List of MOS scales in edos 5 to 30
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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| Step visualization | MOS (name) | Step sizes | Step ratio |
|---|---|---|---|
| ├─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┼─┼┤ | 10L 10s | 2, 1 | 2:1 |
| ├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ | 30edo | 1, 1 | 1:1 |