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

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=MOS Modes=
== Mapping ==
sharpness = 3


==22edo subset==
L = 4 ; s = 1
 
{| class="wikitable center-all"
! Degree
! Notation
! Approximate Ratios
! Approximate Ratios
! Notation
! Degree
|-
| 0
| P1
| <u>1/1</u>
| <u>2/1</u>
| P8
| 22
|-
| 1
| m2
|
|
| M7
| 21
|-
| 2
| ↑m2
| <u>16/15</u>, 15/14
| 28/15, <u>15/8</u>
| ↓M7
| 20
|-
| 3
| ↓M2
| 12/11, <u>11/10</u>, 10/9
| 9/5, <u>20/11</u>, 11/6
| ↑m7
| 19
|-
| 4
| M2
| <u>9/8</u>, <u>8/7</u>
| <u>7/4</u>, <u>16/9</u>
| m7
| 18
|-
| 5
| m3
| <u>7/6</u>
| <u>12/7</u>
| M6
| 17
|-
| 6
| ↑m3
| <u>6/5</u>, 11/9
| 18/11, <u>5/3</u>
| ↓M6
| 16
|-
| 7
| ↓M3
| <u>5/4</u>
| <u>8/5</u>
| ↑m6
| 15
|-
| 8
| M3
| 14/11, <u>9/7</u>
| <u>14/9</u>, 11/7
| m6
| 14
|-
| 9
| P4
| <u>4/3</u>
| <u>3/2</u>
| P5
| 13
|-
| 10
| ↑P4
| 15/11, <u>11/8</u>
| <u>16/11</u>, 22/15
| ↓P5
| 12
|-
| 11
| ↓A4
| colspan="2" | <u>7/5</u>, <u>10/7</u>
| ↑d5
| 11
|}
 
== Rank-2 5-limit temperaments ==
{| class="wikitable center-1 center-2"
!Periods
per 8ve
!Generator
!Temperaments
!5-limit commas
|-
|1
|1\22
|[[Miscellaneous 5-limit temperaments#Chromo|Chromo]]<br>[[Escapade]]
|[[1220703125/1146617856]]<br>[[4294967296/4271484375]]
|-
|1
|3\22
|[[Porcupine]]
|[[250/243]]
|-
|1
|5\22
|[[Orson]]
|[[2109375/2097152]]
|-
|1
|7\22
|[[Magic]]
|[[3125/3072]]
|-
|1
|9\22
|[[Syntonic–diatonic equivalence continuum#Superpyth (5-limit)|Superpyth]]
|[[20480/19683]]
|-
|2
|1\22
|[[Miscellaneous 5-limit temperaments#Comic|Comic]]
|[[5120000/4782969]]
|-
|2
|2\22
|[[Diaschismic family#Diaschismic|Diaschism]]<nowiki/>ic
|[[2048/2025]]
|-
|2
|3\22
|[[Kwazy]]
|[[9010162353515625/9007199254740992]]
|-
|2
|4\22
|[[Miscellaneous 5-limit temperaments#Wizard|Wizard]]
|[[2197265625/2147483648]]
|-
|2
|5\22
|[[Miscellaneous 5-limit temperaments#Doublewide|Doublewide]]
|[[390625/373248]]
|-
|11
|1\22
|[[11th-octave temperaments#Undekapent|Undekapent]]
|[[48828125/45349632]]
|}
 
== MOS Modes ==
{| class="wikitable"
|+
!Period
!Generator
!Necklace
!Proposed Name
|-
| rowspan="2" |22\22
| rowspan="2" |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
|-
| rowspan="2" |22\22
| rowspan="2" |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
|-
| rowspan="4" |22\22
| rowspan="4" |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
|-
| rowspan="2" |22\22
| rowspan="2" |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
|-
| rowspan="2" |11\22
| rowspan="2" |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
|-
| rowspan="2" |11\22
| rowspan="2" |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
|-
| rowspan="3" |11\22
| rowspan="3" |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 ===
{| class="wikitable"
|+
!Necklace
!Proposed Name
|-
|2 2 2 1 2 2 2 2 1 2 2 2
|Hexachordal[12]@22edo
|}

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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