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


==Two periods per octave==
== Two periods per octave ==
 
{| class="wikitable sortable mw-collapsible"
{| class="wikitable"
|-
|-
! 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
| 1\20
| |  
|  
| |  
|  
| |  
|  
| | 60.000
| 60.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\18
| 1\18
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 66.667
| 66.667
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 2\34
| 2\34
| |  
|  
| |  
|  
| |  
|  
| | 70.588
| 70.588
| | [[Vishnu|Vishnu]]
| [[Vishnu]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 7\118
| 7\118
| | 71.186
| 71.186
| | Vishnu
| Vishnu
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\84
| 5\84
| |  
|  
| | 71.429
| 71.429
| | Vishnu
| Vishnu
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\50
| 3\50
| |  
|  
| |  
|  
| | 72.000
| 72.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 1\16
| 1\16
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 75.000
| 75.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 2\30
| 2\30
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 80.000
| 80.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\44
| 3\44
| |  
|  
| |  
|  
| |  
|  
| | 81.818
| 81.818
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 4\58
| 4\58
| |  
|  
| |  
|  
| | 82.759
| 82.759
| | [[Harry|Harry]]
| [[Harry]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|9\130
| 9\130
|83.077
| 83.077
|Harry
| Harry
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\72
| 5\72
| |  
|  
| | 83.333
| 83.333
| | Harry
| Harry
|-
|-
| |  
|  
| |  
|  
| | 1\14
| 1\14
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 85.714
| 85.714
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 2\26
| 2\26
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 92.308
| 92.308
| | [[Injera|Injera]]
| [[Injera]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\38
| 3\38
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 94.737
| 94.737
| | Injera
| Injera
|-
|-
| |  
|  
| | 1\12
| 1\12
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 100.000
| 100.000
| | Injera/[[Diaschismic]]
| Injera/[[Diaschismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|5\58
| 5\58
|
|  
|
|  
|
|  
|103.448
| 103.448
|Diaschismic
| Diaschismic
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 4\46
| 4\46
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 104.348
| 104.348
| | Diaschismic/[[Srutal]]
| Diaschismic/[[Srutal]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|7\80
| 7\80
|
|  
|
|  
|
|  
|105.000
| 105.000
|Srutal
| Srutal
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 3\34
| 3\34
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 105.882
| 105.882
| | Srutal/[[Pajara]]
| Srutal/[[Pajara]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|5\56
| 5\56
|
|  
|
|  
|
|  
|
|  
|107.143
| 107.143
|Pajara
| Pajara
|-
|-
| |  
|  
| |  
|  
| | 2\22
| 2\22
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 109.091
| 109.091
| | Pajara
| Pajara
|-
|-
|
|  
|
|  
|
|  
|3\32
| 3\32
|
|  
|
|  
|
|  
|
|  
|
|  
|112.500
| 112.500
|
|  
|-
|-
| | 1\10
| 1\10
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 120.000
| 120.000
| | [[Octokaidecal]]
| [[Octokaidecal]]
|-
|-
|
|  
|
|  
|3\28
| 3\28
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|128.571
| 128.571
|Octokaidecal
| Octokaidecal
|-
|-
| |  
|  
| | 2\18
| 2\18
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 133.333
| 133.333
| | Octokaidecal
| Octokaidecal
|-
|-
| |  
|  
| |  
|  
| | 3\26
| 3\26
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 138.462
| 138.462
| |  
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|6\60
| 6\60
|
|  
|
|  
|
|  
|
|  
|140.000
| 140.000
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|11\94
| 11\94
|
|  
|
|  
|
|  
|140.126
| 140.126
|Fifive
| Fifive
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|15\128
| 15\128
|
|  
|
|  
|140.625
| 140.625
|Fifive
| Fifive
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 4\34
| 4\34
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 141.176
| 141.176
| | [[Fifive|Fifive]]
| [[Fifive]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|5\42
| 5\42
|
|  
|
|  
|
|  
|
|  
|142.857
| 142.857
|
|  
|-
|-
| | 1\8
| 1\8
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 150.000
| 150.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 4\30
| 4\30
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 160.000
| 160.000
| |  
|  
|-
|-
| |  
|  
| | 3\22
| 3\22
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 163.636
| 163.636
| | [[Hedgehog|Hedgehog]]/[[Echidna]]
| [[Hedgehog]]/[[Echidna]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\80
| 11\80
|
|  
|
|  
|
|  
|
|  
|165.000
| 165.000
|Hedgehog/Echidna
| Hedgehog/Echidna
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 8\58
| 8\58
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 165.517
| 165.517
| | Hedgehog/Echidna
| Hedgehog/Echidna
|-
|-
| |  
|  
| |  
|  
| | 5\36
| 5\36
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 166.667
| 166.667
| |  
|  
|-
|-
| | 2\14
| 2\14
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 171.429
| 171.429
| |  
|  
|-
|-
| |  
|  
| | 3\20
| 3\20
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 180.000
| 180.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 7\46
| 7\46
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 182.609
| 182.609
| | [[Unidec|Unidec]]/[[Hendec]]
| [[Unidec]]/[[Hendec]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 11\72
| 11\72
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 183.333
| 183.333
| | Unidec/Hendec
| Unidec/Hendec
|-
|-
| |  
|  
| |  
|  
| | 4\26
| 4\26
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 184.615
| 184.615
| | Unidec/Hendec
| Unidec/Hendec
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 5\32
| 5\32
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 187.500
| 187.500
| |  
|  
|-
|-
| | 1\6
| 1\6
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 200.000
| 200.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 6\34
| 6\34
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 211.765
| 211.765
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 5\28
| 5\28
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 214.286
| 214.286
| | [[Antikythera]]
| [[Antikythera]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 9\50
| 9\50
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 216.000
| 216.000
| | Antikythera/[[Wizard]]
| Antikythera/[[Wizard]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 13\72
| 13\72
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 216.667
| 216.667
| | Antikythera/Wizard
| Antikythera/Wizard
|-
|-
| |  
|  
| | 4\22
| 4\22
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 218.182
| 218.182
| | Antikythera/Wizard/[[Astrology]]
| Antikythera/Wizard/[[Astrology]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|15\82
| 15\82
|
|  
|
|  
|
|  
|
|  
|219.512
| 219.512
|Astrology
| Astrology
|-
|-
|
|  
|
|  
|
|  
|11\60
| 11\60
|
|  
|
|  
|
|  
|
|  
|
|  
|220.000
| 220.000
|Astrology
| Astrology
|-
|-
|
|  
|
|  
|7\38
| 7\38
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|221.053
| 221.053
|
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 225.000
| 225.000
| | [[Lemba]]
| [[Lemba]]
|-
|-
| |  
|  
| | 5\26
| 5\26
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 230.769
| 230.769
| | Lemba
| Lemba
|-
|-
|
|  
|
|  
|
|  
|12\62
| 12\62
|
|  
|
|  
|
|  
|
|  
|
|  
|232.258
| 232.258
|Lemba
| Lemba
|-
|-
| |  
|  
| |  
|  
| | 7\36
| 7\36
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 233.333
| 233.333
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 9\46
| 9\46
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 234.783
| 234.783
| | [[Echidnic|Echidnic]]
| [[Echidnic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|29\148
| 29\148
|
|  
|
|  
|235.135
| 235.135
|Echidnic
| Echidnic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|20\102
| 20\102
|
|  
|
|  
|
|  
|235.294
| 235.294
|Echidnic
| Echidnic
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\56
| 11\56
|
|  
|
|  
|
|  
|
|  
|235.714
| 235.714
|
|  
|-
|-
| | 2\10
| 2\10
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 240.000
| 240.000
| | [[Decimal|Decimal]]
| [[Decimal]]
|-
|-
| |  
|  
| | 5\24
| 5\24
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 250.000
| 250.000
| | Decimal
| Decimal
|-
|-
|
|  
|
|  
|8\38
| 8\38
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|252.632
| 252.632
|Decimal
| Decimal
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 257.143
| 257.143
| | Decimal
| Decimal
|-
|-
| |  
|  
| | 4\18
| 4\18
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 266.667
| 266.667
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 5\22
| 5\22
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 272.727
| 272.727
| | [[Doublewide|Doublewide]]
| [[Doublewide]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|16\70
| 16\70
|
|  
|
|  
|
|  
|274.286
| 274.286
|Doublewide
| Doublewide
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 11\48
| 11\48
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 275.000
| 275.000
| | Doublewide
| Doublewide
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 6\26
| 6\26
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 276.923
| 276.923
| |  
|  
|-
|-
| | 1\4
| 1\4
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 300.000
| 300.000
| |  
|  
|}
|}


==Three periods per octave==
== Three periods per octave ==
{{todo|complete table|comment=Add hemisemiaug (optimal ETs 18, 24, 42), add landscape microtemperaments}}
{{todo| complete table| comment=Add hemisemiaug (optimal ETs 18, 24, 42), add landscape microtemperaments}}
{| class="wikitable"
{| class="wikitable sortable mw-collapsible"
|-
|-
! colspan="10" | Generator
! colspan="10" | Generator
! | Cents
! Cents
! | Comments
! Comments
|-
|-
| | 0\3
| 0\3
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 0.000
| 0.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\30
| 1\30
|
|  
|
|  
|
|  
| | 40.000
| 40.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\27
| 1\27
| |  
|  
|
|  
|
|  
|
|  
| | 44.444
| 44.444
| | [[Semiaug|Semiaug]]
| [[Semiaug]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 2\51
| 2\51
|
|  
|
|  
|
|  
| | 47.059
| 47.059
| | Semiaug
| Semiaug
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\24
| 1\24
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 50.000
| 50.000
| | Semiaug/[[Augmented family#Hemiug|Hemiug]]
| Semiaug/[[Augmented family#Hemiug| Hemiug]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\45
| 2\45
|
|  
|
|  
|
|  
|
|  
|53.333
| 53.333
|Hemiug
| Hemiug
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 1\21
| 1\21
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 57.143
| 57.143
| | Hemiug
| Hemiug
|-
|-
| |  
|  
| |  
|  
| | 1\18
| 1\18
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 66.667
| 66.667
| |  
|  
|-
|-
| |  
|  
| | 1\15
| 1\15
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 80.000
| 80.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 6\87
| 6\87
|
|  
|
|  
|
|  
| | 82.759
| 82.759
| |  
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|11\159
| 11\159
|
|  
|
|  
|83.019
| 83.019
|[[Tritikleismic]]
| [[Tritikleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|16\231
| 16\231
|
|  
|83.117
| 83.117
|Tritikleismic
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\72
| 5\72
| |  
|  
|
|  
|
|  
|
|  
| | 83.333
| 83.333
| | Tritikleismic
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 4\57
| 4\57
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 84.211
| 84.211
| | Tritikleismic
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 3\42
| 3\42
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 85.714
| 85.714
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 2\27
| 2\27
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 88.889
| 88.889
| |[[Augmented]]/[[Augene]]
| | [[Augmented]]/[[Augene]]
|-
|-
|
|  
|
|  
|
|  
|3\39
| 3\39
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 92.308
|Augmented/Augene/[[Fog]]
| Augmented/Augene/[[Fog]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|4\51
| 4\51
|
|  
|
|  
|
|  
|
|  
|
|  
|94.118
| 94.118
|Augmented/Augene/Fog
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|5\63
| 5\63
|
|  
|
|  
|
|  
|
|  
|95.238
| 95.238
|Augmented/Augene/Fog
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|11\138
| 11\138
|
|  
|
|  
|95.652
| 95.652
|Augmented Augene/Fog
| Augmented Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|6\75
| 6\75
|
|  
|
|  
|
|  
|96
| 96
|Augmented/Augene/Fog
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\87
| 7\87
|
|  
|
|  
|96.552
| 96.552
|Augmented/Augene/[[Misty]]
| Augmented/Augene/[[Misty]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|15\186
| 15\186
|96.774
| 96.774
|Augmented/Augene/Misty
| Augmented/Augene/Misty
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\99
| 8\99
|
|  
|96.97
| 96.97
|Augmented/Augene/Misty
| Augmented/Augene/Misty
|-
|-
| | 1\12
| 1\12
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 100.000
| 100.000
| | Augmented/Augene/[[August]]
| Augmented/Augene/[[August]]
|-
|-
| |  
|  
| |  
|  
| | 3\33
| 3\33
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 109.091
| 109.091
| | August
| August
|-
|-
| |  
|  
| | 2\21
| 2\21
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 114.286
| 114.286
| | August
| August
|-
|-
| |  
|  
| |  
|  
| | 3\30
| 3\30
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 120.000
| 120.000
| |  
|  
|-
|-
| | 1\9
| 1\9
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 133.333
| 133.333
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 4\33
| 4\33
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 145.455
| 145.455
| |  
|  
|-
|-
| |  
|  
| | 3\24
| 3\24
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 150.000
| 150.000
| |[[Triforce]]
| [[Triforce]]
|-
|-
|
|  
|
|  
|5\39
| 5\39
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|153.846
| 153.846
|Triforce
| Triforce
|-
|-
| | 2\15
| 2\15
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 160.000
| 160.000
| | Triforce
| Triforce
|-
|-
| |  
|  
| | 3\21
| 3\21
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 171.429
| 171.429
| |[[Oodako]]
| [[Oodako]]
|-
|-
|
|  
|
|  
|
|  
|7\48
| 7\48
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|175
| 175
|Oodako
| Oodako
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\75
| 11\75
|
|  
|
|  
|
|  
|
|  
|
|  
|176
| 176
|Oodako
| Oodako
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|15\102
| 15\102
|
|  
|
|  
|
|  
|
|  
|176.471
| 176.471
|Oodako
| Oodako
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|19\129
| 19\129
|
|  
|
|  
|
|  
|176.744
| 176.744
|Oodako
| Oodako
|-
|-
|
|  
|
|  
|4\27
| 4\27
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|177.778
| 177.778
|Oodako
| Oodako
|-
|-
| | 1\6
| 1\6
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 200.000
| 200.000
| |  
|  
|}
|}


==Four periods per octave==
== Four periods per octave ==
{| class="wikitable"
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator !! Cents !! Comments
! colspan="6" | Generator
! Cents
! Comments
|-
|-
| 0\4 || || ||  ||  ||  || 0 ||  
| 0\4
|  
|  
|  
|  
|  
| 0
|  
|-
|-
| || ||  || 1\76 || ||  || 15.789 ||  
|  
|  
|  
| 1\76
|  
|  
| 15.789
|  
|-
|-
| || ||  || 1\72 || ||  || 16.667 || [[Quadritikleismic]]
|  
|  
|  
| 1\72
|  
|  
| 16.667
| [[Quadritikleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\212
| 3\212
|16.981
| 16.981
|Quadritikleismic
| Quadritikleismic
|-
|-
| || ||  ||  || 2\140 ||  || 17.143 || Quadritikleismic
|  
|  
|  
|  
| 2\140  
|  
| 17.143  
| Quadritikleismic
|-
|-
| || ||  || 1\68 || ||  || 17.647 || Quadritikleismic
|  
|  
|  
| 1\68  
|  
|  
| 17.647  
| Quadritikleismic
|-
|-
| || ||  || 1\64 || ||  || 18.75 ||  
|  
|  
|  
| 1\64  
|  
|  
| 18.75  
|  
|-
|-
| || ||  || 1\60 || ||  || 20 ||  
|  
|  
|  
| 1\60  
|  
|  
| 20  
|  
|-
|-
| || || || 1\56 ||  ||  || 21.429 ||  
|  
|  
|  
| ...
|  
|  
| ...
|  
|-
|-
| || ||  || 1\52 || ||  || 23.068 ||  
|  
|  
|  
| 1\36
|  
|  
| 33.333
|  
|-
|-
| || ||  || 1\48 ||  ||  || 25 ||  
|  
|  
|  
| 1\32
|  
|  
| 37.5
|  
|-
|-
| || ||  || 1\44 || ||  || 27.273 ||  
|  
|  
|  
| 1\28
|  
|  
| 42.857
|  
|-
|-
| || || || 1\40 ||  ||  || 30 ||  
|  
|  
|  
|  
| 2\52
|  
| 46.154
| [[Hemidim]]
|-
|-
| || || || 1\36 ||  ||  || 33.333 ||  
|  
|  
|  
|  
|  
| 3\76
| 47.368
| Hemidim
|-
|-
| ||  ||  || 1\32 ||  || || 37.5 ||  
|  
|  
| 1\24
|  
|  
|  
| 50
| Hemidim/[[4th-octave temperaments#Darian calendar| Darian calendar]]
|-
|-
| ||  ||  || 1\28 ||  || || 42.857 ||  
|  
| 1\20
|  
|  
|  
|  
| 60
|  
|-
|-
|
| 1\16
|
|  
|
|  
|
|  
|2\52
|  
|
|  
|46.154
| 75
|[[Hemidim]]
|  
|-
|-
|
|  
|
| 2\28
|
|  
|
|  
|
|  
|3\76
|  
|47.368
| 85.714
|Hemidim
| [[Demolished]]
|-
|-
| || || 1\24 ||  ||  ||  || 50 || Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|  
|  
| 3\40
|  
|  
|  
| 90
| Demolished
|-
|-
|  || 1\20 ||  ||  || || || 60 ||  
| 1\12
|  
|  
|  
|  
|  
| 100
| Demolished/[[Diminished]]
|-
|-
| 1\16 || || ||  ||  ||  || 75 ||  
|  
|  
|  
| 14\164
|  
|  
| 102.439
| Diminished
|-
|-
|
|  
|2\28
|  
|
|  
|
|  
|
| 27\316
|
|  
|85.714
| 102.532
|[[Demolished]]
| Diminished/[[Unlit]]
|-
|-
|
|  
|
|  
|3\40
|  
|
|  
|
|  
|
| 40\468
|90
| 102.564
|Demolished
| Diminished/Unlit
|-
|-
| 1\12 || || || ||  ||  || 100 || Demolished/[[Diminished]]
|  
|  
|  
| 13\152
|  
|  
| 102.632
| Diminished/Unlit/[[Undim]]
|-
|-
|
|  
|
|  
|
|  
|14\164
|  
|
|  
|
| 38\444
|102.439
| 102.703
|Diminished
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|
|  
|27\316
| 25\292
|
|  
|102.532
| 102.740
|Diminished/[[Unlit]]
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|
| 12\140
|
|  
|40\468
|  
|102.564
| 102.857
|Diminished/Unlit
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|13\152
| 11\128
|
|  
|
|  
|102.632
| 103.125
|Diminished/Unlit/[[Undim]]
| Diminished
|-
|-
|
|  
|
|  
|
|  
|
| 10\116
|
|  
|38\444
|  
|102.703
| 103.448
|Diminished/Undim
| Diminished
|-
|-
|
|  
|
|  
|
|  
|
| 9\104
|25\292
|  
|
|  
|102.740
| 103.846
|Diminished/Undim
| Diminished
|-
|-
|
|  
|
|  
|
|  
|12\140
| 8\92
|
|  
|
|  
|102.857
| 104.348
|Diminished/Undim
| Diminished
|-
|-
|
|  
|
|  
|
|  
|11\128
| 7\80
|
|  
|
|  
|103.125
| 105
|Diminished
| Diminished/[[Bidia]]
|-
|-
|
|  
|
|  
|
|  
|10\116
|  
|
|  
|
| 20\228
|103.448
| 105.263
|Diminished
| Diminished/Bidia
|-
|-
|
|  
|
|  
|
|  
|9\104
|  
|
| 13\148
|
|  
|103.846
| 105.405
|Diminished
| Diminished/Bidia
|-
|-
|
|  
|
|  
|
|  
|8\92
| 6\68
|
|  
|
|  
|104.348
| 105.882
|Diminished
| Diminished/Bidia
|-
|-
| || ||  || 7\80 ||  ||  || 105 || Diminished/[[Bidia]]
|  
|  
|  
| 5\56
|  
|  
| 107.143
| Diminished/Bidia
|-
|-
|
|  
|
|  
|
| 4\44
|
|  
|
|  
|20\228
|  
|105.263
| 109.091
|Diminished/Bidia
| Diminished
|-
|-
|
|  
|
| 3\32
|
|  
|
|  
|13\148
|  
|
|  
|105.405
| 112.5
|Diminished/Bidia
| Diminished
|-
|-
| ||  ||  || 6\68 || || || 105.882 || Diminished/Bidia
| 2\20
|  
|  
|  
|  
|  
| 120
| Diminished
|-
|-
| ||  ||  || 5\56 || || || 107.143 || Diminished/Bidia
|  
| 3\28
|  
|  
|  
|  
| 128.571
|  
|-
|-
| ||  || 4\44 ||  ||  ||  || 109.091 || Diminished
| 1\8
|-
|  
| || 3\32 ||  ||  ||  ||  || 112.5 || Diminished
|  
|-
|  
| 2\20 ||  ||  ||  ||  ||  || 120 || Diminished
|  
|-
|  
| 1\8 ||  ||  ||  ||  ||  || 150 ||  
| 150  
|  
|}
|}


==Five periods per octave==
== 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)}}
{{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"
{| class="wikitable sortable mw-collapsible"
! colspan="9" |Generator!!Cents !!Comments
! colspan="9" | Generator
! Cents
! Comments
|-
|-
|0\5 ||  || ||
| 0\5  
|
|  
|  
|  
|  
|  
|  
| || 0||
|  
|  
|
|
|
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\140
| 1\140
|
|  
|
|  
|
|  
|8.571
| 8.571
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\135
| 1\135
|
|  
|
|  
|
|  
|8.889
| 8.889
|[[5th-octave temperaments#Slendrismic|Slendrismic]]
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\400
| 3\400
|
|  
|9
| 9
|Slendrismic
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\665
| 5\665
|9.023
| 9.023
|Slendrismic
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\265
| 2\265
|
|  
|
|  
|9.057
| 9.057
|Slendrismic
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\130
| 1\130
|
|  
|
|  
|
|  
|9.231
| 9.231
|Slendrismic/[[Hemipental]]
| Slendroschismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\515
| 4\515
|9.32
| 9.32
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\385
| 3\385
|
|  
|9.351
| 9.351
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\640
| 5\640
|9.375
| 9.375
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\255
| 2\255
|
|  
|
|  
|9.412
| 9.412
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\125
| 1\125
|
|  
|
|  
|
|  
|9.6
| 9.6
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\120
| 1\120
|
|  
|
|  
|
|  
|10
| 10
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\115
| 1\115
|
|  
|
|  
|
|  
|10.435
| 10.435
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|...
| 1\70
|
|  
|
|  
|
|  
|...
| 17.143
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\70
| 1\65
|
|  
|
|  
|
|  
|17.143
| 18.462
|
| [[Pental (temperament)| Pental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\65
|  
|
|  
|
|  
|
| 4\255
|18.462
| 18.824
|[[Pental]]
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\190
|4\255
|  
|18.824
| 18.947
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\190
|  
|
| 5\315
|18.947
| 19.048
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\125
|
|  
|5\315
|  
|19.048
| 19.2
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\125
|  
|
| 3\185
|
|  
|19.2
| 19.459
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\60
|
|  
|3\185
|  
|
|  
|19.459
| 20
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\60
| 1\55
|
|  
|
|  
|
|  
|20
| 21.818
|Pental
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\55
| 1\50
|
|  
|
|  
|
|  
|21.818
| 24
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\50
| 1\45
|
|  
|
|  
|
|  
|24
| 26.67
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\40
|1\45
|  
|
|  
|
|  
|
|  
|26.67
| 30
|
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\35
|1\40
|  
|
|  
|
|  
|
|  
|
|  
|30
| 34.286
|
|  
|-
|-
|
|  
|
|  
|
| 1\30
|1\35
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|34.286
| 40
|
|  
|-
|-
|
|  
|
| 1\25
|1\30
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|40
| 48
|
|  
|-
|-
|
| 1\20
|
|  
|
|  
|2\55
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|43.636
| 60
|
|  
|-
|-
|
|  
|1\25
| 2\35
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|48
| 68.571
|
| [[Coblack]]
|-
|-
|
|  
|
|  
|
|  
|3\70
| 5\85
|
|  
|
|  
|
|  
|
|  
|
|  
|51.429
| 70.588
|
| Coblack
|-
|-
|
|  
|
|  
|2\45
| 3\50
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|53.3
| 72
|
| Coblack
|-
|-
|
|  
|
|  
|
|  
|3\65
|  
|
| 7\115
|
|  
|
|  
|
|  
|
|  
|55.385
| 73.043
|
| Coblack
|-
|-
|1\20
|  
|
|  
|
|  
|
| 4\65
|
|  
|
|  
|
|  
|
|  
|
|  
|60
| 73.846
|
| Coblack
|-
|-
|
| 1\15
|
|  
|
|  
|4\75
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|64
| 80
|
| [[Blackwood]]/[[Blacksmith]]
|-
|-
|
|  
|
|  
|3\55
|  
|
| 5\70
|
|  
|
|  
|
|  
|
|  
|
|  
|65.455
| 85.714
|
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
| 4\55
|5\90
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|66.667
| 87.273
|
| Blackwood/Blacksmith
|-
|-
|
|  
|2\35
|  
|
|  
|
| 7\95
|
|  
|
|  
|
|  
|
|  
|
|  
|68.571
| 88.421
|[[Coblack]]
| Blackwood/Blacksmith
|-
|-
|
|  
|
| 3\40
|
|  
|5\85
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|70.588
| 90
|Coblack
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|3\50
|  
|
| 8\105
|
|  
|
|  
|
|  
|
|  
|
|  
|72
| 91.429
|Coblack
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
| 5\65
|
|  
|7\115
|  
|
|  
|
|  
|
|  
|
|  
|73.043
| 92.308
|Coblack
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
|  
|4\65
| 7\90
|
|  
|
|  
|
|  
|
|  
|
|  
|73.846
| 93.333
|Coblack
| Blackwood/Blacksmith
|-
|-
| 1\15 || ||  ||
| 2\25
|
|  
|  
|  
|  
|  
|  
|  
|  
|  
|  
|  
| || 80||[[Blackwood]]/[[Blacksmith]]
| 96
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
| 5\60
|5\70
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|85.714
| 100
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|
|  
|4\55
|  
|
| 8\95
|
|  
|
|  
|
|  
|
|  
|
|  
|87.273
| 101.053
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|
| 3\35
|
|  
|7\95
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|88.421
| 102.857
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|3\40
|  
|
|  
|
| 7\80
|
|  
|
|  
|
|  
|
|  
|
|  
|90
| 105
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|
|  
|
| 4\45
|8\105
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|91.429
| 106.667
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|
|
|  
|5\65
|  
|
| 5\55
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 109.091
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|7\90
|  
|
| 6\65
|
|  
|
|  
|
|  
|
|  
|93.333
| 110.769
|Blackwood/Blacksmith
| Blackwood/[[Quintosec]]/[[Sengasec]]
|-
|-
|2\25
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 25\270
|96
| 111.111
|Blackwood/Blacksmith
| Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
|
|  
|
|  
|5\60
|  
|
|  
|
|  
|
|  
|
|  
|
| 19\205
|
|  
|100
| 111.220
|Blackwood
| Blackwood/Quintosec/SengasecQintosec
|-
|-
|
|  
|
|  
|
|  
|8\95
|  
|
|  
|
|  
|
| 13\140
|
|  
|
|  
|101.053
| 111.429
|Blackwood
| Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
|
|  
|3\35
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 20\215
|
|  
|102.857
| 111.628
|Blackwood
| Blackwood/Qintosec
|-
|-
|
|  
|
|  
|
|  
|7\80
|  
|
|  
|
| 7\75
|
|  
|
|  
|
|  
|105
| 112
|Blackwood
| Blackwood/[[Qinto]]
|-
|-
|
|  
|
|  
|4\45
|  
|
|  
|
|  
|
|  
|
|  
|
| 15\160
|
|  
|106.667
| 112.5
|Blackwood
| Blackwood/Qinto
|-
|-
|
|  
|
|  
|
|  
|5\55
|  
|
|  
|
|  
|
| 8\85
|
|  
|
|  
|109.091
| 112.941
|Blackwood
| Blackwood/[[Phi as a Generator| Elderthing]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|6\65
|  
|
|  
|
| 9\95
|
|  
|
|  
|110.769
| 113.684
|Blackwood/[[Quintosec]]/[[Sengasec]]
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 10\105
|
|  
|25\270
|  
|111.111
| 114.286
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
| Blackwood
|-
|-
|
| 1\10
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|19\205
|  
|
|  
|111.220
| 120
|Blackwood/Quintosec/SengasecQintosec
| Blackwood
|-
|
|
|
|
|
|
|13\140
|
|
|111.429
|Blackwood/Quintosec/Sengasec/Qintosec
|-
|
|
|
|
|
|
|
|20\215
|
|111.628
|Blackwood/Qintosec
|-
|
|
|
|
|
|7\75
|
|
|
|112
|Blackwood/[[Qinto]]
|-
|
|
|
|
|
|
|
|15\160
|
|112.5
|Blackwood/Qinto
|-
|
|
|
|
|
|
|8\85
|
|
|112.941
|Blackwood/[[Phi as a Generator|Elderthing]]
|-
|
|
|
|
|
|
|9\95
|
|
|113.684
|Blackwood
|-
|
|
|
|
|
|
|10\105
|
|
|114.286
|Blackwood
|-
|1\10
|
|
|
|
|
|
|
|
|120
|Blackwood
|}
|}


==Six periods per octave ==
== Six periods per octave ==
{| class="wikitable"
{| class="wikitable sortable mw-collapsible"
! colspan="7" |Generator!!Cents !!Comments
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|0\6|| || ||  
| 0\6
|
|  
|
|  
|||0||
|  
|  
|  
|  
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|1\288
| 1\288
|
|  
|
|  
|
|  
|4.167
| 4.167
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\282
| 1\282
|
|  
|
|  
|
|  
|4.255
| 4.255
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\276
| 1\276
|2\552
| 2\552
|
|  
|
|  
|4.348
| 4.348
|[[Sextile]]
| [[Sextile]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\822
| 3\822
|
|  
|4.380
| 4.380
|Sextile
| Sextile
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\1092
| 4\1092
|4.396
| 4.396
|Sextile
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\270
| 1\270
|
|  
|
|  
|
|  
|4.444
| 4.444
|Sextile
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\264
| 1\264
|
|  
|
|  
|
|  
|4.545
| 4.545
|
|  
|-
|-
|
|  
|
|  
|
|  
|...
| ...
|
|  
|
|  
|
|  
|...
| ...
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\90
| 1\90
|
|  
|
|  
|
|  
|13.333
| 13.333
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\84
| 1\84
|
|  
|
|  
|
|  
|14.286
| 14.286
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\78
| 1\78
|
|  
|
|  
|
|  
|15.385
| 15.385
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\72
| 1\72
|
|  
|
|  
|
|  
|16.667
| 16.667
|[[Stearnscape]]
| [[Stearnscape]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\282
| 4\282
|17.021
| 17.021
|Stearnscape
| Stearnscape
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\210
| 3\210
|
|  
|17.143
| 17.143
|Stearnscape
| Stearnscape
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\138
| 2\138
|
|  
|
|  
|17.391
| 17.391
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\66
| 1\66
|
|  
|
|  
|
|  
|18.182
| 18.182
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\60
| 1\60
|
|  
|
|  
|
|  
|20
| 20
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\54
| 1\54
|
|  
|
|  
|
|  
|22.222
| 22.222
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\48
| 1\48
|
|  
|
|  
|
|  
|25
| 25
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\42
| 1\42
|
|  
|
|  
|
|  
|28.571
| 28.571
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\36
| 1\36
|
|  
|
|  
|
|  
|33.333
| 33.333
|
|  
|-
|-
|
|  
|
|  
|1\30
| 1\30
|
|  
|
|  
|
|  
|
|  
|40
| 40
|
|  
|-
|-
|
|  
|
| 1\24
|
|  
|2\54
|  
|
|  
|
|  
|
|  
|44.444
| 50
|
|  
|-
|-
|
| 1\18
|1\24
|  
|
|  
|
|  
|
|  
|
|  
|
|50
|  
|  
|-
|
|
|
|3\66
|
|
|
|54.545
|
|-
|
|
|2\42
|
|
|
|
| 57.143
|
|-
|
|
|
|3\60
|
|
|
|60
|
|-
|1\18
|
|
|
|
|
|
| 66.667
| 66.667
|
|  
|-
|-
|
|
|
|4\66
|
|
|
|72.727
|
|-
|
|
|3\48
|
|
|
|
| 75
|  
|  
|-
| 2\30
|
|  
|
|  
|
|  
|5\78
|  
|
|  
|
|
|76.923
|
|-
|
|2\30
|
|
|
|
|
| 80
| 80
|[[Hexe]]
| [[Hexe]]
|-
|-
|
|  
|
|  
|
|  
|5\72
| 5\72
|
|  
|
|  
|
|  
|83.333
| 83.333
|Hexe
| Hexe
|-
|-
|
|  
|
|  
|3\42
| 3\42
|
|  
|
|  
|
|  
|
|  
|85.714
| 85.714
| Hexe
| Hexe
|-
|-
|
|  
|
|  
|
|  
|4\54
| 4\54
|
|  
|
|  
|
|  
|88.889
| 88.889
|Hexe
| Hexe
|-
|-
|1\12
| 1\12
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 100
| 100
|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)}}
== Seven periods per octave ==
{| class="wikitable"
{{todo| complete table| comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
! colspan="8" |Generator!! Cents!!Comments
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
| 0\7|| || ||
| 0\7
|
|  
|
|  
|
|  
| ||0||
|  
|  
|  
|  
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\91
| 1\91
|
|  
|
|  
|
|  
|13.187
| 13.187
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\84
| 1\84
|
|  
|
|  
|
|  
|14.286
| 14.286
|[[Absurdity]]
| [[Absurdity]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\329
| 4\329
|14.59
| 14.59
|Absurdity
| Absurdity
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\245
| 3\245
|
|  
|14.69
| 14.69
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\161
| 2\161
|
|  
|
|  
|14.907
| 14.907
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\77
| 1\77
|
|  
|
|  
|
|  
|15.584
| 15.584
|[[Septant]]
| [[Septant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\301
| 4\301
|15.947
| 15.947
|Septant
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\224
| 3\224
|
|  
|16.071
| 16.071
|Septant
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\147
| 2\147
|
|  
|
|  
|16.327
| 16.327
|Septant
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\70
| 1\70
|
|  
|
|  
|
|  
|17.143
| 17.143
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\63
| 1\63
|
|  
|
|  
|
|  
|19.048
| 19.048
|[[Sevond]]
| [[Sevond]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\119
| 2\119
|
|  
|
|  
|20.168
| 20.168
|Sevond
| Sevond
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\56
| 1\56
|
|  
|
|  
|
|  
|21.429
| 21.429
|Sevond
| Sevond
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\48
| 1\49
|
|  
|
|  
|
|  
|25
| 24.49
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\42
| 1\42
|
|  
|
|  
|
|  
|
|  
|28.571
| 28.571
|[[Mistismic temperaments#Neutron|Neutron]]
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\119
| 3\119
|
|  
|
|  
|30.252
| 30.252
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\196
| 5\196
|
|  
|30.612
| 30.612
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\273
| 7\273
|30.769
| 30.769
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\77
| 2\77
|
|  
|
|  
|
|  
|31.169
| 31.169
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|1\35
| 1\35
|
|  
|
|  
|
|  
|
|  
|
|  
|34.286
| 34.286
|[[Whitewood family#Redwood|Redwood]]
| [[Whitewood family#Redwood| Redwood]]
|-
|-
|
|  
|
|  
|
|  
| 2\63
| 2\63
|
|  
|
|  
|
|  
|
|  
|38.095
| 38.095
|Redwood
| Redwood
|-
|-
|
|  
| 1\28
| 1\28
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|42.857
| 42.857
|Redwood/[[Whitewood]]
| Redwood/[[Whitewood]]
|-
|-
|
|  
|
|  
|
|  
| 3\77
| 3\77
|
|  
|
|  
|
|  
|
|  
| 46.753
| 46.753
|Whitewood
| Whitewood
|-
|-
|
|  
|
|  
|2\49
| 2\49
|
|  
|
|  
|
|  
|
|  
|
|  
|48.980
| 48.980
|Whitewood
| Whitewood
|-
|-
|
|  
|
|  
|
|  
|3\70
| 3\70
|
|  
|
|  
|
|  
|
|  
| 51.429
| 51.429
|Whitewood
| Whitewood
|-
|-
|1\21
| 1\21
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|57.143
| 57.143
|Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal| Septimal]]
|-
|-
|
|  
|
|  
|
|  
| 4\77
| 4\77
|
|  
|
|  
|
|  
|
|  
|62.338
| 62.338
|Jamesbond/Septimal
| Jamesbond/Septimal
|-
|-
|
|  
|
|  
|3\56
| 3\56
|
|  
|
|  
|
|  
|
|  
|
|  
|64.286
| 64.286
| Jamesbond/Septimal
| Jamesbond/Septimal
|-
|-
|
|  
|
|  
|
|  
|5\91
| 5\91
|
|  
|
|  
|
|  
|
|  
|65.934
| 65.934
|Jamesbond/Septimal
| Jamesbond/Septimal
|-
|-
|
|  
|2\35
| 2\35
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 68.571
| 68.571
|Jamesbond/Septimal/[[Greenwood]]
| Jamesbond/Septimal/[[Greenwood]]
|-
|-
|
|  
|
|  
|
|  
|5\84
| 5\84
|
|  
|
|  
|
|  
|
|  
|71.429
| 71.429
|Jamesbond/Septimal/Greenwood
| Jamesbond/Septimal/Greenwood
|-
|-
|
|  
|
|  
|3\49
| 3\49
|
|  
|
|  
|
|  
|
|  
|
|  
| 73.469
| 73.469
|Jamesbond/Septimal/Greenwood
| Jamesbond/Septimal/Greenwood
|-
|-
|
|  
|
|  
|
|  
|4\63
| 4\63
|
|  
|
|  
|
|  
|
|  
|76.190
| 76.190
|Jamesbond/Septimal/Greenwood
| Jamesbond/Septimal/Greenwood
|-
|-
| 1\14
| 1\14
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|85.714
| 85.714
|Jamesbond/Septimal/Greenwood
| Jamesbond/Septimal/Greenwood
|}
|}


==Eight periods per octave==
== Eight periods per octave ==
{{todo|complete table|comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{{todo| complete table| comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable"
{| class="wikitable sortable mw-collapsible"
! colspan="9" |Generator!!Cents!!Comments
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|0\8||  ||
| 0\8
|
|  
|
|  
|
|  
|
|  
|
|  
| ||0||
|  
|  
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\480
|
|  
|1\80
|  
|
|  
|
| 2.5
|15
|  
|
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\472
|
|  
|
|  
|2\152
|  
|
| 2.542
|15.789
| [[Octium]]
|[[Octoid]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\1872
|
|  
|3\224
| 2.564
|16.071
| Octium
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
| 7\3272
|
| 2.567
|16.667
| Octium
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\64
|  
|
| 3\1400
|
|  
|
|  
|
| 2.571
|18.75
| Octium
|
|-
|-
|
|
|
|
|
|
|1\56
|
|
| 1\464
|
|
|
|
|
|
|
| 2.586
|21.429
|
|
|-
|
|
|
|
| …
|
|
|
|
|
|-
|
|  
|  
|  
| 1\96
|  
|  
|
| 12.5
|
|-
|
|
|
|
| 1\88
|  
|  
|  
| 13.635
|  
|-
|-
|
|  
|
|  
|1\48
|  
|
|  
|
| 1\80
|
|  
|
|  
|
|  
|
| 15
|25
|  
|
|-
|-
|
|
|
|
|
|
| 2\152
|
|
| 15.789
| [[Octoid]]
|-
|
|
|
|
|
|
| 3\224
|
| 16.071
| Octoid
|-
|
|
|
|
| 1\72
|
|
|
| 16.667
| Octoid
|-
|
|
|
|
| 1\64
|
|
|
| 18.75
|
|-
|
|
|
| 1\56
|
|
|
|
| 21.429
|
|-
|
|
| 1\48
|
|
|
|
|
| 25
|
|-
|  
| 1\40
| 1\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 30
|30
|  
|
|-
|-
|
|  
|
|  
|2\72
| 2\72
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 33.333
|33.333
|  
|
|-
| 1\32
|
|
|
|
|
|
|
| 37.5
| [[Semidim]]
|-
|-
|1\32
|  
|
|
|
| 3\88
|
|
|
|
|
|
|
|
|
|
|
| 40.909
|37.5
| Semidim
|[[Semidim]]
|-
|  
| 2\56
|  
|  
|  
|  
|  
|  
| 42.857
| Semidim
|-
|
|
| 3\80
|
|
|
|
|
| 45
| Semidim
|-
|-
|
|  
|
|  
|3\88
|  
|
| 4\104
|
|  
|
|  
|
|  
|
|  
|
| 46.154
|40.909
| Semidim
|Semidim
|-
|-
|
|  
|2\56
|  
|
|  
|
|  
|
| 5\128
|
|  
|
|  
|
|  
|
| 46.875
|42.857
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|3\80
|  
|
|
|
| 6\152
|
|
|
|
|
|
|
| 47.368
|45
| Semidim
|Semidim
|-
|
|
|
|
|
| 7\176
|
|
| 47.727
| Semidim
|-
|
|
|
|
|
| 8\200
|
|
| 48
| Semidim
|-
|
|
|
|
|
| 9\224
|
|
| 48.214
| Semidim/[[Octant]]
|-
|
|
|
|
|
|
|
| 28\696
| 48.276
| Semidim/Octant
|-
|
|
|
|
|
|
| 19\472
|
| 48.305
| Semidim/Octant
|-
|
|
|
|
|
| 10\248
|
|
| 48.387
| Semidim
|-
| 1\24
|
|  
|  
|  
|  
|  
|  
| 50
| Semidim
|-
|-
|
| 2\40
|
|  
|
|  
|4\104
|  
|
|  
|
|  
|
|  
|
|  
|
| 60
|46.154
|  
|Semidim
|-
|-
|
| 1\16
|
|
|
|  
|
|  
|5\128
|  
|
|  
|
|  
|
|  
|
| 75
|46.875
|  
|Semidim
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\9
|
|  
|
|  
|
|  
|
|  
|6\152
|  
|
|  
|
|  
|
| 0
|47.368
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\72
|
|  
|7\176
|  
|
|  
|
| 16.667
|47.727
| [[Enneaportent]]
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\200
|  
|
| 4\279
|
| 17.204
|48
| Enneaportent
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|9\224
| 3\207
|
|  
|
| 17.391
|48.214
| Enneaportent
|Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\135
|
|  
|
|  
|28\696
| 17.778
|48.276
| Enneaportent
|Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
| 1\63
|
|  
|
|  
|
|  
|19\472
|  
|
| 19.048
|48.305
| Enneaportent
|Semidim/Octant
|-
|-
|
|  
|
|  
|
| 1\54
|
|  
|
|  
|
|  
|10\248
|  
|
|  
|
| 22.222
|48.387
|  
|Semidim
|-
|-
|1\24
|
|
| 1\45
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 26.667
|50
|  
|Semidim
|-
|-
|
| 1\36
|
|  
|4\88
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 33.333
|54.545
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|
|-
|-
|
| 3\64
|
|
|
|
|
|
|
| 56.250
|  
|  
|
|
| 4\135
|
|
|
|
| 35.556
| No-five tritrizo
|-
|-
|
|  
|
|  
|5\104
| 3\99
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 36.364
|57.692
| No-five tritrizo
|
|-
|-
|2\40
|
|
| 2\63
|
|
|
|
|
|
|
|
|
|
|
|
|
| 38.095
| 60
| [[Niner]]
|
|-
|
|
| 3\90
|
|
|
|
|
| 40
| Niner
|-
| 1\27
|  
|  
|  
|  
|  
|  
|  
| 44.444
| Niner
|-
|
|
| 4\99
|
|
|
|
|
| 48.485
| [[Ennealimmal]]
|-
|
|
|
| 7\171
|
|
|
|
| 49.123
| Ennealimmal
|-
|
| 3\72
|
|
|
|
|
|
| 50
| Ennealimmal
|-
|
|
|
|
|
|
|
| 20\477
| 50.314
| [[Novemkleismic]]
|-
|
|
|
|
|
|
| 17\405
|
| 50.370
| Novemkleismic
|-
|
|
|
|
|
| 14\333
|
|
| 50.451
| Novemkleismic
|-
|
|
|
|
| 11\261
|
|
|
| 50.575
| Novemkleismic
|-
|-
|
|  
|
|  
|5\96
|  
|
| 8\189
|
|  
|
|  
|
|  
|
|  
|
| 50.794
|62.5
| Novemkleismic
|
|-
|-
|
|  
|3\56
|  
|
| 5\117
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 51.282
|64.286
|  
|
|-
|-
|
| 2\45
|
|  
|4\72
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 53.333
|66.667
|  
|
|-
|-
|1\16
| 1\18
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 66.667
|75
|  
|
|}
|}


==Nine periods per octave ==
== Ten periods per octave==
{| class="wikitable"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!! Comments
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|0\9|| || ||  
| 0\10
|  
|  
|  
|  
|  
|  
| 0
|  
|  
|
|
| ||0||
|-
|-
|
| 1\110
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|  
|
| 10.909
|16.667
|  
|[[Enneaportent]]
|-
|-
|
| 1\100
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\279
| 12
|17.204
|  
|Enneaportent
|-
|-
|
|  
|
| 2\190
|
|  
|
|  
|
|  
|
|  
|3\207
|  
|
| 12.632
|17.391
| [[Deca]]
|Enneaportent
|-
|-
|
| 1\90
|
|  
|
|  
|
|  
|
|  
|2\135
|  
|
|  
|
| 13.333
|17.778
| Deca
|Enneaportent
|-
|-
|
| 1\80
|
|  
|
|  
|1\63
|  
|
|  
|
|  
|
|  
|
| 15
|19.048
| Deca
|Enneaportent
|-
|-
|
| 1\70
|
|  
|1\54
|  
|
|  
|
|  
|
|  
|
|  
|
| 17.143
|22.222
|  
|
|-
|-
|
| 1\60
|1\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 20
|26.667
|  
|
|-
|-
|
| 1\50
|
|  
|2\81
|  
|
|  
|
|  
|
|  
|
|  
|
| 24
|29.63
| [[Decimetra]]
|
|-
|-
|1\36
|  
|
|  
|
|  
|
| 4\190
|
|  
|
|  
|
|  
|
| 25.263
|33.333
| Decimetra
|[[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
|-
|-
|
|  
|
|  
|
|  
|4\135
|  
|
| 7\330
|
|  
|
|  
|
| 25.455
|35.556
| Decimetra
|No-five tritrizo
|-
|-
|
|  
|
|  
|3\99
|  
|
|  
|
|  
|
|  
|
| 17\800
|
| 25.5
|36.364
| Decimetra
|No-five tritrizo
|-
|-
|
|  
|2\63
|  
|
|
|
|
|
|
|
| 10\470
|
|
|
| 25.532
|38.095
| Decimetra
|[[Niner]]
|-
|
|
| 3\140
|
|
|
|
| 25.714
| Decimetra
|-
|
| 2\90
|  
|  
|  
|  
|  
| 26.667
| Decimetra
|-
|-
|
| 1\40
|
|3\90
|  
|  
|
|  
|
|  
|
|  
|
|  
|40
|  
|Niner
| 30
| [[Decic]]
|-
|-
|1\27
|
|
|
|
| 3\110
|
|
|
|
|
|
|
|
|
| 32.727
| 44.444
| Decic
|Niner
|-
|
| 2\70
|
|
|
|
|
| 34.286
| Decic
|-
|
|
|
| 4\170
|
|
|
| 28.235
| Decic
|-
|
|
| 3\100
|
|
|
|
| 36
| Decic
|-
| 1\30
|
|
|
|
|
|
| 40
| Decic/[[Decal]]
|-
|
| 3\80
|
|
|
|
|
| 45
| Decal/[[Decistearn]]
|-
|
|  
|  
| 8\210
|  
|  
|  
| 45.714
| Decal/Decistearn
|-
|
|
|
|
| 13\340
|
|
| 45.882
| Decal/Decistearn
|-
|
|
|
|
|
| 18\470
|
| 45.957
| Decal/Decistearn
|-
|
|
|
|
|
|
| 23\600
| 46
| Decal/Decistearn
|-
|
|
| 5\130
|
|
|
|
| 46.154
| Decal/Decistearn
|-
| 2\50
|
|
|
|
|
|
| 48
| Decistearn/[[Decavish]]
|-
|
|
|
|
|
| 11\270
|  
| 48.889
| Decavish
|-
|-
|
|  
|
|  
|4\99
|  
|
|  
|
| 9\220
|
|  
|
|  
|
| 49.091
|48.485
| Decavish
|[[Ennealimmal]]
|-
|-
|
|  
|
|  
|
|  
|7\171
| 7\170
|
|  
|
|  
|
|  
|
| 49.412
|49.123
| Decavish
|Ennealimmal
|-
|-
|
|3\72
|  
|  
|
|  
|
| 5\120
|
|  
|
|  
|
|  
|  
| 50
| 50
|Ennealimmal
| Decavish
|-
|
| 3\70
|
|
|
|
|
| 51.429
| Decavish
|-
|-
|
|  
|
|  
|
| 4\90
|
|  
|
|  
|
|  
|
|  
|20\477
| 53.333
|50.314
|  
|[[Novemkleismic]]
|-
|-
|
|  
|
|  
|
|  
|
| 5\110
|
|  
|
|  
|17\405
|  
|
| 54.545
|50.370
|  
|Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 6\130
|14\333
|  
|
|  
|
| 55.385
|50.451
| [[Decoid]]
|Novemkleismic
|-
|-
|
| 1\20
|
|
|
|  
|
|  
|11\261
|  
|
|  
|
|  
|
| 60
|50.575
|  
|Novemkleismic
|}
 
== Eleven periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\11
|
|  
|
|  
|8\189
|  
|
|  
|
|  
|
|  
|
| 0
|50.794
|  
|Novemkleismic
|-
|-
|
|  
|
| 1\55
|5\117
|  
|
|  
|
|  
|
|  
|
|  
|
| 21.818
|51.282
|  
|
|-
|-
|2\45
| 1\44
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 27.273
|53.333
|  
|  
|-
|-
|
|  
|
| 2\77
|5\108
|  
|
|  
|
|  
|
|  
|
|  
|
| 31.169
|55.556
|  
|
|-
|-
|
| 1\33
|3\63
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 36.364
|57.143
|  
|
|-
|-
|
|
|4\81
|  
|  
|
| 3\88
|
|  
|
|  
|
|  
|59.259
|  
|
|
| 40.909
|  
|-
|-
|1\18
| 2\55
|
|
|
|
|
|
|
|
|
|
|
|
|
| 42.636
| 66.667
| [[Hendecatonic]]
|
|-
|
| 3\77
|
|
|
|
|
| 46.753
| Hendecatonic
|-
|
|
|
| 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==
==Twelve periods per octave==
See also: [[Compton family]]
{{See also| Compton family}}
 
{| class="wikitable sortable mw-collapsible"
{| class="wikitable"
! colspan="8" | Generator
! colspan="8" |Generator!!Cents!!Comments
! Cents
! Comments
|-
|-
|0\12|| || ||
| 0\12
|
|
|  
|  
|  
|  
|  
|  
| 0
|  
|  
|
|||0||
|-
|-
|
|  
|
|  
|
|  
|1\636
| 1\636
|
|  
|
|  
|
|  
|
|  
|1.887
| 1.887
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\624
| 1\624
|
|  
|
|  
|
|  
|
|  
|1.923
| 1.923
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\1236
| 2\1236
|
|  
|
|  
|
|  
|1.942
| 1.942
|[[Atomic]]
| [[Atomic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\1848
| 3\1848
|
|  
|
|  
|1.948
| 1.948
|Atomic
| Atomic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\2460
| 4\2460
|
|  
|1.951
| 1.951
|Atomic
| Atomic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\3072
| 5\3072
|1.953
| 1.953
|Atomic
| Atomic
|-
|-
|
|  
|
|  
|
|  
|1\612
| 1\612
|
|  
|
|  
|
|  
|
|  
|1.961
| 1.961
|Atomic
| Atomic
|-
|-
|
|  
|
|  
|
|  
|1\600
| 1\600
|
|  
|
|  
|
|  
|
|  
|2
| 2
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\588
| 1\588
|
|  
|
|  
|
|  
|
|  
|2.041
| 2.041
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\576
| 1\576
|
|  
|
|  
|
|  
|
|  
|2.083
| 2.083
|
|  
|-
|-
|
|  
|
|  
|
|  
|...
| ...
|
|  
|
|  
|
|  
|
|  
|...
| ...
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\108
| 1\108
|
|  
|
|  
|
|  
|
|  
|11.111
| 11.111
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\96
| 1\96
|
|  
|
|  
|
|  
|
|  
|12.5
| 12.5
|
| [[Compton]]
|-
|-
|
|  
|
|  
|
|  
|1\84
| 1\84
|
|  
|
|  
|
|  
|
|  
|14.286
| 14.286
|[[Compton]]
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\240
| 3\240
|
|  
|
|  
|15
| 15
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\636
| 8\636
|15.094
| 15.094
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\396
| 5\396
|
|  
|15.152
| 15.152
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
| 7\552
|15.217
| 15.217
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\156
| 2\156
|
|  
|
|  
|
|  
|15.385
| 15.385
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\540
| 7\540
|15.556
| 15.556
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\384
| 5\384
|
|  
|15.625
| 15.625
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\612
| 8\612
|15.686
| 15.686
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\228
| 3\228
|
|  
|
|  
|15.789
| 15.789
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
| 7\528
|15.909
| 15.909
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\300
| 4\300
|
|  
|16
| 16
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\372
| 5\372
|16.129
| 16.129
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|1\72
| 1\72
|
|  
|
|  
|
|  
|
|  
|16.667
| 16.667
|Compton
| Compton
|-
|-
|
|  
|
|  
|1\60
| 1\60
|
|  
|
|  
|
|  
|
|  
|
|  
|20
| 20
|
| Compton
|-
|-
|
|  
|
|  
|
|  
|2\108
| 2\108
|
|  
|
|  
|
|  
|
|  
|22.222
| 22.222
|
|  
|-
|-
|
|  
|1\48
| 1\48
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|25
| 25
|[[Catler]]
| [[Catler]]
|-
|-
|
|  
|
|  
|
|  
|3\132
| 3\132
|
|  
|
|  
|
|  
|
|  
| 27.273
| 27.273
|Catler
| Catler
|-
|-
|
|  
|
|  
| 2\84
| 2\84
|
|  
|
|  
|
|  
|
|  
|
|  
|28.571
| 28.571
|Catler
| Catler
|-
|-
|
|  
|
|  
|
|  
|3\120
| 3\120
|
|  
|
|  
|
|  
|
|  
|30
| 30
|Catler
| Catler
|-
|-
|1\36
| 1\36
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|33.333
| 33.333
|Catler/[[Catnip]]
| Catler/[[Catnip]]
|-
|-
|
|  
|
|  
|
|  
|4\132
| 4\132
|
|  
|
|  
|
|  
|
|  
|36.364
| 36.364
|Catnip
| Catnip
|-
|-
|
|  
|
|  
|3\96
| 3\96
|
|  
|
|  
|
|  
|
|  
|
|  
|37.5
| 37.5
| Catnip
| Catnip
|-
|-
|
|  
|
|  
|
|  
|5\156
| 5\156
|
|  
|
|  
|
|  
|
|  
|38.462
| 38.462
|Catnip
| Catnip
|-
|-
|
|  
|2\60
| 2\60
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|40
| 40
|Catnip
| Catnip
|-
|-
|
|  
|
|  
|
|  
|5\144
| 5\144
|
|  
|
|  
|
|  
|
|  
|41.667
| 41.667
|
|  
|-
|-
|
|  
|
|  
|3\84
| 3\84
|
|  
|
|  
|
|  
|
|  
|
|  
| 42.857
| 42.857
| [[Magnesium]]
| [[Magnesium]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|16\444
| 16\444
|43.243
| 43.243
|Magnesium
| Magnesium
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|13\360
| 13\360
|
|  
|43.333
| 43.333
|Magnesium
| Magnesium
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|10\276
| 10\276
|
|  
|
|  
|43.378
| 43.378
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|7\192
| 7\192
|
|  
|
|  
|
|  
|43.75
| 43.75
|
|  
|-
|-
|
|  
|
|  
|
|  
|4\108
| 4\108
|
|  
|
|  
|
|  
|
|  
|44.444
| 44.444
|
|  
|-
|-
|1\24
| 1\24
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 50
| 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"