼─┼─┼─┤ | 2L 8s (jaric) | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┤ | 10L 2s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\22 and 1\22 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼┼─────────┼┤ | 2L 2s | 10, 1 | 10:1 |- | ├────────┼┼┼────────┼┼┤ | 2L 4s (malic) | 9, 1 | 9:1 |- | ├───────┼┼┼┼───────┼┼┼┤ | 2L 6s (subaric) | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼──────┼┼┼┼┤ | 2L 8s (jaric) | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼─────┼┼┼┼┼┤ | 2L 10s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼────┼┼┼┼┼┼┤ | 2L 12s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┤ | 2L 14s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┤ | 2L 16s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┤ | 2L 18s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 22edo | 1, 1 | 1:1 |}

23edo

These are all moment of symmetry scales in 23edo.
Single-period MOS scales

Generators 12\23 and 11\23
Step visualization MOS (name) Step sizes Step ratio
├───────────┼──────────┤ 1L 1s 12, 11 12:11
├┼──────────┼──────────┤ 2L 1s 11, 1 11:1
├┼┼─────────┼┼─────────┤ 2L 3s 10, 1 10:1
├┼┼┼────────┼┼┼────────┤ 2L 5s (antidiatonic) 9, 1 9:1
├┼┼┼┼───────┼┼┼┼───────┤ 2L 7s (balzano) 8, 1 8:1
├┼┼┼┼┼──────┼┼┼┼┼──────┤ 2L 9s 7, 1 7:1
├┼┼┼┼┼┼─────┼┼┼┼┼┼─────┤ 2L 11s 6, 1 6:1
├┼┼┼┼┼┼┼────┼┼┼┼┼┼┼────┤ 2L 13s 5, 1 5:1
├┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼───┤ 2L 15s 4, 1 4:1
├┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼──┤ 2L 17s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼─┤ 2L 19s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 23edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 13\23 and 10\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼─────────┤ | 1L 1s | 13, 10 | 13:10 |- | ├──┼─────────┼─────────┤ | 2L 1s | 10, 3 | 10:3 |- | ├──┼──┼──────┼──┼──────┤ | 2L 3s | 7, 3 | 7:3 |- | ├──┼──┼──┼───┼──┼──┼───┤ | 2L 5s (antidiatonic) | 4, 3 | 4:3 |- | ├──┼──┼──┼──┼┼──┼──┼──┼┤ | 7L 2s (armotonic) | 3, 1 | 3:1 |- | ├─┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┼┼┤ | 7L 9s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\23 and 9\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼────────┤ | 1L 1s | 14, 9 | 14:9 |- | ├────┼────────┼────────┤ | 2L 1s | 9, 5 | 9:5 |- | ├────┼────┼───┼────┼───┤ | 3L 2s | 5, 4 | 5:4 |- | ├┼───┼┼───┼───┼┼───┼───┤ | 5L 3s (oneirotonic) | 4, 1 | 4:1 |- | ├┼┼──┼┼┼──┼┼──┼┼┼──┼┼──┤ | 5L 8s | 3, 1 | 3:1 |- | ├┼┼┼─┼┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┤ | 5L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\23 and 8\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼───────┤ | 1L 1s | 15, 8 | 15:8 |- | ├──────┼───────┼───────┤ | 2L 1s | 8, 7 | 8:7 |- | ├──────┼──────┼┼──────┼┤ | 3L 2s | 7, 1 | 7:1 |- | ├─────┼┼─────┼┼┼─────┼┼┤ | 3L 5s (checkertonic) | 6, 1 | 6:1 |- | ├────┼┼┼────┼┼┼┼────┼┼┼┤ | 3L 8s | 5, 1 | 5:1 |- | ├───┼┼┼┼───┼┼┼┼┼───┼┼┼┼┤ | 3L 11s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼──┼┼┼┼┼┼──┼┼┼┼┼┤ | 3L 14s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼─┼┼┼┼┼┼┼─┼┼┼┼┼┼┤ | 3L 17s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\23 and 7\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼──────┤ | 1L 1s | 16, 7 | 16:7 |- | ├────────┼──────┼──────┤ | 1L 2s | 9, 7 | 9:7 |- | ├─┼──────┼──────┼──────┤ | 3L 1s | 7, 2 | 7:2 |- | ├─┼─┼────┼─┼────┼─┼────┤ | 3L 4s (mosh) | 5, 2 | 5:2 |- | ├─┼─┼─┼──┼─┼─┼──┼─┼─┼──┤ | 3L 7s (sephiroid) | 3, 2 | 3:2 |- | ├─┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┼┤ | 10L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\23 and 6\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼─────┤ | 1L 1s | 17, 6 | 17:6 |- | ├──────────┼─────┼─────┤ | 1L 2s | 11, 6 | 11:6 |- | ├────┼─────┼─────┼─────┤ | 3L 1s | 6, 5 | 6:5 |- | ├────┼────┼┼────┼┼────┼┤ | 4L 3s (smitonic) | 5, 1 | 5:1 |- | ├───┼┼───┼┼┼───┼┼┼───┼┼┤ | 4L 7s | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┤ | 4L 11s | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ | 4L 15s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\23 and 5\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼────┤ | 1L 1s | 18, 5 | 18:5 |- | ├────────────┼────┼────┤ | 1L 2s | 13, 5 | 13:5 |- | ├───────┼────┼────┼────┤ | 1L 3s | 8, 5 | 8:5 |- | ├──┼────┼────┼────┼────┤ | 4L 1s | 5, 3 | 5:3 |- | ├──┼──┼─┼──┼─┼──┼─┼──┼─┤ | 5L 4s (semiquartal) | 3, 2 | 3:2 |- | ├┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┤ | 9L 5s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\23 and 4\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼───┤ | 1L 1s | 19, 4 | 19:4 |- | ├──────────────┼───┼───┤ | 1L 2s | 15, 4 | 15:4 |- | ├──────────┼───┼───┼───┤ | 1L 3s | 11, 4 | 11:4 |- | ├──────┼───┼───┼───┼───┤ | 1L 4s | 7, 4 | 7:4 |- | ├──┼───┼───┼───┼───┼───┤ | 5L 1s (machinoid) | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┼──┼┼──┼┼──┼┤ | 6L 5s | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ | 6L 11s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\23 and 3\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼──┤ | 1L 1s | 20, 3 | 20:3 |- | ├────────────────┼──┼──┤ | 1L 2s | 17, 3 | 17:3 |- | ├─────────────┼──┼──┼──┤ | 1L 3s | 14, 3 | 14:3 |- | ├──────────┼──┼──┼──┼──┤ | 1L 4s | 11, 3 | 11:3 |- | ├───────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 8, 3 | 8:3 |- | ├────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼──┼──┼──┼──┤ | 7L 1s (pine) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ | 8L 7s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\23 and 2\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼─┤ | 1L 1s | 21, 2 | 21:2 |- | ├──────────────────┼─┼─┤ | 1L 2s | 19, 2 | 19:2 |- | ├────────────────┼─┼─┼─┤ | 1L 3s | 17, 2 | 17:2 |- | ├──────────────┼─┼─┼─┼─┤ | 1L 4s | 15, 2 | 15:2 |- | ├────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 13, 2 | 13:2 |- | ├──────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 11L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\23 and 1\23 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼┤ | 1L 1s | 22, 1 | 22:1 |- | ├────────────────────┼┼┤ | 1L 2s | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┤ | 1L 3s | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┤ | 1L 4s | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 23edo | 1, 1 | 1:1 |}

24edo

These are all moment of symmetry scales in 24edo.
Single-period MOS scales

Generators 13\24 and 11\24
Step visualization MOS (name) Step sizes Step ratio
├────────────┼──────────┤ 1L 1s 13, 11 13:11
├─┼──────────┼──────────┤ 2L 1s 11, 2 11:2
├─┼─┼────────┼─┼────────┤ 2L 3s 9, 2 9:2
├─┼─┼─┼──────┼─┼─┼──────┤ 2L 5s (antidiatonic) 7, 2 7:2
├─┼─┼─┼─┼────┼─┼─┼─┼────┤ 2L 7s (balzano) 5, 2 5:2
├─┼─┼─┼─┼─┼──┼─┼─┼─┼─┼──┤ 2L 9s 3, 2 3:2
├─┼─┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┼┤ 11L 2s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 24edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 14\24 and 10\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼─────────┤ | 1L 1s | 14, 10 | 7:5 |- | ├───┼─────────┼─────────┤ | 2L 1s | 10, 4 | 5:2 |- | ├───┼───┼─────┼───┼─────┤ | 2L 3s | 6, 4 | 3:2 |- | ├───┼───┼───┼─┼───┼───┼─┤ | 5L 2s (diatonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 12edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\24 and 9\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼────────┤ | 1L 1s | 15, 9 | 5:3 |- | ├─────┼────────┼────────┤ | 2L 1s | 9, 6 | 3:2 |- | ├─────┼─────┼──┼─────┼──┤ | 3L 2s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┤ | 8edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\24 and 8\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼───────┤ | 1L 1s | 16, 8 | 2:1 |- | ├───────┼───────┼───────┤ | 3edo | 8, 8 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\24 and 7\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼──────┤ | 1L 1s | 17, 7 | 17:7 |- | ├─────────┼──────┼──────┤ | 1L 2s | 10, 7 | 10:7 |- | ├──┼──────┼──────┼──────┤ | 3L 1s | 7, 3 | 7:3 |- | ├──┼──┼───┼──┼───┼──┼───┤ | 3L 4s (mosh) | 4, 3 | 4:3 |- | ├──┼──┼──┼┼──┼──┼┼──┼──┼┤ | 7L 3s (dicoid) | 3, 1 | 3:1 |- | ├─┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┼┼┤ | 7L 10s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 24edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\24 and 6\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼─────┤ | 1L 1s | 18, 6 | 3:1 |- | ├───────────┼─────┼─────┤ | 1L 2s | 12, 6 | 2:1 |- | ├─────┼─────┼─────┼─────┤ | 4edo | 6, 6 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\24 and 5\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼────┤ | 1L 1s | 19, 5 | 19:5 |- | ├─────────────┼────┼────┤ | 1L 2s | 14, 5 | 14:5 |- | ├────────┼────┼────┼────┤ | 1L 3s | 9, 5 | 9:5 |- | ├───┼────┼────┼────┼────┤ | 4L 1s | 5, 4 | 5:4 |- | ├───┼───┼┼───┼┼───┼┼───┼┤ | 5L 4s (semiquartal) | 4, 1 | 4:1 |- | ├──┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┤ | 5L 9s | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 5L 14s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 24edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\24 and 4\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼───┤ | 1L 1s | 20, 4 | 5:1 |- | ├───────────────┼───┼───┤ | 1L 2s | 16, 4 | 4:1 |- | ├───────────┼───┼───┼───┤ | 1L 3s | 12, 4 | 3:1 |- | ├───────┼───┼───┼───┼───┤ | 1L 4s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┼───┤ | 6edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\24 and 3\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼──┤ | 1L 1s | 21, 3 | 7:1 |- | ├─────────────────┼──┼──┤ | 1L 2s | 18, 3 | 6:1 |- | ├──────────────┼──┼──┼──┤ | 1L 3s | 15, 3 | 5:1 |- | ├───────────┼──┼──┼──┼──┤ | 1L 4s | 12, 3 | 4:1 |- | ├────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┤ | 8edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\24 and 2\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼─┤ | 1L 1s | 22, 2 | 11:1 |- | ├───────────────────┼─┼─┤ | 1L 2s | 20, 2 | 10:1 |- | ├─────────────────┼─┼─┼─┤ | 1L 3s | 18, 2 | 9:1 |- | ├───────────────┼─┼─┼─┼─┤ | 1L 4s | 16, 2 | 8:1 |- | ├─────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 12edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\24 and 1\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼┤ | 1L 1s | 23, 1 | 23:1 |- | ├─────────────────────┼┼┤ | 1L 2s | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┤ | 1L 3s | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┤ | 1L 4s | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 24edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 7\24 and 5\24
Step visualization MOS (name) Step sizes Step ratio
├──────┼────┼──────┼────┤ 2L 2s 7, 5 7:5
├─┼────┼────┼─┼────┼────┤ 4L 2s (citric) 5, 2 5:2
├─┼─┼──┼─┼──┼─┼─┼──┼─┼──┤ 4L 6s (lime) 3, 2 3:2
├─┼─┼─┼┼─┼─┼┼─┼─┼─┼┼─┼─┼┤ 10L 4s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 24edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 8\24 and 4\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼───┼───────┼───┤ | 2L 2s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┼───┤ | 6edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\24 and 3\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼──┼────────┼──┤ | 2L 2s | 9, 3 | 3:1 |- | ├─────┼──┼──┼─────┼──┼──┤ | 2L 4s (malic) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┤ | 8edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\24 and 2\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼─┼─────────┼─┤ | 2L 2s | 10, 2 | 5:1 |- | ├───────┼─┼─┼───────┼─┼─┤ | 2L 4s (malic) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─────┼─┼─┼─┤ | 2L 6s (subaric) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼───┼─┼─┼─┼─┤ | 2L 8s (jaric) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 12edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\24 and 1\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼┼──────────┼┤ | 2L 2s | 11, 1 | 11:1 |- | ├─────────┼┼┼─────────┼┼┤ | 2L 4s (malic) | 10, 1 | 10:1 |- | ├────────┼┼┼┼────────┼┼┼┤ | 2L 6s (subaric) | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼───────┼┼┼┼┤ | 2L 8s (jaric) | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼──────┼┼┼┼┼┤ | 2L 10s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼─────┼┼┼┼┼┼┤ | 2L 12s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┤ | 2L 14s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┤ | 2L 16s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┤ | 2L 18s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┤ | 2L 20s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 24edo | 1, 1 | 1:1 |}
3 periods

Generators 5\24 and 3\24
Step visualization MOS (name) Step sizes Step ratio
├────┼──┼────┼──┼────┼──┤ 3L 3s (triwood) 5, 3 5:3
├─┼──┼──┼─┼──┼──┼─┼──┼──┤ 6L 3s (hyrulic) 3, 2 3:2
├─┼─┼┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼┤ 9L 6s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 24edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 6\24 and 2\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼─┼─────┼─┼─────┼─┤ | 3L 3s (triwood) | 6, 2 | 3:1 |- | ├───┼─┼─┼───┼─┼─┼───┼─┼─┤ | 3L 6s (tcherepnin) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 12edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 7\24 and 1\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼┼──────┼┼──────┼┤ | 3L 3s (triwood) | 7, 1 | 7:1 |- | ├─────┼┼┼─────┼┼┼─────┼┼┤ | 3L 6s (tcherepnin) | 6, 1 | 6:1 |- | ├────┼┼┼┼────┼┼┼┼────┼┼┼┤ | 3L 9s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼───┼┼┼┼┼───┼┼┼┼┤ | 3L 12s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼──┼┼┼┼┼┼──┼┼┼┼┼┤ | 3L 15s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┼┼┼┼┼┼┤ | 3L 18s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 24edo | 1, 1 | 1:1 |}
4 periods

Generators 4\24 and 2\24
Step visualization MOS (name) Step sizes Step ratio
├───┼─┼───┼─┼───┼─┼───┼─┤ 4L 4s (tetrawood) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 12edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\24 and 1\24 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼┼────┼┼────┼┼────┼┤ | 4L 4s (tetrawood) | 5, 1 | 5:1 |- | ├───┼┼┼───┼┼┼───┼┼┼───┼┼┤ | 4L 8s | 4, 1 | 4:1 |- | ├──┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┤ | 4L 12s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ | 4L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 24edo | 1, 1 | 1:1 |}
6 periods

Generators 3\24 and 1\24
Step visualization MOS (name) Step sizes Step ratio
├──┼┼──┼┼──┼┼──┼┼──┼┼──┼┤ 6L 6s 3, 1 3:1
├─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ 6L 12s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 24edo 1, 1 1:1


8 periods

Generators 2\24 and 1\24
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ 8L 8s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 24edo 1, 1 1:1

25edo

These are all moment of symmetry scales in 25edo.
Single-period MOS scales

Generators 13\25 and 12\25
Step visualization MOS (name) Step sizes Step ratio
├────────────┼───────────┤ 1L 1s 13, 12 13:12
├┼───────────┼───────────┤ 2L 1s 12, 1 12:1
├┼┼──────────┼┼──────────┤ 2L 3s 11, 1 11:1
├┼┼┼─────────┼┼┼─────────┤ 2L 5s (antidiatonic) 10, 1 10:1
├┼┼┼┼────────┼┼┼┼────────┤ 2L 7s (balzano) 9, 1 9:1
├┼┼┼┼┼───────┼┼┼┼┼───────┤ 2L 9s 8, 1 8:1
├┼┼┼┼┼┼──────┼┼┼┼┼┼──────┤ 2L 11s 7, 1 7:1
├┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼─────┤ 2L 13s 6, 1 6:1
├┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼────┤ 2L 15s 5, 1 5:1
├┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼───┤ 2L 17s 4, 1 4:1
├┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼──┤ 2L 19s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼─┤ 2L 21s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 25edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 14\25 and 11\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼──────────┤ | 1L 1s | 14, 11 | 14:11 |- | ├──┼──────────┼──────────┤ | 2L 1s | 11, 3 | 11:3 |- | ├──┼──┼───────┼──┼───────┤ | 2L 3s | 8, 3 | 8:3 |- | ├──┼──┼──┼────┼──┼──┼────┤ | 2L 5s (antidiatonic) | 5, 3 | 5:3 |- | ├──┼──┼──┼──┼─┼──┼──┼──┼─┤ | 7L 2s (armotonic) | 3, 2 | 3:2 |- | ├┼─┼┼─┼┼─┼┼─┼─┼┼─┼┼─┼┼─┼─┤ | 9L 7s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 15\25 and 10\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼─────────┤ | 1L 1s | 15, 10 | 3:2 |- | ├────┼─────────┼─────────┤ | 2L 1s | 10, 5 | 2:1 |- | ├────┼────┼────┼────┼────┤ | 5edo | 5, 5 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\25 and 9\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼────────┤ | 1L 1s | 16, 9 | 16:9 |- | ├──────┼────────┼────────┤ | 2L 1s | 9, 7 | 9:7 |- | ├──────┼──────┼─┼──────┼─┤ | 3L 2s | 7, 2 | 7:2 |- | ├────┼─┼────┼─┼─┼────┼─┼─┤ | 3L 5s (checkertonic) | 5, 2 | 5:2 |- | ├──┼─┼─┼──┼─┼─┼─┼──┼─┼─┼─┤ | 3L 8s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼┼─┼─┼─┼─┼┼─┼─┼─┼─┤ | 11L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\25 and 8\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼───────┤ | 1L 1s | 17, 8 | 17:8 |- | ├────────┼───────┼───────┤ | 1L 2s | 9, 8 | 9:8 |- | ├┼───────┼───────┼───────┤ | 3L 1s | 8, 1 | 8:1 |- | ├┼┼──────┼┼──────┼┼──────┤ | 3L 4s (mosh) | 7, 1 | 7:1 |- | ├┼┼┼─────┼┼┼─────┼┼┼─────┤ | 3L 7s (sephiroid) | 6, 1 | 6:1 |- | ├┼┼┼┼────┼┼┼┼────┼┼┼┼────┤ | 3L 10s | 5, 1 | 5:1 |- | ├┼┼┼┼┼───┼┼┼┼┼───┼┼┼┼┼───┤ | 3L 13s | 4, 1 | 4:1 |- | ├┼┼┼┼┼┼──┼┼┼┼┼┼──┼┼┼┼┼┼──┤ | 3L 16s | 3, 1 | 3:1 |- | ├┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┤ | 3L 19s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\25 and 7\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼──────┤ | 1L 1s | 18, 7 | 18:7 |- | ├──────────┼──────┼──────┤ | 1L 2s | 11, 7 | 11:7 |- | ├───┼──────┼──────┼──────┤ | 3L 1s | 7, 4 | 7:4 |- | ├───┼───┼──┼───┼──┼───┼──┤ | 4L 3s (smitonic) | 4, 3 | 4:3 |- | ├┼──┼┼──┼──┼┼──┼──┼┼──┼──┤ | 7L 4s | 3, 1 | 3:1 |- | ├┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┤ | 7L 11s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\25 and 6\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼─────┤ | 1L 1s | 19, 6 | 19:6 |- | ├────────────┼─────┼─────┤ | 1L 2s | 13, 6 | 13:6 |- | ├──────┼─────┼─────┼─────┤ | 1L 3s | 7, 6 | 7:6 |- | ├┼─────┼─────┼─────┼─────┤ | 4L 1s | 6, 1 | 6:1 |- | ├┼┼────┼┼────┼┼────┼┼────┤ | 4L 5s (gramitonic) | 5, 1 | 5:1 |- | ├┼┼┼───┼┼┼───┼┼┼───┼┼┼───┤ | 4L 9s | 4, 1 | 4:1 |- | ├┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┼──┤ | 4L 13s | 3, 1 | 3:1 |- | ├┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┤ | 4L 17s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\25 and 5\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼────┤ | 1L 1s | 20, 5 | 4:1 |- | ├──────────────┼────┼────┤ | 1L 2s | 15, 5 | 3:1 |- | ├─────────┼────┼────┼────┤ | 1L 3s | 10, 5 | 2:1 |- | ├────┼────┼────┼────┼────┤ | 5edo | 5, 5 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\25 and 4\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼───┤ | 1L 1s | 21, 4 | 21:4 |- | ├────────────────┼───┼───┤ | 1L 2s | 17, 4 | 17:4 |- | ├────────────┼───┼───┼───┤ | 1L 3s | 13, 4 | 13:4 |- | ├────────┼───┼───┼───┼───┤ | 1L 4s | 9, 4 | 9:4 |- | ├────┼───┼───┼───┼───┼───┤ | 1L 5s (antimachinoid) | 5, 4 | 5:4 |- | ├┼───┼───┼───┼───┼───┼───┤ | 6L 1s (archaeotonic) | 4, 1 | 4:1 |- | ├┼┼──┼┼──┼┼──┼┼──┼┼──┼┼──┤ | 6L 7s | 3, 1 | 3:1 |- | ├┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┤ | 6L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\25 and 3\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼──┤ | 1L 1s | 22, 3 | 22:3 |- | ├──────────────────┼──┼──┤ | 1L 2s | 19, 3 | 19:3 |- | ├───────────────┼──┼──┼──┤ | 1L 3s | 16, 3 | 16:3 |- | ├────────────┼──┼──┼──┼──┤ | 1L 4s | 13, 3 | 13:3 |- | ├─────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 10, 3 | 10:3 |- | ├──────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 7, 3 | 7:3 |- | ├───┼──┼──┼──┼──┼──┼──┼──┤ | 1L 7s (antipine) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼──┼──┼──┼──┼──┤ | 8L 1s (subneutralic) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┤ | 8L 9s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\25 and 2\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼─┤ | 1L 1s | 23, 2 | 23:2 |- | ├────────────────────┼─┼─┤ | 1L 2s | 21, 2 | 21:2 |- | ├──────────────────┼─┼─┼─┤ | 1L 3s | 19, 2 | 19:2 |- | ├────────────────┼─┼─┼─┼─┤ | 1L 4s | 17, 2 | 17:2 |- | ├──────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 15, 2 | 15:2 |- | ├────────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 13, 2 | 13:2 |- | ├──────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 11s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 12L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 24\25 and 1\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────┼┤ | 1L 1s | 24, 1 | 24:1 |- | ├──────────────────────┼┼┤ | 1L 2s | 23, 1 | 23:1 |- | ├─────────────────────┼┼┼┤ | 1L 3s | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┼┤ | 1L 4s | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 23s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}
Multi-period MOS scales
5 periods

Generators 3\25 and 2\25
Step visualization MOS (name) Step sizes Step ratio
├──┼─┼──┼─┼──┼─┼──┼─┼──┼─┤ 5L 5s (pentawood) 3, 2 3:2
├┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┤ 10L 5s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 25edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 4\25 and 1\25 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───┼┼───┼┼───┼┼───┼┼───┼┤ | 5L 5s (pentawood) | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┤ | 5L 10s | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 5L 15s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 25edo | 1, 1 | 1:1 |}

26edo

These are all moment of symmetry scales in 26edo.
Single-period MOS scales

Generators 14\26 and 12\26
Step visualization MOS (name) Step sizes Step ratio
├─────────────┼───────────┤ 1L 1s 14, 12 7:6
├─┼───────────┼───────────┤ 2L 1s 12, 2 6:1
├─┼─┼─────────┼─┼─────────┤ 2L 3s 10, 2 5:1
├─┼─┼─┼───────┼─┼─┼───────┤ 2L 5s (antidiatonic) 8, 2 4:1
├─┼─┼─┼─┼─────┼─┼─┼─┼─────┤ 2L 7s (balzano) 6, 2 3:1
├─┼─┼─┼─┼─┼───┼─┼─┼─┼─┼───┤ 2L 9s 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 13edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 15\26 and 11\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼──────────┤ | 1L 1s | 15, 11 | 15:11 |- | ├───┼──────────┼──────────┤ | 2L 1s | 11, 4 | 11:4 |- | ├───┼───┼──────┼───┼──────┤ | 2L 3s | 7, 4 | 7:4 |- | ├───┼───┼───┼──┼───┼───┼──┤ | 5L 2s (diatonic) | 4, 3 | 4:3 |- | ├┼──┼┼──┼┼──┼──┼┼──┼┼──┼──┤ | 7L 5s | 3, 1 | 3:1 |- | ├┼┼─┼┼┼─┼┼┼─┼┼─┼┼┼─┼┼┼─┼┼─┤ | 7L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\26 and 10\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼─────────┤ | 1L 1s | 16, 10 | 8:5 |- | ├─────┼─────────┼─────────┤ | 2L 1s | 10, 6 | 5:3 |- | ├─────┼─────┼───┼─────┼───┤ | 3L 2s | 6, 4 | 3:2 |- | ├─┼───┼─┼───┼───┼─┼───┼───┤ | 5L 3s (oneirotonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 13edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\26 and 9\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼────────┤ | 1L 1s | 17, 9 | 17:9 |- | ├───────┼────────┼────────┤ | 2L 1s | 9, 8 | 9:8 |- | ├───────┼───────┼┼───────┼┤ | 3L 2s | 8, 1 | 8:1 |- | ├──────┼┼──────┼┼┼──────┼┼┤ | 3L 5s (checkertonic) | 7, 1 | 7:1 |- | ├─────┼┼┼─────┼┼┼┼─────┼┼┼┤ | 3L 8s | 6, 1 | 6:1 |- | ├────┼┼┼┼────┼┼┼┼┼────┼┼┼┼┤ | 3L 11s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼───┼┼┼┼┼┼───┼┼┼┼┼┤ | 3L 14s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼──┼┼┼┼┼┼┼──┼┼┼┼┼┼┤ | 3L 17s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┤ | 3L 20s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\26 and 8\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼───────┤ | 1L 1s | 18, 8 | 9:4 |- | ├─────────┼───────┼───────┤ | 1L 2s | 10, 8 | 5:4 |- | ├─┼───────┼───────┼───────┤ | 3L 1s | 8, 2 | 4:1 |- | ├─┼─┼─────┼─┼─────┼─┼─────┤ | 3L 4s (mosh) | 6, 2 | 3:1 |- | ├─┼─┼─┼───┼─┼─┼───┼─┼─┼───┤ | 3L 7s (sephiroid) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 13edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\26 and 7\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼──────┤ | 1L 1s | 19, 7 | 19:7 |- | ├───────────┼──────┼──────┤ | 1L 2s | 12, 7 | 12:7 |- | ├────┼──────┼──────┼──────┤ | 3L 1s | 7, 5 | 7:5 |- | ├────┼────┼─┼────┼─┼────┼─┤ | 4L 3s (smitonic) | 5, 2 | 5:2 |- | ├──┼─┼──┼─┼─┼──┼─┼─┼──┼─┼─┤ | 4L 7s | 3, 2 | 3:2 |- | ├┼─┼─┼┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┤ | 11L 4s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\26 and 6\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼─────┤ | 1L 1s | 20, 6 | 10:3 |- | ├─────────────┼─────┼─────┤ | 1L 2s | 14, 6 | 7:3 |- | ├───────┼─────┼─────┼─────┤ | 1L 3s | 8, 6 | 4:3 |- | ├─┼─────┼─────┼─────┼─────┤ | 4L 1s | 6, 2 | 3:1 |- | ├─┼─┼───┼─┼───┼─┼───┼─┼───┤ | 4L 5s (gramitonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 13edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\26 and 5\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼────┤ | 1L 1s | 21, 5 | 21:5 |- | ├───────────────┼────┼────┤ | 1L 2s | 16, 5 | 16:5 |- | ├──────────┼────┼────┼────┤ | 1L 3s | 11, 5 | 11:5 |- | ├─────┼────┼────┼────┼────┤ | 1L 4s | 6, 5 | 6:5 |- | ├┼────┼────┼────┼────┼────┤ | 5L 1s (machinoid) | 5, 1 | 5:1 |- | ├┼┼───┼┼───┼┼───┼┼───┼┼───┤ | 5L 6s | 4, 1 | 4:1 |- | ├┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┤ | 5L 11s | 3, 1 | 3:1 |- | ├┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┤ | 5L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\26 and 4\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼───┤ | 1L 1s | 22, 4 | 11:2 |- | ├─────────────────┼───┼───┤ | 1L 2s | 18, 4 | 9:2 |- | ├─────────────┼───┼───┼───┤ | 1L 3s | 14, 4 | 7:2 |- | ├─────────┼───┼───┼───┼───┤ | 1L 4s | 10, 4 | 5:2 |- | ├─────┼───┼───┼───┼───┼───┤ | 1L 5s (antimachinoid) | 6, 4 | 3:2 |- | ├─┼───┼───┼───┼───┼───┼───┤ | 6L 1s (archaeotonic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 13edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\26 and 3\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼──┤ | 1L 1s | 23, 3 | 23:3 |- | ├───────────────────┼──┼──┤ | 1L 2s | 20, 3 | 20:3 |- | ├────────────────┼──┼──┼──┤ | 1L 3s | 17, 3 | 17:3 |- | ├─────────────┼──┼──┼──┼──┤ | 1L 4s | 14, 3 | 14:3 |- | ├──────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 11, 3 | 11:3 |- | ├───────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 8, 3 | 8:3 |- | ├────┼──┼──┼──┼──┼──┼──┼──┤ | 1L 7s (antipine) | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼──┼──┼──┼──┼──┤ | 8L 1s (subneutralic) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ | 9L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 24\26 and 2\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────┼─┤ | 1L 1s | 24, 2 | 12:1 |- | ├─────────────────────┼─┼─┤ | 1L 2s | 22, 2 | 11:1 |- | ├───────────────────┼─┼─┼─┤ | 1L 3s | 20, 2 | 10:1 |- | ├─────────────────┼─┼─┼─┼─┤ | 1L 4s | 18, 2 | 9:1 |- | ├───────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 16, 2 | 8:1 |- | ├─────────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 11s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 13edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 25\26 and 1\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────────┼┤ | 1L 1s | 25, 1 | 25:1 |- | ├───────────────────────┼┼┤ | 1L 2s | 24, 1 | 24:1 |- | ├──────────────────────┼┼┼┤ | 1L 3s | 23, 1 | 23:1 |- | ├─────────────────────┼┼┼┼┤ | 1L 4s | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 23s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 24s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 7\26 and 6\26
Step visualization MOS (name) Step sizes Step ratio
├──────┼─────┼──────┼─────┤ 2L 2s 7, 6 7:6
├┼─────┼─────┼┼─────┼─────┤ 4L 2s (citric) 6, 1 6:1
├┼┼────┼┼────┼┼┼────┼┼────┤ 4L 6s (lime) 5, 1 5:1
├┼┼┼───┼┼┼───┼┼┼┼───┼┼┼───┤ 4L 10s 4, 1 4:1
├┼┼┼┼──┼┼┼┼──┼┼┼┼┼──┼┼┼┼──┤ 4L 14s 3, 1 3:1
├┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼─┤ 4L 18s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 26edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 8\26 and 5\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼────┼───────┼────┤ | 2L 2s | 8, 5 | 8:5 |- | ├──┼────┼────┼──┼────┼────┤ | 4L 2s (citric) | 5, 3 | 5:3 |- | ├──┼──┼─┼──┼─┼──┼──┼─┼──┼─┤ | 6L 4s (lemon) | 3, 2 | 3:2 |- | ├┼─┼┼─┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼─┤ | 10L 6s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\26 and 4\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼───┼────────┼───┤ | 2L 2s | 9, 4 | 9:4 |- | ├────┼───┼───┼────┼───┼───┤ | 2L 4s (malic) | 5, 4 | 5:4 |- | ├┼───┼───┼───┼┼───┼───┼───┤ | 6L 2s (ekic) | 4, 1 | 4:1 |- | ├┼┼──┼┼──┼┼──┼┼┼──┼┼──┼┼──┤ | 6L 8s | 3, 1 | 3:1 |- | ├┼┼┼─┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┼┼┼─┤ | 6L 14s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\26 and 3\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼──┼─────────┼──┤ | 2L 2s | 10, 3 | 10:3 |- | ├──────┼──┼──┼──────┼──┼──┤ | 2L 4s (malic) | 7, 3 | 7:3 |- | ├───┼──┼──┼──┼───┼──┼──┼──┤ | 2L 6s (subaric) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼──┼┼──┼──┼──┼──┤ | 8L 2s (taric) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┼┼─┤ | 8L 10s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\26 and 2\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼─┼──────────┼─┤ | 2L 2s | 11, 2 | 11:2 |- | ├────────┼─┼─┼────────┼─┼─┤ | 2L 4s (malic) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼──────┼─┼─┼─┤ | 2L 6s (subaric) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼────┼─┼─┼─┼─┤ | 2L 8s (jaric) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼──┼─┼─┼─┼─┼─┤ | 2L 10s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┼─┤ | 12L 2s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\26 and 1\26 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼┼───────────┼┤ | 2L 2s | 12, 1 | 12:1 |- | ├──────────┼┼┼──────────┼┼┤ | 2L 4s (malic) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼─────────┼┼┼┤ | 2L 6s (subaric) | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼────────┼┼┼┼┤ | 2L 8s (jaric) | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼───────┼┼┼┼┼┤ | 2L 10s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼──────┼┼┼┼┼┼┤ | 2L 12s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼┤ | 2L 14s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼┤ | 2L 16s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼┤ | 2L 18s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼┤ | 2L 20s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼┤ | 2L 22s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 26edo | 1, 1 | 1:1 |}

27edo

These are all moment of symmetry scales in 27edo.
Single-period MOS scales

Generators 14\27 and 13\27
Step visualization MOS (name) Step sizes Step ratio
├─────────────┼────────────┤ 1L 1s 14, 13 14:13
├┼────────────┼────────────┤ 2L 1s 13, 1 13:1
├┼┼───────────┼┼───────────┤ 2L 3s 12, 1 12:1
├┼┼┼──────────┼┼┼──────────┤ 2L 5s (antidiatonic) 11, 1 11:1
├┼┼┼┼─────────┼┼┼┼─────────┤ 2L 7s (balzano) 10, 1 10:1
├┼┼┼┼┼────────┼┼┼┼┼────────┤ 2L 9s 9, 1 9:1
├┼┼┼┼┼┼───────┼┼┼┼┼┼───────┤ 2L 11s 8, 1 8:1
├┼┼┼┼┼┼┼──────┼┼┼┼┼┼┼──────┤ 2L 13s 7, 1 7:1
├┼┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼┼─────┤ 2L 15s 6, 1 6:1
├┼┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼┼────┤ 2L 17s 5, 1 5:1
├┼┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼┼───┤ 2L 19s 4, 1 4:1
├┼┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼┼──┤ 2L 21s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼┼─┤ 2L 23s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 27edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 15\27 and 12\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────┼───────────┤ | 1L 1s | 15, 12 | 5:4 |- | ├──┼───────────┼───────────┤ | 2L 1s | 12, 3 | 4:1 |- | ├──┼──┼────────┼──┼────────┤ | 2L 3s | 9, 3 | 3:1 |- | ├──┼──┼──┼─────┼──┼──┼─────┤ | 2L 5s (antidiatonic) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 9edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 16\27 and 11\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼──────────┤ | 1L 1s | 16, 11 | 16:11 |- | ├────┼──────────┼──────────┤ | 2L 1s | 11, 5 | 11:5 |- | ├────┼────┼─────┼────┼─────┤ | 2L 3s | 6, 5 | 6:5 |- | ├────┼────┼────┼┼────┼────┼┤ | 5L 2s (diatonic) | 5, 1 | 5:1 |- | ├───┼┼───┼┼───┼┼┼───┼┼───┼┼┤ | 5L 7s | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼──┼┼┼┼──┼┼┼──┼┼┼┤ | 5L 12s | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼─┼┼┼┼┼─┼┼┼┼─┼┼┼┼┤ | 5L 17s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\27 and 10\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼─────────┤ | 1L 1s | 17, 10 | 17:10 |- | ├──────┼─────────┼─────────┤ | 2L 1s | 10, 7 | 10:7 |- | ├──────┼──────┼──┼──────┼──┤ | 3L 2s | 7, 3 | 7:3 |- | ├───┼──┼───┼──┼──┼───┼──┼──┤ | 3L 5s (checkertonic) | 4, 3 | 4:3 |- | ├┼──┼──┼┼──┼──┼──┼┼──┼──┼──┤ | 8L 3s | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┤ | 8L 11s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\27 and 9\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼────────┤ | 1L 1s | 18, 9 | 2:1 |- | ├────────┼────────┼────────┤ | 3edo | 9, 9 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\27 and 8\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼───────┤ | 1L 1s | 19, 8 | 19:8 |- | ├──────────┼───────┼───────┤ | 1L 2s | 11, 8 | 11:8 |- | ├──┼───────┼───────┼───────┤ | 3L 1s | 8, 3 | 8:3 |- | ├──┼──┼────┼──┼────┼──┼────┤ | 3L 4s (mosh) | 5, 3 | 5:3 |- | ├──┼──┼──┼─┼──┼──┼─┼──┼──┼─┤ | 7L 3s (dicoid) | 3, 2 | 3:2 |- | ├┼─┼┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼┼─┼─┤ | 10L 7s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\27 and 7\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼──────┤ | 1L 1s | 20, 7 | 20:7 |- | ├────────────┼──────┼──────┤ | 1L 2s | 13, 7 | 13:7 |- | ├─────┼──────┼──────┼──────┤ | 3L 1s | 7, 6 | 7:6 |- | ├─────┼─────┼┼─────┼┼─────┼┤ | 4L 3s (smitonic) | 6, 1 | 6:1 |- | ├────┼┼────┼┼┼────┼┼┼────┼┼┤ | 4L 7s | 5, 1 | 5:1 |- | ├───┼┼┼───┼┼┼┼───┼┼┼┼───┼┼┼┤ | 4L 11s | 4, 1 | 4:1 |- | ├──┼┼┼┼──┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┤ | 4L 15s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┤ | 4L 19s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\27 and 6\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼─────┤ | 1L 1s | 21, 6 | 7:2 |- | ├──────────────┼─────┼─────┤ | 1L 2s | 15, 6 | 5:2 |- | ├────────┼─────┼─────┼─────┤ | 1L 3s | 9, 6 | 3:2 |- | ├──┼─────┼─────┼─────┼─────┤ | 4L 1s | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 9edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\27 and 5\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼────┤ | 1L 1s | 22, 5 | 22:5 |- | ├────────────────┼────┼────┤ | 1L 2s | 17, 5 | 17:5 |- | ├───────────┼────┼────┼────┤ | 1L 3s | 12, 5 | 12:5 |- | ├──────┼────┼────┼────┼────┤ | 1L 4s | 7, 5 | 7:5 |- | ├─┼────┼────┼────┼────┼────┤ | 5L 1s (machinoid) | 5, 2 | 5:2 |- | ├─┼─┼──┼─┼──┼─┼──┼─┼──┼─┼──┤ | 5L 6s | 3, 2 | 3:2 |- | ├─┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┤ | 11L 5s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\27 and 4\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼───┤ | 1L 1s | 23, 4 | 23:4 |- | ├──────────────────┼───┼───┤ | 1L 2s | 19, 4 | 19:4 |- | ├──────────────┼───┼───┼───┤ | 1L 3s | 15, 4 | 15:4 |- | ├──────────┼───┼───┼───┼───┤ | 1L 4s | 11, 4 | 11:4 |- | ├──────┼───┼───┼───┼───┼───┤ | 1L 5s (antimachinoid) | 7, 4 | 7:4 |- | ├──┼───┼───┼───┼───┼───┼───┤ | 6L 1s (archaeotonic) | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┼──┼┼──┼┼──┼┼──┼┤ | 7L 6s | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ | 7L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 24\27 and 3\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────┼──┤ | 1L 1s | 24, 3 | 8:1 |- | ├────────────────────┼──┼──┤ | 1L 2s | 21, 3 | 7:1 |- | ├─────────────────┼──┼──┼──┤ | 1L 3s | 18, 3 | 6:1 |- | ├──────────────┼──┼──┼──┼──┤ | 1L 4s | 15, 3 | 5:1 |- | ├───────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 12, 3 | 4:1 |- | ├────────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┼──┼──┼──┼──┤ | 1L 7s (antipine) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 9edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 25\27 and 2\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────────┼─┤ | 1L 1s | 25, 2 | 25:2 |- | ├──────────────────────┼─┼─┤ | 1L 2s | 23, 2 | 23:2 |- | ├────────────────────┼─┼─┼─┤ | 1L 3s | 21, 2 | 21:2 |- | ├──────────────────┼─┼─┼─┼─┤ | 1L 4s | 19, 2 | 19:2 |- | ├────────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 17, 2 | 17:2 |- | ├──────────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 15, 2 | 15:2 |- | ├────────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 13, 2 | 13:2 |- | ├──────────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 11s | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 12s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 13L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 26\27 and 1\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────────┼┤ | 1L 1s | 26, 1 | 26:1 |- | ├────────────────────────┼┼┤ | 1L 2s | 25, 1 | 25:1 |- | ├───────────────────────┼┼┼┤ | 1L 3s | 24, 1 | 24:1 |- | ├──────────────────────┼┼┼┼┤ | 1L 4s | 23, 1 | 23:1 |- | ├─────────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 23s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 24s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 25s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}
Multi-period MOS scales
3 periods

Generators 5\27 and 4\27
Step visualization MOS (name) Step sizes Step ratio
├────┼───┼────┼───┼────┼───┤ 3L 3s (triwood) 5, 4 5:4
├┼───┼───┼┼───┼───┼┼───┼───┤ 6L 3s (hyrulic) 4, 1 4:1
├┼┼──┼┼──┼┼┼──┼┼──┼┼┼──┼┼──┤ 6L 9s 3, 1 3:1
├┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┤ 6L 15s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 27edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 6\27 and 3\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼──┼─────┼──┼─────┼──┤ | 3L 3s (triwood) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 9edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 7\27 and 2\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼─┼──────┼─┼──────┼─┤ | 3L 3s (triwood) | 7, 2 | 7:2 |- | ├────┼─┼─┼────┼─┼─┼────┼─┼─┤ | 3L 6s (tcherepnin) | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼──┼─┼─┼─┼──┼─┼─┼─┤ | 3L 9s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼┼─┼─┼─┼─┼┼─┼─┼─┼─┤ | 12L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\27 and 1\27 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼┼───────┼┼───────┼┤ | 3L 3s (triwood) | 8, 1 | 8:1 |- | ├──────┼┼┼──────┼┼┼──────┼┼┤ | 3L 6s (tcherepnin) | 7, 1 | 7:1 |- | ├─────┼┼┼┼─────┼┼┼┼─────┼┼┼┤ | 3L 9s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼────┼┼┼┼┼────┼┼┼┼┤ | 3L 12s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼───┼┼┼┼┼┼───┼┼┼┼┼┤ | 3L 15s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼──┼┼┼┼┼┼┼──┼┼┼┼┼┼┤ | 3L 18s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┤ | 3L 21s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 27edo | 1, 1 | 1:1 |}
9 periods

Generators 2\27 and 1\27
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ 9L 9s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 27edo 1, 1 1:1

28edo

These are all moment of symmetry scales in 28edo.
Single-period MOS scales

Generators 15\28 and 13\28
Step visualization MOS (name) Step sizes Step ratio
├──────────────┼────────────┤ 1L 1s 15, 13 15:13
├─┼────────────┼────────────┤ 2L 1s 13, 2 13:2
├─┼─┼──────────┼─┼──────────┤ 2L 3s 11, 2 11:2
├─┼─┼─┼────────┼─┼─┼────────┤ 2L 5s (antidiatonic) 9, 2 9:2
├─┼─┼─┼─┼──────┼─┼─┼─┼──────┤ 2L 7s (balzano) 7, 2 7:2
├─┼─┼─┼─┼─┼────┼─┼─┼─┼─┼────┤ 2L 9s 5, 2 5:2
├─┼─┼─┼─┼─┼─┼──┼─┼─┼─┼─┼─┼──┤ 2L 11s 3, 2 3:2
├─┼─┼─┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┼─┼┤ 13L 2s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 28edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 16\28 and 12\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼───────────┤ | 1L 1s | 16, 12 | 4:3 |- | ├───┼───────────┼───────────┤ | 2L 1s | 12, 4 | 3:1 |- | ├───┼───┼───────┼───┼───────┤ | 2L 3s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┼───┼───┤ | 7edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\28 and 11\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼──────────┤ | 1L 1s | 17, 11 | 17:11 |- | ├─────┼──────────┼──────────┤ | 2L 1s | 11, 6 | 11:6 |- | ├─────┼─────┼────┼─────┼────┤ | 3L 2s | 6, 5 | 6:5 |- | ├┼────┼┼────┼────┼┼────┼────┤ | 5L 3s (oneirotonic) | 5, 1 | 5:1 |- | ├┼┼───┼┼┼───┼┼───┼┼┼───┼┼───┤ | 5L 8s | 4, 1 | 4:1 |- | ├┼┼┼──┼┼┼┼──┼┼┼──┼┼┼┼──┼┼┼──┤ | 5L 13s | 3, 1 | 3:1 |- | ├┼┼┼┼─┼┼┼┼┼─┼┼┼┼─┼┼┼┼┼─┼┼┼┼─┤ | 5L 18s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\28 and 10\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼─────────┤ | 1L 1s | 18, 10 | 9:5 |- | ├───────┼─────────┼─────────┤ | 2L 1s | 10, 8 | 5:4 |- | ├───────┼───────┼─┼───────┼─┤ | 3L 2s | 8, 2 | 4:1 |- | ├─────┼─┼─────┼─┼─┼─────┼─┼─┤ | 3L 5s (checkertonic) | 6, 2 | 3:1 |- | ├───┼─┼─┼───┼─┼─┼─┼───┼─┼─┼─┤ | 3L 8s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 14edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\28 and 9\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼────────┤ | 1L 1s | 19, 9 | 19:9 |- | ├─────────┼────────┼────────┤ | 1L 2s | 10, 9 | 10:9 |- | ├┼────────┼────────┼────────┤ | 3L 1s | 9, 1 | 9:1 |- | ├┼┼───────┼┼───────┼┼───────┤ | 3L 4s (mosh) | 8, 1 | 8:1 |- | ├┼┼┼──────┼┼┼──────┼┼┼──────┤ | 3L 7s (sephiroid) | 7, 1 | 7:1 |- | ├┼┼┼┼─────┼┼┼┼─────┼┼┼┼─────┤ | 3L 10s | 6, 1 | 6:1 |- | ├┼┼┼┼┼────┼┼┼┼┼────┼┼┼┼┼────┤ | 3L 13s | 5, 1 | 5:1 |- | ├┼┼┼┼┼┼───┼┼┼┼┼┼───┼┼┼┼┼┼───┤ | 3L 16s | 4, 1 | 4:1 |- | ├┼┼┼┼┼┼┼──┼┼┼┼┼┼┼──┼┼┼┼┼┼┼──┤ | 3L 19s | 3, 1 | 3:1 |- | ├┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼─┤ | 3L 22s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\28 and 8\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼───────┤ | 1L 1s | 20, 8 | 5:2 |- | ├───────────┼───────┼───────┤ | 1L 2s | 12, 8 | 3:2 |- | ├───┼───────┼───────┼───────┤ | 3L 1s | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┼───┼───┤ | 7edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\28 and 7\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼──────┤ | 1L 1s | 21, 7 | 3:1 |- | ├─────────────┼──────┼──────┤ | 1L 2s | 14, 7 | 2:1 |- | ├──────┼──────┼──────┼──────┤ | 4edo | 7, 7 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\28 and 6\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼─────┤ | 1L 1s | 22, 6 | 11:3 |- | ├───────────────┼─────┼─────┤ | 1L 2s | 16, 6 | 8:3 |- | ├─────────┼─────┼─────┼─────┤ | 1L 3s | 10, 6 | 5:3 |- | ├───┼─────┼─────┼─────┼─────┤ | 4L 1s | 6, 4 | 3:2 |- | ├───┼───┼─┼───┼─┼───┼─┼───┼─┤ | 5L 4s (semiquartal) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 14edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\28 and 5\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼────┤ | 1L 1s | 23, 5 | 23:5 |- | ├─────────────────┼────┼────┤ | 1L 2s | 18, 5 | 18:5 |- | ├────────────┼────┼────┼────┤ | 1L 3s | 13, 5 | 13:5 |- | ├───────┼────┼────┼────┼────┤ | 1L 4s | 8, 5 | 8:5 |- | ├──┼────┼────┼────┼────┼────┤ | 5L 1s (machinoid) | 5, 3 | 5:3 |- | ├──┼──┼─┼──┼─┼──┼─┼──┼─┼──┼─┤ | 6L 5s | 3, 2 | 3:2 |- | ├┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┤ | 11L 6s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 24\28 and 4\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────┼───┤ | 1L 1s | 24, 4 | 6:1 |- | ├───────────────────┼───┼───┤ | 1L 2s | 20, 4 | 5:1 |- | ├───────────────┼───┼───┼───┤ | 1L 3s | 16, 4 | 4:1 |- | ├───────────┼───┼───┼───┼───┤ | 1L 4s | 12, 4 | 3:1 |- | ├───────┼───┼───┼───┼───┼───┤ | 1L 5s (antimachinoid) | 8, 4 | 2:1 |- | ├───┼───┼───┼───┼───┼───┼───┤ | 7edo | 4, 4 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 25\28 and 3\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────────┼──┤ | 1L 1s | 25, 3 | 25:3 |- | ├─────────────────────┼──┼──┤ | 1L 2s | 22, 3 | 22:3 |- | ├──────────────────┼──┼──┼──┤ | 1L 3s | 19, 3 | 19:3 |- | ├───────────────┼──┼──┼──┼──┤ | 1L 4s | 16, 3 | 16:3 |- | ├────────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 13, 3 | 13:3 |- | ├─────────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 10, 3 | 10:3 |- | ├──────┼──┼──┼──┼──┼──┼──┼──┤ | 1L 7s (antipine) | 7, 3 | 7:3 |- | ├───┼──┼──┼──┼──┼──┼──┼──┼──┤ | 1L 8s (antisubneutralic) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 9L 1s (sinatonic) | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┤ | 9L 10s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 26\28 and 2\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────────┼─┤ | 1L 1s | 26, 2 | 13:1 |- | ├───────────────────────┼─┼─┤ | 1L 2s | 24, 2 | 12:1 |- | ├─────────────────────┼─┼─┼─┤ | 1L 3s | 22, 2 | 11:1 |- | ├───────────────────┼─┼─┼─┼─┤ | 1L 4s | 20, 2 | 10:1 |- | ├─────────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 18, 2 | 9:1 |- | ├───────────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 16, 2 | 8:1 |- | ├─────────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 11s | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 12s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 14edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 27\28 and 1\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────────┼┤ | 1L 1s | 27, 1 | 27:1 |- | ├─────────────────────────┼┼┤ | 1L 2s | 26, 1 | 26:1 |- | ├────────────────────────┼┼┼┤ | 1L 3s | 25, 1 | 25:1 |- | ├───────────────────────┼┼┼┼┤ | 1L 4s | 24, 1 | 24:1 |- | ├──────────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 23, 1 | 23:1 |- | ├─────────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 23s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 24s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 25s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 26s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 8\28 and 6\28
Step visualization MOS (name) Step sizes Step ratio
├───────┼─────┼───────┼─────┤ 2L 2s 8, 6 4:3
├─┼─────┼─────┼─┼─────┼─────┤ 4L 2s (citric) 6, 2 3:1
├─┼─┼───┼─┼───┼─┼─┼───┼─┼───┤ 4L 6s (lime) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 14edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 9\28 and 5\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼────┼────────┼────┤ | 2L 2s | 9, 5 | 9:5 |- | ├───┼────┼────┼───┼────┼────┤ | 4L 2s (citric) | 5, 4 | 5:4 |- | ├───┼───┼┼───┼┼───┼───┼┼───┼┤ | 6L 4s (lemon) | 4, 1 | 4:1 |- | ├──┼┼──┼┼┼──┼┼┼──┼┼──┼┼┼──┼┼┤ | 6L 10s | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼─┼┼┼┼─┼┼┼┤ | 6L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\28 and 4\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼───┼─────────┼───┤ | 2L 2s | 10, 4 | 5:2 |- | ├─────┼───┼───┼─────┼───┼───┤ | 2L 4s (malic) | 6, 4 | 3:2 |- | ├─┼───┼───┼───┼─┼───┼───┼───┤ | 6L 2s (ekic) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 14edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\28 and 3\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼──┼──────────┼──┤ | 2L 2s | 11, 3 | 11:3 |- | ├───────┼──┼──┼───────┼──┼──┤ | 2L 4s (malic) | 8, 3 | 8:3 |- | ├────┼──┼──┼──┼────┼──┼──┼──┤ | 2L 6s (subaric) | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼──┼─┼──┼──┼──┼──┤ | 8L 2s (taric) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼┼─┼─┼┼─┼┼─┼┼─┼┤ | 10L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\28 and 2\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼─┼───────────┼─┤ | 2L 2s | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─────────┼─┼─┤ | 2L 4s (malic) | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼───────┼─┼─┼─┤ | 2L 6s (subaric) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─────┼─┼─┼─┼─┤ | 2L 8s (jaric) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼───┼─┼─┼─┼─┼─┤ | 2L 10s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 14edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\28 and 1\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼┼────────────┼┤ | 2L 2s | 13, 1 | 13:1 |- | ├───────────┼┼┼───────────┼┼┤ | 2L 4s (malic) | 12, 1 | 12:1 |- | ├──────────┼┼┼┼──────────┼┼┼┤ | 2L 6s (subaric) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼─────────┼┼┼┼┤ | 2L 8s (jaric) | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼────────┼┼┼┼┼┤ | 2L 10s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼───────┼┼┼┼┼┼┤ | 2L 12s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼──────┼┼┼┼┼┼┼┤ | 2L 14s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼┼┤ | 2L 16s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼┼┤ | 2L 18s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼┼┤ | 2L 20s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼┼┤ | 2L 22s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼┼┤ | 2L 24s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}
4 periods

Generators 4\28 and 3\28
Step visualization MOS (name) Step sizes Step ratio
├───┼──┼───┼──┼───┼──┼───┼──┤ 4L 4s (tetrawood) 4, 3 4:3
├┼──┼──┼┼──┼──┼┼──┼──┼┼──┼──┤ 8L 4s 3, 1 3:1
├┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┼┼┼─┼┼─┤ 8L 12s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 28edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\28 and 2\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼─┼────┼─┼────┼─┼────┼─┤ | 4L 4s (tetrawood) | 5, 2 | 5:2 |- | ├──┼─┼─┼──┼─┼─┼──┼─┼─┼──┼─┼─┤ | 4L 8s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┤ | 12L 4s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 6\28 and 1\28 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────┼┼─────┼┼─────┼┼─────┼┤ | 4L 4s (tetrawood) | 6, 1 | 6:1 |- | ├────┼┼┼────┼┼┼────┼┼┼────┼┼┤ | 4L 8s | 5, 1 | 5:1 |- | ├───┼┼┼┼───┼┼┼┼───┼┼┼┼───┼┼┼┤ | 4L 12s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┤ | 4L 16s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┤ | 4L 20s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 28edo | 1, 1 | 1:1 |}
7 periods

Generators 3\28 and 1\28
Step visualization MOS (name) Step sizes Step ratio
├──┼┼──┼┼──┼┼──┼┼──┼┼──┼┼──┼┤ 7L 7s 3, 1 3:1
├─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┤ 7L 14s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 28edo 1, 1 1:1

29edo

These are all moment of symmetry scales in 29edo.
Single-period MOS scales

Generators 15\29 and 14\29
Step visualization MOS (name) Step sizes Step ratio
├──────────────┼─────────────┤ 1L 1s 15, 14 15:14
├┼─────────────┼─────────────┤ 2L 1s 14, 1 14:1
├┼┼────────────┼┼────────────┤ 2L 3s 13, 1 13:1
├┼┼┼───────────┼┼┼───────────┤ 2L 5s (antidiatonic) 12, 1 12:1
├┼┼┼┼──────────┼┼┼┼──────────┤ 2L 7s (balzano) 11, 1 11:1
├┼┼┼┼┼─────────┼┼┼┼┼─────────┤ 2L 9s 10, 1 10:1
├┼┼┼┼┼┼────────┼┼┼┼┼┼────────┤ 2L 11s 9, 1 9:1
├┼┼┼┼┼┼┼───────┼┼┼┼┼┼┼───────┤ 2L 13s 8, 1 8:1
├┼┼┼┼┼┼┼┼──────┼┼┼┼┼┼┼┼──────┤ 2L 15s 7, 1 7:1
├┼┼┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼┼┼─────┤ 2L 17s 6, 1 6:1
├┼┼┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼┼┼────┤ 2L 19s 5, 1 5:1
├┼┼┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼┼┼───┤ 2L 21s 4, 1 4:1
├┼┼┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼┼┼──┤ 2L 23s 3, 1 3:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼┼┼─┤ 2L 25s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 29edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 16\29 and 13\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────┼────────────┤ | 1L 1s | 16, 13 | 16:13 |- | ├──┼────────────┼────────────┤ | 2L 1s | 13, 3 | 13:3 |- | ├──┼──┼─────────┼──┼─────────┤ | 2L 3s | 10, 3 | 10:3 |- | ├──┼──┼──┼──────┼──┼──┼──────┤ | 2L 5s (antidiatonic) | 7, 3 | 7:3 |- | ├──┼──┼──┼──┼───┼──┼──┼──┼───┤ | 2L 7s (balzano) | 4, 3 | 4:3 |- | ├──┼──┼──┼──┼──┼┼──┼──┼──┼──┼┤ | 9L 2s | 3, 1 | 3:1 |- | ├─┼┼─┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┼┼─┼┼┤ | 9L 11s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 17\29 and 12\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼───────────┤ | 1L 1s | 17, 12 | 17:12 |- | ├────┼───────────┼───────────┤ | 2L 1s | 12, 5 | 12:5 |- | ├────┼────┼──────┼────┼──────┤ | 2L 3s | 7, 5 | 7:5 |- | ├────┼────┼────┼─┼────┼────┼─┤ | 5L 2s (diatonic) | 5, 2 | 5:2 |- | ├──┼─┼──┼─┼──┼─┼─┼──┼─┼──┼─┼─┤ | 5L 7s | 3, 2 | 3:2 |- | ├┼─┼─┼┼─┼─┼┼─┼─┼─┼┼─┼─┼┼─┼─┼─┤ | 12L 5s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\29 and 11\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼──────────┤ | 1L 1s | 18, 11 | 18:11 |- | ├──────┼──────────┼──────────┤ | 2L 1s | 11, 7 | 11:7 |- | ├──────┼──────┼───┼──────┼───┤ | 3L 2s | 7, 4 | 7:4 |- | ├──┼───┼──┼───┼───┼──┼───┼───┤ | 5L 3s (oneirotonic) | 4, 3 | 4:3 |- | ├──┼──┼┼──┼──┼┼──┼┼──┼──┼┼──┼┤ | 8L 5s | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼─┼┼┼─┼┼┼─┼┼─┼┼┼─┼┼┤ | 8L 13s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\29 and 10\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼─────────┤ | 1L 1s | 19, 10 | 19:10 |- | ├────────┼─────────┼─────────┤ | 2L 1s | 10, 9 | 10:9 |- | ├────────┼────────┼┼────────┼┤ | 3L 2s | 9, 1 | 9:1 |- | ├───────┼┼───────┼┼┼───────┼┼┤ | 3L 5s (checkertonic) | 8, 1 | 8:1 |- | ├──────┼┼┼──────┼┼┼┼──────┼┼┼┤ | 3L 8s | 7, 1 | 7:1 |- | ├─────┼┼┼┼─────┼┼┼┼┼─────┼┼┼┼┤ | 3L 11s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼────┼┼┼┼┼┼────┼┼┼┼┼┤ | 3L 14s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼───┼┼┼┼┼┼┼───┼┼┼┼┼┼┤ | 3L 17s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┤ | 3L 20s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┤ | 3L 23s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\29 and 9\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼────────┤ | 1L 1s | 20, 9 | 20:9 |- | ├──────────┼────────┼────────┤ | 1L 2s | 11, 9 | 11:9 |- | ├─┼────────┼────────┼────────┤ | 3L 1s | 9, 2 | 9:2 |- | ├─┼─┼──────┼─┼──────┼─┼──────┤ | 3L 4s (mosh) | 7, 2 | 7:2 |- | ├─┼─┼─┼────┼─┼─┼────┼─┼─┼────┤ | 3L 7s (sephiroid) | 5, 2 | 5:2 |- | ├─┼─┼─┼─┼──┼─┼─┼─┼──┼─┼─┼─┼──┤ | 3L 10s | 3, 2 | 3:2 |- | ├─┼─┼─┼─┼─┼┼─┼─┼─┼─┼┼─┼─┼─┼─┼┤ | 13L 3s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\29 and 8\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼───────┤ | 1L 1s | 21, 8 | 21:8 |- | ├────────────┼───────┼───────┤ | 1L 2s | 13, 8 | 13:8 |- | ├────┼───────┼───────┼───────┤ | 3L 1s | 8, 5 | 8:5 |- | ├────┼────┼──┼────┼──┼────┼──┤ | 4L 3s (smitonic) | 5, 3 | 5:3 |- | ├─┼──┼─┼──┼──┼─┼──┼──┼─┼──┼──┤ | 7L 4s | 3, 2 | 3:2 |- | ├─┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼┼─┼─┼┼─┼┤ | 11L 7s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\29 and 7\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼──────┤ | 1L 1s | 22, 7 | 22:7 |- | ├──────────────┼──────┼──────┤ | 1L 2s | 15, 7 | 15:7 |- | ├───────┼──────┼──────┼──────┤ | 1L 3s | 8, 7 | 8:7 |- | ├┼──────┼──────┼──────┼──────┤ | 4L 1s | 7, 1 | 7:1 |- | ├┼┼─────┼┼─────┼┼─────┼┼─────┤ | 4L 5s (gramitonic) | 6, 1 | 6:1 |- | ├┼┼┼────┼┼┼────┼┼┼────┼┼┼────┤ | 4L 9s | 5, 1 | 5:1 |- | ├┼┼┼┼───┼┼┼┼───┼┼┼┼───┼┼┼┼───┤ | 4L 13s | 4, 1 | 4:1 |- | ├┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┼──┤ | 4L 17s | 3, 1 | 3:1 |- | ├┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┼─┤ | 4L 21s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\29 and 6\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼─────┤ | 1L 1s | 23, 6 | 23:6 |- | ├────────────────┼─────┼─────┤ | 1L 2s | 17, 6 | 17:6 |- | ├──────────┼─────┼─────┼─────┤ | 1L 3s | 11, 6 | 11:6 |- | ├────┼─────┼─────┼─────┼─────┤ | 4L 1s | 6, 5 | 6:5 |- | ├────┼────┼┼────┼┼────┼┼────┼┤ | 5L 4s (semiquartal) | 5, 1 | 5:1 |- | ├───┼┼───┼┼┼───┼┼┼───┼┼┼───┼┼┤ | 5L 9s | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┤ | 5L 14s | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ | 5L 19s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 24\29 and 5\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────┼────┤ | 1L 1s | 24, 5 | 24:5 |- | ├──────────────────┼────┼────┤ | 1L 2s | 19, 5 | 19:5 |- | ├─────────────┼────┼────┼────┤ | 1L 3s | 14, 5 | 14:5 |- | ├────────┼────┼────┼────┼────┤ | 1L 4s | 9, 5 | 9:5 |- | ├───┼────┼────┼────┼────┼────┤ | 5L 1s (machinoid) | 5, 4 | 5:4 |- | ├───┼───┼┼───┼┼───┼┼───┼┼───┼┤ | 6L 5s | 4, 1 | 4:1 |- | ├──┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┤ | 6L 11s | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 6L 17s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 25\29 and 4\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────────┼───┤ | 1L 1s | 25, 4 | 25:4 |- | ├────────────────────┼───┼───┤ | 1L 2s | 21, 4 | 21:4 |- | ├────────────────┼───┼───┼───┤ | 1L 3s | 17, 4 | 17:4 |- | ├────────────┼───┼───┼───┼───┤ | 1L 4s | 13, 4 | 13:4 |- | ├────────┼───┼───┼───┼───┼───┤ | 1L 5s (antimachinoid) | 9, 4 | 9:4 |- | ├────┼───┼───┼───┼───┼───┼───┤ | 1L 6s (onyx) | 5, 4 | 5:4 |- | ├┼───┼───┼───┼───┼───┼───┼───┤ | 7L 1s (pine) | 4, 1 | 4:1 |- | ├┼┼──┼┼──┼┼──┼┼──┼┼──┼┼──┼┼──┤ | 7L 8s | 3, 1 | 3:1 |- | ├┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼┼─┤ | 7L 15s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 26\29 and 3\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────────┼──┤ | 1L 1s | 26, 3 | 26:3 |- | ├──────────────────────┼──┼──┤ | 1L 2s | 23, 3 | 23:3 |- | ├───────────────────┼──┼──┼──┤ | 1L 3s | 20, 3 | 20:3 |- | ├────────────────┼──┼──┼──┼──┤ | 1L 4s | 17, 3 | 17:3 |- | ├─────────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 14, 3 | 14:3 |- | ├──────────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 11, 3 | 11:3 |- | ├───────┼──┼──┼──┼──┼──┼──┼──┤ | 1L 7s (antipine) | 8, 3 | 8:3 |- | ├────┼──┼──┼──┼──┼──┼──┼──┼──┤ | 1L 8s (antisubneutralic) | 5, 3 | 5:3 |- | ├─┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 9L 1s (sinatonic) | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ | 10L 9s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 27\29 and 2\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────────┼─┤ | 1L 1s | 27, 2 | 27:2 |- | ├────────────────────────┼─┼─┤ | 1L 2s | 25, 2 | 25:2 |- | ├──────────────────────┼─┼─┼─┤ | 1L 3s | 23, 2 | 23:2 |- | ├────────────────────┼─┼─┼─┼─┤ | 1L 4s | 21, 2 | 21:2 |- | ├──────────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 19, 2 | 19:2 |- | ├────────────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 17, 2 | 17:2 |- | ├──────────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 15, 2 | 15:2 |- | ├────────────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 13, 2 | 13:2 |- | ├──────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 11s | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 12s | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 13s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 14L 1s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 28\29 and 1\29 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────────┼┤ | 1L 1s | 28, 1 | 28:1 |- | ├──────────────────────────┼┼┤ | 1L 2s | 27, 1 | 27:1 |- | ├─────────────────────────┼┼┼┤ | 1L 3s | 26, 1 | 26:1 |- | ├────────────────────────┼┼┼┼┤ | 1L 4s | 25, 1 | 25:1 |- | ├───────────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 24, 1 | 24:1 |- | ├──────────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 23, 1 | 23:1 |- | ├─────────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 23s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 24s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 25s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 26s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 27s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 29edo | 1, 1 | 1:1 |}

30edo

These are all moment of symmetry scales in 30edo.
Single-period MOS scales

Generators 16\30 and 14\30
Step visualization MOS (name) Step sizes Step ratio
├───────────────┼─────────────┤ 1L 1s 16, 14 8:7
├─┼─────────────┼─────────────┤ 2L 1s 14, 2 7:1
├─┼─┼───────────┼─┼───────────┤ 2L 3s 12, 2 6:1
├─┼─┼─┼─────────┼─┼─┼─────────┤ 2L 5s (antidiatonic) 10, 2 5:1
├─┼─┼─┼─┼───────┼─┼─┼─┼───────┤ 2L 7s (balzano) 8, 2 4:1
├─┼─┼─┼─┼─┼─────┼─┼─┼─┼─┼─────┤ 2L 9s 6, 2 3:1
├─┼─┼─┼─┼─┼─┼───┼─┼─┼─┼─┼─┼───┤ 2L 11s 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 15edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 17\30 and 13\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────┼────────────┤ | 1L 1s | 17, 13 | 17:13 |- | ├───┼────────────┼────────────┤ | 2L 1s | 13, 4 | 13:4 |- | ├───┼───┼────────┼───┼────────┤ | 2L 3s | 9, 4 | 9:4 |- | ├───┼───┼───┼────┼───┼───┼────┤ | 2L 5s (antidiatonic) | 5, 4 | 5:4 |- | ├───┼───┼───┼───┼┼───┼───┼───┼┤ | 7L 2s (armotonic) | 4, 1 | 4:1 |- | ├──┼┼──┼┼──┼┼──┼┼┼──┼┼──┼┼──┼┼┤ | 7L 9s | 3, 1 | 3:1 |- | ├─┼┼┼─┼┼┼─┼┼┼─┼┼┼┼─┼┼┼─┼┼┼─┼┼┼┤ | 7L 16s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 18\30 and 12\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────┼───────────┤ | 1L 1s | 18, 12 | 3:2 |- | ├─────┼───────────┼───────────┤ | 2L 1s | 12, 6 | 2:1 |- | ├─────┼─────┼─────┼─────┼─────┤ | 5edo | 6, 6 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 19\30 and 11\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────┼──────────┤ | 1L 1s | 19, 11 | 19:11 |- | ├───────┼──────────┼──────────┤ | 2L 1s | 11, 8 | 11:8 |- | ├───────┼───────┼──┼───────┼──┤ | 3L 2s | 8, 3 | 8:3 |- | ├────┼──┼────┼──┼──┼────┼──┼──┤ | 3L 5s (checkertonic) | 5, 3 | 5:3 |- | ├─┼──┼──┼─┼──┼──┼──┼─┼──┼──┼──┤ | 8L 3s | 3, 2 | 3:2 |- | ├─┼─┼┼─┼┼─┼─┼┼─┼┼─┼┼─┼─┼┼─┼┼─┼┤ | 11L 8s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 20\30 and 10\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────┼─────────┤ | 1L 1s | 20, 10 | 2:1 |- | ├─────────┼─────────┼─────────┤ | 3edo | 10, 10 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 21\30 and 9\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────┼────────┤ | 1L 1s | 21, 9 | 7:3 |- | ├───────────┼────────┼────────┤ | 1L 2s | 12, 9 | 4:3 |- | ├──┼────────┼────────┼────────┤ | 3L 1s | 9, 3 | 3:1 |- | ├──┼──┼─────┼──┼─────┼──┼─────┤ | 3L 4s (mosh) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 10edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 22\30 and 8\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────┼───────┤ | 1L 1s | 22, 8 | 11:4 |- | ├─────────────┼───────┼───────┤ | 1L 2s | 14, 8 | 7:4 |- | ├─────┼───────┼───────┼───────┤ | 3L 1s | 8, 6 | 4:3 |- | ├─────┼─────┼─┼─────┼─┼─────┼─┤ | 4L 3s (smitonic) | 6, 2 | 3:1 |- | ├───┼─┼───┼─┼─┼───┼─┼─┼───┼─┼─┤ | 4L 7s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 15edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 23\30 and 7\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────┼──────┤ | 1L 1s | 23, 7 | 23:7 |- | ├───────────────┼──────┼──────┤ | 1L 2s | 16, 7 | 16:7 |- | ├────────┼──────┼──────┼──────┤ | 1L 3s | 9, 7 | 9:7 |- | ├─┼──────┼──────┼──────┼──────┤ | 4L 1s | 7, 2 | 7:2 |- | ├─┼─┼────┼─┼────┼─┼────┼─┼────┤ | 4L 5s (gramitonic) | 5, 2 | 5:2 |- | ├─┼─┼─┼──┼─┼─┼──┼─┼─┼──┼─┼─┼──┤ | 4L 9s | 3, 2 | 3:2 |- | ├─┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┼┼─┼─┼─┼┤ | 13L 4s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 24\30 and 6\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────┼─────┤ | 1L 1s | 24, 6 | 4:1 |- | ├─────────────────┼─────┼─────┤ | 1L 2s | 18, 6 | 3:1 |- | ├───────────┼─────┼─────┼─────┤ | 1L 3s | 12, 6 | 2:1 |- | ├─────┼─────┼─────┼─────┼─────┤ | 5edo | 6, 6 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 25\30 and 5\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────────┼────┤ | 1L 1s | 25, 5 | 5:1 |- | ├───────────────────┼────┼────┤ | 1L 2s | 20, 5 | 4:1 |- | ├──────────────┼────┼────┼────┤ | 1L 3s | 15, 5 | 3:1 |- | ├─────────┼────┼────┼────┼────┤ | 1L 4s | 10, 5 | 2:1 |- | ├────┼────┼────┼────┼────┼────┤ | 6edo | 5, 5 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 26\30 and 4\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────────────────┼───┤ | 1L 1s | 26, 4 | 13:2 |- | ├─────────────────────┼───┼───┤ | 1L 2s | 22, 4 | 11:2 |- | ├─────────────────┼───┼───┼───┤ | 1L 3s | 18, 4 | 9:2 |- | ├─────────────┼───┼───┼───┼───┤ | 1L 4s | 14, 4 | 7:2 |- | ├─────────┼───┼───┼───┼───┼───┤ | 1L 5s (antimachinoid) | 10, 4 | 5:2 |- | ├─────┼───┼───┼───┼───┼───┼───┤ | 1L 6s (onyx) | 6, 4 | 3:2 |- | ├─┼───┼───┼───┼───┼───┼───┼───┤ | 7L 1s (pine) | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 15edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 27\30 and 3\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────────────────────┼──┤ | 1L 1s | 27, 3 | 9:1 |- | ├───────────────────────┼──┼──┤ | 1L 2s | 24, 3 | 8:1 |- | ├────────────────────┼──┼──┼──┤ | 1L 3s | 21, 3 | 7:1 |- | ├─────────────────┼──┼──┼──┼──┤ | 1L 4s | 18, 3 | 6:1 |- | ├──────────────┼──┼──┼──┼──┼──┤ | 1L 5s (antimachinoid) | 15, 3 | 5:1 |- | ├───────────┼──┼──┼──┼──┼──┼──┤ | 1L 6s (onyx) | 12, 3 | 4:1 |- | ├────────┼──┼──┼──┼──┼──┼──┼──┤ | 1L 7s (antipine) | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┼──┼──┼──┼──┼──┤ | 1L 8s (antisubneutralic) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 10edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 28\30 and 2\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────────────────────┼─┤ | 1L 1s | 28, 2 | 14:1 |- | ├─────────────────────────┼─┼─┤ | 1L 2s | 26, 2 | 13:1 |- | ├───────────────────────┼─┼─┼─┤ | 1L 3s | 24, 2 | 12:1 |- | ├─────────────────────┼─┼─┼─┼─┤ | 1L 4s | 22, 2 | 11:1 |- | ├───────────────────┼─┼─┼─┼─┼─┤ | 1L 5s (antimachinoid) | 20, 2 | 10:1 |- | ├─────────────────┼─┼─┼─┼─┼─┼─┤ | 1L 6s (onyx) | 18, 2 | 9:1 |- | ├───────────────┼─┼─┼─┼─┼─┼─┼─┤ | 1L 7s (antipine) | 16, 2 | 8:1 |- | ├─────────────┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 8s (antisubneutralic) | 14, 2 | 7:1 |- | ├───────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 9s (antisinatonic) | 12, 2 | 6:1 |- | ├─────────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 10s | 10, 2 | 5:1 |- | ├───────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 11s | 8, 2 | 4:1 |- | ├─────┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 12s | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 1L 13s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 15edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 29\30 and 1\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────────────────────┼┤ | 1L 1s | 29, 1 | 29:1 |- | ├───────────────────────────┼┼┤ | 1L 2s | 28, 1 | 28:1 |- | ├──────────────────────────┼┼┼┤ | 1L 3s | 27, 1 | 27:1 |- | ├─────────────────────────┼┼┼┼┤ | 1L 4s | 26, 1 | 26:1 |- | ├────────────────────────┼┼┼┼┼┤ | 1L 5s (antimachinoid) | 25, 1 | 25:1 |- | ├───────────────────────┼┼┼┼┼┼┤ | 1L 6s (onyx) | 24, 1 | 24:1 |- | ├──────────────────────┼┼┼┼┼┼┼┤ | 1L 7s (antipine) | 23, 1 | 23:1 |- | ├─────────────────────┼┼┼┼┼┼┼┼┤ | 1L 8s (antisubneutralic) | 22, 1 | 22:1 |- | ├────────────────────┼┼┼┼┼┼┼┼┼┤ | 1L 9s (antisinatonic) | 21, 1 | 21:1 |- | ├───────────────────┼┼┼┼┼┼┼┼┼┼┤ | 1L 10s | 20, 1 | 20:1 |- | ├──────────────────┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 11s | 19, 1 | 19:1 |- | ├─────────────────┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 12s | 18, 1 | 18:1 |- | ├────────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 13s | 17, 1 | 17:1 |- | ├───────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 14s | 16, 1 | 16:1 |- | ├──────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 15s | 15, 1 | 15:1 |- | ├─────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 16s | 14, 1 | 14:1 |- | ├────────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 17s | 13, 1 | 13:1 |- | ├───────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 18s | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 19s | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 20s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 21s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 22s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 23s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 24s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 25s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 26s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 27s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 1L 28s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}
Multi-period MOS scales
2 periods

Generators 8\30 and 7\30
Step visualization MOS (name) Step sizes Step ratio
├───────┼──────┼───────┼──────┤ 2L 2s 8, 7 8:7
├┼──────┼──────┼┼──────┼──────┤ 4L 2s (citric) 7, 1 7:1
├┼┼─────┼┼─────┼┼┼─────┼┼─────┤ 4L 6s (lime) 6, 1 6:1
├┼┼┼────┼┼┼────┼┼┼┼────┼┼┼────┤ 4L 10s 5, 1 5:1
├┼┼┼┼───┼┼┼┼───┼┼┼┼┼───┼┼┼┼───┤ 4L 14s 4, 1 4:1
├┼┼┼┼┼──┼┼┼┼┼──┼┼┼┼┼┼──┼┼┼┼┼──┤ 4L 18s 3, 1 3:1
├┼┼┼┼┼┼─┼┼┼┼┼┼─┼┼┼┼┼┼┼─┼┼┼┼┼┼─┤ 4L 22s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 30edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 9\30 and 6\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼─────┼────────┼─────┤ | 2L 2s | 9, 6 | 3:2 |- | ├──┼─────┼─────┼──┼─────┼─────┤ | 4L 2s (citric) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 10edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 10\30 and 5\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────┼────┼─────────┼────┤ | 2L 2s | 10, 5 | 2:1 |- | ├────┼────┼────┼────┼────┼────┤ | 6edo | 5, 5 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 11\30 and 4\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────────┼───┼──────────┼───┤ | 2L 2s | 11, 4 | 11:4 |- | ├──────┼───┼───┼──────┼───┼───┤ | 2L 4s (malic) | 7, 4 | 7:4 |- | ├──┼───┼───┼───┼──┼───┼───┼───┤ | 6L 2s (ekic) | 4, 3 | 4:3 |- | ├──┼──┼┼──┼┼──┼┼──┼──┼┼──┼┼──┼┤ | 8L 6s | 3, 1 | 3:1 |- | ├─┼┼─┼┼┼─┼┼┼─┼┼┼─┼┼─┼┼┼─┼┼┼─┼┼┤ | 8L 14s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 12\30 and 3\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────────┼──┼───────────┼──┤ | 2L 2s | 12, 3 | 4:1 |- | ├────────┼──┼──┼────────┼──┼──┤ | 2L 4s (malic) | 9, 3 | 3:1 |- | ├─────┼──┼──┼──┼─────┼──┼──┼──┤ | 2L 6s (subaric) | 6, 3 | 2:1 |- | ├──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤ | 10edo | 3, 3 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 13\30 and 2\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────────┼─┼────────────┼─┤ | 2L 2s | 13, 2 | 13:2 |- | ├──────────┼─┼─┼──────────┼─┼─┤ | 2L 4s (malic) | 11, 2 | 11:2 |- | ├────────┼─┼─┼─┼────────┼─┼─┼─┤ | 2L 6s (subaric) | 9, 2 | 9:2 |- | ├──────┼─┼─┼─┼─┼──────┼─┼─┼─┼─┤ | 2L 8s (jaric) | 7, 2 | 7:2 |- | ├────┼─┼─┼─┼─┼─┼────┼─┼─┼─┼─┼─┤ | 2L 10s | 5, 2 | 5:2 |- | ├──┼─┼─┼─┼─┼─┼─┼──┼─┼─┼─┼─┼─┼─┤ | 2L 12s | 3, 2 | 3:2 |- | ├┼─┼─┼─┼─┼─┼─┼─┼┼─┼─┼─┼─┼─┼─┼─┤ | 14L 2s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 14\30 and 1\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├─────────────┼┼─────────────┼┤ | 2L 2s | 14, 1 | 14:1 |- | ├────────────┼┼┼────────────┼┼┤ | 2L 4s (malic) | 13, 1 | 13:1 |- | ├───────────┼┼┼┼───────────┼┼┼┤ | 2L 6s (subaric) | 12, 1 | 12:1 |- | ├──────────┼┼┼┼┼──────────┼┼┼┼┤ | 2L 8s (jaric) | 11, 1 | 11:1 |- | ├─────────┼┼┼┼┼┼─────────┼┼┼┼┼┤ | 2L 10s | 10, 1 | 10:1 |- | ├────────┼┼┼┼┼┼┼────────┼┼┼┼┼┼┤ | 2L 12s | 9, 1 | 9:1 |- | ├───────┼┼┼┼┼┼┼┼───────┼┼┼┼┼┼┼┤ | 2L 14s | 8, 1 | 8:1 |- | ├──────┼┼┼┼┼┼┼┼┼──────┼┼┼┼┼┼┼┼┤ | 2L 16s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼┼┼┼┼┼─────┼┼┼┼┼┼┼┼┼┤ | 2L 18s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼┼┼┼┼┼────┼┼┼┼┼┼┼┼┼┼┤ | 2L 20s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼┼┼┼┼┼───┼┼┼┼┼┼┼┼┼┼┼┤ | 2L 22s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼┼┼┼┼┤ | 2L 24s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 2L 26s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}
3 periods

Generators 6\30 and 4\30
Step visualization MOS (name) Step sizes Step ratio
├─────┼───┼─────┼───┼─────┼───┤ 3L 3s (triwood) 6, 4 3:2
├─┼───┼───┼─┼───┼───┼─┼───┼───┤ 6L 3s (hyrulic) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 15edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 7\30 and 3\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├──────┼──┼──────┼──┼──────┼──┤ | 3L 3s (triwood) | 7, 3 | 7:3 |- | ├───┼──┼──┼───┼──┼──┼───┼──┼──┤ | 3L 6s (tcherepnin) | 4, 3 | 4:3 |- | ├┼──┼──┼──┼┼──┼──┼──┼┼──┼──┼──┤ | 9L 3s | 3, 1 | 3:1 |- | ├┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┼┼┼─┼┼─┼┼─┤ | 9L 12s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 8\30 and 2\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───────┼─┼───────┼─┼───────┼─┤ | 3L 3s (triwood) | 8, 2 | 4:1 |- | ├─────┼─┼─┼─────┼─┼─┼─────┼─┼─┤ | 3L 6s (tcherepnin) | 6, 2 | 3:1 |- | ├───┼─┼─┼─┼───┼─┼─┼─┼───┼─┼─┼─┤ | 3L 9s | 4, 2 | 2:1 |- | ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ | 15edo | 2, 2 | 1:1 |}{| class="wikitable center-all" |+ style="font-size: 105%;" | Generators 9\30 and 1\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────────┼┼────────┼┼────────┼┤ | 3L 3s (triwood) | 9, 1 | 9:1 |- | ├───────┼┼┼───────┼┼┼───────┼┼┤ | 3L 6s (tcherepnin) | 8, 1 | 8:1 |- | ├──────┼┼┼┼──────┼┼┼┼──────┼┼┼┤ | 3L 9s | 7, 1 | 7:1 |- | ├─────┼┼┼┼┼─────┼┼┼┼┼─────┼┼┼┼┤ | 3L 12s | 6, 1 | 6:1 |- | ├────┼┼┼┼┼┼────┼┼┼┼┼┼────┼┼┼┼┼┤ | 3L 15s | 5, 1 | 5:1 |- | ├───┼┼┼┼┼┼┼───┼┼┼┼┼┼┼───┼┼┼┼┼┼┤ | 3L 18s | 4, 1 | 4:1 |- | ├──┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┼──┼┼┼┼┼┼┼┤ | 3L 21s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┼─┼┼┼┼┼┼┼┼┤ | 3L 24s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}
5 periods

Generators 4\30 and 2\30
Step visualization MOS (name) Step sizes Step ratio
├───┼─┼───┼─┼───┼─┼───┼─┼───┼─┤ 5L 5s (pentawood) 4, 2 2:1
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤ 15edo 2, 2 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 5\30 and 1\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├────┼┼────┼┼────┼┼────┼┼────┼┤ | 5L 5s (pentawood) | 5, 1 | 5:1 |- | ├───┼┼┼───┼┼┼───┼┼┼───┼┼┼───┼┼┤ | 5L 10s | 4, 1 | 4:1 |- | ├──┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┼──┼┼┼┤ | 5L 15s | 3, 1 | 3:1 |- | ├─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ | 5L 20s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}
6 periods

Generators 3\30 and 2\30
Step visualization MOS (name) Step sizes Step ratio
├──┼─┼──┼─┼──┼─┼──┼─┼──┼─┼──┼─┤ 6L 6s 3, 2 3:2
├┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┼┼─┼─┤ 12L 6s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 30edo 1, 1 1:1

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Generators 4\30 and 1\30 |- ! Step visualization ! MOS (name) ! Step sizes ! Step ratio |- | ├───┼┼───┼┼───┼┼───┼┼───┼┼───┼┤ | 6L 6s | 4, 1 | 4:1 |- | ├──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┼──┼┼┤ | 6L 12s | 3, 1 | 3:1 |- | ├─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┼─┼┼┼┤ | 6L 18s | 2, 1 | 2:1 |- | ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |}
10 periods

Generators 2\30 and 1\30
Step visualization MOS (name) Step sizes Step ratio
├─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ 10L 10s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 30edo 1, 1 1:1