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


==22edo subset==
L = 4 ; s = 1


=== Generator: 2\22, Period 2\22 ===
{| class="wikitable center-all"
{| class="wikitable"
! Degree
!Name
! Notation
!Intervals
! Approximate Ratios
!Alteration
! Approximate Ratios
|-
! Notation
|10L 2s (2:1)
! Degree
|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)
| 0
|2 7 2 2 7 2
| P1
|2 7 2 7 2 2
| <u>1/1</u>
| <u>2/1</u>
| P8
| 22
|-
|-
|2L 2s (9:2)
| 1
|9 2 9 2
| m2
|9 2 2 9
|}
 
=== Generator: 5\22, Period 1\22 ===
{| class="wikitable"
!Name
!Intervals
!Alteration
|-
|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
|
|
| M7
| 21
|-
|-
|4L 1s (5:2)
| 2
|5 5 2 5 5
| ↑m2
|
| <u>16/15</u>, 15/14
| 28/15, <u>15/8</u>
| ↓M7
| 20
|-
|-
|1L 3s (7:5)
| 3
|5 7 5 5
| ↓M2
|
| 12/11, <u>11/10</u>, 10/9
| 9/5, <u>20/11</u>, 11/6
| ↑m7
| 19
|-
|-
|1L 2s (12:5)
| 4
|5 12 5
| M2
|
| <u>9/8</u>, <u>8/7</u>
| <u>7/4</u>, <u>16/9</u>
| m7
| 18
|-
|-
|1L 1s (17:5)
| 5
|17 5
| m3
|
| <u>7/6</u>
|}
| <u>12/7</u>
 
| M6
=== Generator: 5\22, Period 1\22 ===
| 17
{| class="wikitable"
!Name
!Intervals
!Alteration
|-
|-
|9L 4s (2:1)
| 6
|2 1 2 2 1 2 2 2 1 2 2 1 2
| ↑m3
|
| <u>6/5</u>, 11/9
| 18/11, <u>5/3</u>
| ↓M6
| 16
|-
|-
|4L 5s (3:2)
| 7
|2 3 2 3 2 3 2 3 2
| ↓M3
|
| <u>5/4</u>
| <u>8/5</u>
| ↑m6
| 15
|-
|-
|4L 1s (5:2)
| 8
|5 5 2 5 5
| M3
|
| 14/11, <u>9/7</u>
| <u>14/9</u>, 11/7
| m6
| 14
|-
|-
|1L 3s (7:5)
| 9
|5 7 5 5
| P4
|
| <u>4/3</u>
| <u>3/2</u>
| P5
| 13
|-
|-
|1L 2s (12:5)
| 10
|5 12 5
| ↑P4
|
| 15/11, <u>11/8</u>
| <u>16/11</u>, 22/15
| ↓P5
| 12
|-
|-
|1L 1s (17:5)
| 11
|17 5
| ↓A4
|
| colspan="2" | <u>7/5</u>, <u>10/7</u>
| ↑d5
| 11
|}
|}


=== Generator: 5\22, Period 1\22 ===
== Rank-2 5-limit temperaments ==
{| class="wikitable"
{| class="wikitable center-1 center-2"
!Name
!Periods
!Intervals
per 8ve
!Alteration
!Generator
|-
!Temperaments
|9L 4s (2:1)
!5-limit commas
|2 1 2 2 1 2 2 2 1 2 2 1 2
|
|-
|-
|4L 5s (3:2)
|1
|2 3 2 3 2 3 2 3 2
|1\22
|
|[[Miscellaneous 5-limit temperaments#Chromo|Chromo]]<br>[[Escapade]]
|[[1220703125/1146617856]]<br>[[4294967296/4271484375]]
|-
|-
|4L 1s (5:2)
|1
|5 5 2 5 5
|3\22
|
|[[Porcupine]]
|[[250/243]]
|-
|-
|1L 3s (7:5)
|1
|5 7 5 5
|5\22
|
|[[Orson]]
|[[2109375/2097152]]
|-
|-
|1L 2s (12:5)
|1
|5 12 5
|7\22
|
|[[Magic]]
|[[3125/3072]]
|-
|-
|1L 1s (17:5)
|1
|17 5
|9\22
|
|[[Syntonic–diatonic equivalence continuum#Superpyth (5-limit)|Superpyth]]
|}
|[[20480/19683]]
 
=== Generator: 5\22, Period 1\22 ===
{| class="wikitable"
!Name
!Intervals
!Alteration
|-
|-
|9L 4s (2:1)
|2
|2 1 2 2 1 2 2 2 1 2 2 1 2
|1\22
|
|[[Miscellaneous 5-limit temperaments#Comic|Comic]]
|[[5120000/4782969]]
|-
|-
|4L 5s (3:2)
|2
|2 3 2 3 2 3 2 3 2
|2\22
|
|[[Diaschismic family#Diaschismic|Diaschism]]<nowiki/>ic
|[[2048/2025]]
|-
|-
|4L 1s (5:2)
|2
|5 5 2 5 5
|3\22
|
|[[Kwazy]]
|[[9010162353515625/9007199254740992]]
|-
|-
|1L 3s (7:5)
|2
|5 7 5 5
|4\22
|
|[[Miscellaneous 5-limit temperaments#Wizard|Wizard]]
|[[2197265625/2147483648]]
|-
|-
|1L 2s (12:5)
|2
|5 12 5
|5\22
|
|[[Miscellaneous 5-limit temperaments#Doublewide|Doublewide]]
|[[390625/373248]]
|-
|-
|1L 1s (17:5)
|11
|17 5
|1\22
|
|[[11th-octave temperaments#Undekapent|Undekapent]]
|[[48828125/45349632]]
|}
|}


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


=== Generator: 5\22, Period 1\22 ===
=== Non-MOS modes ===
{| class="wikitable"
{| class="wikitable"
!Name
|+
!Intervals
!Necklace
!Alteration
!Proposed Name
|-
|-
|9L 4s (2:1)
|2 2 2 1 2 2 2 2 1 2 2 2
|2 1 2 2 1 2 2 2 1 2 2 1 2
|Hexachordal[12]@22edo
|
|-
|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
|
|}
|}
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