Xenharmonic Wiki

Map of rank-2 temperaments: Difference between revisions

← Older edit
VisualWikitext
ArrowHead294 (talk | contribs)
14,512 edits
m Text replacement - "lendrism" to "lendroschism"
 
(19 intermediate revisions by 2 users not shown)
Line 1: Line 1:
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]].
Since this is the largest subset, it has its own page: [[map of linear temperaments]].


Line 926: Line 926:
|}
|}


==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 sortable mw-collapsible"
{| 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
| |
| |
|
|
|
| | 50.000
| | Semiaug/[[Augmented family#Hemiug|Hemiug]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\24
|2\45
|  
|
|  
|
|  
|
|  
|
|  
|53.333
| 50.000
|Hemiug
| Semiaug/[[Augmented family#Hemiug| Hemiug]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 1\21
|  
| |  
|  
| |
| 2\45
| |  
|  
|
|  
|
|  
|
|  
| | 57.143
| 53.333
| | Hemiug
| Hemiug
|-
|-
| |
|  
| |
|  
| | 1\18
|  
| |
| 1\21
| |
|  
| |
|  
| |
|  
|
|  
|
|  
|
|  
| | 66.667
| 57.143
| |  
| Hemiug
|-
| |  
| | 1\15
| |
| |
| |
| |
| |
|
|
|
| | 80.000
| |
|-
| |
| |
| |
| |
| |
| |
| | 6\87
|
|
|
| | 82.759
| |
|-
|
|
|
|
|
|
|
|11\159
|
|
|83.019
|[[Tritikleismic]]
|-
|-
|
|  
|
|  
|
| 1\18
|
|  
|
|  
|
|  
|
|  
|
|  
|16\231
|  
|
|  
|83.117
| 66.667
|Tritikleismic
|  
|-
|-
| |  
|  
| |
| 1\15
| |  
|  
| |  
|  
| |  
|  
| | 5\72
|  
| |  
|  
|
|  
|
|  
|
|  
| | 83.333
| 80.000
| | Tritikleismic
|  
|-
|-
| |
|  
| |
|  
| |
|  
| |
|  
| | 4\57
|  
| |
|  
| |
| 6\87
|
|  
|
|  
|
|  
| | 84.211
| 82.759
| | Tritikleismic
|  
|-
| |  
| |  
| |  
| | 3\42
| |
| |
| |
|
|
|
| | 85.714
| |
|-
| |
| |
| | 2\27
| |
| |
| |
| |
|
|
|
| | 88.889
| |[[Augmented]]/[[Augene]]
|-
|
|
|
|3\39
|
|
|
|
|
|
|92.308
|Augmented/Augene/[[Fog]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|4\51
|  
|
|  
|
|  
|
| 11\159
|
|  
|
|  
|94.118
| 83.019
|Augmented/Augene/Fog
| [[Tritikleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|5\63
|  
|
|  
|
|  
|
| 16\231
|
|  
|95.238
| 83.117
|Augmented/Augene/Fog
| Tritikleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 5\72
|
|  
|11\138
|  
|
|  
|
|  
|95.652
| 83.333
|Augmented Augene/Fog
| Tritikleismic
|-
|
|
|
|
|
|
|6\75
|
|
|
|96
|Augmented/Augene/Fog
|-
|
|
|
|
|
|
|
|7\87
|
|
|96.552
|Augmented/Augene/[[Misty]]
|-
|
|
|
|
|
|
|
|
|
|15\186
|96.774
|Augmented/Augene/Misty
|-
|
|
|
|
|
|
|
|
|8\99
|
|96.97
|Augmented/Augene/Misty
|-
| | 1\12
| |
| |
| |
| |
| |
| |
|
|
|
| | 100.000
| | Augmented/Augene/[[August]]
|-
|-
| |  
|  
| |  
|  
| | 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]]/[[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
| |  
| |  
| |
| |
| |
| |
|
|
|
| | 160.000
| | Triforce
|-
| |
| | 3\21
| |
| |
| |
| |
| |
|
|
|
| | 171.429
| |[[Oodako]]
|-
|
|
|
|7\48
|
|
|
|
|
|
|175
|Oodako
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\75
|  
|
|  
|
| 6\75
|
|  
|
|  
|
|  
|176
| 96
|Oodako
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|15\102
|  
|
|  
|
| 7\87
|
|  
|
|  
|176.471
| 96.552
|Oodako
| Augmented/Augene/[[Misty]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|19\129
|  
|
|  
|
|  
|
| 15\186
|176.744
| 96.774
|Oodako
| Augmented/Augene/Misty
|-
|-
|
|  
|
|  
|4\27
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\99
|
|  
|177.778
| 96.97
|Oodako
| Augmented/Augene/Misty
|-
| | 1\6
| |
| |  
| |
| |
| |
| |
|
|
|
| | 200.000
| |
|}
 
==Four periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator !! Cents !! Comments
|-
|-
| 0\4 || || || || || || 0 ||  
| 1\12
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 100.000
| Augmented/Augene/[[August]]
|-
|-
| || || || 1\76 || || || 15.789 ||  
|  
|  
| 3\33
|  
|  
|  
|  
|  
|  
|  
| 109.091
| August
|-
|-
| ||  ||  || 1\72 ||  ||  || 16.667 || [[Quadritikleismic]]
|  
|-
| 2\21
|
|  
|
|  
|
|  
|
|  
|
|  
|3\212
|  
|16.981
|  
|Quadritikleismic
|  
|-
| 114.286
| ||  ||  ||  || 2\140 ||  || 17.143 || Quadritikleismic
| August
|-
|-
| || || || 1\68 || || || 17.647 || Quadritikleismic
|  
|  
| 3\30
|  
|  
|  
|  
|  
|  
|  
| 120.000
|  
|-
|-
| || || || 1\64 || || || 18.75 ||  
| 1\9
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 133.333
|  
|-
|-
| || ||  || 1\60 ||  ||  || 20 ||  
|  
|-
|  
|  ||  ||  || ... ||  ||  || ... ||  
| 4\33
|-
|  
|  ||  ||  || 1\36 ||  ||  || 33.333 ||  
|  
|-
|  
| ||  ||  || 1\32 ||  ||  || 37.5 ||  
|  
|  
|  
|  
| 145.455
|  
|-
|-
| || || || 1\28 || || || 42.857 ||  
|  
| 3\24
|  
|  
|  
|  
|  
|  
|  
|  
| 150.000
| [[Triforce]]
|-
|-
|
|
|
|
|
| 5\39
|
|
|2\52
|  
|
|  
|46.154
|  
|[[Hemidim]]
|  
|  
|  
| 153.846
| Triforce
|-
|-
|
| 2\15
|
|  
|
|  
|
|  
|
|  
|3\76
|  
|47.368
|  
|Hemidim
|  
|-
|  
| ||  || 1\24 ||  ||  ||  || 50 || Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|  
|-
| 160.000
|  || 1\20 ||  ||  ||  ||  || 60 ||  
| Triforce
|-
| 1\16 ||  ||  ||  ||  ||  || 75 ||  
|-
|
|2\28
|
|
|
|
|85.714
|[[Demolished]]
|-
|
|
|3\40
|
|
|
|90
|Demolished
|-
|-
| 1\12 ||  ||  ||  ||  ||  || 100 || Demolished/[[Diminished]]
|  
|-
| 3\21
|
|  
|
|
|14\164
|
|
|102.439
|Diminished
|-
|
|
|
|
|27\316
|
|102.532
|Diminished/[[Unlit]]
|-
|
|
|
|
|
|40\468
|102.564
|Diminished/Unlit
|-
|
|
|
|13\152
|
|
|102.632
|Diminished/Unlit/[[Undim]]
|-
|
|
|
|
|
|38\444
|102.703
|Diminished/Undim
|-
|
|
|
|
|25\292
|
|102.740
|Diminished/Undim
|-
|
|
|
|12\140
|
|
|102.857
|Diminished/Undim
|-
|
|
|
|11\128
|
|
|103.125
|Diminished
|-
|
|
|
|10\116
|
|
|103.448
|Diminished
|-
|
|
|
|9\104
|
|
|103.846
|Diminished
|-
|
|
|
|8\92
|
|
|104.348
|Diminished
|-
|  ||  ||  || 7\80 ||  ||  || 105 || Diminished/[[Bidia]]
|-
|
|
|
|
|
|20\228
|105.263
|Diminished/Bidia
|-
|
|
|
|
|13\148
|
|105.405
|Diminished/Bidia
|-
|  ||  ||  || 6\68 ||  ||  || 105.882 || Diminished/Bidia
|-
|  ||  ||  || 5\56 ||  ||  || 107.143 || Diminished/Bidia
|-
|  ||  || 4\44 ||  ||  ||  || 109.091 || Diminished
|-
|  || 3\32 ||  ||  ||  ||  || 112.5 || Diminished
|-
| 2\20 ||  ||  ||  ||  ||  || 120 || Diminished
|-
|
|3\28
|
|
|
|
|128.571
|
|-
| 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 sortable mw-collapsible"
! colspan="9" |Generator!!Cents !!Comments
|-
|0\5 ||  || ||
|
|  
|  
|  
|  
|  
|  
| || 0||
|  
|-
|  
|
|  
|
|  
|
| 171.429
|
| [[Oodako]]
|
|1\140
|
|
|
|8.571
|
|-
|
|
|
|
|
|1\135
|
|
|
|8.889
|[[5th-octave temperaments#Slendrismic|Slendrismic]]
|-
|-
|
|  
|
|  
|
|  
|
| 7\48
|
|  
|
|  
|
|  
|3\400
|  
|
|  
|9
|  
|Slendrismic
| 175
| Oodako
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 11\75
|
|  
|
|  
|
|  
|5\665
|  
|9.023
|  
|Slendrismic
| 176
| Oodako
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 15\102
|2\265
|  
|
|  
|
|  
|9.057
|  
|Slendrismic
| 176.471
| Oodako
|-
|-
|
|
|
|
|
|1\130
|
|
|
|9.231
|Slendrismic/[[Hemipental]]
|-
|
|
|
|
|
|
|
|
|4\515
|9.32
|Hemipental
|-
|
|
|
|
|
|
|
|3\385
|
|9.351
|Hemipental
|-
|
|
|
|
|
|
|
|
|5\640
|9.375
|Hemipental
|-
|
|
|
|
|
|
|2\255
|
|
|9.412
|Hemipental
|-
|
|
|
|
|
|1\125
|
|
|
|9.6
|Hemipental
|-
|
|
|
|
|
|1\120
|
|
|
|10
|
|-
|
|
|
|
|
|1\115
|
|
|
|10.435
|
|-
|
|
|
|
|
|...
|
|
|
|...
|
|-
|
|
|
|
|
|1\70
|
|
|
|17.143
|
|-
|
|
|
|
|
|1\65
|
|
|
|18.462
|[[Pental (temperament)|Pental]]
|-
|
|
|
|
|
|
|
|
|4\255
|18.824
|Pental
|-
|
|
|
|
|
|
|
|3\190
|
|18.947
|Pental
|-
|
|
|
|
|
|
|
|
|5\315
|19.048
|Pental
|-
|
|
|
|
|
|
|2\125
|
|
|19.2
|Pental
|-
|
|
|
|
|
|
|
|3\185
|
|19.459
|Pental
|-
|
|
|
|
|
|1\60
|
|
|
|20
|Pental
|-
|
|
|
|
|
|1\55
|
|
|
|21.818
|
|-
|
|
|
|
|
|1\50
|
|
|
|24
|
|-
|
|
|
|
|
|1\45
|
|
|
|26.67
|
|-
|
|
|
|
|1\40
|
|
|
|
|30
|
|-
|
|
|
|1\35
|
|
|
|
|
|34.286
|
|-
|
|
|1\30
|
|
|
|
|
|
|40
|
|-
|
|1\25
|
|
|
|
|
|
|
|48
|
|-
|1\20
|
|
|
|
|
|
|
|
|60
|
|-
|
|2\35
|
|
|
|
|
|
|
|68.571
|[[Coblack]]
|-
|
|
|
|5\85
|
|
|
|
|
|70.588
|Coblack
|-
|
|
|3\50
|
|
|
|
|
|
|72
|Coblack
|-
|
|
|
|
|7\115
|
|
|
|
|73.043
|Coblack
|-
|
|
|
|4\65
|
|
|
|
|
|73.846
|Coblack
|-
| 1\15 ||  ||  ||
|
|  
|  
|  
|  
|  
|  
| || 80||[[Blackwood]]/[[Blacksmith]]
|  
|  
|  
| 19\129
|  
|
|
| 176.744
| Oodako
|-
|-
|
|  
|
|  
|
| 4\27
|5\70
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|85.714
|  
|Blackwood/Blacksmith
| 177.778
| Oodako
|-
|-
|
| 1\6
|
|  
|4\55
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|87.273
|  
|Blackwood/Blacksmith
| 200.000
|
|}
 
== Four periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator
! Cents
! Comments
|-
|-
|
| 0\4
|
|  
|
|  
|7\95
|  
|
|  
|
|  
|
| 0
|
|  
|
|88.421
|Blackwood/Blacksmith
|-
|-
|
|  
|3\40
|  
|
|  
|
| 1\76
|
|  
|
|  
|
| 15.789
|
|  
|
|90
|Blackwood/Blacksmith
|-
|
|
|
|8\105
|
|
|
|
|
|91.429
|Blackwood/Blacksmith
|-
|
|
|5\65
|
|
|
|
|
|
|92.308
|Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
|  
|7\90
| 1\72
|
|  
|
|  
|
| 16.667
|
| [[Quadritikleismic]]
|
|93.333
|Blackwood/Blacksmith
|-
|-
|2\25
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\212
|
| 16.981
|
| Quadritikleismic
|
|96
|Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|5\60
|  
|
|  
|
| 2\140
|
|  
|
| 17.143
|
| Quadritikleismic
|
|100
|Blackwood
|-
|-
|
|  
|
|  
|
|  
|8\95
| 1\68
|
|  
|
|  
|
| 17.647
|
| Quadritikleismic
|
|101.053
|Blackwood
|-
|-
|
|  
|3\35
|  
|
|  
|
| 1\64
|
|  
|
|  
|
| 18.75
|
|  
|
|102.857
|Blackwood
|-
|-
|
|  
|
|  
|
|  
|7\80
| 1\60
|
|  
|
|  
|
| 20
|
|  
|
|105
|Blackwood
|-
|-
|
|  
|
|  
|4\45
|  
|
| ...
|
|  
|
|  
|
| ...
|
|  
|
|106.667
|Blackwood
|-
|-
|
|  
|
|  
|
|  
|5\55
| 1\36
|
|  
|
|  
|
| 33.333
|
|  
|
|109.091
|Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 1\32
|6\65
|  
|
|  
|
| 37.5
|
|  
|
|110.769
|Blackwood/[[Quintosec]]/[[Sengasec]]
|-
|-
|
|  
|
|  
|
|  
|
| 1\28
|
|  
|
|  
|
| 42.857
|
|  
|25\270
|111.111
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 2\52
|
|  
|
| 46.154
|19\205
| [[Hemidim]]
|
|111.220
|Blackwood/Quintosec/SengasecQintosec
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\76
|13\140
| 47.368
|
| Hemidim
|
|111.429
|Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
|
|  
|
|  
|
| 1\24
|
|  
|
|  
|
|  
|
| 50
|20\215
| Hemidim/[[4th-octave temperaments#Darian calendar| Darian calendar]]
|
|111.628
|Blackwood/Qintosec
|-
|-
|
|  
|
| 1\20
|
|  
|
|  
|
|  
|7\75
|  
|
| 60
|
|  
|
|112
|Blackwood/[[Qinto]]
|-
|-
|
| 1\16
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 75
|15\160
|  
|
|112.5
|Blackwood/Qinto
|-
|-
|
|  
|
| 2\28
|
|  
|
|  
|
|  
|
|  
|8\85
| 85.714
|
| [[Demolished]]
|
|112.941
|Blackwood/[[Phi as a Generator|Elderthing]]
|-
|-
|
|  
|
|  
|
| 3\40
|
|  
|
|  
|
|  
|9\95
| 90
|
| Demolished
|
|113.684
|Blackwood
|-
|-
|
| 1\12
|
|  
|
|  
|
|  
|
|  
|
|  
|10\105
| 100
|
| Demolished/[[Diminished]]
|
|114.286
|Blackwood
|-
|-
|1\10
|  
|
|  
|
|  
|
| 14\164
|
|  
|
|  
|
| 102.439
|
| Diminished
|
|120
|Blackwood
|}
 
==Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" |Generator!!Cents !!Comments
|-
|-
|0\6||  || ||  
|  
|
|  
|
|  
|||0||
|  
| 27\316
|  
| 102.532
| Diminished/[[Unlit]]
|-
|-
|
|  
|
|  
|
|  
|1\288
|  
|
|  
|
| 40\468
|
| 102.564
|4.167
| Diminished/Unlit
|
|-
|-
|
|  
|
|  
|
|  
|1\282
| 13\152
|
|  
|
|  
|
| 102.632
|4.255
| Diminished/Unlit/[[Undim]]
|
|-
|-
|
|  
|
|  
|
|  
|1\276
|  
|2\552
|  
|
| 38\444
|
| 102.703
|4.348
| Diminished/Undim
|[[Sextile]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 25\292
|3\822
|  
|
| 102.740
|4.380
| Diminished/Undim
|Sextile
|-
|-
|
|  
|
|  
|
|  
|
| 12\140
|
|  
|
|  
|4\1092
| 102.857
|4.396
| Diminished/Undim
|Sextile
|-
|
|
|
|1\270
|
|
|
|4.444
|Sextile
|-
|
|
|
|1\264
|
|
|
|4.545
|
|-
|-
|
|  
|
|  
|
|  
|...
| 11\128
|
|  
|
|  
|
| 103.125
|...
| Diminished
|
|-
|-
|
|  
|
|  
|
|  
|1\90
| 10\116
|
|  
|
|  
|
| 103.448
|13.333
| Diminished
|
|-
|-
|
|  
|
|  
|
|  
|1\84
| 9\104
|
|  
|
|  
|
| 103.846
|14.286
| Diminished
|
|-
|-
|
|  
|
|  
|
|  
|1\78
| 8\92
|
|  
|
|  
|
| 104.348
|15.385
| Diminished
|
|-
|-
|
|  
|
|  
|
|  
|1\72
| 7\80
|
|  
|
|  
|
| 105
|16.667
| Diminished/[[Bidia]]
|[[Stearnscape]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 20\228
|4\282
| 105.263
|17.021
| Diminished/Bidia
|Stearnscape
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 13\148
|3\210
|  
|
| 105.405
|17.143
| Diminished/Bidia
|Stearnscape
|-
|-
|
|  
|
|  
|
|  
|
| 6\68
|2\138
|  
|
|  
|
| 105.882
|17.391
| Diminished/Bidia
|
|-
|-
|
|  
|
|  
|
|  
|1\66
| 5\56
|
|  
|
|  
|
| 107.143
|18.182
| Diminished/Bidia
|
|-
|-
|
|  
|
|  
|
| 4\44
|1\60
|  
|
|  
|
|  
|
| 109.091
|20
| Diminished
|
|-
|-
|
|  
|
| 3\32
|
|  
|1\54
|  
|
|  
|
|  
|
| 112.5
|22.222
| Diminished
|
|-
|-
|
| 2\20
|
|  
|
|  
|1\48
|  
|
|  
|
|  
|
| 120
|25
| Diminished
|
|-
|
|
|
|1\42
|
|
|
|28.571
|
|-
|
|
|
|1\36
|
|
|
|33.333
|
|-
|
|
|1\30
|
|
|
|
|40
|
|-
|-
|
|  
|1\24
| 3\28
|
|  
|
|  
|
|  
|
|  
|
| 128.571
|50
|  
|  
|-
|-
|1\18
| 1\8
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 150
| 66.667
|  
|
|-
|
|2\30
|
|
|
|
|
| 80
|[[Hexe]]
|-
|
|
|
|5\72
|
|
|
|83.333
|Hexe
|-
|
|
|3\42
|
|
|
|
|85.714
| Hexe
|-
|
|
|
|4\54
|
|
|
|88.889
|Hexe
|-
|1\12
|
|
|
|
|
|
| 100
|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)}}
== 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"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!! Cents!!Comments
! colspan="9" | Generator
! Cents
! Comments
|-
|-
| 0\7|| || ||
| 0\5
|
|  
|
|  
|
|  
| ||0||
|  
|  
|  
|  
|  
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\91
|  
|
| 1\140
|
|  
|
|  
|13.187
|  
|
| 8.571
|-
|  
|
|
|
|
|1\84
|
|
|
|14.286
|[[Absurdity]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\135
|
|  
|4\329
|  
|14.59
|  
|Absurdity
| 8.889
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|
|
|
|  
|
|  
|
|  
|
|  
|
|  
|3\245
|  
|
| 3\400
|14.69
|  
|
| 9
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\161
|  
|
|  
|
|  
|14.907
| 5\665
|
| 9.023
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\77
|  
|
|  
|
| 2\265
|
|  
|15.584
|  
|[[Septant]]
| 9.057
|-
| Slendroschismic
|
|
|
|
|
|
|
|4\301
|15.947
|Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\130
|3\224
|  
|
|  
|16.071
|  
|Septant
| 9.231
| Slendroschismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\147
|  
|
|  
|
|  
|16.327
| 4\515
|Septant
| 9.32
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\70
|  
|
|  
|
|  
|
| 3\385
|17.143
|  
|
| 9.351
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\63
|  
|
|  
|
|  
|
|  
|19.048
| 5\640
|[[Sevond]]
| 9.375
|-
| Hemipental
|
|
|
|
|
|2\119
|
|
|20.168
|Sevond
|-
|
|
|
|
|1\56
|
|
|
|21.429
|Sevond
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\49
|  
|
|  
|
| 2\255
|
|  
|24.49
|  
|
| 9.412
| Hemipental
|-
|-
|
|
|
|
|
|  
|1\42
|  
|
|  
|
| 1\125
|
|  
|
|  
|28.571
|  
|[[Mistismic temperaments#Neutron|Neutron]]
| 9.6
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\119
| 1\120
|
|  
|
|  
|30.252
|  
|Neutron
| 10
|
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\115
|5\196
|  
|
|  
|30.612
|  
|Neutron
| 10.435
|-
|  
|
|
|
|
|
|
|
|7\273
|30.769
|Neutron
|-
|
|
|
|
|2\77
|
|
|
|31.169
|Neutron
|-
|-
|
|  
|
|  
|1\35
|  
|
|  
|
|  
|
| 1\70
|
|  
|
|  
|34.286
|  
|[[Whitewood family#Redwood|Redwood]]
| 17.143
|  
|-
|-
|
|  
|
|  
|
|  
| 2\63
|  
|
|  
|
| 1\65
|
|  
|
|  
|38.095
|  
|Redwood
| 18.462
| [[Pental (temperament)| Pental]]
|-
|-
|
|  
| 1\28
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|42.857
| 4\255
|Redwood/[[Whitewood]]
| 18.824
| Pental
|-
|-
|
|  
|
|  
|
|  
| 3\77
|  
|
|  
|
|  
|
|  
|
| 3\190
| 46.753
|  
|Whitewood
| 18.947
| Pental
|-
|-
|
|  
|
|  
|2\49
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|48.980
| 5\315
|Whitewood
| 19.048
| Pental
|-
|-
|
|  
|
|  
|
|  
|3\70
|  
|
|  
|
|  
|
| 2\125
|
|  
| 51.429
|  
|Whitewood
| 19.2
| Pental
|-
|-
|1\21
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\185
|57.143
|  
|Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| 19.459
| Pental
|-
|-
|
|  
|
|  
|
|  
| 4\77
|  
|
|  
|
| 1\60
|
|  
|
|  
|62.338
|  
|Jamesbond/Septimal
| 20
| Pental
|-
|-
|
|  
|
|  
|3\56
|  
|
|  
|
|  
|
| 1\55
|
|  
|
|  
|64.286
|  
| Jamesbond/Septimal
| 21.818
|  
|-
|-
|
|  
|
|  
|
|  
|5\91
|  
|
|  
|
| 1\50
|
|  
|
|  
|65.934
|  
|Jamesbond/Septimal
| 24
|  
|-
|-
|
|  
|2\35
|  
|
|  
|
|  
|
|  
|
| 1\45
|
|  
|
|  
| 68.571
|  
|Jamesbond/Septimal/[[Greenwood]]
| 26.67
|-
|  
|
|
|
|5\84
|
|
|
|
|71.429
|Jamesbond/Septimal/Greenwood
|-
|
|
|3\49
|
|
|
|
|
| 73.469
|Jamesbond/Septimal/Greenwood
|-
|-
|
|  
|
|  
|
|  
|4\63
|  
|
| 1\40
|
|  
|
|  
|
|  
|76.190
|  
|Jamesbond/Septimal/Greenwood
| 30
|  
|-
|-
| 1\14
|  
|
|  
|
|  
|
| 1\35
|
|  
|
|  
|
|  
|
|  
|85.714
|  
|Jamesbond/Septimal/Greenwood
| 34.286
|}
|  
 
==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="9" |Generator!!Cents!!Comments
|-
|-
|0\8||  ||
|  
|
|  
|
| 1\30
|
|  
|
|  
|
|  
| ||0||
|  
|-
|  
|
|  
|
| 40
|
|  
|
|
|
|1\80
|
|
|15
|
|-
|
|
|
|
|
|
|
|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
|
|
|
|
|
|
|
|30
|
|-
|-
|
|  
|
| 1\25
|2\72
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|33.333
| 48
|
|  
|-
|-
|1\32
| 1\20
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|37.5
| 60
|[[Semidim]]
|  
|-
|-
|
|  
|
| 2\35
|3\88
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|40.909
| 68.571
|Semidim
| [[Coblack]]
|-
|
|2\56
|
|
|
|
|
|
|
|42.857
|Semidim
|-
|
|
|3\80
|
|
|
|
|
|
|45
|Semidim
|-
|-
|
|  
|
|  
|
|  
|4\104
| 5\85
|
|  
|
|  
|
|  
|
|  
|
|  
|46.154
| 70.588
|Semidim
| Coblack
|-
|-
|
|  
|
|  
|
| 3\50
|
|  
|5\128
|  
|
|  
|
|  
|
|  
|
|  
|46.875
| 72
|Semidim
| Coblack
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 7\115
|6\152
|  
|
|  
|
|  
|
|  
|47.368
| 73.043
|Semidim
| Coblack
|-
|-
|
|  
|
|  
|
|  
|
| 4\65
|
|  
|
|  
|7\176
|  
|
|  
|
|  
|47.727
| 73.846
|Semidim
| Coblack
|-
|
|
|
|
|
|
|8\200
|
|
|48
|Semidim
|-
|-
|
| 1\15
|
|  
|
|  
|
|  
|
|  
|
|  
|9\224
|  
|
|  
|
|  
|48.214
| 80
|Semidim/[[Octant]]
| [[Blackwood]]/[[Blacksmith]]
|-
|-
|
|  
|
|  
|
|  
|
| 5\70
|
|  
|
|  
|
|  
|
|  
|28\696
|  
|48.276
| 85.714
|Semidim/Octant
| Blackwood/Blacksmith
|-
|
|
|
|
|
|
|
|19\472
|
|48.305
|Semidim/Octant
|-
|
|
|
|
|
|
|10\248
|
|
|48.387
|Semidim
|-
|-
|1\24
|
|
|
|
|
|
|
|
|50
|Semidim
|-
|2\40
|
|
|
|
|
|
|
|
| 60
|
|-
|1\16
|
|
|
|
|
|
|
|
|75
|
|}
==Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!! Comments
|-
|0\9||  || ||
|  
|  
|
|  
|
| 4\55
| ||0||
|  
|-
|  
|
|  
|
|  
|
|  
|
|  
|1\72
| 87.273
|
| Blackwood/Blacksmith
|
|
|16.667
|[[Enneaportent]]
|-
|
|
|
|
|
|
|
|4\279
|17.204
|Enneaportent
|-
|-
|
|
|
|
|
|
|3\207
|
|17.391
|Enneaportent
|-
|
|
|
|
|
|2\135
|
|
|17.778
|Enneaportent
|-
|
|
|
|1\63
|
|
|
|
|19.048
|Enneaportent
|-
|
|
|1\54
|
|
|
|
|
|22.222
|
|-
|
|1\45
|
|
|
|
|
|
|26.667
|
|-
|1\36
|
|
|
|
|
|
|
|33.333
|[[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
|-
|
|
|
|4\135
|
|
|
|
|35.556
|No-five tritrizo
|-
|
|
|3\99
|
|
|
|
|
|36.364
|No-five tritrizo
|-
|
|2\63
|
|
|
|
|
|
|38.095
|[[Niner]]
|-
|
|
|3\90
|  
|  
|
|
|
|
|40
|Niner
|-
|1\27
|
|
|
|
|
|
|
| 44.444
|Niner
|-
|
|
|4\99
|
|
|
|
|
|48.485
|[[Ennealimmal]]
|-
|
|
|
|7\171
|
|
|
|
|49.123
|Ennealimmal
|-
|
|3\72
|  
|  
|
|  
|
| 7\95
|
|  
|
|  
|
|  
| 50
|  
|Ennealimmal
|  
|-
| 88.421
|
| Blackwood/Blacksmith
|
|
|
|
|
|
|20\477
|50.314
|[[Novemkleismic]]
|-
|
|
|
|
|
|
|17\405
|
|50.370
|Novemkleismic
|-
|
|
|
|
|
|14\333
|
|
|50.451
|Novemkleismic
|-
|
|
|
|
|11\261
|
|
|
|50.575
|Novemkleismic
|-
|
|
|
|8\189
|
|
|
|
|50.794
|Novemkleismic
|-
|
|
|5\117
|
|
|
|
|
|51.282
|
|-
|-
|2\45
|
|
|
|
|
|
|
|53.333
|  
|  
| 3\40
|
|
|
|
|
|
|
| 90
| Blackwood/Blacksmith
|-
|-
|1\18
|
|
|
|
|
|
|
| 66.667
|
|}
==Twelve periods per octave==
See also: [[Compton family]]
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!!Comments
|-
|0\12||  || ||
|
|  
|  
|
|  
|||0||
|  
| 8\105
|  
|  
|  
|
|
| 91.429
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
| 5\65
|1\636
|  
|
|  
|
|  
|
|  
|
|  
|1.887
|  
|
| 92.308
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
|  
|1\624
| 7\90
|
|  
|
|  
|
|  
|
|  
|1.923
|  
|
| 93.333
|-
| Blackwood/Blacksmith
|
|
|
|
|2\1236
|
|
|
|1.942
|[[Atomic]]
|-
|
|
|
|
|
|3\1848
|
|
|1.948
|Atomic
|-
|
|
|
|
|
|
|4\2460
|
|1.951
|Atomic
|-
|-
|
| 2\25
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\3072
|  
|1.953
|  
|Atomic
| 96
| Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|
| 5\60
|1\612
|  
|
|  
|
|  
|
|  
|
|  
|1.961
|  
|Atomic
| 100
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|1\600
| 8\95
|
|  
|
|  
|
|  
|
|  
|2
|  
|
| 101.053
| Blackwood
|-
|-
|
|  
|
| 3\35
|
|  
|1\588
|  
|
|  
|
|  
|
|  
|
|  
|2.041
|  
|
| 102.857
|-
| Blackwood
|
|
|
|1\576
|
|
|
|
|2.083
|
|-
|
|
|
|...
|
|
|
|
|...
|
|-
|-
|
|  
|
|  
|
|  
|1\108
| 7\80
|
|  
|
|  
|
|  
|
|  
|11.111
|  
|
| 105
| Blackwood
|-
|-
|
|  
|
|  
|
| 4\45
|1\96
|  
|
|  
|
|  
|
|  
|
|  
|12.5
|  
|[[Compton]]
| 106.667
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|1\84
| 5\55
|
|  
|
|  
|
|  
|
|  
|14.286
|  
|Compton
| 109.091
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 6\65
|3\240
|  
|
|  
|
|  
|15
|  
|Compton
| 110.769
|-
| Blackwood/[[Quintosec]]/[[Sengasec]]
|
|
|
|
|
|
|
|8\636
|15.094
|Compton
|-
|
|
|
|
|
|
|5\396
|
|15.152
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
|  
|15.217
| 25\270
|Compton
| 111.111
| Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\156
|  
|
|  
|
|  
|
| 19\205
|15.385
|  
|Compton
| 111.220
| Blackwood/Quintosec/SengasecQintosec
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 13\140
|7\540
|  
|15.556
|  
|Compton
| 111.429
| Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\384
|  
|
| 20\215
|15.625
|  
|Compton
| 111.628
|-
| Blackwood/Qintosec
|
|
|
|
|
|
|
|8\612
|15.686
|Compton
|-
|
|
|
|
|
|3\228
|
|
|15.789
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\75
|
|  
|7\528
|  
|15.909
|  
|Compton
| 112
| Blackwood/[[Qinto]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\300
|  
|
| 15\160
|16
|  
|Compton
| 112.5
| Blackwood/Qinto
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\85
|5\372
|  
|16.129
|  
|Compton
| 112.941
| Blackwood/[[Phi as a Generator| Elderthing]]
|-
|-
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|  
|
| 9\95
|
|  
|16.667
|  
|Compton
| 113.684
|-
| Blackwood
|
|
|1\60
|
|
|
|
|
|20
|Compton
|-
|
|
|
|2\108
|
|
|
|
|22.222
|
|-
|
|1\48
|
|
|
|
|
|
|25
|[[Catler]]
|-
|-
|
|  
|
|  
|
|  
|3\132
|  
|
|  
|
|  
|
| 10\105
|
|  
| 27.273
|  
|Catler
| 114.286
| Blackwood
|-
|-
|
| 1\10
|
|
| 2\84
|
|
|  
|
|  
|
|  
|
|  
|
|  
|28.571
|  
|Catler
| 120
| Blackwood
|}
 
== Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\6
|
|  
|
|  
|3\120
|  
|
|  
|
|  
|
|  
|
| 0
|30
|  
|Catler
|-
|1\36
|
|
|
|
|
|
|
|33.333
|Catler/[[Catnip]]
|-
|
|
|
|4\132
|
|
|
|
|36.364
|Catnip
|-
|
|
|3\96
|
|
|
|
|
|37.5
| Catnip
|-
|-
|
|  
|
|  
|
|  
|5\156
| 1\288
|
|  
|
|  
|
|  
|
| 4.167
|38.462
|  
|Catnip
|-
|-
|
|  
|2\60
|  
|
|  
|
| 1\282
|
|  
|
|  
|
|  
|
| 4.255
|40
|  
|Catnip
|-
|-
|
|  
|
|  
|
|  
|5\144
| 1\276
|
| 2\552
|
|  
|
|  
|
| 4.348
|41.667
| [[Sextile]]
|
|-
|-
|
|  
|
|  
|3\84
|  
|
|  
|
|  
|
| 3\822
|
|  
|
| 4.380
| 42.857
| Sextile
| [[Magnesium]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\1092
|16\444
| 4.396
|43.243
| Sextile
|Magnesium
|-
|
|
|
|
|
|
|13\360
|
|43.333
|Magnesium
|-
|-
|
|  
|
|  
|
|  
|
| 1\270
|
|  
|10\276
|  
|
|  
|
| 4.444
|43.378
| Sextile
|
|-
|-
|
|  
|
|  
|
|  
|
| 1\264
|7\192
|  
|
|  
|
|  
|
| 4.545
|43.75
|  
|
|-
|-
|
|  
|
|  
|
|  
|4\108
| ...
|
|  
|
|  
|
|  
|
| ...
|44.444
|  
|
|-
|-
|1\24
|
|
|
|
|
|
| 1\90
|
|
|
|
|
|
|
| 13.333
| 50
|
|
|-
|}
|
 
|
== See also ==
|
| 1\84
|
|
|
| 14.286
|
|-
|
|
|
| 1\78
|
|
|
| 15.385
|
|-
|
|
|
| 1\72
|
|
|
| 16.667
| [[Stearnscape]]
|-
|
|
|
|
|
|
| 4\282
| 17.021
| Stearnscape
|-
|
|
|
|
|
| 3\210
|
| 17.143
| Stearnscape
|-
|
|
|
|
| 2\138
|
|
| 17.391
|
|-
|
|
|
| 1\66
|
|
|
| 18.182
|
|-
|
|
|
| 1\60
|
|
|
| 20
|
|-
|
|
|
| 1\54
|
|
|
| 22.222
|
|-
|
|
|
| 1\48
|
|
|
| 25
|
|-
|
|
|
| 1\42
|
|
|
| 28.571
|
|-
|
|
|
| 1\36
|
|
|
| 33.333
|
|-
|
|
| 1\30
|
|
|
|
| 40
|
|-
|
| 1\24
|  
|  
|  
|
|
| 50
|
|-
| 1\18
|
|
|
|
|
|
| 66.667
|
|-
|
| 2\30
|
|
|
|
|
| 80
| [[Hexe]]
|-
|
|
|
| 5\72
|
|
|
| 83.333
| Hexe
|-
|
|
| 3\42
|
|
|
|
| 85.714
| Hexe
|-
|
|
|
| 4\54
|
|
|
| 88.889
| Hexe
|-
| 1\12
|  
|  
|  
|  
|  
|  
| 100
| Hexe
|}


*[[Fractional-octave temperaments]]: Lists dozens more temperaments beyond what can be listed here.
== 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
|
|
|
|
|
|
|
| 0
|
|-
|
|
|
|
| 1\91
|
|
|
| 13.187
|
|-
|
|
|
|
| 1\84
|
|
|
| 14.286
| [[Absurdity]]
|-
|
|
|
|
|
|
|
| 4\329
| 14.59
| Absurdity
|-
|
|
|
|
|
|
| 3\245
|
| 14.69
|
|-
|
|
|
|
|
| 2\161
|
|
| 14.907
|
|-
|
|
|
|
| 1\77
|
|
|
| 15.584
| [[Septant]]
|-
|
|
|
|
|
|
|
| 4\301
| 15.947
| Septant
|-
|
|
|
|
|
|
| 3\224
|
| 16.071
| Septant
|-
|
|
|
|
|
| 2\147
|
|
| 16.327
| Septant
|-
|
|
|
|
| 1\70
|
|
|
| 17.143
|
|-
|
|
|
|
| 1\63
|
|
|
| 19.048
| [[Sevond]]
|-
|
|
|
|
|
| 2\119
|
|
| 20.168
| Sevond
|-
|
|
|
|
| 1\56
|
|
|
| 21.429
| Sevond
|-
|
|
|
|
| 1\49
|
|
|
| 24.49
|
|-
|
|
|
| 1\42
|
|
|
|
| 28.571
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|
|
|
|
|
| 3\119
|
|
| 30.252
| Neutron
|-
|
|
|
|
|
|
| 5\196
|
| 30.612
| Neutron
|-
|
|
|
|
|
|
|
| 7\273
| 30.769
| Neutron
|-
|
|
|
|
| 2\77
|
|
|
| 31.169
| Neutron
|-
|
|
| 1\35
|
|
|
|
|
| 34.286
| [[Whitewood family#Redwood| Redwood]]
|-
|
|
|
| 2\63
|
|
|
|
| 38.095
| Redwood
|-
|
| 1\28
|
|
|
|
|
|
| 42.857
| Redwood/[[Whitewood]]
|-
|
|
|
| 3\77
|
|
|
|
| 46.753
| Whitewood
|-
|
|
| 2\49
|
|
|
|
|
| 48.980
| Whitewood
|-
|
|
|
| 3\70
|
|
|
|
| 51.429
| Whitewood
|-
| 1\21
|
|
|
|
|
|
|
| 57.143
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal| Septimal]]
|-
|
|
|
| 4\77
|
|
|
|
| 62.338
| Jamesbond/Septimal
|-
|
|
| 3\56
|
|
|
|
|
| 64.286
| Jamesbond/Septimal
|-
|
|
|
| 5\91
|
|
|
|
| 65.934
| Jamesbond/Septimal
|-
|
| 2\35
|
|
|
|
|
|
| 68.571
| Jamesbond/Septimal/[[Greenwood]]
|-
|
|
|
| 5\84
|
|
|
|
| 71.429
| Jamesbond/Septimal/Greenwood
|-
|
|
| 3\49
|
|
|
|
|
| 73.469
| Jamesbond/Septimal/Greenwood
|-
|
|
|
| 4\63
|
|
|
|
| 76.190
| Jamesbond/Septimal/Greenwood
|-
| 1\14
|
|
|
|
|
|
|
| 85.714
| Jamesbond/Septimal/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 sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
| 0\8
|
|
|
|
|
|
|
| 0
|
|-
|
|
|
|
| 1\480
|
|
|
| 2.5
|
|-
|
|
|
|
| 1\472
|
|
|
| 2.542
| [[Octium]]
|-
|
|
|
|
|
|
| 4\1872
|
| 2.564
| Octium
|-
|
|
|
|
|
|
|
| 7\3272
| 2.567
| Octium
|-
|
|
|
|
|
| 3\1400
|
|
| 2.571
| Octium
|-
|
|
|
|
| 1\464
|
|
|
| 2.586
|
|-
|
|
|
|
| …
|
|
|
|
|
|-
|
|
|
|
| 1\96
|
|
|
| 12.5
|
|-
|
|
|
|
| 1\88
|
|
|
| 13.635
|
|-
|
|
|
|
| 1\80
|
|
|
| 15
|
|-
|
|
|
|
|
| 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
|
|
|
|
|
|
| 30
|
|-
|
|
| 2\72
|
|
|
|
|
| 33.333
|
|-
| 1\32
|
|
|
|
|
|
|
| 37.5
| [[Semidim]]
|-
|
|
| 3\88
|
|
|
|
|
| 40.909
| Semidim
|-
|
| 2\56
|
|
|
|
|
|
| 42.857
| Semidim
|-
|
|
| 3\80
|
|
|
|
|
| 45
| Semidim
|-
|
|
|
| 4\104
|
|
|
|
| 46.154
| Semidim
|-
|
|
|
|
| 5\128
|
|
|
| 46.875
| Semidim
|-
|
|
|
|
| 6\152
|
|
|
| 47.368
| 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
|
|
|
|
|
|
|
| 60
|
|-
| 1\16
|
|
|
|
|
|
|
| 75
|
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
| 0\9
|
|
|
|
|
|
|
| 0
|
|-
|
|
|
|
| 1\72
|
|
|
| 16.667
| [[Enneaportent]]
|-
|
|
|
|
|
|
|
| 4\279
| 17.204
| Enneaportent
|-
|
|
|
|
|
|
| 3\207
|
| 17.391
| Enneaportent
|-
|
|
|
|
|
| 2\135
|
|
| 17.778
| Enneaportent
|-
|
|
|
| 1\63
|
|
|
|
| 19.048
| Enneaportent
|-
|
|
| 1\54
|
|
|
|
|
| 22.222
|
|-
|
| 1\45
|
|
|
|
|
|
| 26.667
|
|-
| 1\36
|
|
|
|
|
|
|
| 33.333
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|
|
|
| 4\135
|
|
|
|
| 35.556
| No-five tritrizo
|-
|
|
| 3\99
|
|
|
|
|
| 36.364
| No-five tritrizo
|-
|
| 2\63
|
|
|
|
|
|
| 38.095
| [[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
|-
|
|
|
| 8\189
|
|
|
|
| 50.794
| Novemkleismic
|-
|
|
| 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\110
|
|
|
|
|
|
| 10.909
|
|-
| 1\100
|
|
|
|
|
|
| 12
|
|-
|
| 2\190
|
|
|
|
|
| 12.632
| [[Deca]]
|-
| 1\90
|
|
|
|
|
|
| 13.333
| Deca
|-
| 1\80
|
|
|
|
|
|
| 15
| Deca
|-
| 1\70
|
|
|
|
|
|
| 17.143
|
|-
| 1\60
|
|
|
|
|
|
| 20
|
|-
| 1\50
|
|
|
|
|
|
| 24
| [[Decimetra]]
|-
|
|
|
| 4\190
|
|
|
| 25.263
| Decimetra
|-
|
|
|
|
| 7\330
|
|
| 25.455
| Decimetra
|-
|
|
|
|
|
|
| 17\800
| 25.5
| Decimetra
|-
|
|
|
|
|
| 10\470
|
| 25.532
| Decimetra
|-
|
|
| 3\140
|
|
|
|
| 25.714
| Decimetra
|-
|
| 2\90
|
|
|
|
|
| 26.667
| Decimetra
|-
| 1\40
|
|
|
|
|
|
| 30
| [[Decic]]
|-
|
|
| 3\110
|
|
|
|
| 32.727
| Decic
|-
|
| 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
|-
|
|
|
|
| 9\220
|
|
| 49.091
| Decavish
|-
|
|
|
| 7\170
|
|
|
| 49.412
| Decavish
|-
|
|
| 5\120
|
|
|
|
| 50
| Decavish
|-
|
| 3\70
|
|
|
|
|
| 51.429
| Decavish
|-
|
|
| 4\90
|
|
|
|
| 53.333
|
|-
|
|
|
| 5\110
|
|
|
| 54.545
|
|-
|
|
|
|
| 6\130
|
|
| 55.385
| [[Decoid]]
|-
| 1\20
|
|
|
|
|
|
| 60
|
|}
 
== Eleven periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
| 0\11
|
|
|
|
|
|
| 0
|
|-
|
| 1\55
|
|
|
|
|
| 21.818
|
|-
| 1\44
|
|
|
|
|
|
| 27.273
|
|-
|
| 2\77
|
|
|
|
|
| 31.169
|
|-
| 1\33
|
|
|
|
|
|
| 36.364
|
|-
|
| 3\88
|
|
|
|
|
| 40.909
|
|-
| 2\55
|
|
|
|
|
|
| 42.636
| [[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==
{{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 ==
* [[Fractional-octave temperaments]] – lists dozens more temperaments beyond what can be 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"