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

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Line 1: Line 1:
= Mapping =
== Mapping ==
sharpness = 3
sharpness = 3
L = 4 ; s = 1
L = 4 ; s = 1


Line 159: Line 160:
|}
|}


= MOS Modes =
== MOS Modes ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!Period
!Period
!Generator
!Generator
!Mode
!Necklace
!Name
!Proposed Name
!Alteration
|-
|-
|22\22
| rowspan="2" |22\22
|3\22
| rowspan="2" |3\22
|3 3 3 3 1 3 3 3
|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]@22edo
|Porcupine[8]
|-
Porcupine[15]
|1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
|
|Porcupine[15]@22edo
|-
|-
|22\22
| rowspan="2" |22\22
|5\22
| rowspan="2" |5\22
|2 3 2 3 2 3 2 3 2
|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]@22edo
|Orson[9]
|-
Orson[13]
|2 1 2 1 2 1 2 2 1 2 1 2 1 2
|
|Orson[13]@22edo
|-
|-
|22\22
| rowspan="4" |22\22
|7\22
| rowspan="4" |7\22
|1 5 1 1 5 1 1 1 5 1
|1 5 1 1 5 1 1 1 5 1
1 1 4 1 1 1 4 1 1 1 4 1 1
|Magic[10]@22edo
 
|-
1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1
|1 1 4 1 1 1 4 1 1 1 4 1 1
 
|Magic[13]@22edo
1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1
|-
|Magic[10]
|1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1
Magic[13]
|Magic[16]@22edo
 
|-
Magic[16]
|1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1
 
|Magic[19]@22edo
Magic[19]
|
|-
|-
|22\22
| rowspan="2" |22\22
|9\22
| rowspan="2" |9\22
|1 3 1 3 1 3 1 1 3 1 3 1
|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]@22edo
|Superpyth[12]
|-
Superpyth[17]
|1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1
|
|Superpyth[17]@22edo
|-
|-
|11\22
|11\22
|2\22
|2\22
|2 2 2 1 2 2 2 2 2 1 2 2
|2 2 2 1 2 2 2 2 2 1 2 2
|Diaschismic[12]
|Diaschismic[12]@22edo
|2 2 2 1 2 2 2 2 1 2 2 2
|-
|-
|11\22
| rowspan="2" |11\22
|3\22
| rowspan="2" |3\22
|3 3 2 3 3 3 2 3
|3 3 2 3 3 3 2 3
2 1 2 1 2 1 2 2 1 2 1 2 1 2
|Kwazy[8]@22edo
|Kwazy[8]
|-
Kwazy[14]
|2 1 2 1 2 1 2 2 1 2 1 2 1 2
|
|Kwazy[14]@22edo
|-
|-
|11\22
| rowspan="2" |11\22
|4\22
| rowspan="2" |4\22
|3 1 3 1 3 3 1 3 1 3
|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]@22edo
|Wizard[10]
|-
Wizard[16]
|1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1
|
|Wizard[16]@22edo
|-
|-
|11\22
| rowspan="3" |11\22
|5\22
| rowspan="3" |5\22
|1 4 1 4 1 1 4 1 4 1
|1 4 1 4 1 1 4 1 4 1
1 3 1 1 1 3 1 1 3 1 1 1 3 1
|Doublewide[10]@22edo
 
|-
1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1
|1 3 1 1 1 3 1 1 3 1 1 1 3 1
|Doublewide[10]
|Doublewide[14]@22edo
Doublewide[14]
|-
 
|1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1
Doublewide[18]
|Doublewide[18]@22edo
|
|-
|-
|2\22
|2\22
Line 246: Line 242:
|2 2 2 2 2 2 2 2 2 2 2
|2 2 2 2 2 2 2 2 2 2 2
|11edo
|11edo
|
|-
|-
|1\22
|1\22
Line 252: Line 247:
|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
|22edo
|22edo
|
|}
|}


==1edo subset==
=== Non-MOS modes ===
 
=== Period: 22\22, Generator: 22\22 ===
{| class="wikitable"
{| class="wikitable"
!Name
|+
!Intervals
!Necklace
|-
!Proposed Name
|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==
=== 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
|2 2 2 1 2 2 2 2 1 2 2 2
|-
|Hexachordal[12]@22edo
|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 18:38, 3 July 2026

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 Necklace Proposed Name
22\22 3\22 3 3 3 3 1 3 3 3 Porcupine[8]@22edo
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 Porcupine[15]@22edo
22\22 5\22 2 3 2 3 2 3 2 3 2 Orson[9]@22edo
2 1 2 1 2 1 2 2 1 2 1 2 1 2 Orson[13]@22edo
22\22 7\22 1 5 1 1 5 1 1 1 5 1 Magic[10]@22edo
1 1 4 1 1 1 4 1 1 1 4 1 1 Magic[13]@22edo
1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1 Magic[16]@22edo
1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 Magic[19]@22edo
22\22 9\22 1 3 1 3 1 3 1 1 3 1 3 1 Superpyth[12]@22edo
1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1 Superpyth[17]@22edo
11\22 2\22 2 2 2 1 2 2 2 2 2 1 2 2 Diaschismic[12]@22edo
11\22 3\22 3 3 2 3 3 3 2 3 Kwazy[8]@22edo
2 1 2 1 2 1 2 2 1 2 1 2 1 2 Kwazy[14]@22edo
11\22 4\22 3 1 3 1 3 3 1 3 1 3 Wizard[10]@22edo
1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 Wizard[16]@22edo
11\22 5\22 1 4 1 4 1 1 4 1 4 1 Doublewide[10]@22edo
1 3 1 1 1 3 1 1 3 1 1 1 3 1 Doublewide[14]@22edo
1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 Doublewide[18]@22edo
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

Non-MOS modes

Necklace Proposed Name
2 2 2 1 2 2 2 2 1 2 2 2 Hexachordal[12]@22edo
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