View source for Map of rank-2 temperaments

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.

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

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

==Two periods per octave==

{| class="wikitable"
|-
! colspan="12" | Generator
! | Cents
! | Comments
|-
| | 0\2
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 0
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\26
| | 46.154
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\24
| | 
| | 50.000
| | [[Shrutar|Shrutar]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 2\46
| | 52.174
| | Shrutar
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\22
| | 
| | 
| | 54.545
| | Shrutar
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\20
| | 
| | 
| | 
| | 60.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\18
| | 
| | 
| | 
| | 
| | 66.667
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 2\34
| | 
| | 
| | 
| | 70.588
| | [[Vishnu|Vishnu]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\118
| | 71.186
| | Vishnu
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 5\84
| | 
| | 71.429
| | Vishnu
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 3\50
| | 
| | 
| | 72.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\16
| | 
| | 
| | 
| | 
| | 
| | 75.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 2\30
| | 
| | 
| | 
| | 
| | 80.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 3\44
| | 
| | 
| | 
| | 81.818
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 4\58
| | 
| | 
| | 82.759
| | [[Harry|Harry]]
|-
|
|
|
|
|
|
|
|
|
|
|
|9\130
|83.077
|Harry
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 5\72
| | 
| | 83.333
| | Harry
|-
| | 
| | 
| | 
| | 
| | 
| | 1\14
| | 
| | 
| | 
| | 
| | 
| | 
| | 85.714
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 2\26
| | 
| | 
| | 
| | 
| | 
| | 92.308
| | [[Injera|Injera]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 3\38
| | 
| | 
| | 
| | 
| | 94.737
| | Injera
|-
| | 
| | 
| | 
| | 
| | 1\12
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 100.000
| | [[Srutal|Srutal]]/[[pajara|pajara]]/injera
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 4\46
| | 
| | 
| | 
| | 
| | 104.348
| | Srutal/pajara/[[Diaschismic|diaschismic]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 3\34
| | 
| | 
| | 
| | 
| | 
| | 105.882
| | Srutal/pajara/diaschismic
|-
| | 
| | 
| | 
| | 
| | 
| | 2\22
| | 
| | 
| | 
| | 
| | 
| | 
| | 109.091
| | Srutal/pajara
|-
|
|
|
|
|
|
|3\32
|
|
|
|
|
|112.500
|
|-
| | 
| | 
| | 
| | 1\10
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 120.000
| | [[Octokaidecal]]/[[Nimona]]
|-
|
|
|
|
|
|3\28
|
|
|
|
|
|
|128.571
|Octokaidecal/Nimona
|-
| | 
| | 
| | 
| | 
| | 2\18
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 133.333
| | Octokaidecal/Nimona
|-
| | 
| | 
| | 
| | 
| | 
| | 3\26
| | 
| | 
| | 
| | 
| | 
| | 
| | 138.462
| | 
|-
|
|
|
|
|
|
|
|6\60
|
|
|
|
|140.000
|
|-
|
|
|
|
|
|
|
|
|11\94
|
|
|
|140.126
|Fifive
|-
|
|
|
|
|
|
|
|
|
|15\128
|
|
|140.625
|Fifive
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 4\34
| | 
| | 
| | 
| | 
| | 
| | 141.176
| | [[Fifive|Fifive]]
|-
|
|
|
|
|
|
|
|5\42
|
|
|
|
|142.857
|
|-
| | 
| | 
| | 1\8
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 150.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 4\30
| | 
| | 
| | 
| | 
| | 
| | 
| | 160.000
| | 
|-
| | 
| | 
| | 
| | 
| | 3\22
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 163.636
| | [[Hedgehog|Hedgehog]]/[[Echidna|echidna]]
|-
|
|
|
|
|
|
|
|11\80
|
|
|
|
|165.000
|Hedgehog/echidna
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 8\58
| | 
| | 
| | 
| | 
| | 
| | 165.517
| | Hedgehog/echidna
|-
| | 
| | 
| | 
| | 
| | 
| | 5\36
| | 
| | 
| | 
| | 
| | 
| | 
| | 166.667
| | 
|-
| | 
| | 
| | 
| | 2\14
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 171.429
| | 
|-
| | 
| | 
| | 
| | 
| | 3\20
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 180.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\46
| | 
| | 
| | 
| | 
| | 
| | 182.609
| | [[Unidec|Unidec]]/[[Hendec|hendec]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 11\72
| | 
| | 
| | 
| | 
| | 183.333
| | Unidec/hendec
|-
| | 
| | 
| | 
| | 
| | 
| | 4\26
| | 
| | 
| | 
| | 
| | 
| | 
| | 184.615
| | Unidec/hendec
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 5\32
| | 
| | 
| | 
| | 
| | 
| | 187.500
| | 
|-
| | 
| | 1\6
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 200.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\34
| | 
| | 
| | 
| | 
| | 
| | 211.765
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 5\28
| | 
| | 
| | 
| | 
| | 
| | 
| | 214.286
| | [[Antikythera]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 9\50
| | 
| | 
| | 
| | 
| | 
| | 216.000
| | Antikythera/[[Wizard]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 13\72
| | 
| | 
| | 
| | 
| | 216.667
| | Antikythera/Wizard
|-
| | 
| | 
| | 
| | 
| | 4\22
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 218.182
| | Antikythera/Wizard/[[Astrology]]
|-
|
|
|
|
|
|
|
|15\82
|
|
|
|
|219.512
|Astrology
|-
|
|
|
|
|
|
|11\60
|
|
|
|
|
|220.000
|Astrology
|-
|
|
|
|
|
|7\38
|
|
|
|
|
|
|221.053
|
|-
| | 
| | 
| | 
| | 3\16
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 225.000
| | 
|-
| | 
| | 
| | 
| | 
| | 5\26
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 230.769
| | [[Lemba|Lemba]]
|-
|
|
|
|
|
|
|12\62
|
|
|
|
|
|232.258
|Lemba
|-
| | 
| | 
| | 
| | 
| | 
| | 7\36
| | 
| | 
| | 
| | 
| | 
| | 
| | 233.333
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 9\46
| | 
| | 
| | 
| | 
| | 
| | 234.783
| | [[Echidnic|Echidnic]]
|-
|
|
|
|
|
|
|
|
|
|29\148
|
|
|235.135
|Echidnic
|-
|
|
|
|
|
|
|
|
|20\102
|
|
|
|235.294
|Echidnic
|-
|
|
|
|
|
|
|
|11\56
|
|
|
|
|235.714
|
|-
| | 
| | 
| | 2\10
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 240.000
| | [[Decimal|Decimal]]
|-
| | 
| | 
| | 
| | 
| | 5\24
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 250.000
| | Decimal
|-
|
|
|
|
|
|8\38
|
|
|
|
|
|
|252.632
|Decimal
|-
| | 
| | 
| | 
| | 3\14
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 257.143
| | Decimal
|-
| | 
| | 
| | 
| | 
| | 4\18
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 266.667
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 5\22
| | 
| | 
| | 
| | 
| | 
| | 
| | 272.727
| | [[Doublewide|Doublewide]]
|-
|
|
|
|
|
|
|
|
|16\70
|
|
|
|274.286
|Doublewide
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 11\48
| | 
| | 
| | 
| | 
| | 275.000
| | Doublewide
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\26
| | 
| | 
| | 
| | 
| | 
| | 276.923
| | 
|-
| | 1\4
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 300.000
| | 
|}

==Three periods per octave==

{| class="wikitable"
|-
! colspan="9" | Generator
!
! | Cents
! | Comments
|-
| | 0\3
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
|
| | 0
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\30
|
| | 40.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\27
| | 
|
| | 44.444
| | [[Semiaug|Semiaug]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 2\51
|
| | 47.059
| | Semiaug
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\24
| | 
| | 
|
| | 50.000
| | Semiaug
|-
| | 
| | 
| | 
| | 
| | 
| | 1\21
| | 
| | 
| | 
|
| | 57.143
| | 
|-
| | 
| | 
| | 
| | 
| | 1\18
| | 
| | 
| | 
| | 
|
| | 66.667
| | 
|-
| | 
| | 
| | 
| | 1\15
| | 
| | 
| | 
| | 
| | 
|
| | 80.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\87
|
| | 82.759
| | 
|-
|
|
|
|
|
|
|
|
|
|11\159
|83.019
|[[Tritikleismic]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 5\72
| | 
|
| | 83.333
| | Tritikleismic
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 4\57
| | 
| | 
|
| | 84.2105
| | Tritikleismic
|-
| | 
| | 
| | 
| | 
| | 
| | 3\42
| | 
| | 
| | 
|
| | 85.714
| | 
|-
| | 
| | 
| | 
| | 
| | 2\27
| | 
| | 
| | 
| | 
|
| | 88.889
| |[[Augmented]]/[[augene]]
|-
|
|
|
|
|
|3\39
|
|
|
|
|92.308
|Augmented/augene
|-
| | 
| | 
| | 1\12
| | 
| | 
| | 
| | 
| | 
| | 
|
| | 100.000
| | Augmented/augene/[[august]]
|-
| | 
| | 
| | 
| | 
| | 3\33
| | 
| | 
| | 
| | 
|
| | 109.091
| | August
|-
| | 
| | 
| | 
| | 2\21
| | 
| | 
| | 
| | 
| | 
|
| | 114.286
| | August
|-
| | 
| | 
| | 
| | 
| | 3\30
| | 
| | 
| | 
| | 
|
| | 120.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 4\39
| | 
| | 
| | 
|
| | 123.077
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 5\48
| | 
| | 
|
| | 125.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\57
| | 
|
| | 126.316
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\66
|
| | 127.273
| | 
|-
| | 
| | 1\9
| | 
| | 
| | 
| | 
| | 
| | 
| | 
|
| | 133.333
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 8\69
|
| | 139.134
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\60
| | 
|
| | 140.000
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\51
| | 
| | 
|
| | 141.176
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 5\42
| | 
| | 
| | 
|
| | 142.857
| | 
|-
| | 
| | 
| | 
| | 
| | 4\33
| | 
| | 
| | 
| | 
|
| | 145.4545
| | 
|-
| | 
| | 
| | 
| | 3\24
| | 
| | 
| | 
| | 
| | 
|
| | 150.000
| |[[Triforce]]
|-
|
|
|
|
|5\39
|
|
|
|
|
|153.846
|Triforce
|-
| | 
| | 
| | 2\15
| | 
| | 
| | 
| | 
| | 
| | 
|
| | 160.000
| | Triforce
|-
| | 
| | 
| | 
| | 3/21
| | 
| | 
| | 
| | 
| | 
|
| | 171.429
| | 
|-
| | 
| | 
| | 
| | 
| | 4/27
| | 
| | 
| | 
| | 
|
| | 177.778
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 5/33
| | 
| | 
| | 
|
| | 181.818
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\39
| | 
| | 
|
| | 184.615
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\45
| | 
|
| | 186.667
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 8\51
|
| | 118.235
| | 
|-
| | 1\6
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
|
| | 200.000
| | 
|}

==Four periods per octave==

{| class="wikitable"
|-
! colspan="18" | Generator
! | Cents
! | Comments
|-
| | 0\4
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 0
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\76
| | 15.78947
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\72
| | 
| | 16.<u>6</u>
| | [[Quadritikleismic|Quadritikleismic]]
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 2\140
| | 17.14286
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\68
| | 
| | 
| | 17.64706
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\64
| | 
| | 
| | 
| | 18.75
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\60
| | 
| | 
| | 
| | 
| | 20
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\56
| | 
| | 
| | 
| | 
| | 
| | 21.42857
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\52
| | 
| | 
| | 
| | 
| | 
| | 
| | 23.06792
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\48
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 25
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\44
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 27.<u>27</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\40
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 30
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\36
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 33.<u>3</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 1\32
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 37.5
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 1\28
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 42.85714
| | 
|-
| | 
| | 
| | 
| | 
| | 1\24
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 50
| | 
|-
| | 
| | 
| | 
| | 1\20
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 60
| | 
|-
| | 
| | 
| | 1\16
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 75
| | [[Diminished|Diminished]]
|-
| | 
| | 
| | 
| | 2\28
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 85.<u>714285</u>
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 3\40
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 90
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 4\52
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 92.30769
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 5\64
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 93.75
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\76
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 94.73684
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\88
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 95.<u>45</u>
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 8\100
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 96
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 9\112
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 96.42857
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 10\124
| | 
| | 
| | 
| | 
| | 
| | 
| | 96.77419
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 11\136
| | 
| | 
| | 
| | 
| | 
| | 97.08852
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 12\148
| | 
| | 
| | 
| | 
| | 97.<u>297</u>
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 13\160
| | 
| | 
| | 
| | 97.5
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 14\172
| | 
| | 
| | 97.67442
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 15\184
| | 
| | 97.82609
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 16\196
| | 97.95918
| | Diminished
|-
| | 
| | 1\12
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 100
| | Diminished
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 17\200
| | 102
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 16\188
| | 
| | 102.12766
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 15\176
| | 
| | 
| | 102.<u>27</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 14\164
| | 
| | 
| | 
| | 102.<u>43902</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 13\152
| | 
| | 
| | 
| | 
| | 102.63158
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 12\140
| | 
| | 
| | 
| | 
| | 
| | 102.85714
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 11\128
| | 
| | 
| | 
| | 
| | 
| | 
| | 103.125
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 10\116
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 103.448275
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 9\104
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 103.84615
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 8\92
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 104.34783
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\80
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 105
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\68
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 105.88235
| | [[Bidia|Bidia]]
|-
| | 
| | 
| | 
| | 
| | 
| | 5\56
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 107.14286
| | 
|-
| | 
| | 
| | 
| | 
| | 4\44
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 109.<u>09</u>
| | 
|-
| | 
| | 
| | 
| | 3\32
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 112.5
| | 
|-
| | 
| | 
| | 2\20
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 120
| | 
|-
| | 
| | 
| | 
| | 3\28
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 128.57143
| | 
|-
| | 
| | 
| | 
| | 
| | 4\36
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 133.<u>3</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 5\44
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 136.<u>36</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 6\52
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 138.46154
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 7\60
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 140
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 8\68
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 141.17646
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 9\76
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 142.10526
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 10\84
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 142.85714
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 11\92
| | 
| | 
| | 
| | 
| | 
| | 
| | 143.47826
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 12\100
| | 
| | 
| | 
| | 
| | 
| | 144
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 13\108
| | 
| | 
| | 
| | 
| | 144.<u>4</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 14\116
| | 
| | 
| | 
| | 144.82759
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 15\124
| | 
| | 
| | 145.16129
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 16\132
| | 
| | 145.<u>45</u>
| | 
|-
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 17\140
| | 145.<u>714285</u>
| | 
|-
| | 1\8
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 
| | 150
| | 
|}

==Five periods per octave==
<ul><li>[[Blackwood|Blackwood]]/[[blacksmith|blacksmith]] - The prime 3, and in blacksmith also 7, is represented using [[5edo|5edo]]. The generator gets you to all intervals of 5.</li><li>Elderthing - generator of phi. Two generators up to 3, two down to 7, other primes are more complex. (One generator up or one down are ambiguous 13.)</li></ul>
==Six periods per octave==
<ul><li>[[Hexe|Hexe]] - The 2.5.7 subgroup is represented using [[6edo|6edo]], and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to [[12edo|12edo]].</li></ul>
==Seven periods per octave==
<ul><li>[[Whitewood|Whitewood]] - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5.</li><li>[[Jamesbond|Jamesbond]]/[[septimal|septimal]] - The 5-limit (and in septimal the prime 11) is represented using [[7edo|7edo]], and the generator is only used for intervals of 7.</li><li>[[Sevond|Sevond]] - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.</li><li>[[Absurdity|Absurdity]] - A complex temperament (perhaps "absurdly" so).</li></ul>
==Eight periods per octave==
<ul><li>[[Octoid|Octoid]] - 16-cent generator, sub-cent accuracy.</li></ul>
==Nine periods per octave==
<ul><li>[[Ennealimmal|Ennealimmal]] - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate.</li></ul>
==Twelve periods per octave==
See also: [[Pythagorean_family|Pythagorean family]]

Temperaments in this family are interesting because they can be thought of as [[12edo|12edo]] with microtonal alterations.

<ul><li>[[Compton|Compton]] - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called [[waage|waage]]), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of [[72edo|72edo]] might make this more concrete.</li><li>[[Catler|Catler]] - 5-limit as in 12edo; intervals of 7 are off by one generator.</li><li>[[Atomic|Atomic]] - Does not temper out the schisma, so 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.</li></ul>
[[Category:Rank 2]]
[[Category:Lists of temperaments]]