User:Contribution/Exploring Selected Modes in 22-EDO

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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 M7 21
2 ↑m2 16/15, 15/14 28/15, 15/8 ↓M7 20
3 ↓M2 12/11, 11/10, 10/9 9/5, 20/11, 11/6 ↑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, 11/9 18/11, 5/3 ↓M6 16
7 ↓M3 5/4 8/5 ↑m6 15
8 M3 14/11, 9/7 14/9, 11/7 m6 14
9 P4 4/3 3/2 P5 13
10 ↑P4 15/11, 11/8 16/11, 22/15 ↓P5 12
11 ↓A4 7/5, 10/7 ↑d5 11

Rank-2 5-limit temperaments

Periods

per 8ve

Generator Temperaments 5-limit commas
1 1\22 Chromo
Escapade 		1220703125/1146617856
4294967296/4271484375
1 3\22 Porcupine 250/243
1 5\22 Orson 2109375/2097152
1 7\22 Magic 3125/3072
1 9\22 Superpyth 20480/19683
2 1\22 Comic 5120000/4782969
2 2\22 Diaschismic 2048/2025
2 3\22 Kwazy 9010162353515625/9007199254740992
2 4\22 Wizard 2197265625/2147483648
2 5\22 Doublewide 390625/373248
11 1\22 Undekapent 48828125/45349632

MOS Modes

Period Generator Mode Name Alteration
22\22 3\22 3 3 3 3 1 3 3 3

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

Porcupine[8]

Porcupine[15]

22\22 5\22 2 3 2 3 2 3 2 3 2

2 1 2 1 2 1 2 2 1 2 1 2 1 2

Orson[9]

Orson[13]

22\22 7\22 1 5 1 1 5 1 1 1 5 1

1 1 4 1 1 1 4 1 1 1 4 1 1

1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1

1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1

Magic[10]

Magic[13]

Magic[16]

Magic[19]

22\22 9\22 1 3 1 3 1 3 1 1 3 1 3 1

1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1

Superpyth[12]

Superpyth[17]

11\22 2\22 2 2 2 1 2 2 2 2 2 1 2 2 Diaschismic[12] 2 2 2 1 2 2 2 2 1 2 2 2
11\22 3\22 3 3 2 3 3 3 2 3

2 1 2 1 2 1 2 2 1 2 1 2 1 2

Kwazy[8]

Kwazy[14]

11\22 4\22 3 1 3 1 3 3 1 3 1 3

1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1

Wizard[10]

Wizard[16]

11\22 5\22 1 4 1 4 1 1 4 1 4 1

1 3 1 1 1 3 1 1 3 1 1 1 3 1

1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1

Doublewide[10]

Doublewide[14]

Doublewide[18]

2\22 2\22 2 2 2 2 2 2 2 2 2 2 2 11edo
1\22 1\22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 22edo

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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