User:Contribution/Exploring Selected Modes in 22-EDO: Difference between revisions

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=MOS Modes=
= Mapping =
sharpness = 3
L = 4 ; s = 1
{| class="wikitable center-all"
! Degree
! Notation
! Approximate Ratios
! Approximate Ratios
! Notation
! Degree
|-
| 0
| P1
| 1/1
| 2/1
| P8
| 22
|-
| 1
| m2
| 32/31
| 31/16
| M7
| 21
|-
| 2
| ↑m2
| 16/15
| 15/8
| ↓M7
| 20
|-
| 3
| ↓M2
| 11/10
| 20/11
| ↑m7
| 19
|-
| 4
| M2
| 9/8, 8/7
| 7/4, 16/9
| m7
| 18
|-
| 5
| m3
| 7/6
| 12/7
| M6
| 17
|-
| 6
| ↑m3
| 6/5
| 5/3
| ↓M6
| 16
|-
| 7
| ↓M3
| 5/4
| 8/5
| ↑m6
| 15
|-
| 8
| M3
| 9/7
| 14/9
| m6
| 14
|-
| 9
| P4
| 4/3
| 3/2
| P5
| 13
|-
| 10
| ↑P4
| 11/8
| 16/11
| ↓P5
| 12
|-
| 11
| ↓A4
| colspan="2" | 7/5, 10/7
| ↑d5
| 11
|}
 
 
= MOS Modes =
 
==1edo subset==
 
=== Period: 22\22, Generator: 22\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|1L 0s (22:0)
|22
|}
 
==2edo subset==
 
=== Period: 11\22, Generator: 11\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|2L 0s (11:0)
|11 11
|}
 
==11edo subset==
 
=== Period: 2\22, Generator: 2\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|11L 0s (2:0)
|2 2 2 2 2 2 2 2 2 2 2
|}
 
=== Period: 22\22, Generator: 2\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|1L 9s (4:2)
|2 2 2 2 4 2 2 2 2 2
|-
|1L 8s (6:2)
|2 2 2 2 6 2 2 2 2
|-
|1L 7s (8:2)
|2 2 2 8 2 2 2 2
|-
|1L 6s (10:2)
|2 2 2 10 2 2 2
|-
|1L 5s (12:2)
|2 2 12 2 2 2
|-
|1L 4s (14:2)
|2 2 14 2 2
|-
|1L 3s (16:2)
|2 16 2 2
|-
|1L 2s (18:2)
|2 18 2
|-
|1L 1s (20:2)
|20 2
|}
 
=== Period: 22\22, Generator: 4\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|5L 1s (4:2)
|4 4 4 2 4 4
|-
|1L 4s (6:4)
|4 4 6 4 4
|-
|1L 3s (10:4)
|4 10 4 4
|-
|1L 2s (14:4)
|4 14 4
|-
|1L 1s (18:4)
|18 4
|}
 
=== Period: 22\22, Generator: 6\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|4L 3s (4:2)
|4 2 4 2 4 2 4
|-
|3L 1s (6:4)
|6 6 4 6
|-
|1L 2s (10:6)
|6 10 6
|-
|1L 1s (16:6)
|16 6
|}
 
=== Period: 22\22, Generator: 8\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|3L 5s (4:2)
|2 4 2 4 2 2 4 2
|-
|3L 2s (6:2)
|6 2 6 2 6
|-
|2L 1s (8:6)
|8 6 8
|-
|1L 1s (14:8)
|14 8
|}
 
=== Period: 22\22, Generator: 10\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|2L 7s (4:2)
|2 2 4 2 2 2 4 2 2
|-
|2L 5s (6:2)
|2 6 2 2 2 6 2
|-
|2L 3s (8:2)
|2 8 2 8 2
|-
|2L 1s (10:2)
|10 2 10
|-
|1L 1s (12:10)
|12 10
|}


==22edo subset==
==22edo subset==
=== Period: 1\22, Generator: 1\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|22L 0s (1:0)
|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
|}
=== Period: 11\22, Generator: 1\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|2L 18s (2:1)
|1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
|-
|2L 16s (3:1)
|1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1
|-
|2L 14s (4:1)
|1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1
|-
|2L 12s (5:1)
|1 1 1 5 1 1 1 1 1 1 5 1 1 1
|-
|2L 10s (6:1)
|1 1 6 1 1 1 1 1 6 1 1 1
|-
|2L 8s (7:1)
|1 1 7 1 1 1 1 7 1 1
|-
|2L 6s (8:1)
|1 8 1 1 1 8 1 1
|-
|2L 4s (9:1)
|1 9 1 1 9 1
|-
|2L 2s (10:1)
|10 1 10 1
|}
=== Period: 11\22, Generator: 2\22 ===
{| class="wikitable"
!Name
!Intervals
!Alteration
|-
|10L 2s (2:1)
|2 2 2 1 2 2 2 2 2 1 2 2
|2 2 2 1 2 2 2 2 1 2 2 2
|-
|2L 8s (3:2)
|2 2 3 2 2 2 2 3 2 2
|2 2 3 2 2 2 3 2 2 2
|-
|2L 6s (5:2)
|2 5 2 2 2 5 2 2
|2 2 5 2 2 5 2 2
|-
|2L 4s (7:2)
|2 7 2 2 7 2
|2 7 2 7 2 2
|-
|2L 2s (9:2)
|9 2 9 2
|9 2 2 9
|}
=== Period: 11\22, Generator: 3\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|8L 6s (2:1)
|2 1 2 1 2 1 2 2 1 2 1 2 1 2
|-
|6L 2s (3:2)
|3 3 2 3 3 3 2 3
|-
|2L 4s (5:3)
|3 5 3 3 5 3
|-
|2L 2s (8:3)
|8 3 8 3
|}
=== Period: 11\22, Generator: 4\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|6L 10s (2:1)
|1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1
|-
|6L 4s (3:1)
|3 1 3 1 3 3 1 3 1 3
|-
|4L 2s (4:3)
|4 3 4 4 3 4
|-
|2L 2s (7:4)
|7 4 7 4
|}
=== Period: 11\22, Generator: 5\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|4L 14s (2:1)
|1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1
|-
|4L 10s (3:1)
|1 3 1 1 1 3 1 1 3 1 1 1 3 1
|-
|4L 6s (4:1)
|1 4 1 4 1 1 4 1 4 1
|-
|4L 2s (5:1)
|5 1 5 5 1 5
|-
|2L 2s (6:5)
|6 5 6 5
|}
=== Period: 22\22, Generator: 1\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|1L 20s (2:1)
|1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
|-
|1L 19s (3:1)
|1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
|-
|1L 18s (4:1)
|1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1
|-
|1L 17s (5:1)
|1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1
|-
|1L 16s (6:1)
|1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1
|-
|1L 15s (7:1)
|1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1
|-
|1L 14s (8:1)
|1 1 1 1 1 1 1 8 1 1 1 1 1 1 1
|-
|1L 13s (9:1)
|1 1 1 1 1 1 9 1 1 1 1 1 1 1
|-
|1L 12s (10:1)
|1 1 1 1 1 1 10 1 1 1 1 1 1
|-
|1L 11s (11:1)
|1 1 1 1 1 11 1 1 1 1 1 1
|-
|1L 10s (12:1)
|1 1 1 1 1 12 1 1 1 1 1
|-
|1L 9s (13:1)
|1 1 1 1 13 1 1 1 1 1
|-
|1L 8s (14:1)
|1 1 1 1 14 1 1 1 1
|-
|1L 7s (15:1)
|1 1 1 15 1 1 1 1
|-
|1L 6s (16:1)
|1 1 1 16 1 1 1
|-
|1L 5s (17:1)
|1 1 17 1 1 1
|-
|1L 4s (18:1)
|1 1 18 1 1
|-
|1L 3s (19:1)
|1 19 1 1
|-
|1L 2s (20:1)
|1 20 1
|-
|1L 1s (21:1)
|21 1
|}
=== Period: 22\22, Generator: 3\22 ===
{| class="wikitable"
!Name
!Intervals
!Alteration
!Alteration
!Alteration
|-
|7L 8s (2:1)
|1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
|
|
|
|-
|7L 1s (3:1)
|3 3 3 3 1 3 3 3
|
|
|
|-
|1L 6s (4:3)
|3 3 3 4 3 3 3
|3 4 3 3 3 4 2
|3 3 4 2 4 3 3
|2 4 3 3 3 4 3
|-
|1L 5s (7:3)
|3 3 7 3 3 3
|
|
|
|-
|1L 4s (10:3)
|3 3 10 3 3
|
|
|
|-
|1L 3s (13:3)
|3 13 3 3
|
|
|
|-
|1L 2s (16:3)
|3 16 3
|
|
|
|-
|1L 1s (19:3)
|19 3
|
|
|
|}
=== Period: 22\22, Generator: 5\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|9L 4s (2:1)
|2 1 2 2 1 2 2 2 1 2 2 1 2
|-
|4L 5s (3:2)
|2 3 2 3 2 3 2 3 2
|-
|4L 1s (5:2)
|5 5 2 5 5
|-
|1L 3s (7:5)
|5 7 5 5
|-
|1L 2s (12:5)
|5 12 5
|-
|1L 1s (17:5)
|17 5
|}
=== Period: 22\22, Generator: 7\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|3L 16s (2:1)
|1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1
|-
|3L 13s (3:1)
|1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1
|-
|3L 10s (4:1)
|1 1 4 1 1 1 4 1 1 1 4 1 1
|-
|3L 7s (5:1)
|1 5 1 1 5 1 1 1 5 1
|-
|3L 4s (6:1)
|1 6 1 6 1 6 1
|-
|3L 1s (7:1)
|7 7 1 7
|-
|1L 2s (8:7)
|7 8 7
|-
|1L 1s (15:7)
|15 7
|}
=== Period: 22\22, Generator: 9\22 ===
{| class="wikitable"
!Name
!Intervals
|-
|5L 12s (2:1)
|1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1
|-
|5L 7s (3:1)
|1 3 1 3 1 3 1 1 3 1 3 1
|-
|5L 2s (4:1)
|4 1 4 4 4 1 4
|-
|2L 3s (5:4)
|4 5 4 5 4
|-
|2L 1s (9:4)
|9 4 9
|-
|1L 1s (13:9)
|13 9
|}

Latest revision as of 23:33, 18 October 2025

Mapping

sharpness = 3 L = 4 ; s = 1

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 22
1 m2 32/31 31/16 M7 21
2 ↑m2 16/15 15/8 ↓M7 20
3 ↓M2 11/10 20/11 ↑m7 19
4 M2 9/8, 8/7 7/4, 16/9 m7 18
5 m3 7/6 12/7 M6 17
6 ↑m3 6/5 5/3 ↓M6 16
7 ↓M3 5/4 8/5 ↑m6 15
8 M3 9/7 14/9 m6 14
9 P4 4/3 3/2 P5 13
10 ↑P4 11/8 16/11 ↓P5 12
11 ↓A4 7/5, 10/7 ↑d5 11


MOS Modes

1edo subset

Period: 22\22, Generator: 22\22

Name Intervals
1L 0s (22:0) 22

2edo subset

Period: 11\22, Generator: 11\22

Name Intervals
2L 0s (11:0) 11 11

11edo subset

Period: 2\22, Generator: 2\22

Name Intervals
11L 0s (2:0) 2 2 2 2 2 2 2 2 2 2 2

Period: 22\22, Generator: 2\22

Name Intervals
1L 9s (4:2) 2 2 2 2 4 2 2 2 2 2
1L 8s (6:2) 2 2 2 2 6 2 2 2 2
1L 7s (8:2) 2 2 2 8 2 2 2 2
1L 6s (10:2) 2 2 2 10 2 2 2
1L 5s (12:2) 2 2 12 2 2 2
1L 4s (14:2) 2 2 14 2 2
1L 3s (16:2) 2 16 2 2
1L 2s (18:2) 2 18 2
1L 1s (20:2) 20 2

Period: 22\22, Generator: 4\22

Name Intervals
5L 1s (4:2) 4 4 4 2 4 4
1L 4s (6:4) 4 4 6 4 4
1L 3s (10:4) 4 10 4 4
1L 2s (14:4) 4 14 4
1L 1s (18:4) 18 4

Period: 22\22, Generator: 6\22

Name Intervals
4L 3s (4:2) 4 2 4 2 4 2 4
3L 1s (6:4) 6 6 4 6
1L 2s (10:6) 6 10 6
1L 1s (16:6) 16 6

Period: 22\22, Generator: 8\22

Name Intervals
3L 5s (4:2) 2 4 2 4 2 2 4 2
3L 2s (6:2) 6 2 6 2 6
2L 1s (8:6) 8 6 8
1L 1s (14:8) 14 8

Period: 22\22, Generator: 10\22

Name Intervals
2L 7s (4:2) 2 2 4 2 2 2 4 2 2
2L 5s (6:2) 2 6 2 2 2 6 2
2L 3s (8:2) 2 8 2 8 2
2L 1s (10:2) 10 2 10
1L 1s (12:10) 12 10

22edo subset

Period: 1\22, Generator: 1\22

Name Intervals
22L 0s (1:0) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Period: 11\22, Generator: 1\22

Name Intervals
2L 18s (2:1) 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
2L 16s (3:1) 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1
2L 14s (4:1) 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1
2L 12s (5:1) 1 1 1 5 1 1 1 1 1 1 5 1 1 1
2L 10s (6:1) 1 1 6 1 1 1 1 1 6 1 1 1
2L 8s (7:1) 1 1 7 1 1 1 1 7 1 1
2L 6s (8:1) 1 8 1 1 1 8 1 1
2L 4s (9:1) 1 9 1 1 9 1
2L 2s (10:1) 10 1 10 1

Period: 11\22, Generator: 2\22

Name Intervals Alteration
10L 2s (2:1) 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2
2L 8s (3:2) 2 2 3 2 2 2 2 3 2 2 2 2 3 2 2 2 3 2 2 2
2L 6s (5:2) 2 5 2 2 2 5 2 2 2 2 5 2 2 5 2 2
2L 4s (7:2) 2 7 2 2 7 2 2 7 2 7 2 2
2L 2s (9:2) 9 2 9 2 9 2 2 9

Period: 11\22, Generator: 3\22

Name Intervals
8L 6s (2:1) 2 1 2 1 2 1 2 2 1 2 1 2 1 2
6L 2s (3:2) 3 3 2 3 3 3 2 3
2L 4s (5:3) 3 5 3 3 5 3
2L 2s (8:3) 8 3 8 3

Period: 11\22, Generator: 4\22

Name Intervals
6L 10s (2:1) 1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1
6L 4s (3:1) 3 1 3 1 3 3 1 3 1 3
4L 2s (4:3) 4 3 4 4 3 4
2L 2s (7:4) 7 4 7 4

Period: 11\22, Generator: 5\22

Name Intervals
4L 14s (2:1) 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1
4L 10s (3:1) 1 3 1 1 1 3 1 1 3 1 1 1 3 1
4L 6s (4:1) 1 4 1 4 1 1 4 1 4 1
4L 2s (5:1) 5 1 5 5 1 5
2L 2s (6:5) 6 5 6 5

Period: 22\22, Generator: 1\22

Name Intervals
1L 20s (2:1) 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
1L 19s (3:1) 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
1L 18s (4:1) 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1
1L 17s (5:1) 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1
1L 16s (6:1) 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1
1L 15s (7:1) 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1
1L 14s (8:1) 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1
1L 13s (9:1) 1 1 1 1 1 1 9 1 1 1 1 1 1 1
1L 12s (10:1) 1 1 1 1 1 1 10 1 1 1 1 1 1
1L 11s (11:1) 1 1 1 1 1 11 1 1 1 1 1 1
1L 10s (12:1) 1 1 1 1 1 12 1 1 1 1 1
1L 9s (13:1) 1 1 1 1 13 1 1 1 1 1
1L 8s (14:1) 1 1 1 1 14 1 1 1 1
1L 7s (15:1) 1 1 1 15 1 1 1 1
1L 6s (16:1) 1 1 1 16 1 1 1
1L 5s (17:1) 1 1 17 1 1 1
1L 4s (18:1) 1 1 18 1 1
1L 3s (19:1) 1 19 1 1
1L 2s (20:1) 1 20 1
1L 1s (21:1) 21 1

Period: 22\22, Generator: 3\22

Name Intervals Alteration Alteration Alteration
7L 8s (2:1) 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
7L 1s (3:1) 3 3 3 3 1 3 3 3
1L 6s (4:3) 3 3 3 4 3 3 3 3 4 3 3 3 4 2 3 3 4 2 4 3 3 2 4 3 3 3 4 3
1L 5s (7:3) 3 3 7 3 3 3
1L 4s (10:3) 3 3 10 3 3
1L 3s (13:3) 3 13 3 3
1L 2s (16:3) 3 16 3
1L 1s (19:3) 19 3

Period: 22\22, Generator: 5\22

Name Intervals
9L 4s (2:1) 2 1 2 2 1 2 2 2 1 2 2 1 2
4L 5s (3:2) 2 3 2 3 2 3 2 3 2
4L 1s (5:2) 5 5 2 5 5
1L 3s (7:5) 5 7 5 5
1L 2s (12:5) 5 12 5
1L 1s (17:5) 17 5

Period: 22\22, Generator: 7\22

Name Intervals
3L 16s (2:1) 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1
3L 13s (3:1) 1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1
3L 10s (4:1) 1 1 4 1 1 1 4 1 1 1 4 1 1
3L 7s (5:1) 1 5 1 1 5 1 1 1 5 1
3L 4s (6:1) 1 6 1 6 1 6 1
3L 1s (7:1) 7 7 1 7
1L 2s (8:7) 7 8 7
1L 1s (15:7) 15 7

Period: 22\22, Generator: 9\22

Name Intervals
5L 12s (2:1) 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1
5L 7s (3:1) 1 3 1 3 1 3 1 1 3 1 3 1
5L 2s (4:1) 4 1 4 4 4 1 4
2L 3s (5:4) 4 5 4 5 4
2L 1s (9:4) 9 4 9
1L 1s (13:9) 13 9
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