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Map of rank-2 temperaments: Difference between revisions

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This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only rank-2 temperaments not appearing here should be ones like [[Bohlen-Pierce|Bohlen-Pierce]] that completely lack octaves.
This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only rank-2 temperaments not appearing here should be ones like [[Bohlen–Pierce]] that completely lack octaves.


Please make sure each fraction of an octave is always the [[mediant|mediant]] of the ones directly above and below.
Please make sure each fraction of an octave is always the [[mediant]] of the ones directly above and below.


==One period per octave==
Interactive maps of ''all'' linear temperaments with octave, half-octave, third-octave, or tritave period that are logged on the wiki are available [https://hkm2685.github.io/temperament-map/rank2/viewer/ here].  
Since this is the largest subset, it has its own page: [[Map_of_linear_temperaments|Map of linear temperaments]].


==Two periods per octave==
== One period per octave ==
Since this is the largest subset, it has its own page: [[map of linear temperaments]].


{| class="wikitable"
== Two periods per octave ==
{| class="wikitable sortable mw-collapsible"
|-
|-
! colspan="9" | Generator
! colspan="9" | Generator
! | Cents
! Cents
! | Comments
! Comments
|-
|-
| | 0\2
| 0\2
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 0.000
| 0.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\26
| 1\26
| | 46.154
| 46.154
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\24
| 1\24
| |  
|  
| | 50.000
| 50.000
| | [[Shrutar|Shrutar]]
| [[Shrutar]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 2\46
| 2\46
| | 52.174
| 52.174
| | Shrutar
| Shrutar
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\22
| 1\22
| |  
|  
| |  
|  
| | 54.545
| 54.545
| | Shrutar
| Shrutar
|-
| |
| |
| |
| |
| |
| | 1\20
| |
| |
| |
| | 60.000
| |
|-
| |
| |
| |
| |
| | 1\18
| |
| |
| |
| |
| | 66.667
| |
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 2\34
| 1\20
| |  
|  
| |  
|  
| |  
|  
| | 70.588
| 60.000
| | [[Vishnu|Vishnu]]
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 1\18
| |  
|  
| |  
|  
| |  
|  
| | 7\118
|  
| | 71.186
| 66.667
| | Vishnu
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 2\34
| |  
|  
| | 5\84
|  
| |  
|  
| | 71.429
| 70.588
| | Vishnu
| [[Vishnu]]
|-
|-
| |
|  
| |
|  
| |
|  
| |
|  
| |  
|  
| |  
|  
| | 3\50
|  
| |  
|  
| |  
| 7\118
| | 72.000
| 71.186
| |  
| Vishnu
|-
| |
| |
| |
| | 1\16
| |
| |
| |
| |
| |
| | 75.000
| |
|-
| |
| |
| |
| |
| | 2\30
| |
| |
| |
| |
| | 80.000
| |
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\44
|  
| |  
|  
| |
| 5\84
| |  
|  
| | 81.818
| 71.429
| |
| Vishnu
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 4\58
| 3\50
| |  
|  
| |  
|  
| | 82.759
| 72.000
| | [[Harry|Harry]]
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\16
|
|  
|
|  
|
|  
|
|  
|9\130
|  
|83.077
| 75.000
|Harry
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 2\30
| |  
|  
| |  
|  
| | 5\72
|  
| |  
|  
| | 83.333
| 80.000
| | Harry
|  
|-
|-
| |  
|  
| |  
|  
| | 1\14
|  
| |  
|  
| |  
|  
| |
| 3\44
| |  
|  
| |  
|  
| |  
|  
| | 85.714
| 81.818
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 2\26
|  
| |  
|  
| |  
|  
| |
| 4\58
| |  
|  
| |  
|  
| | 92.308
| 82.759
| | [[Injera|Injera]]
| [[Harry]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\38
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 9\130
| | 94.737
| 83.077
| | Injera
| Harry
|-
|-
| |  
|  
| | 1\12
|  
| |
|  
| |
|  
| |
|  
| |
|  
| |
|  
| |
| 5\72
| |
|  
| | 100.000
| 83.333
| | Injera/[[Diaschismic]]
| Harry
|-
|
|
|
|
|
|5\58
|
|
|
|103.448
|Diaschismic
|-
|-
| |  
|  
| |  
|  
| |
| 1\14
| |  
|  
| | 4\46
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 104.348
| 85.714
| | Diaschismic/[[Srutal]]
|  
|-
|-
|
|  
|
|  
|
|  
|
| 2\26
|
|  
|7\80
|  
|
|  
|
|  
|
|  
|105.000
| 92.308
|Srutal
| [[Injera]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 3\34
|  
| |  
| 3\38
| |  
|  
| |  
|  
| |
|  
| |  
|  
| | 105.882
| 94.737
| | Srutal/[[Pajara]]
| Injera
|-
|-
|
|  
|
| 1\12
|
|  
|
|  
|5\56
|  
|
|  
|
|  
|
|  
|
|  
|107.143
| 100.000
|Pajara
| Injera/[[Diaschismic]]
|-
|-
| |  
|  
| |  
|  
| | 2\22
|  
| |  
|  
| |  
|  
| |
| 5\58
| |  
|  
| |  
|  
| |  
|  
| | 109.091
| 103.448
| | Pajara
| Diaschismic
|-
|-
|
|  
|
|  
|
|  
|3\32
|  
|
| 4\46
|
|  
|
|  
|
|  
|
|  
|112.500
| 104.348
|
| Diaschismic/[[Srutal]]
|-
|-
| | 1\10
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 7\80
| |  
|  
| |  
|  
| |  
|  
| | 120.000
| 105.000
| | [[Octokaidecal]]
| Srutal
|-
|-
|
|
|
|  
|3\28
|  
|
| 3\34
|
|  
|
|  
|
|  
|
|  
|
|  
|128.571
| 105.882
|Octokaidecal
| Srutal/[[Pajara]]
|-
|-
| |  
|  
| | 2\18
|  
| |  
|  
| |  
|  
| |
| 5\56
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 133.333
| 107.143
| | Octokaidecal
| Pajara
|-
|-
| |  
|  
| |  
|  
| | 3\26
| 2\22
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 138.462
| 109.091
| |
| Pajara
|-
|-
|
|  
|
|  
|
|  
|
| 3\32
|6\60
|  
|
|  
|
|  
|
|  
|
|  
|140.000
| 112.500
|
|  
|-
|-
|
| 1\10
|
|  
|
|  
|
|  
|
|  
|11\94
|  
|
|  
|
|  
|
|  
|140.126
| 120.000
|Fifive
| [[Octokaidecal]]
|-
|-
|
|  
|
|  
|
| 3\28
|
|  
|
|  
|
|  
|15\128
|  
|
|  
|
|  
|140.625
| 128.571
|Fifive
| Octokaidecal
|-
|-
| |  
|  
| |
| 2\18
| |  
|  
| | 4\34
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 141.176
| 133.333
| | [[Fifive|Fifive]]
| Octokaidecal
|-
|-
|
|  
|
|  
|
| 3\26
|
|  
|5\42
|  
|
|  
|
|  
|
|  
|
|  
|142.857
| 138.462
|
|  
|-
|-
| | 1\8
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 6\60
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 150.000
| 140.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 4\30
|  
| |  
|  
| |  
|  
| |
| 11\94
| |  
|  
| |  
|  
| |  
|  
| | 160.000
| 140.126
| |
| Fifive
|-
|-
| |
|  
| | 3\22
|  
| |
|  
| |
|  
| |
|  
| |
|  
| |  
| 15\128
| |
|  
| |  
|  
| | 163.636
| 140.625
| | [[Hedgehog|Hedgehog]]/[[Echidna]]
| Fifive
|-
|
|
|
|
|11\80
|
|
|
|
|165.000
|Hedgehog/Echidna
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 8\58
| 4\34
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 165.517
| 141.176
| | Hedgehog/Echidna
| [[Fifive]]
|-
|-
| |  
|  
| |  
|  
| | 5\36
|  
| |  
|  
| |  
| 5\42
| |  
|  
| |  
|  
| |
|  
| |
|  
| | 166.667
| 142.857
| |  
|  
|-
|-
| | 2\14
| 1\8
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 171.429
| 150.000
| |  
|  
|-
|-
| |  
|  
| | 3\20
|  
| |  
| 4\30
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
|  
| |  
|  
| | 180.000
| 160.000
| |  
|  
|-
|-
| |  
|  
| |
| 3\22
| |  
|  
| | 7\46
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 182.609
| 163.636
| | [[Unidec|Unidec]]/[[Hendec]]
| [[Hedgehog]]/[[Echidna]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 11\72
| 11\80
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 183.333
| 165.000
| | Unidec/Hendec
| Hedgehog/Echidna
|-
|-
| |  
|  
| |  
|  
| | 4\26
|  
| |  
| 8\58
| |  
|  
| |  
|  
| |  
|  
| |
|  
| |  
|  
| | 184.615
| 165.517
| | Unidec/Hendec
| Hedgehog/Echidna
|-
|-
| |
|  
| |  
|  
| |  
| 5\36
| | 5\32
|  
| |
|  
| |
|  
| |
|  
| |
|  
| |
|  
| | 187.500
| 166.667
| |
|  
|-
| | 1\6
| |
| |
| |  
| |  
| |  
| |  
| |  
| |  
| | 200.000
| |
|-
| |
| |
| |
| | 6\34
| |
| |
| |
| |
| |
| | 211.765
| |
|-
| |
| |
| | 5\28
| |
| |
| |
| |
| |
| |
| | 214.286
| | [[Antikythera]]
|-
|-
| |
| 2\14
| |  
|  
| |  
|  
| | 9\50
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 216.000
| 171.429
| | Antikythera/[[Wizard]]
|  
|-
|-
| |  
|  
| |
| 3\20
| |  
|  
| |  
|  
| | 13\72
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 216.667
| 180.000
| | Antikythera/Wizard
|  
|-
|-
| |  
|  
| | 4\22
|  
| |  
|  
| |
| 7\46
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 218.182
| 182.609
| | Antikythera/Wizard/[[Astrology]]
| [[Unidec]]/[[Hendec]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|15\82
| 11\72
|
|  
|
|  
|
|  
|
|  
|219.512
| 183.333
|Astrology
| Unidec/Hendec
|-
|-
|
|  
|
|  
|
| 4\26
|11\60
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|220.000
| 184.615
|Astrology
| Unidec/Hendec
|-
|-
|
|  
|
|  
|7\38
|  
|
| 5\32
|
|  
|
|  
|
|  
|
|  
|
|  
|221.053
| 187.500
|
|  
|-
|-
| |
| 1\6
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 225.000
| 200.000
| | [[Lemba]]
|  
|-
|-
| |  
|  
| | 5\26
|  
| |  
|  
| |
| 6\34
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 230.769
| 211.765
| | Lemba
|  
|-
|-
|
|  
|
|  
|
| 5\28
|12\62
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|232.258
| 214.286
|Lemba
| [[Antikythera]]
|-
|-
| |  
|  
| |  
|  
| | 7\36
|  
| |  
| 9\50
| |  
|  
| |  
|  
| |  
|  
| |
|  
| |  
|  
| | 233.333
| 216.000
| |
| Antikythera/[[Wizard]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 9\46
|  
| |
| 13\72
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 234.783
| 216.667
| | [[Echidnic|Echidnic]]
| Antikythera/Wizard
|-
|-
|
|  
|
| 4\22
|
|  
|
|  
|
|  
|
|  
|29\148
|  
|
|  
|
|  
|235.135
| 218.182
|Echidnic
| Antikythera/Wizard/[[Astrology]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 15\82
|20\102
|  
|
|  
|
|  
|
|  
|235.294
| 219.512
|Echidnic
| Astrology
|-
|-
|
|  
|
|  
|
|  
|
| 11\60
|11\56
|  
|
|  
|
|  
|
|  
|
|  
|235.714
| 220.000
|
| Astrology
|-
|-
| | 2\10
|  
| |  
|  
| |
| 7\38
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 240.000
| 221.053
| | [[Decimal|Decimal]]
|  
|-
|-
| |  
|  
| | 5\24
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 250.000
| 225.000
| | Decimal
| [[Lemba]]
|-
|-
|
|  
|
| 5\26
|8\38
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|252.632
| 230.769
|Decimal
| Lemba
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |
| 12\62
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 257.143
| 232.258
| | Decimal
| Lemba
|-
|-
| |
|  
| | 4\18
|  
| |
| 7\36
| |
|  
| |
|  
| |
|  
| |
|  
| |
|  
| |  
|  
| | 266.667
| 233.333
| |
|  
|-
| |
| |
| | 5\22
| |
| |  
| |  
| |
| |
| |
| | 272.727
| | [[Doublewide|Doublewide]]
|-
|
|
|
|
|
|16\70
|
|
|
|274.286
|Doublewide
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |
| 9\46
| | 11\48
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 275.000
| 234.783
| | Doublewide
| [[Echidnic]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 6\26
|  
| |  
|  
| |  
|  
| |
| 29\148
| |  
|  
| |  
|  
| | 276.923
| 235.135
| |
| Echidnic
|-
|-
| | 1\4
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 20\102
| |  
|  
| |  
|  
| |  
|  
| | 300.000
| 235.294
| |
| Echidnic
|}
 
==Three periods per octave==
{{todo|complete table|comment=Add hemisemiaug (optimal ETs 18, 24, 42), add landscape microtemperaments}}
{| class="wikitable"
|-
! colspan="10" | Generator
! | Cents
! | Comments
|-
|-
| | 0\3
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 11\56
| |
|  
| |  
|  
|
|  
|
|  
|
| 235.714
| | 0.000
|  
| |  
|-
|-
| |
| 2\10
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\30
|  
|
|  
|
|  
|
| 240.000
| | 40.000
| [[Decimal]]
| |
|-
|-
| |  
|  
| |
| 5\24
| |
|  
| |  
|  
| |  
|  
| | 1\27
|  
| |  
|  
|
|  
|
|  
|
| 250.000
| | 44.444
| Decimal
| | [[Semiaug|Semiaug]]
|-
|-
| |  
|  
| |  
|  
| |
| 8\38
| |  
|  
| |  
|  
| |  
|  
| | 2\51
|  
|
|  
|
|  
|
| 252.632
| | 47.059
| Decimal
| | Semiaug
|-
|-
| |
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\24
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
| 257.143
| | 50.000
| Decimal
| | Semiaug/[[Augmented family#Hemiug|Hemiug]]
|-
|-
|
|  
|
| 4\18
|
|  
|
|  
|
|  
|2\45
|  
|
|  
|
|  
|
|  
|
| 266.667
|53.333
|  
|Hemiug
|-
|-
| |
|  
| |  
|  
| |  
| 5\22
| | 1\21
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
| 272.727
| | 57.143
| [[Doublewide]]
| | Hemiug
|-
|-
| |  
|  
| |  
|  
| | 1\18
|  
| |  
|  
| |  
|  
| |
| 16\70
| |
|  
|
|  
|
|  
|
| 274.286
| | 66.667
| Doublewide
| |
|-
|-
| |  
|  
| | 1\15
|  
| |  
|  
| |  
|  
| |
| 11\48
| |
|  
| |  
|  
|
|  
|
|  
|
| 275.000
| | 80.000
| Doublewide
| |
|-
|-
| |  
|  
| |  
|
| |  
|
| |  
| 6\26
| |  
|  
| |  
|  
| | 6\87
|  
|
|  
|
|  
|
| 276.923
| | 82.759
|  
| |  
|-
| 1\4
|  
|  
|  
|  
|  
|  
|  
|  
| 300.000
|
|}
 
== Three periods per octave ==
{{todo| complete table| comment=Add hemisemiaug (optimal ETs 18, 24, 42), add landscape microtemperaments}}
{| class="wikitable sortable mw-collapsible"
|-
|-
|
! colspan="10" | Generator
|
! Cents
|
! Comments
|
|
|
|
|11\159
|
|
|83.019
|[[Tritikleismic]]
|-
|-
|
| 0\3
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|16\231
|  
|
|  
|83.117
| 0.000
|Tritikleismic
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\72
|  
| |  
| 1\30
|
|  
|
|  
|
|  
| | 83.333
| 40.000
| | Tritikleismic
|  
|-
|-
| |
|  
| |
|  
| |
|  
| |
|  
| | 4\57
|  
| |
| 1\27
| |
|  
|
|  
|
|  
|
|  
| | 84.211
| 44.444
| | Tritikleismic
| [[Hemiaug]]
|-
| |  
| |  
| |
| | 3\42
| |  
| |  
| |  
|
|
|
| | 85.714
| |
|-
|-
| |  
|  
| |  
|  
| | 2\27
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 2\51
|
|  
|
|  
|
|  
| | 88.889
| 47.059
| |[[Augmented]]/[[Augene]]
| Hemiaug
|-
|-
|
|  
|
|  
|
|  
|3\39
|  
|
| 1\24
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 50.000
|Augmented/Augene/[[Fog]]
| Hemiaug/[[Hemiug]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|4\51
|  
|
| 2\45
|
|  
|
|  
|
|  
|
|  
|94.118
| 53.333
|Augmented/Augene/Fog
| Hemiug
|-
|-
|
|  
|
|  
|
|  
|
| 1\21
|
|  
|5\63
|  
|
|  
|
|  
|
|  
|
|  
|95.238
| 57.143
|Augmented/Augene/Fog
| Hemiug
|-
|-
|
|  
|
|  
|
| 1\18
|
|  
|
|  
|
|  
|
|  
|11\138
|  
|
|  
|
|  
|95.652
| 66.667
|Augmented Augene/Fog
|  
|-
|-
|
|  
|
| 1\15
|
|  
|
|  
|
|  
|
|  
|6\75
|  
|
|  
|
|  
|
|  
|96
| 80.000
|Augmented/Augene/Fog
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 6\87
|7\87
|  
|
|  
|
|  
|96.552
| 82.759
|Augmented/Augene/[[Misty]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 11\159
|
|  
|15\186
|  
|96.774
| 83.019
|Augmented/Augene/Misty
| [[Tritikleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\99
| 16\231
|
|  
|96.97
| 83.117
|Augmented/Augene/Misty
| Tritikleismic
|-
|-
| | 1\12
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 5\72
| |  
|  
|
|  
|
|  
|
|  
| | 100.000
| 83.333
| | Augmented/Augene/[[August]]
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| | 3\33
|  
| |  
|  
| |
| 4\57
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 109.091
| 84.211
| | August
| Tritikleismic
|-
|-
| |  
|  
| | 2\21
|  
| |  
|  
| |
| 3\42
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 114.286
| 85.714
| | August
|  
|-
|-
| |  
|  
| |  
|  
| | 3\30
| 2\27
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 120.000
| 88.889
| |  
| | [[Augmented (temperament)|Augmented]]/[[Augene]]
|-
|-
| | 1\9
|  
| |  
|  
| |  
|  
| |
| 3\39
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 133.333
| 92.308
| |
| Augmented/Augene/[[Fog]]
|-
|-
| |  
|  
| |  
|  
| | 4\33
|  
| |  
|  
| |  
| 4\51
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 145.455
| 94.118
| |
| Augmented/Augene/Fog
|-
|-
| |  
|  
| | 3\24
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 5\63
| |  
|  
|
|  
|
|  
|
|  
| | 150.000
| 95.238
| |[[Triforce]]
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|5\39
|  
|
|  
|
|  
|
|  
|
|  
|
| 11\138
|
|  
|
|  
|153.846
| 95.652
|Triforce
| Augmented/Augene/Fog
|-
|-
| | 2\15
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 6\75
|
|  
|
|  
|
|  
| | 160.000
| 96
| | Triforce
| Augmented/Augene/Fog
|-
|-
| |  
|  
| | 3\21
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
| 7\87
|
|  
|
|  
| | 171.429
| 96.552
| |[[Oodako]]
| Augmented/Augene/[[Misty]]
|-
|-
|
|  
|
|  
|
|  
|7\48
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 15\186
|175
| 96.774
|Oodako
| Augmented/Augene/Misty
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\75
|  
|
|  
|
|  
|
|  
|
| 8\99
|
|  
|176
| 96.97
|Oodako
| Augmented/Augene/Misty
|-
|-
|
| 1\12
|
|  
|
|  
|
|  
|
|  
|15\102
|  
|
|  
|
|  
|
|  
|
|  
|176.471
| 100.000
|Oodako
| Augmented/Augene/[[August]]
|-
|-
|
|  
|
|  
|
| 3\33
|
|  
|
|  
|
|  
|19\129
|  
|
|  
|
|  
|
|  
|176.744
| 109.091
|Oodako
| August
|-
|-
|
|  
|
| 2\21
|4\27
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|177.778
| 114.286
|Oodako
| August
|-
|-
| | 1\6
|  
| |  
|  
| |
| 3\30
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 200.000
| 120.000
| |
|  
|}
 
==Four periods per octave==
{| class="wikitable"
! colspan="7" | Generator !! Cents !! Comments
|-
|-
| 0\4 || || || || ||
| 1\9
| || 0 ||  
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 133.333
|  
|-
|-
| || || || 1\76 || ||
|  
| || 15.789 ||  
|  
| 4\33
|  
|  
|  
|  
|  
|  
|  
| 145.455
|  
|-
|-
| || || || 1\72 || || 
|  
| || 16.667 || [[Quadritikleismic]]
| 3\24
|  
|  
|  
|  
|  
|  
|  
|  
| 150.000
| [[Triforce]]/[[Augment]]
|-
|-
| || || || || 2\140 ||
|  
| || 17.143 || Quadritikleismic
|  
| 5\39
|  
|  
|  
|  
|  
|  
|  
| 153.846
| Triforce/Augment
|-
|-
| || || || 1\68 || ||
| 2\15
| || 17.647 || Quadritikleismic
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 160.000
| Triforce/Augment
|-
|-
| || || || 1\64 || ||
|  
| || 18.75 ||  
| 3\21
|  
|  
|  
|  
|  
|  
|  
|  
| 171.429
| [[Oodako]]/Augment
|-
|-
| || ||  || 1\60 || ||
|  
| || 20 ||  
|  
|-
|  
| ||  ||  || 1\56 ||  || 
| 7\48
| || 21.429 ||
|  
|  
|  
|  
|  
|  
| 175
| Oodako/Augment
|-
|-
| || || || 1\52 || ||
|  
| || 23.068 ||
|  
|  
|  
| 11\75
|  
|  
|  
|  
|  
| 176
| Oodako
|-
|-
| || || || 1\48 || ||
|  
| || 25 ||
|  
|  
|  
|  
| 15\102
|  
|  
|  
|  
| 176.471
| Oodako
|-
|-
| || || || 1\44 || ||
|  
| || 27.273 ||  
|  
|  
|  
|  
|  
| 19\129
|  
|  
|  
| 176.744
| Oodako
|-
|-
| ||  ||  || 1\40 || ||
|  
| || 30 ||  
|  
|-
| 4\27
| ||  ||  || 1\36 ||  || 
|  
| || 33.333 ||  
|  
|  
|  
|  
|  
|  
| 177.778
| Oodako
|-
|-
| || || || 1\32 || ||
| 1\6
| || 37.5 ||  
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 200.000
|  
|}
 
== Four periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator
! Cents
! Comments
|-
|-
| ||  ||  || 1\28 || ||
| 0\4
| || 42.857 ||  
|  
|  
|  
|  
|  
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\76
|2\52
|  
|
|  
|
| 15.789
|46.154
|  
|[[Hemidim]]
|-
|-
|
|  
|
|  
|
|  
|
| 1\72
|
|  
|3\76
|  
|
| 16.667
|47.368
| [[Quadritikleismic]]
|Hemidim
|-
|-
| || || 1\24 || ||  || 
|  
| || 50 || Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|  
|  
|  
|  
| 3\212
| 16.981
| Quadritikleismic
|-
|-
| || 1\20 || ||  ||  ||
|  
| || 60 ||
|  
|  
|  
| 2\140
|  
| 17.143
| Quadritikleismic
|-
|-
| 1\16 || || || ||  || 
|  
| || 75 ||
|  
|  
| 1\68
|  
|  
| 17.647
| Quadritikleismic
|-
|-
|
|  
|2\28
|  
|
|  
|
| 1\64
|
|  
|
|  
|
| 18.75
|85.714
|  
|[[Demolished]]
|-
|-
|
|  
|
|  
|3\40
|  
|
| 1\60
|
|  
|
|  
|
| 20
|90
|  
|Demolished
|-
|-
| 1\12 || || ||  ||  ||
|  
| || 100 || Demolished/[[Diminished]]
|  
|  
| ...
|  
|  
| ...
|  
|-
|-
|
|  
|
|  
|
|  
|14\164
| 1\36
|
|  
|
|  
|
| 33.333
|102.439
|  
|Diminished
|-
|-
|
|  
|
|  
|
|  
|
| 1\32
|27\316
|  
|
|  
|
| 37.5
|102.532
|  
|Diminished/[[Unlit]]
|-
|-
|
|  
|
|  
|
|  
|
| 1\28
|
|  
|40\468
|  
|
| 42.857
|102.564
|  
|Diminished/Unlit
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 2\52
|
|  
|53\620
| 46.154
|102.581
| [[Hemidim]]
|Diminished/Unlit
|-
|-
|
|  
|
|  
|
|  
|13\152
|  
|
|  
|
| 3\76
|
| 47.368
|102.632
| Hemidim
|Diminished/Unlit/[[Undim]]
|-
|-
|
|  
|
|  
|
| 1\24
|
|  
|
|  
|
|  
|51\596
| 50
|102.685
| Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|Diminished/Undim
|-
|-
|
|  
|
| 1\20
|
|  
|
|  
|
|  
|38\444
|  
|
| 60
|102.703
|  
|Diminished/Undim
|-
|-
|
| 1\16
|
|  
|
|  
|
|  
|25\292
|  
|
|  
|
| 75
|102.740
|  
|Diminished/Undim
|-
|-
|
|  
|
| 2\28
|
|  
|12\140
|  
|
|  
|
|  
|
| 85.714
|102.857
| [[Demolished]]
|Diminished/Undim
|-
|-
|
|  
|
|  
|
| 3\40
|11\128
|  
|
|  
|
|  
|
| 90
|103.125
| Demolished
|Diminished
|-
|-
|
| 1\12
|
|  
|
|  
|10\116
|  
|
|  
|
|  
|
| 100
|103.448
| Demolished/[[Diminished (temperament)|Diminished]]
|Diminished
|-
|-
|
|  
|
|  
|
|  
|9\104
| 14\164
|
|  
|
|  
|
| 102.439
|103.846
| Diminished
|Diminished
|-
|-
|
|  
|
|  
|
|  
|8\92
|  
|
| 27\316
|
|  
|
| 102.532
|104.348
| Diminished/[[Unlit]]
|Diminished
|-
|-
| || || || 7\80 ||  ||  
|  
| || 105 || Diminished/[[Bidia]]
|  
|  
|  
|  
| 40\468
| 102.564
| Diminished/Unlit
|-
|-
|
|  
|
|  
|
|  
|
| 13\152
|
|  
|20\228
|  
|
| 102.632
|105.263
| Diminished/Unlit/[[Undim]]
|Diminished/Bidia
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 38\444
|33\376
| 102.703
|105.319
| Diminished/Undim
|Diminished/Bidia
|-
|-
|
|  
|
|  
|
|  
|
|  
|13\148
| 25\292
|
|  
|
| 102.740
|105.405
| Diminished/Undim
|Diminished/Bidia
|-
|-
| || ||  || 6\68 ||  ||  
|  
| || 105.882 || Diminished/Bidia
|  
|  
| 12\140
|  
|  
| 102.857
| Diminished/Undim
|-
|-
| || ||  || 5\56 ||  ||  
|  
| || 107.143 || Diminished/Bidia
|  
|  
| 11\128
|  
|  
| 103.125
| Diminished
|-
|-
| || || 4\44 ||  ||  ||  
|  
| || 109.091 || Diminished
|  
|  
| 10\116
|  
|  
| 103.448
| Diminished
|-
|-
|  || 3\32 ||  ||  ||  ||
| || 112.5 || Diminished
|-
| 2\20 ||  ||  ||  ||  ||
| || 120 || Diminished
|-
| 1\8 ||  ||  ||  ||  ||
| || 150 ||
|}
==Five periods per octave==
{{todo|complete table|comment=add trisedodge (optimal ETs 15, 50, 65, 80, 340, 405) and countdown (15, 35, 50, 65, 210, 275, 340)}}
{| class="wikitable"
! colspan="9" |Generator!!Cents !!Comments
|-
|0\5 ||  || ||
|
|  
|  
|  
|  
|  
|  
| || 0||
| 9\104
|  
|  
| 103.846
| Diminished
|-
|-
|
|  
|
|  
|
|
|
| 8\92
|
|  
|1\140
|
|
| 104.348
|
| Diminished
|
|-
|8.571
|  
|
|  
|  
| 7\80
|  
|  
| 105
| Diminished/[[Bidia]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\135
| 20\228
|
| 105.263
|
| Diminished/Bidia
|
|8.889
|[[5th-octave temperaments#Slendrismic|Slendrismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 13\148
|
|  
|
| 105.405
|3\400
| Diminished/Bidia
|
|9
|Slendrismic
|-
|-
|
|  
|
|  
|
|  
|
| 6\68
|
|  
|
|  
|2\265
| 105.882
|
| Diminished/Bidia
|
|9.057
|Slendrismic
|-
|-
|
|  
|
|  
|
|  
|
| 5\56
|
|  
|1\130
|  
|
| 107.143
|
| Diminished/Bidia
|
|9.231
|Slendrismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
| 4\44
|
|  
|
|  
|
|  
|
| 109.091
|3\385
| Diminished
|
|9.351
|Hemipental
|-
|-
|
|  
|
| 3\32
|
|  
|
|  
|
|  
|
|  
|2\255
| 112.5
|
| Diminished
|
|9.412
|Hemipental
|-
|-
|
| 2\20
|
|  
|
|  
|
|  
|
|  
|1\125
|  
|
| 120
|
| Diminished
|
|9.6
|Hemipental
|-
|-
|
|  
|
| 3\28
|
|  
|
|  
|
|  
|1\120
|  
|
| 128.571
|
|  
|
|10
|
|-
|-
|
| 1\8
|
|  
|
|  
|
|  
|
|  
|1\115
|  
|
| 150
|
|  
|
|}
|10.435
 
|
== Five periods per octave ==
{{todo| complete table| comment=add trisedodge (optimal ETs 15, 50, 65, 80, 340, 405) and countdown (15, 35, 50, 65, 210, 275, 340)}}
{| class="wikitable sortable mw-collapsible"
! colspan="9" | Generator
! Cents
! Comments
|-
|-
|
| 0\5
|
|  
|
|  
|
|  
|
|  
|...
|  
|
|  
|
|  
|
|  
|...
| 0
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\70
| 1\140
|
|  
|
|  
|
|  
|17.143
| 8.571
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\65
| 1\135
|
|  
|
|  
|
|  
|18.462
| 8.889
|[[Pental]]
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\190
| 3\400
|
|  
|18.947
| 9
|Pental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\125
|  
|
|  
|
| 5\665
|19.2
| 9.023
|Pental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\265
|3\185
|  
|
|  
|19.459
| 9.057
|Pental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\60
| 1\130
|
|  
|
|  
|
|  
|20
| 9.231
|Pental
| Slendroschismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\55
|  
|
|  
|
|  
|
| 4\515
|21.818
| 9.32
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\50
|  
|
|  
|
| 3\385
|
|  
|24
| 9.351
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\45
|  
|
|  
|
|  
|
| 5\640
|26.67
| 9.375
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\40
|  
|
|  
|
| 2\255
|
|  
|
|  
|30
| 9.412
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|1\35
|  
|
|  
|
| 1\125
|
|  
|
|  
|
|  
|34.286
| 9.6
|
| Hemipental
|-
|-
|
|  
|
|  
|1\30
|  
|
|  
|
|  
|
| 1\120
|
|  
|
|  
|
|  
|40
| 10
|
|  
|-
|-
|
|  
|
|  
|
|  
|2\55
|  
|
|  
|
| 1\115
|
|  
|
|  
|
|  
|43.636
| 10.435
|
|  
|-
|-
|
|  
|1\25
|  
|
|  
|
|  
|
|  
|
| 1\70
|
|  
|
|  
|
|  
|48
| 17.143
|
|  
|-
|-
|
|  
|
|  
|
|  
|3\70
|  
|
|  
|
| 1\65
|
|  
|
|  
|
|  
|51.429
| 18.462
|
| [[Pental (temperament)| Pental]]
|-
|-
|
|  
|
|  
|2\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\255
|53.3
| 18.824
|
| Pental
|-
|-
|
|  
|
|  
|
|  
|3\65
|  
|
|  
|
|  
|
|  
|
| 3\190
|
|  
|55.385
| 18.947
|
| Pental
|-
|-
|1\20
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 5\315
|60
| 19.048
|
| Pental
|-
|-
|
|  
|
|  
|
|  
|4\75
|  
|
|  
|
|  
|
| 2\125
|
|  
|
|  
|64
| 19.2
|
| Pental
|-
|-
|
|  
|
|  
|3\55
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\185
|
|  
|65.455
| 19.459
|
| Pental
|-
|-
|
|  
|
|  
|
|  
|5\90
|  
|
|  
|
| 1\60
|
|  
|
|  
|
|  
|66.667
| 20
|
| Pental
|-
|-
|
|  
|2\35
|  
|
|  
|
|  
|
|  
|
| 1\55
|
|  
|
|  
|
|  
|68.571
| 21.818
|[[Coblack]]
|  
|-
|-
|
|  
|
|  
|
|  
|5\85
|  
|
|  
|
| 1\50
|
|  
|
|  
|
|  
|70.588
| 24
|Coblack
| [[Cloudtone]]
|-
|-
|
|  
|
|  
|3\50
|  
|
|  
|
|  
|
| 1\45
|
|  
|
|  
|
|  
|72
| 26.67
|Coblack
| Cloudtone
|-
|-
|
|  
|
|  
|
|  
|
|  
|7\115
| 1\40
|
|  
|
|  
|
|  
|
|  
|73.043
| 30
|Coblack
| Cloudtone
|-
|-
|
|  
|
|  
|
|  
|4\65
| 1\35
|
|  
|
|  
|
|  
|
|  
|
|  
|73.846
| 34.286
|Coblack
|  
|-
|-
| 1\15 ||  ||  ||
|
|  
|  
|  
|  
| 1\30
|
|
|
|
|
|
| 40
|  
|  
| || 80||[[Blackwood]]/[[Blacksmith]]
|-
|
|
|
|5\70
|
|
|
|
|
|85.714
|Blackwood/Blacksmith
|-
|-
|
|  
|
| 1\25
|4\55
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|87.273
| 48
|Blackwood/Blacksmith
|  
|-
|-
|
| 1\20
|
|  
|
|  
|7\95
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|88.421
| 60
|Blackwood/Blacksmith
|  
|-
|-
|
|  
|3\40
| 2\35
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|90
| 68.571
|Blackwood/Blacksmith
| [[Coblack]]
|-
|-
|
|  
|
|  
|
|  
|8\105
| 5\85
|
|  
|
|  
|
|  
|
|  
|
|  
|91.429
| 70.588
|Blackwood/Blacksmith
| Coblack
|-
|-
|
|  
|
|  
|5\65
| 3\50
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 72
|Blackwood/Blacksmith
| Coblack
|-
|-
|
|
|
|  
|
|  
|7\90
|  
|
| 7\115
|
|  
|
|  
|
|  
|
|  
|93.333
| 73.043
|Blackwood/Blacksmith
| Coblack
|-
|-
|2\25
|  
|
|  
|
|  
|
| 4\65
|
|  
|
|  
|
|  
|
|  
|
|  
|96
| 73.846
|Blackwood/Blacksmith
| Coblack
|-
|-
|
| 1\15
|
|  
|5\60
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|100
| 80
|Blackwood
| [[Blackwood]]
|-
|-
|
|  
|
|  
|
|  
|8\95
| 5\70
|
|  
|
|  
|
|  
|
|  
|
|  
|101.053
| 85.714
|Blackwood
| Blackwood
|-
|-
|
|  
|3\35
|  
|
| 4\55
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|102.857
| 87.273
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|7\80
| 7\95
|
|  
|
|  
|
|  
|
|  
|
|  
|105
| 88.421
|Blackwood
| Blackwood
|-
|-
|
|  
|
| 3\40
|4\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|106.667
| 90
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|5\55
| 8\105
|
|  
|
|  
|
|  
|
|  
|
|  
|109.091
| 91.429
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
| 5\65
|
|  
|6\65
|  
|
|  
|
|  
|
|  
|
|  
|110.769
| 92.308
|Blackwood/[[Quintosec]]/[[Sengasec]]
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 7\90
|
|  
|
|  
|
|  
|
|  
|25\270
|  
|
| 93.333
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
| Blackwood
|-
|-
|
| 2\25
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|19\205
|  
|
|  
|
| 96
|Blackwood/Quintosec/SengasecQintosec
| Blackwood
|-
|-
|
|  
|
|  
|
| 5\60
|
|  
|
|  
|
|  
|13\140
|  
|
|  
|
|  
|
| 100
|Blackwood/Quintosec/Sengasec/Qintosec
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 8\95
|
|  
|
|  
|
|  
|20\215
|  
|
|  
|
| 101.053
|Blackwood/Qintosec
| Blackwood
|-
|-
|
|  
|
| 3\35
|
|  
|
|  
|
|  
|7\75
|  
|
|  
|
|  
|
|  
|112
| 102.857
|Blackwood/[[Qinto]]
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 7\80
|
|  
|
|  
|
|  
|15\160
|  
|
|  
|
| 105
|Blackwood/Qinto
| Blackwood
|-
|-
|
|  
|
|  
|
| 4\45
|
|  
|
|  
|
|  
|8\85
|  
|
|  
|
|  
|112.941
| 106.667
|Blackwood/[[Phi as a Generator|Elderthing]]
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 5\55
|
|  
|
|  
|9\95
|  
|
|  
|
|  
|113.684
| 109.091
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 6\65
|
|  
|10\105
|  
|
|  
|
|  
|114.286
| 110.769
|Blackwood
| Blackwood/[[Quintosec]]/[[Sengasec]]
|-
|-
|1\10
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 25\270
|120
| 111.111
|Blackwood
| Blackwood/Quintosec/Sengasec/[[Qintosec]]
|}
 
==Six periods per octave ==
{| class="wikitable"
! colspan="7" |Generator!!Cents !!Comments
|-
|-
|0\6||  || ||  
|  
|
|  
|
|  
|||0||
|  
|-
|  
|
|  
|
|  
|
| 19\205
|1\288
|  
|
| 111.220
|
| Blackwood/Quintosec/SengasecQintosec
|
|4.167
|
|-
|-
|
|  
|
|  
|
|  
|1\282
|  
|
|  
|
|
|
| 13\140
|4.255
|  
|
|  
| 111.429
| Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
|
|  
|
|  
|
|  
|1\276
|  
|2\552
|  
|
|  
|
|  
|4.348
| 20\215
|[[Sextile]]
|
| 111.628
| Blackwood/Qintosec
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\822
| 7\75
|
|  
|4.380
|  
|Sextile
|  
| 112
| Blackwood/[[Qinto]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\1092
|  
|4.396
| 15\160
|Sextile
|
| 112.5
| Blackwood/Qinto
|-
|-
|
|  
|
|  
|
|  
|1\270
|  
|
|  
|
|
|
| 8\85
|4.444
|  
|Sextile
|  
| 112.941
| Blackwood/[[Phi as a Generator|Elderthing]]
|-
|-
|
|  
|
|  
|
|  
|1\264
|  
|
|  
|
|
|
| 9\95
|4.545
|  
|
|  
| 113.684
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|...
|  
|
|  
|
|
|
| 10\105
|...
|  
|
|  
| 114.286
| Blackwood
|-
|-
|
| 1\10
|
|
|
|
|1\90
|
|
|  
|
|  
|
|  
|13.333
|  
|
|  
| 120
| Blackwood
|}
 
== Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\6
|
|  
|
|  
|1\84
|  
|
|  
|
|  
|
|  
|14.286
| 0
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\78
| 1\288
|
|  
|
|  
|
|  
|15.385
| 4.167
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\72
| 1\282
|
|  
|
|  
|
|  
|16.667
| 4.255
|[[Stearnscape]]
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\276
|
| 2\552
|
|  
|4\282
|  
|17.021
| 4.348
|Stearnscape
| [[Sextile]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\210
| 3\822
|
|  
|17.143
| 4.380
|Stearnscape
| Sextile
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\138
|  
|
|  
|
| 4\1092
|17.391
| 4.396
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\66
| 1\270
|
|  
|
|  
|
|  
|18.182
| 4.444
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\60
| 1\264
|
|  
|
|  
|
|  
|20
| 4.545
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\54
| ...
|
|  
|
|  
|
|  
|22.222
| ...
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\48
| 1\90
|
|  
|
|  
|
|  
|25
| 13.333
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\42
| 1\84
|
|  
|
|  
|
|  
|28.571
| 14.286
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\36
| 1\78
|
|  
|
|  
|
|  
|33.333
| 15.385
|
|  
|-
|-
|
|
|
|  
|1\30
|  
|
| 1\72
|
|  
|
|  
|
|  
|40
| 16.667
|
| [[Stearnscape]]
|-
|-
|
|  
|
|  
|
|  
|2\54
|  
|
|  
|
|  
|
| 4\282
|44.444
| 17.021
|
| Stearnscape
|-
|-
|
|1\24
|
|
|
|
|
|50
|  
|  
|
|
|
|
| 3\210
|
| 17.143
| Stearnscape
|-
|-
|
|  
|
|  
|
|  
|3\66
|  
|
| 2\138
|
|  
|
|  
|54.545
| 17.391
|
|  
|-
|-
|
|  
|
|  
|2\42
|  
|
| 1\66
|
|  
|
|  
|
|  
| 57.143
| 18.182
|
|  
|-
|-
|
|  
|
|  
|
|  
|3\60
| 1\60
|
|  
|
|  
|
|  
|60
| 20
|
|  
|-
|-
|1\18
|  
|
|  
|
|  
|
| 1\54
|
|  
|
|  
|
|  
| 66.667
| 22.222
|
|  
|-
|-
|
|  
|
|  
|
|  
|4\66
| 1\48
|
|  
|
|  
|
|  
|72.727
| 25
|
|  
|-
|-
|
|  
|
|  
|3\48
|  
|
| 1\42
|
|  
|
|  
|
|  
| 75
| 28.571
|  
|  
|-
|-
|
|  
|
|  
|
|  
|5\78
| 1\36
|
|  
|
|  
|
|  
|76.923
| 33.333
|
|  
|-
|-
|
|  
|2\30
|  
|
| 1\30
|
|  
|
|  
|
|  
|
|  
| 80
| 40
|[[Hexe]]
|  
|-
|-
|
|  
|
| 1\24
|
|  
|5\72
|  
|
|  
|
|  
|
|  
|83.333
| 50
|Hexe
| [[Hemisemiaug]]
|-
|-
|
|
|
|
|3\42
|2\42
|
|
|
|
|
|
|
|
|85.714
|57.143
| Hexe
|Hemisemiaug
|-
|-
| 1\18
|
|
|
|
|
|
|4\54
|
|
|
|
|
|
|88.889
| 66.667
|Hexe
| Hemisemiaug
|-
|-
|1\12
|  
|
| 2\30
|
|  
|
|  
|
|  
|
|  
|
|  
| 100
| 80
|Hexe
| [[Hexe]]
|}
==Seven periods per octave==
{{todo|complete table|comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
{| class="wikitable"
! colspan="8" |Generator!! Cents!!Comments
|-
|-
| 0\7||  || ||
|  
|
|  
|
|  
|
| 5\72
| ||0||
|  
|  
|  
| 83.333
| Hexe
|-
|-
|
|  
|
|  
|
| 3\42
|
|  
|1\91
|  
|
|  
|
|  
|
| 85.714
|13.187
| Hexe
|
|-
|-
|
|  
|
|  
|
|  
|
| 4\54
|1\84
|  
|
|  
|
|  
|
| 88.889
|14.286
| Hexe
|[[Absurdity]]
|-
|-
|
| 1\12
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\329
| 100
|14.59
| Hexe
|Absurdity
|}
 
== Seven periods per octave ==
{{todo| complete table| comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\7
|
|  
|
|  
|
|  
|
|  
|
|  
|3\245
|  
|
|  
|14.69
| 0
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\91
|2\161
|  
|
|  
|
|  
|14.907
| 13.187
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\77
| 1\84
|
|  
|
|  
|
|  
|15.584
| 14.286
|[[Septant]]
| [[Absurdity]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\301
| 4\329
|15.947
| 14.59
|Septant
| Absurdity
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\224
| 3\245
|
|  
|16.071
| 14.69
|Septant
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\147
| 2\161
|
|  
|
|  
|16.327
| 14.907
|Septant
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\70
| 1\77
|
|  
|
|  
|
|  
|17.143
| 15.584
|
| [[Septant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\63
|  
|
|  
|
|  
|
| 4\301
|19.048
| 15.947
|[[Sevond]]
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\119
|  
|
| 3\224
|
|  
|20.168
| 16.071
|Sevond
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\56
|  
|
| 2\147
|
|  
|
|  
|21.429
| 16.327
|Sevond
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\48
| 1\70
|
|  
|
|  
|
|  
|25
| 17.143
|
|  
|-
|-
|
|
|
|  
|
|  
|1\42
|  
|
| 1\63
|
|  
|
|  
|
|  
|28.571
| 19.048
|[[Mistismic temperaments#Neutron|Neutron]]
| [[Sevond]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\119
| 2\119
|
|  
|
|  
|30.252
| 20.168
|Neutron
| Sevond
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\56
|
|  
|5\196
|  
|
|  
|30.612
| 21.429
|Neutron
| Sevond
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\49
|
|  
|
|  
|7\273
|  
|30.769
| 24.49
|Neutron
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\42
|2\77
|  
|
|  
|
|  
|
|  
|31.169
| 28.571
|Neutron
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|
|  
|
|  
|1\35
|  
|
|  
|
|  
|
| 3\119
|
|  
|
|  
|34.286
| 30.252
|[[Whitewood family#Redwood|Redwood]]
| Neutron
|-
|-
|
|  
|
|  
|
|  
| 2\63
|  
|
|  
|
|  
|
| 5\196
|
|  
|38.095
| 30.612
|Redwood
| Neutron
|-
|-
|
|  
| 1\28
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\273
|42.857
| 30.769
|Redwood/[[Whitewood]]
| Neutron
|-
|-
|
|  
|
|  
|
|  
| 3\77
|  
|
| 2\77
|
|  
|
|  
|
|  
| 46.753
| 31.169
|Whitewood
| Neutron
|-
|-
|
|  
|
|  
|2\49
| 1\35
|
|  
|
|  
|
|  
|
|  
|
|  
|48.980
| 34.286
|Whitewood
| [[Whitewood family#Redwood| Redwood]]
|-
|-
|
|  
|
|  
|
|  
|3\70
| 2\63
|
|  
|
|  
|
|  
|
|  
| 51.429
| 38.095
|Whitewood
| Redwood
|-
|-
|1\21
|
|
| 1\28
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|57.143
| 42.857
|Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| Redwood/[[Whitewood]]
|-
|-
|
|  
|
|  
|
|  
| 4\77
| 3\77
|
|  
|
|  
|
|  
|
|  
|62.338
| 46.753
|Jamesbond/Septimal
| Whitewood
|-
|-
|
|  
|
|  
|3\56
| 2\49
|
|  
|
|  
|
|  
|
|  
|
|  
|64.286
| 48.980
| Jamesbond/Septimal
| Whitewood
|-
|-
|
|  
|
|  
|
|  
|5\91
| 3\70
|
|  
|
|  
|
|  
|
|  
|65.934
| 51.429
|Jamesbond/Septimal
| Whitewood
|-
|-
|
| 1\21
|2\35
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 68.571
| 57.143
|Jamesbond/Septimal/[[Greenwood]]
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Austinpowers|Austinpowers]]
|-
|-
|
|  
|
|  
|
|  
|5\84
| 4\77
|
|  
|
|  
|
|  
|
|  
|71.429
| 62.338
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers
|-
|-
|
|  
|
|  
|3\49
| 3\56
|
|  
|
|  
|
|  
|
|  
|
|  
| 73.469
| 64.286
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers
|-
|-
|
|  
|
|  
|
|  
|4\63
| 5\91
|
|  
|
|  
|
|  
|
|  
|76.190
| 65.934
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers
|-
|-
| 1\14
|  
|
| 2\35
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|85.714
| 68.571
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/[[Greenwood]]
|}
 
==Eight periods per octave==
{{todo|complete table|comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable"
! colspan="9" |Generator!!Cents!!Comments
|-
|-
|0\8|| ||
|  
|
|  
|
|  
|
| 5\84
|
|  
|
|  
| ||0||
|  
|  
| 71.429
| Jamesbond/Austinpowers/Greenwood
|-
|-
|
|  
|
|  
|
| 3\49
|
|  
|
|  
|
|  
|1\80
|  
|
|  
|
| 73.469
|15
| Jamesbond/Austinpowers/Greenwood
|
|-
|-
|
|  
|
|  
|
|  
|
| 4\63
|
|  
|
|  
|
|  
|2\152
|  
|
| 76.190
|15.789
| Jamesbond/Austinpowers/Greenwood
|[[Octoid]]
|-
|-
|
| 1\14
|
|
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\224
| 85.714
|16.071
| Jamesbond/Austinpowers/Greenwood
|Octoid
|}
 
== Eight periods per octave ==
{{todo| complete table| comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\8
|
|  
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|  
|
| 0
|16.667
|  
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\64
| 1\480
|
|  
|
|  
|
|  
|
| 2.5
|18.75
|  
|
|-
|-
|
|
|
|  
|
|  
|1\56
|  
|
| 1\472
|
|  
|
|  
|
|  
|
| 2.542
|21.429
| [[Octium]]
|
|-
|-
|
|  
|
|  
|1\48
|  
|
|  
|
|  
|
|  
|
| 4\1872
|
|  
|
| 2.564
|25
| Octium
|
|-
|-
|
|  
| 1\40
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\3272
|
| 2.567
|30
| Octium
|
|-
|-
|
|  
|
|  
|2\72
|  
|
|  
|
|  
|
| 3\1400
|
|  
|
|  
|
| 2.571
|33.333
| Octium
|
|-
|-
|1\32
|  
|
|  
|
|  
|
|  
|
| 1\464
|
|  
|
|  
|
|  
|
| 2.586
|37.5
|  
|[[Semidim]]
|-
|-
|
|  
|
|  
|3\88
|  
|
|  
|
| …
|
|  
|
|  
|
|  
|
|  
|40.909
|  
|Semidim
|-
|-
|
|  
|2\56
|  
|
|  
|
|  
|
| 1\96
|
|  
|
|  
|
|  
|
| 12.5
|42.857
|  
|Semidim
|-
|-
|
|  
|
|  
|3\80
|  
|
|  
|
| 1\88
|
|  
|
|  
|
|  
|
| 13.635
|45
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|4\104
|  
|
| 1\80
|
|  
|
|  
|
|  
|
| 15
|46.154
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|5\128
|  
|
| 2\152
|
|  
|
|  
|
| 15.789
|46.875
| [[Octoid]]
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|6\152
|  
|
| 3\224
|
|  
|
| 16.071
|47.368
| Octoid
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\72
|
|  
|7\176
|  
|
|  
|
| 16.667
|47.727
| Octoid
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\64
|
|  
|8\200
|  
|
|  
|
| 18.75
|48
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
| 1\56
|
|  
|
|  
|9\224
|  
|
|  
|
| 21.429
|48.214
|  
|Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
| 1\48
|
|  
|
|  
|
|  
|
|  
|
|  
|28\696
| 25
|48.276
|  
|Semidim/Octant
|-
|-
|
|  
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|
|  
|19\472
|  
|
| 30
|48.305
|  
|Semidim/Octant
|-
|-
|
|  
|
|  
|
| 2\72
|
|  
|
|  
|
|  
|10\248
|  
|
|  
|
| 33.333
|48.387
|  
|Semidim
|-
|-
|1\24
| 1\32
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 37.5
|50
| [[Semidim]]
|Semidim
|-
|-
|
|  
|
|  
|4\88
| 3\88
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 40.909
|54.545
| Semidim
|
|-
|-
|
| 3\64
|
|
|
|
|
|
|
| 56.250
|  
|  
| 2\56
|
|
|
|
|
|
| 42.857
| Semidim
|-
|-
|
|  
|
|  
|5\104
| 3\80
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 45
|57.692
| Semidim
|
|-
|-
|2\40
|  
|
|  
|
|  
|
| 4\104
|
|  
|
|  
|
|  
|
|  
|
| 46.154
| 60
| Semidim
|
|-
|-
|
|  
|
|  
|5\96
|  
|
|  
|
| 5\128
|
|  
|
|  
|
|  
|
| 46.875
|62.5
| Semidim
|
|-
|-
|
|  
|3\56
|  
|
|  
|
|  
|
| 6\152
|
|  
|
|  
|
|  
|
| 47.368
|64.286
| Semidim
|
|-
|-
|
|  
|
|  
|4\72
|  
|
|  
|
|  
|
| 7\176
|
|  
|
|  
|
| 47.727
|66.667
| Semidim
|
|-
|-
|1\16
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\200
|
|  
|
|  
|
| 48
|75
| Semidim
|
|}
 
==Nine periods per octave ==
{| class="wikitable"
! colspan="8" |Generator!!Cents!! Comments
|-
|-
|0\9||  || ||
|  
|  
|
|  
|
|  
| ||0||
|  
|  
| 9\224
|  
|  
| 48.214
| Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|  
|
| 28\696
|16.667
| 48.276
|[[Enneaportent]]
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 19\472
|4\279
|  
|17.204
| 48.305
|Enneaportent
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 10\248
|3\207
|  
|
|  
|17.391
| 48.387
|Enneaportent
| Semidim
|-
|-
|
| 1\24
|
|  
|
|  
|
|  
|
|  
|2\135
|  
|
|  
|
|  
|17.778
| 50
|Enneaportent
| Semidim
|-
|-
|
| 2\40
|
|  
|
|  
|1\63
|  
|
|  
|
|  
|
|  
|
|  
|19.048
| 60
|Enneaportent
|  
|-
|-
|
| 1\16
|
|
|1\54
|
|
|  
|
|  
|
|  
|
|  
|
|  
|22.222
| 75
|
|  
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\9
|1\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|26.667
| 0
|
|  
|-
|-
|
|  
|
|  
|2\81
|  
|
|  
|
| 1\72
|
|  
|
|  
|
|  
|29.63
| 16.667
|
| [[Enneaportent]]
|-
|-
|1\36
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\279
|33.333
| 17.204
|[[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|4\135
|  
|
|  
|
|  
|
| 3\207
|
|  
|35.556
| 17.391
|No-five tritrizo
| Enneaportent
|-
|-
|
|  
|
|  
|3\99
|  
|
|  
|
|  
|
| 2\135
|
|  
|
|  
|36.364
| 17.778
|No-five tritrizo
| Enneaportent
|-
|-
|
|  
|2\63
|  
|
|  
|
| 1\63
|
|  
|
|  
|
|  
|
|  
|38.095
| 19.048
|[[Niner]]
| Enneaportent
|-
|-
|
|
|3\90
|  
|  
|
|  
|
| 1\54
|
|  
|
|  
|40
|  
|Niner
|  
|
| 22.222
|
|-
|-
|1\27
|
|
| 1\45
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 44.444
| 26.667
|Niner
|  
|-
|-
|
| 1\36
|
|  
|4\99
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|48.485
| 33.333
|[[Ennealimmal]]
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|-
|
|  
|
|  
|
|  
|7\171
| 4\135
|
|  
|
|  
|
|  
|
|  
|49.123
| 35.556
|Ennealimmal
| No-five tritrizo
|-
|-
|
|3\72
|  
|  
|
|  
|
| 3\99
|
|  
|
|  
|
|  
| 50
|  
|Ennealimmal
|  
| 36.364
| No-five tritrizo
|-
|-
|
|  
|
| 2\63
|
|  
|
|  
|
|  
|
|  
|
|  
|20\477
|  
|50.314
| 38.095
|[[Novemkleismic]]
| [[Niner]]
|-
|-
|
|  
|
|  
|
| 3\90
|
|  
|
|  
|
|  
|17\405
|  
|
|  
|50.370
| 40
|Novemkleismic
| Niner
|-
|-
|
| 1\27
|
|  
|
|  
|
|  
|
|  
|14\333
|  
|
|  
|
|  
|50.451
| 44.444
|Novemkleismic
| Niner
|-
|-
|
|  
|
|  
|
| 4\99
|
|  
|11\261
|  
|
|  
|
|  
|
|  
|50.575
| 48.485
|Novemkleismic
| [[Ennealimmal]]
|-
|-
|
|  
|
|  
|
|  
|8\189
| 7\171
|
|  
|
|  
|
|  
|
|  
|50.794
| 49.123
|Novemkleismic
| Ennealimmal
|-
|-
|
|  
|
| 3\72
|5\117
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|51.282
| 50
|
| Ennealimmal
|-
|-
|2\45
|
|
|
|
|
|
|
|53.333
|  
|  
|
|
|
|
|
|
| 20\477
| 50.314
| [[Novemkleismic]]
|-
|-
|
|  
|
|  
|5\108
|  
|
|  
|
|  
|
|  
|
| 17\405
|
|  
|55.556
| 50.370
|
| Novemkleismic
|-
|-
|
|  
|3\63
|  
|
|  
|
|  
|
|  
|
| 14\333
|
|  
|
|  
|57.143
| 50.451
|
| Novemkleismic
|-
|-
|
|
|4\81
|  
|  
|
|  
|
|  
|
|  
|
| 11\261
|59.259
|  
|
|
|
| 50.575
| Novemkleismic
|-
|-
|1\18
|  
|
|  
|
|  
|
| 8\189
|
|  
|
|  
|
|  
|
|  
| 66.667
| 50.794
|
| Novemkleismic
|}
 
==Twelve periods per octave==
See also: [[Compton family]]
 
{| class="wikitable"
! colspan="8" |Generator!!Cents!!Comments
|-
|-
|0\12||  || ||
|
|  
|  
|
|  
|||0||
| 5\117
|  
|  
|  
|
|
| 51.282
|  
|-
|-
| 2\45
|
|
|
|
|
|
|
| 53.333
|
|-
| 1\18
|
|
|
|
|
|
|
| 66.667
|
|}
== Ten periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
| 0\10
|
|
|
|
|
|
| 0
|
|-
|1\140
|
|
|
|
|1\636
|
|
|
|
|
|
|
|
|1.887
|
|
|8.571
|[[Decoid]]
|-
|-
|
|
|2\270
|
|
|
|
|1\624
|
|
|
|
|
|
|
|8.888
|1.923
|Decoid
|
|-
|-
|1\130
|
|
|
|
|
|
|
|
|2\1236
|
|
|
|
|
|9.231
|1.942
|Decoid
|[[Atomic]]
|-
|-
|1\120
|
|
|
|
Line 4,013: Line 4,010:
|
|
|
|
|3\1848
|
|
|10
|
|
|1.948
|Atomic
|-
|-
|
| 1\110
|
|  
|
|  
|
|  
|
|  
|
|  
|4\2460
|  
|
| 10.909
|1.951
|  
|Atomic
|-
|-
|
| 1\100
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\3072
| 12
|1.953
|  
|Atomic
|-
|-
|
|  
|
| 2\190
|
|  
|1\612
|  
|
|  
|
|  
|
|  
|
| 12.632
|1.961
| [[Deca]]
|Atomic
|-
|-
|
| 1\90
|
|  
|
|  
|1\600
|  
|
|  
|
|  
|
|  
|
| 13.333
|2
| Deca
|
|-
|-
|
| 1\80
|
|  
|
|  
|1\588
|  
|
|  
|
|  
|
|  
|
| 15
|2.041
| Deca
|
|-
|-
|
| 1\70
|
|  
|
|  
|1\576
|  
|
|  
|
|  
|
|  
|
| 17.143
|2.083
|  
|
|-
|-
|
| 1\60
|
|  
|
|  
|...
|  
|
|  
|
|  
|
|  
|
| 20
|...
|  
|
|-
|-
|
| 1\50
|
|  
|
|  
|1\108
|  
|
|  
|
|  
|
|  
|
| 24
|11.111
| [[Decimetra]]
|
|-
|-
|
|  
|
|  
|
|  
|1\96
| 4\190
|
|  
|
|  
|
|  
|
| 25.263
|12.5
| Decimetra
|
|-
|-
|
|  
|
|  
|
|  
|1\84
|  
|
| 7\330
|
|  
|
|  
|
| 25.455
|14.286
| Decimetra
|[[Compton]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\240
|  
|
| 17\800
|
| 25.5
|15
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 10\470
|
|  
|8\636
| 25.532
|15.094
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
| 3\140
|
|  
|
|  
|
|  
|5\396
|  
|
| 25.714
|15.152
| Decimetra
|Compton
|-
|-
|
|  
|
| 2\90
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
| 26.667
|15.217
| Decimetra
|Compton
|-
|-
|
| 1\40
|
|  
|
|  
|
|  
|2\156
|  
|
|  
|
|  
|
| 30
|15.385
| [[Decic]]
|Compton
|-
|-
|
|  
|
|  
|
| 3\110
|
|  
|
|  
|
|  
|
|  
|7\540
| 32.727
|15.556
| Decic
|Compton
|-
|-
|
|  
|
| 2\70
|
|  
|
|  
|
|  
|
|  
|5\384
|  
|
| 34.286
|15.625
| Decic
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 4\170
|
|  
|
|  
|
|  
|8\612
| 28.235
|15.686
| Decic
|Compton
|-
|-
|
|  
|
|  
|
| 3\100
|
|  
|
|  
|3\228
|  
|
|  
|
| 36
|15.789
| Decic
|Compton
|-
|-
|
| 1\30
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
| 40
|15.909
| Decic/[[Decal]]
|Compton
|-
|-
|
|  
|
| 3\80
|
|  
|
|  
|
|  
|
|  
|4\300
|  
|
| 45
|16
| Decal/[[Decistearn]]
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 8\210
|
|  
|
|  
|
|  
|5\372
| 45.714
|16.129
| Decal/Decistearn
|Compton
|-
|-
|
|  
|
|  
|
|  
|1\72
|  
|
| 13\340
|
|  
|
|  
|
| 45.882
|16.667
| Decal/Decistearn
|Compton
|-
|-
|
|  
|
|  
|1\60
|  
|
|  
|
|  
|
| 18\470
|
|  
|
| 45.957
|20
| Decal/Decistearn
|
|-
|-
|
|  
|
|  
|
|  
|2\108
|  
|
|  
|
|  
|
| 23\600
|
| 46
|22.222
| Decal/Decistearn
|
|-
|-
|
|  
|1\48
|  
|
| 5\130
|
|  
|
|  
|
|  
|
|  
|
| 46.154
|25
| Decal/Decistearn
|[[Catler]]
|-
|-
|
| 2\50
|
|  
|
|  
|3\132
|  
|
|  
|
|  
|
|  
|
| 48
| 27.273
| Decistearn/[[Decavish]]
|Catler
|-
|-
|
|  
|
|  
| 2\84
|  
|
|  
|
|  
|
| 11\270
|
|  
|
| 48.889
|28.571
| Decavish
|Catler
|-
|-
|
|  
|
|  
|
|  
|3\120
|  
|
| 9\220
|
|  
|
|  
|
| 49.091
|30
| Decavish
|Catler
|-
|-
|1\36
|  
|
|  
|
|  
|
| 7\170
|
|  
|
|  
|
|  
|
| 49.412
|33.333
| Decavish
|Catler/[[Catnip]]
|-
|-
|
|  
|
|  
|
| 5\120
|4\132
|  
|
|  
|
|  
|
|  
|
| 50
|36.364
| Decavish
|Catnip
|-
|-
|
|  
|
| 3\70
|3\96
|  
|
|  
|
|  
|
|  
|
|  
|
| 51.429
|37.5
| Decavish
| Catnip
|-
|-
|
|  
|
|  
|
| 4\90
|5\156
|  
|
|  
|
|  
|
|  
|
| 53.333
|38.462
|  
|Catnip
|-
|-
|
|  
|2\60
|  
|
|  
|
| 5\110
|
|  
|
|  
|
|  
|
| 54.545
|40
|  
|Catnip
|-
|-
|
|  
|
|  
|
|  
|5\144
|  
|
| 6\130
|
|  
|
|  
|
| 55.385
|41.667
|
|
|-
|-
|
| 1\20
|
|
|3\84
|  
|
|  
|
|  
|
|  
|
|  
|
| 60
| 42.857
|  
| [[Magnesium]]
|}
 
== Eleven periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\11
|
|
|
|  
|
|  
|
|  
|
|  
|
|  
|16\444
| 0
|43.243
|  
|Magnesium
|-
|
| 1\55
|
|
|
|
|
| 21.818
|
|-
| 1\44
|
|
|
|
|
|
| 27.273
|  
|-
|-
|
|
|
| 2\77
|
|
|
|
|
|
|
|
|13\360
|
|
| 31.169
|43.333
|
|Magnesium
|-
|-
| 1\33
|
|
|
|
|
|
|
|
|
|
|10\276
|
|
| 36.364
|
|
|43.378
|-
|
|
|-
| 3\88
|
|
|
|
|
|
|
|
|7\192
|
|
| 40.909
|
|
|
|-
|43.75
| 2\55
|
|
|-
|
|
|
|
|
|
|
|4\108
|
|
| 42.636
|
| [[Hendecatonic (temperament)|Hendecatonic]]
|
|-
|
|
|44.444
| 3\77
|
|
|-
|
|1\24
|
|
|
|
|
|
| 46.753
|
| Hendecatonic
|
|-
|
|
|
|
| 50
|
|
| 7\176
|
|
|
| 47.727
| Hendecatonic
|-
|
|
|
|
| 11\275
|
|
| 48
| Hendecatonic
|-
|
|
| 4\99
|
|
|
|
| 48.485
| Hendecatonic / [[cohendecatonic]]
|-
|
|
|
|
| 9\220
|
|
| 49.091
| Cohendecatonic
|-
|
|
|
|
|
| 14\341
|
| 49.267
| Cohendecatonic
|-
|
|
|
| 5\121
|
|
|
| 49.587
| Cohendecatonic
|-
|
|
|
|
| 6\143
|
|
| 50.350
|
|-
|
|
|
|
|
| 7\165
|
| 50.909
|
|-
|
|
|
|
|
|
| 8\187
| 51.337
| [[Undeka]]
|-
|
|
|
|
|
|
| 9\209
| 51.675
| Undeka
|-
|
|
|
|
|
|
| 10\231
| 51.948
| Undeka
|-
|
|
|
|
|
|
| 11\253
| 52.174
| Undeka
|-
| 1\22
|
|
|
|
|
|
| 54.545
| Undeka
|}
 
==Twelve periods per octave==
{{See also| Compton family}}
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
| 0\12
|
|
|
|
|
|
|
| 0
|
|-
|
|
|
| 1\636
|
|
|
|
| 1.887
|
|-
|
|
|
| 1\624
|
|
|
|
| 1.923
|
|-
|
|
|
|
| 2\1236
|
|
|
| 1.942
| [[Atomic]]
|-
|
|
|
|
|
| 3\1848
|
|
| 1.948
| Atomic
|-
|
|
|
|
|
|
| 4\2460
|
| 1.951
| Atomic
|-
|
|
|
|
|
|
|
| 5\3072
| 1.953
| Atomic
|-
|
|
|
| 1\612
|
|
|
|
| 1.961
| Atomic
|-
|
|
|
| 1\600
|
|
|
|
| 2
|
|-
|
|
|
| 1\588
|
|
|
|
| 2.041
|
|-
|
|
|
| 1\576
|
|
|
|
| 2.083
|
|-
|
|
|
| ...
|
|
|
|
| ...
|
|-
|
|
|
| 1\108
|
|
|
|
| 11.111
|
|-
|
|
|
| 1\96
|
|
|
|
| 12.5
| [[Compton]]
|-
|
|
|
| 1\84
|
|
|
|
| 14.286
| Compton
|-
|
|
|
|
|
| 3\240
|
|
| 15
| Compton
|-
|
|
|
|
|
|
|
| 8\636
| 15.094
| Compton
|-
|
|
|
|
|
|
| 5\396
|
| 15.152
| Compton
|-
|
|
|
|
|
|
|
| 7\552
| 15.217
| Compton
|-
|
|
|
|
| 2\156
|
|
|
| 15.385
| Compton
|-
|
|
|
|
|
|
|
| 7\540
| 15.556
| Compton
|-
|
|
|
|
|
|
| 5\384
|
| 15.625
| Compton
|-
|
|
|
|
|
|
|
| 8\612
| 15.686
| Compton
|-
|
|
|
|
|
| 3\228
|
|
| 15.789
| Compton
|-
|
|
|
|
|
|
|
| 7\528
| 15.909
| Compton
|-
|
|
|
|
|
|
| 4\300
|
| 16
| Compton
|-
|
|
|
|
|
|
|
| 5\372
| 16.129
| Compton
|-
|
|
|
| 1\72
|
|
|
|
| 16.667
| Compton
|-
|
|
| 1\60
|
|
|
|
|
| 20
| Compton
|-
|
|
|
| 2\108
|
|
|
|
| 22.222
|
|-
|
| 1\48
|
|
|
|
|
|
| 25
| [[Catler]]
|-
|
|
|
| 3\132
|
|
|
|
| 27.273
| Catler
|-
|
|
| 2\84
|
|
|
|
|
| 28.571
| Catler
|-
|
|
|
| 3\120
|
|
|
|
| 30
| Catler
|-
| 1\36
|
|
|
|
|
|
|
| 33.333
| Catler/[[Catnip]]
|-
|
|
|
| 4\132
|
|
|
|
| 36.364
| Catnip
|-
|
|
| 3\96
|
|
|
|
|
| 37.5
| Catnip
|-
|
|
|
| 5\156
|
|
|
|
| 38.462
| Catnip
|-
|
| 2\60
|
|
|
|
|
|
| 40
| Catnip
|-
|
|
|
| 5\144
|
|
|
|
| 41.667
|
|-
|
|
| 3\84
|
|
|
|
|
| 42.857
| [[Magnesium]]
|-
|
|
|
|
|
|
|
| 16\444
| 43.243
| Magnesium
|-
|  
|  
|  
|  
|  
|  
| 13\360
|  
| 43.333
| Magnesium
|-
|  
|  
|  
|  
|  
| 10\276
|  
|  
| 43.378
|  
|-
|  
|  
|  
|  
| 7\192
|  
|  
|  
| 43.75
|  
|-
|  
|  
|  
| 4\108
|  
|  
|  
|  
| 44.444
|  
|-
| 1\24
|  
|  
|  
|  
|  
|  
|  
| 50
|  
|}
|}


== See also ==
== See also ==
 
* [[Fractional-octave temperaments]] – lists dozens more temperaments beyond what can be listed here.
*[[Fractional-octave temperaments]]: Lists dozens more temperaments that have not yet been listed here.


[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Lists of temperaments]]
[[Category:Lists of temperaments]]
Retrieved from "https://en.xen.wiki/w/Map_of_rank-2_temperaments"