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Map of rank-2 temperaments: Difference between revisions

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


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


==One period per octave==
Interactive maps of ''all'' linear temperaments with octave, half-octave, third-octave, or tritave period that are logged on the wiki are available [https://hkm2685.github.io/temperament-map/rank2/viewer/ here].
 
== 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 928:
|}
|}


==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"
|-
|-
Line 971: Line 973:
|  
|  
| 44.444
| 44.444
| [[Semiaug]]
| [[Hemiaug]]
|-
|-
|  
|  
Line 984: Line 986:
|  
|  
| 47.059
| 47.059
| Semiaug
| Hemiaug
|-
|-
|  
|  
Line 997: Line 999:
|  
|  
| 50.000
| 50.000
| Semiaug/[[Augmented family#Hemiug|Hemiug]]
| Hemiaug/[[Hemiug]]
|-
|-
|  
|  
Line 1,140: Line 1,142:
|  
|  
| 88.889
| 88.889
| | [[Augmented]]/[[Augene]]
| | [[Augmented (temperament)|Augmented]]/[[Augene]]
|-
|-
|  
|  
Line 1,192: Line 1,194:
|  
|  
| 95.652
| 95.652
| Augmented Augene/Fog
| Augmented/Augene/Fog
|-
|-
|  
|  
Line 1,335: Line 1,337:
|  
|  
| 150.000
| 150.000
| [[Triforce]]
| [[Triforce]]/[[Augment]]
|-
|-
|  
|  
Line 1,348: Line 1,350:
|  
|  
| 153.846
| 153.846
| Triforce
| Triforce/Augment
|-
|-
| 2\15
| 2\15
Line 1,361: Line 1,363:
|  
|  
| 160.000
| 160.000
| Triforce
| Triforce/Augment
|-
|-
|  
|  
Line 1,374: Line 1,376:
|  
|  
| 171.429
| 171.429
| [[Oodako]]
| [[Oodako]]/Augment
|-
|-
|  
|  
Line 1,387: Line 1,389:
|  
|  
| 175
| 175
| Oodako
| Oodako/Augment
|-
|-
|  
|  
Line 1,455: Line 1,457:
|}
|}


==Four periods per octave==
== Four periods per octave ==
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator
! colspan="6" | Generator
Line 1,497: Line 1,499:
| Quadritikleismic
| Quadritikleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
| 2\140  
| 2\140  
|
|  
| 17.143  
| 17.143  
| Quadritikleismic
| Quadritikleismic
|-
|-
|
|  
|
|  
|
|  
| 1\68  
| 1\68  
|
|  
|
|  
| 17.647  
| 17.647  
| Quadritikleismic
| Quadritikleismic
|-
|-
|
|  
|
|  
|
|  
| 1\64  
| 1\64  
|
|  
|
|  
| 18.75  
| 18.75  
|  
|  
|-
|-
|
|  
|
|  
|
|  
| 1\60  
| 1\60  
|
|  
|
|  
| 20  
| 20  
|  
|  
|-
|-
|
|  
|
|  
|
|  
| ...  
| ...  
|
|  
|
|  
| ...  
| ...  
|  
|  
|-
|-
|
|  
|
|  
|
|  
| 1\36  
| 1\36  
|
|  
|
|  
| 33.333  
| 33.333  
|  
|  
|-
|-
|
|  
|
|  
|
|  
| 1\32  
| 1\32  
|
|  
|
|  
| 37.5  
| 37.5  
|  
|  
|-
|-
| 
| 
| 
| 1\28
| 
| 
| 42.857
|  
|  
|-
|
|
| 1\28
|
|
| 42.857
|
|-
|  
|  
|  
|  
Line 1,587: Line 1,589:
| Hemidim
| Hemidim
|-
|-
|
|  
|
|  
| 1\24  
| 1\24  
|
|  
|
|  
|
|  
| 50  
| 50  
| Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
| Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|-
|-
|
|  
| 1\20  
| 1\20  
|
|  
|
|  
|
|  
|
|  
| 60  
| 60  
|  
|  
|-
|-
| 1\16  
| 1\16  
|
|  
|
|  
|
|  
|
|  
|
|  
| 75  
| 75  
|  
|  
Line 1,633: Line 1,635:
|-
|-
| 1\12  
| 1\12  
|
|  
|
|  
|
|  
|
|  
|
|  
| 100  
| 100  
| Demolished/[[Diminished]]
| Demolished/[[Diminished (temperament)|Diminished]]
|-
|-
|  
|  
Line 1,740: Line 1,742:
| Diminished
| Diminished
|-
|-
|
|  
|
|  
|
|  
| 7\80  
| 7\80  
|
|  
|
|  
| 105  
| 105  
| Diminished/[[Bidia]]
| Diminished/[[Bidia]]
Line 1,767: Line 1,769:
| Diminished/Bidia
| Diminished/Bidia
|-
|-
|
|  
|
|  
|
|  
| 6\68  
| 6\68  
|
|  
|
|  
| 105.882  
| 105.882  
| Diminished/Bidia
| Diminished/Bidia
|-
|-
|
|  
|
|  
|
|  
| 5\56  
| 5\56  
|
|  
|
|  
| 107.143  
| 107.143  
| Diminished/Bidia
| Diminished/Bidia
|-
|-
|
|  
|
|  
| 4\44  
| 4\44  
|
|  
|
|  
|
|  
| 109.091  
| 109.091  
| Diminished
| Diminished
|-
|-
|
|  
| 3\32  
| 3\32  
|
|  
|
|  
|
|  
|
|  
| 112.5  
| 112.5  
| Diminished
| Diminished
|-
|-
| 2\20  
| 2\20  
|
|  
|
|  
|
|  
|
|  
|
|  
| 120  
| 120  
| Diminished
| Diminished
Line 1,822: Line 1,824:
|-
|-
| 1\8  
| 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 sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="9" | Generator
! colspan="9" | Generator
Line 1,839: Line 1,841:
|-
|-
| 0\5  
| 0\5  
|
|  
|  
|  
|  
|  
Line 1,872: Line 1,874:
|  
|  
| 8.889
| 8.889
| [[5th-octave temperaments#Slendrismic|Slendrismic]]
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|  
|  
Line 1,884: Line 1,886:
|  
|  
| 9
| 9
| Slendrismic
| Slendroschismic
|-
|-
|  
|  
Line 1,896: Line 1,898:
| 5\665
| 5\665
| 9.023
| 9.023
| Slendrismic
| Slendroschismic
|-
|-
|  
|  
Line 1,908: Line 1,910:
|  
|  
| 9.057
| 9.057
| Slendrismic
| Slendroschismic
|-
|-
|  
|  
Line 1,920: Line 1,922:
|  
|  
| 9.231
| 9.231
| Slendrismic/[[Hemipental]]
| Slendroschismic/[[Hemipental]]
|-
|-
|  
|  
Line 2,004: Line 2,006:
|  
|  
| 10.435
| 10.435
|
|-
|
|
|
|
|
| ...
|
|
|
| ...
|  
|  
|-
|-
Line 2,040: Line 2,030:
|  
|  
| 18.462
| 18.462
| [[Pental (temperament)|Pental]]
| [[Pental (temperament)| Pental]]
|-
|-
|  
|  
Line 2,136: Line 2,126:
|  
|  
| 24
| 24
|  
| [[Cloudtone]]
|-
|-
|  
|  
Line 2,148: Line 2,138:
|  
|  
| 26.67
| 26.67
|  
| Cloudtone
|-
|-
|  
|  
Line 2,160: Line 2,150:
|  
|  
| 30
| 30
|  
| Cloudtone
|-
|-
|  
|  
Line 2,271: Line 2,261:
|-
|-
| 1\15  
| 1\15  
|
|  
|
|  
|  
|  
|  
|  
Line 2,280: Line 2,270:
|  
|  
| 80
| 80
| [[Blackwood]]/[[Blacksmith]]
| [[Blackwood]]
|-
|-
|  
|  
Line 2,292: Line 2,282:
|  
|  
| 85.714
| 85.714
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,304: Line 2,294:
|  
|  
| 87.273
| 87.273
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,316: Line 2,306:
|  
|  
| 88.421
| 88.421
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,328: Line 2,318:
|  
|  
| 90
| 90
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,340: Line 2,330:
|  
|  
| 91.429
| 91.429
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,352: Line 2,342:
|  
|  
| 92.308
| 92.308
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,364: Line 2,354:
|  
|  
| 93.333
| 93.333
| Blackwood/Blacksmith
| Blackwood
|-
|-
| 2\25
| 2\25
Line 2,376: Line 2,366:
|  
|  
| 96
| 96
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,583: Line 2,573:
|}
|}


==Six periods per octave ==
== Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! colspan="7" | Generator
Line 2,590: Line 2,580:
|-
|-
| 0\6
| 0\6
|
|  
|  
|  
|  
|  
Line 2,827: Line 2,817:
|  
|  
| 50
| 50
|  
| [[Hemisemiaug]]
|-
|
|
|2\42
|
|
|
|
|57.143
|Hemisemiaug
|-
|-
| 1\18
| 1\18
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 66.667
| 66.667
|  
| Hemisemiaug
|-
|-
|  
|  
Line 2,890: Line 2,890:
|}
|}


==Seven periods per octave==
== 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)}}
{{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"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!! Cents!!Comments
! 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\49
| 1\49
|
|  
|
|  
|
|  
|24.49
| 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#Austinpowers|Austinpowers]]
|-
|-
|
|  
|
|  
|
|  
| 4\77
| 4\77
|
|  
|
|  
|
|  
|
|  
|62.338
| 62.338
|Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|
|  
|
|  
|3\56
| 3\56
|
|  
|
|  
|
|  
|
|  
|
|  
|64.286
| 64.286
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|
|  
|
|  
|
|  
|5\91
| 5\91
|
|  
|
|  
|
|  
|
|  
|65.934
| 65.934
|Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|
|  
|2\35
| 2\35
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 68.571
| 68.571
|Jamesbond/Septimal/[[Greenwood]]
| Jamesbond/Austinpowers/[[Greenwood]]
|-
|-
|
|  
|
|  
|
|  
|5\84
| 5\84
|
|  
|
|  
|
|  
|
|  
|71.429
| 71.429
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
|
|  
|
|  
|3\49
| 3\49
|
|  
|
|  
|
|  
|
|  
|
|  
| 73.469
| 73.469
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
|
|  
|
|  
|
|  
|4\63
| 4\63
|
|  
|
|  
|
|  
|
|  
|76.190
| 76.190
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
| 1\14
| 1\14
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|85.714
| 85.714
|Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/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)}}
 
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="9" |Generator!!Cents!!Comments
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|0\8||  ||
| 0\8
|
|  
|
|  
|
|  
|
|  
|
|  
| ||0||
|  
|  
| 0
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\80
|
|
|1\80
|  
|
|  
|
| 15
|15
|  
|
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\152
|
|
|2\152
|  
|
| 15.789
|15.789
| [[Octoid]]
|[[Octoid]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\224
|
|
|3\224
| 16.071
|16.071
| Octoid
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\72
|1\72
|  
|
|  
|
|  
|
| 16.667
|16.667
| Octoid
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\64
| 1\64
|
|  
|
|  
|
|  
|
| 18.75
|18.75
|  
|
|-
|-
|
|  
|
|  
|
|  
|1\56
| 1\56
|
|  
|
|  
|
|  
|
|  
|
| 21.429
|21.429
|  
|
|-
|-
|
|  
|
|  
|1\48
| 1\48
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 25
|25
|  
|
|-
|-
|
|  
| 1\40
| 1\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 30
|30
|  
|
|-
|-
|
|  
|
|  
|2\72
| 2\72
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 33.333
|33.333
|  
|
|-
|-
|1\32
| 1\32
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 37.5
|37.5
| [[Semidim]]
|[[Semidim]]
|-
|-
|
|  
|
|  
|3\88
| 3\88
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 40.909
|40.909
| Semidim
|Semidim
|-
|-
|
|  
|2\56
| 2\56
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 42.857
|42.857
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|3\80
| 3\80
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 45
|45
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|
|  
|4\104
| 4\104
|
|  
|
|  
|
|  
|
|  
|
| 46.154
|46.154
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|5\128
| 5\128
|
|  
|
|  
|
|  
|
| 46.875
|46.875
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 6\152
|6\152
|  
|
|  
|
|  
|
| 47.368
|47.368
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\176
|7\176
|  
|
|  
|
| 47.727
|47.727
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\200
|8\200
|  
|
|  
|
| 48
|48
| Semidim
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 9\224
|9\224
|  
|
|  
|
| 48.214
|48.214
| Semidim/[[Octant]]
|Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 28\696
|28\696
| 48.276
|48.276
| Semidim/Octant
|Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 19\472
|19\472
|  
|
| 48.305
|48.305
| Semidim/Octant
|Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 10\248
|10\248
|  
|
|  
|
| 48.387
|48.387
| Semidim
|Semidim
|-
|-
|1\24
| 1\24
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 50
|50
| Semidim
|Semidim
|-
|-
|2\40
| 2\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 60
| 60
|
|  
|-
|-
|1\16
| 1\16
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 75
|75
|  
|
|}
|}


==Nine periods per octave ==
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!! Comments
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|0\9|| || ||  
| 0\9
|  
|  
|  
|  
|  
|  
|
| 0
|  
|  
|
|
| ||0||
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\72
| 1\72
|
|  
|
|  
|
|  
|16.667
| 16.667
|[[Enneaportent]]
| [[Enneaportent]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\279
| 4\279
|17.204
| 17.204
|Enneaportent
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\207
| 3\207
|
|  
|17.391
| 17.391
|Enneaportent
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\135
| 2\135
|
|  
|
|  
|17.778
| 17.778
|Enneaportent
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|1\63
| 1\63
|
|  
|
|  
|
|  
|
|  
|19.048
| 19.048
|Enneaportent
| Enneaportent
|-
|-
|
|  
|
|  
|1\54
| 1\54
|
|  
|
|  
|
|  
|
|  
|
|  
|22.222
| 22.222
|
|  
|-
|-
|
|  
|1\45
| 1\45
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|26.667
| 26.667
|
|  
|-
|-
|1\36
| 1\36
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|33.333
| 33.333
|[[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|-
|
|  
|
|  
|
|  
|4\135
| 4\135
|
|  
|
|  
|
|  
|
|  
|35.556
| 35.556
|No-five tritrizo
| No-five tritrizo
|-
|-
|
|  
|
|  
|3\99
| 3\99
|
|  
|
|  
|
|  
|
|  
|
|  
|36.364
| 36.364
|No-five tritrizo
| No-five tritrizo
|-
|-
|
|  
|2\63
| 2\63
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|38.095
| 38.095
|[[Niner]]
| [[Niner]]
|-
|-
|
|
|3\90
|  
|  
|
|
|
| 3\90
|
|
|
|  
|40
|  
|Niner
|  
|  
| 40
| Niner
|-
|-
|1\27
| 1\27
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 44.444
| 44.444
|Niner
| Niner
|-
|-
|
|  
|
|  
|4\99
| 4\99
|
|  
|
|  
|
|  
|
|  
|
|  
|48.485
| 48.485
|[[Ennealimmal]]
| [[Ennealimmal]]
|-
|-
|
|  
|
|  
|
|  
|7\171
| 7\171
|
|  
|
|  
|
|  
|
|  
|49.123
| 49.123
|Ennealimmal
| Ennealimmal
|-
|-
|
|3\72
|  
|  
|
| 3\72
|
|
|
|  
|
|  
|
|  
|  
|  
| 50
| 50
|Ennealimmal
| Ennealimmal
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|20\477
| 20\477
|50.314
| 50.314
|[[Novemkleismic]]
| [[Novemkleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|17\405
| 17\405
|
|  
|50.370
| 50.370
|Novemkleismic
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|14\333
| 14\333
|
|  
|
|  
|50.451
| 50.451
|Novemkleismic
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\261
| 11\261
|
|  
|
|  
|
|  
|50.575
| 50.575
|Novemkleismic
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|8\189
| 8\189
|
|  
|
|  
|
|  
|
|  
|50.794
| 50.794
|Novemkleismic
| Novemkleismic
|-
|-
|
|  
|
|  
|5\117
| 5\117
|
|  
|
|  
|
|  
|
|  
|
|  
|51.282
| 51.282
|
|-
|2\45
|
|
|
|
|
|
|
|53.333
|  
|  
|-
|-
|1\18
| 2\45
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 53.333
|
|-
| 1\18
|  
|  
|  
|  
|  
|  
|  
| 66.667
| 66.667
|
|  
|}
|}


==Twelve periods per octave==
== Ten periods per octave==
See also: [[Compton family]]
 
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!!Comments
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|0\12|| || ||
| 0\10
|
|  
|  
|  
|  
|  
|  
| 0
|  
|  
|
|||0||
|-
|-
|1\140
|
|
|
|
|
|
|1\636
|
|
|
|
|
|
|
|8.571
|1.887
|[[Decoid]]
|
|-
|-
|
|
|2\270
|
|
|
|
|1\624
|
|
|
|
|
|
|
|8.888
|1.923
|Decoid
|
|-
|-
|1\130
|
|
|
|
|
|
|
|
|2\1236
|
|
|
|
|
|9.231
|1.942
|Decoid
|[[Atomic]]
|-
|-
|1\120
|
|
|
|
Line 3,915: Line 3,912:
|
|
|
|
|3\1848
|
|
|10
|
|
|1.948
|Atomic
|-
|-
|
| 1\110
|
|  
|
|  
|
|  
|
|  
|
|  
|4\2460
|  
|
| 10.909
|1.951
|  
|Atomic
|-
|-
|
| 1\100
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\3072
| 12
|1.953
|  
|Atomic
|-
|-
|
|  
|
| 2\190
|
|  
|1\612
|  
|
|  
|
|  
|
|  
|
| 12.632
|1.961
| [[Deca]]
|Atomic
|-
|-
|
| 1\90
|
|  
|
|  
|1\600
|  
|
|  
|
|  
|
|  
|
| 13.333
|2
| Deca
|
|-
|-
|
| 1\80
|
|  
|
|  
|1\588
|  
|
|  
|
|  
|
|  
|
| 15
|2.041
| Deca
|
|-
|-
|
| 1\70
|
|  
|
|  
|1\576
|  
|
|  
|
|  
|
|  
|
| 17.143
|2.083
|  
|
|-
|-
|
| 1\60
|
|  
|
|  
|...
|  
|
|  
|
|  
|
|  
|
| 20
|...
|  
|
|-
|-
|
| 1\50
|
|  
|
|  
|1\108
|  
|
|  
|
|  
|
|  
|
| 24
|11.111
| [[Decimetra]]
|
|-
|-
|
|  
|
|  
|
|  
|1\96
| 4\190
|
|  
|
|  
|
|  
|
| 25.263
|12.5
| Decimetra
|[[Compton]]
|-
|-
|
|  
|
|  
|
|  
|1\84
|  
|
| 7\330
|
|  
|
|  
|
| 25.455
|14.286
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\240
|  
|
| 17\800
|
| 25.5
|15
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 10\470
|
|  
|8\636
| 25.532
|15.094
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
| 3\140
|
|  
|
|  
|
|  
|5\396
|  
|
| 25.714
|15.152
| Decimetra
|Compton
|-
|-
|
|  
|
| 2\90
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
| 26.667
|15.217
| Decimetra
|Compton
|-
|-
|
| 1\40
|
|  
|
|  
|
|  
|2\156
|  
|
|  
|
|  
|
| 30
|15.385
| [[Decic]]
|Compton
|-
|-
|
|  
|
|  
|
| 3\110
|
|  
|
|  
|
|  
|
|  
|7\540
| 32.727
|15.556
| Decic
|Compton
|-
|-
|
|  
|
| 2\70
|
|  
|
|  
|
|  
|
|  
|5\384
|  
|
| 34.286
|15.625
| Decic
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 4\170
|
|  
|
|  
|
|  
|8\612
| 28.235
|15.686
| Decic
|Compton
|-
|-
|
|  
|
|  
|
| 3\100
|
|  
|
|  
|3\228
|  
|
|  
|
| 36
|15.789
| Decic
|Compton
|-
|-
|
| 1\30
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
| 40
|15.909
| Decic/[[Decal]]
|Compton
|-
|-
|
|  
|
| 3\80
|
|  
|
|  
|
|  
|
|  
|4\300
|  
|
| 45
|16
| Decal/[[Decistearn]]
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 8\210
|
|  
|
|  
|
|  
|5\372
| 45.714
|16.129
| Decal/Decistearn
|Compton
|-
|-
|
|  
|
|  
|
|  
|1\72
|  
|
| 13\340
|
|  
|
|  
|
| 45.882
|16.667
| Decal/Decistearn
|Compton
|-
|-
|
|  
|
|  
|1\60
|  
|
|  
|
|  
|
| 18\470
|
|  
|
| 45.957
|20
| Decal/Decistearn
|Compton
|-
|-
|
|  
|
|  
|
|  
|2\108
|  
|
|  
|
|  
|
| 23\600
|
| 46
|22.222
| Decal/Decistearn
|
|-
|-
|
|  
|1\48
|  
|
| 5\130
|
|  
|
|  
|
|  
|
|  
|
| 46.154
|25
| Decal/Decistearn
|[[Catler]]
|-
|-
|
| 2\50
|
|  
|
|  
|3\132
|  
|
|  
|
|  
|
|  
|
| 48
| 27.273
| Decistearn/[[Decavish]]
|Catler
|-
|-
|
|  
|
|  
| 2\84
|  
|
|  
|
|  
|
| 11\270
|
|  
|
| 48.889
|28.571
| Decavish
|Catler
|-
|-
|
|  
|
|  
|
|  
|3\120
|  
|
| 9\220
|
|  
|
|  
|
| 49.091
|30
| Decavish
|Catler
|-
|-
|1\36
|  
|
|  
|
|  
|
| 7\170
|
|  
|
|  
|
|  
|
| 49.412
|33.333
| Decavish
|Catler/[[Catnip]]
|-
|-
|
|  
|
|  
|
| 5\120
|4\132
|  
|
|  
|
|  
|
|  
|
| 50
|36.364
| Decavish
|Catnip
|-
|-
|
|  
|
| 3\70
|3\96
|  
|
|  
|
|  
|
|  
|
|  
|
| 51.429
|37.5
| Decavish
| Catnip
|-
|-
|
|  
|
|  
|
| 4\90
|5\156
|  
|
|  
|
|  
|
|  
|
| 53.333
|38.462
|  
|Catnip
|-
|-
|
|  
|2\60
|  
|
|  
|
| 5\110
|
|  
|
|  
|
|  
|
| 54.545
|40
|  
|Catnip
|-
|-
|
|  
|
|  
|
|  
|5\144
|  
|
| 6\130
|
|  
|
|  
|
| 55.385
|41.667
|
|
|-
|-
|
| 1\20
|
|
|3\84
|  
|
|  
|
|  
|
|  
|
|  
|
| 60
| 42.857
|  
| [[Magnesium]]
|}
 
== Eleven periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\11
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|16\444
| 0
|43.243
|  
|Magnesium
|-
|-
|
|
|
| 1\55
|
|
|
|
|
|
|
|
|13\360
|
|
| 21.818
|43.333
|
|Magnesium
|-
|-
| 1\44
|
|
|
|
|
|
|
|
|
|
|10\276
|
|
| 27.273
|
|
|43.378
|-
|
|
|-
| 2\77
|
|
|
|
|
|
|
|
|7\192
|
|
| 31.169
|
|
|
|-
|43.75
| 1\33
|
|
|-
|
|
|
|
|
|
|
|4\108
|
|
| 36.364
|
|
|
|-
|
|
|44.444
| 3\88
|
|
|-
|
|1\24
|
|
|
|
|
|
| 40.909
|
|
|
|-
|
| 2\55
|
|
| 50
|
|
|
|
|
|
| 42.636
| [[Hendecatonic (temperament)|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 ==
== See also ==
 
* [[Fractional-octave temperaments]] – lists dozens more temperaments beyond what can be listed here.
*[[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"