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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.
 
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 ==
== One period per octave ==
Line 927: Line 929:


== 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 1,497: 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  
| 1\28  
|
|  
|
|  
| 42.857  
| 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  
|  
|  
Line 1,832: Line 1,834:


== 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 2,028: Line 2,030:
|  
|  
| 18.462
| 18.462
| [[Pental (temperament)|Pental]]
| [[Pental (temperament)| Pental]]
|-
|-
|  
|  
Line 2,124: Line 2,126:
|  
|  
| 24
| 24
|  
| [[Cloudtone]]
|-
|-
|  
|  
Line 2,136: Line 2,138:
|  
|  
| 26.67
| 26.67
|  
| Cloudtone
|-
|-
|  
|  
Line 2,148: Line 2,150:
|  
|  
| 30
| 30
|  
| Cloudtone
|-
|-
|  
|  
Line 2,259: Line 2,261:
|-
|-
| 1\15  
| 1\15  
|
|  
|
|  
|  
|  
|  
|  
Line 2,268: Line 2,270:
|  
|  
| 80
| 80
| [[Blackwood]]/[[Blacksmith]]
| [[Blackwood]]
|-
|-
|  
|  
Line 2,280: Line 2,282:
|  
|  
| 85.714
| 85.714
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,292: Line 2,294:
|  
|  
| 87.273
| 87.273
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,304: Line 2,306:
|  
|  
| 88.421
| 88.421
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,316: Line 2,318:
|  
|  
| 90
| 90
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,328: Line 2,330:
|  
|  
| 91.429
| 91.429
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,340: Line 2,342:
|  
|  
| 92.308
| 92.308
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,352: Line 2,354:
|  
|  
| 93.333
| 93.333
| Blackwood/Blacksmith
| Blackwood
|-
|-
| 2\25
| 2\25
Line 2,364: Line 2,366:
|  
|  
| 96
| 96
| Blackwood/Blacksmith
| Blackwood
|-
|-
|  
|  
Line 2,578: Line 2,580:
|-
|-
| 0\6
| 0\6
|
|  
|  
|  
|  
|  
Line 2,815: Line 2,817:
|  
|  
| 50
| 50
|  
| [[Hemisemiaug]]
|-
|
|
|2\42
|
|
|
|
|57.143
|Hemisemiaug
|-
|-
| 1\18
| 1\18
|
|
|
|
|
|
| 66.667
| Hemisemiaug
|-
|  
|  
| 2\30
|  
|  
|  
|  
Line 2,824: Line 2,846:
|  
|  
|  
|  
| 66.667
| 80
|
|-
|
| 2\30
|
|
|
|
|
| 80
| [[Hexe]]
| [[Hexe]]
|-
|-
Line 2,879: Line 2,891:


== 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
! colspan="8" | Generator
Line 2,886: Line 2,898:
|-
|-
| 0\7
| 0\7
|
|  
|  
|  
|  
|  
Line 3,059: Line 3,071:
|  
|  
| 28.571
| 28.571
| [[Mistismic temperaments#Neutron|Neutron]]
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|  
|  
Line 3,114: Line 3,126:
|  
|  
| 34.286
| 34.286
| [[Whitewood family#Redwood|Redwood]]
| [[Whitewood family#Redwood| Redwood]]
|-
|-
|  
|  
Line 3,180: Line 3,192:
|  
|  
| 57.143
| 57.143
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Austinpowers|Austinpowers]]
|-
|-
|  
|  
Line 3,191: Line 3,203:
|  
|  
| 62.338
| 62.338
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|  
|  
Line 3,202: Line 3,214:
|  
|  
| 64.286
| 64.286
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|  
|  
Line 3,213: Line 3,225:
|  
|  
| 65.934
| 65.934
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|  
|  
Line 3,224: Line 3,236:
|  
|  
| 68.571
| 68.571
| Jamesbond/Septimal/[[Greenwood]]
| Jamesbond/Austinpowers/[[Greenwood]]
|-
|-
|  
|  
Line 3,235: Line 3,247:
|  
|  
| 71.429
| 71.429
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
|  
|  
Line 3,246: Line 3,258:
|  
|  
| 73.469
| 73.469
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
|  
|  
Line 3,257: Line 3,269:
|  
|  
| 76.190
| 76.190
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
| 1\14
| 1\14
Line 3,268: Line 3,280:
|  
|  
| 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) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! colspan="8" | Generator
Line 3,279: Line 3,291:
|-
|-
| 0\8
| 0\8
|
|  
|  
|  
|  
|  
Line 3,289: Line 3,301:
|  
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\480
| 1\480
|
|  
|
|  
|
|  
|2.5
| 2.5
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\472
| 1\472
|
|  
|
|  
|
|  
|2.542
| 2.542
|[[Octium]]
| [[Octium]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\1872
| 4\1872
|
|  
|2.564
| 2.564
|Octium
| Octium
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\3272
| 7\3272
|2.567
| 2.567
|Octium
| Octium
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\1400
| 3\1400
|
|  
|
|  
|2.571
| 2.571
|Octium
| Octium
|-
|
|
|
|
|1\464
|
|
|
|2.586
|
|-
|
|
|
|
|…
|
|
|
|
|
|-
|
|
|
|
|1\96
|
|
|
|12.5
|
|-
|
|
|
|
|1\88
|
|
|
|13.635
|
|-
|-
|  
|  
Line 3,392: Line 3,360:
|  
|  
|  
|  
| 1\80
| 1\464
|
|
|  
|  
| 2.586
|  
|  
|-
|  
|  
| 15
|  
|  
|-
|  
|  
|  
|  
| …
|  
|  
|  
|  
|  
|  
| 2\152
|  
|  
|  
|  
| 15.789
|[[Octoid]]
|-
|-
|  
|  
Line 3,414: Line 3,382:
|  
|  
|  
|  
| 1\96
|  
|  
|  
|  
| 3\224
|  
|  
| 16.071
| 12.5
|
|-
|
|
|
|
| 1\88
|
|
|
| 13.635
|
|-
|
|
|
|
| 1\80
|
|
|
| 15
|
|-
|
|
|
|
|
| 2\152
|
|
| 15.789
| [[Octoid]]
|-
|
|
|
|
|
|
| 3\224
|
| 16.071
| Octoid
| Octoid
|-
|-
Line 3,671: Line 3,683:
|-
|-
| 0\9
| 0\9
|
|  
|  
|  
|  
|  
Line 3,767: Line 3,779:
|  
|  
| 33.333
| 33.333
| [[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|-
|  
|  
Line 3,948: Line 3,960:
== Ten periods per octave==
== Ten periods per octave==
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="7" |Generator
! colspan="7" | Generator
!Cents
! Cents
!Comments
! Comments
|-
|-
|0\10
| 0\10
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|0
| 0
|
|  
|-
|-
|1\110
|1\140
|
|
|
|
Line 3,969: Line 3,981:
|
|
|
|
|10.909
|8.571
|
|[[Decoid]]
|-
|-
|1\100
|
|
|2\270
|
|
|
|
Line 3,979: Line 3,991:
|
|
|
|
|12
|8.888
|
|Decoid
|-
|-
|1\130
|
|
|2\190
|
|
|
|
Line 3,989: Line 4,001:
|
|
|
|
|12.632
|9.231
|[[Deca]]
|Decoid
|-
|-
|1\90
|1\120
|
|
|
|
|
|
|
|13.333
|Deca
|-
|1\80
|
|
|
|
Line 4,008: Line 4,011:
|
|
|
|
|10
|
|
|15
|Deca
|-
|-
|1\70
| 1\110
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|17.143
| 10.909
|
|  
|-
|-
|1\60
| 1\100
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|20
| 12
|
|  
|-
|-
|1\50
|  
|
| 2\190
|
|  
|
|  
|
|  
|
|  
|
|  
|24
| 12.632
|[[Decimetra]]
| [[Deca]]
|-
|-
|
| 1\90
|
|  
|
|  
|4\190
|  
|
|  
|
|  
|
|  
|25.263
| 13.333
|Decimetra
| Deca
|-
|-
|
| 1\80
|
|  
|
|  
|
|  
|7\330
|  
|
|  
|
|  
|25.455
| 15
|Decimetra
| Deca
|-
|-
|
| 1\70
|
|  
|
|  
|
|  
|
|  
|
|  
|17\800
|  
|25.5
| 17.143
|Decimetra
|  
|-
|-
|
| 1\60
|
|  
|
|  
|
|  
|
|  
|10\470
|  
|
|  
|25.532
| 20
|Decimetra
|  
|-
|-
|
| 1\50
|
|  
|3\140
|  
|
|  
|
|  
|
|  
|
|  
|25.714
| 24
|Decimetra
| [[Decimetra]]
|-
|-
|
|  
|2\90
|  
|
|  
|
| 4\190
|
|  
|
|  
|
|  
|26.667
| 25.263
|Decimetra
| Decimetra
|-
|-
|1\40
|  
|
|  
|
|  
|
|  
|
| 7\330
|
|  
|
|  
|30
| 25.455
|[[Decic]]
| Decimetra
|-
|
|
|3\110
|
|
|
|
|32.727
|Decic
|-
|-
|  
|  
|2\70
|
|
|
|  
|  
|  
|  
|34.286
|  
|Decic
|
|
| 17\800
| 25.5
| Decimetra
|-
|-
|
|  
|
|  
|
|  
|4\170
|  
|
|  
|
| 10\470
|
|  
|28.235
| 25.532
|Decic
| Decimetra
|-
|-
|
|  
|
|  
|3\100
| 3\140
|
|  
|
|  
|
|  
|
|  
|36
| 25.714
|Decic
| Decimetra
|-
|-
|1\30
|  
|
| 2\90
|
|  
|
|  
|
|  
|
|  
|
|  
|40
| 26.667
|Decic/[[Decal]]
| Decimetra
|-
|-
|
| 1\40
|3\80
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|45
| 30
|Decal/[[Decistearn]]
| [[Decic]]
|-
|-
|
|  
|
|  
|
| 3\110
|8\210
|  
|
|  
|
|  
|
|  
|45.714
| 32.727
|Decal/Decistearn
| Decic
|-
|-
|
|  
|
| 2\70
|
|  
|
|  
|13\340
|  
|
|  
|
|  
|45.882
| 34.286
|Decal/Decistearn
| Decic
|-
|-
|
|  
|
|  
|
|  
|
| 4\170
|
|  
|18\470
|  
|
|  
|45.957
| 28.235
|Decal/Decistearn
| Decic
|-
|-
|
|  
|
|  
|
| 3\100
|
|  
|
|  
|
|  
|23\600
|  
|46
| 36
|Decal/Decistearn
| Decic
|-
|-
|
| 1\30
|
|  
|5\130
|  
|
|  
|
|  
|
|  
|
|  
|46.154
| 40
|Decal/Decistearn
| Decic/[[Decal]]
|-
|-
|2\50
|  
|
| 3\80
|
|  
|
|  
|
|  
|
|  
|
|  
|48
| 45
|Decistearn/[[Decavish]]
| Decal/[[Decistearn]]
|-
|-
|
|  
|
|  
|
|  
|
| 8\210
|
|  
|11\270
|  
|
|  
|48.889
| 45.714
|Decavish
| Decal/Decistearn
|-
|-
|
|  
|
|  
|
|  
|
|  
|9\220
| 13\340
|
|  
|
|  
|49.091
| 45.882
|Decavish
| Decal/Decistearn
|-
|-
|
|  
|
|  
|
|  
|7\170
|  
|
|  
|
| 18\470
|
|  
|49.412
| 45.957
|Decavish
| Decal/Decistearn
|-
|-
|
|  
|
|  
|5\120
|  
|
|  
|
|  
|
|  
|
| 23\600
|50
| 46
|Decavish
| Decal/Decistearn
|-
|-
|
|  
|3\70
|  
|
| 5\130
|
|  
|
|  
|
|  
|
|  
|51.429
| 46.154
|Decavish
| Decal/Decistearn
|-
|-
|
| 2\50
|
|  
|4\90
|  
|
|  
|
|  
|
|  
|
|  
|53.333
| 48
|
| Decistearn/[[Decavish]]
|-
|-
|
|  
|
|  
|
|  
|5\110
|  
|
|  
|
| 11\270
|
|  
|54.545
| 48.889
|
| Decavish
|-
|-
|
|  
|
|  
|
|  
|
|  
|6\130
| 9\220
|
|  
|
|  
|55.385
| 49.091
|[[Decoid]]
| Decavish
|-
|-
|1\20
|  
|
|  
|
|  
|
| 7\170
|
|  
|
|  
|
|  
|60
| 49.412
|
| Decavish
|}
 
== Eleven periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" |Generator
!Cents
!Comments
|-
|-
|0\11
|  
|
|
| 5\120
|  
|  
|  
|  
|  
|  
|  
|
| 50
|
| Decavish
|0
|
|-
|-
|
|  
|1\55
| 3\70
|
|  
|
|  
|
|  
|
|  
|
|  
|21.818
| 51.429
|
| Decavish
|-
|-
|1\44
|  
|
|  
|
| 4\90
|
|  
|
|  
|
|  
|
|  
|27.273
| 53.333
|
|  
|-
|-
|
|2\77
|
|
|
|  
|  
|
|  
| 31.169
|  
| 5\110
|
|
|
| 54.545
|  
|  
|-
|-
|1\33
|  
|
|  
|
|  
|
|  
|
| 6\130
|
|  
|
|  
|36.364
| 55.385
|
|
|-
|-
|
| 1\20
|3\88
|
|
|
|
|  
|
|  
|
|  
|
|  
|40.909
| 60
|
|  
|}
 
== Eleven periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|2\55
| 0\11
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|42.636
| 0
|[[Hendecatonic]]
|  
|-
|-
|
|  
|3\77
| 1\55
|
|  
|
|  
|
|  
|
|  
|
|  
|46.753
| 21.818
|Hendecatonic
|  
|-
|-
|
| 1\44
|
|  
|
|  
|7\176
|  
|
|  
|
|  
|
|  
|47.727
| 27.273
|Hendecatonic
|  
|-
|-
|
|  
|
| 2\77
|
|  
|
|  
|11\275
|  
|
|  
|
|  
|48
| 31.169
|Hendecatonic
|  
|-
|-
|
| 1\33
|
|  
|4\99
|  
|
|  
|
|  
|
|  
|
|  
|48.485
| 36.364
|Hendecatonic/[[Cohendecatonic]]
|  
|-
|-
|
|  
|
| 3\88
|
|  
|
|  
|9\220
|  
|
|  
|
|  
|49.091
| 40.909
|Cohendecatonic
|  
|-
|-
|
| 2\55
|
|  
|
|  
|
|  
|
|  
|14\341
|  
|
|  
|49.267
| 42.636
|Cohendecatonic
| [[Hendecatonic (temperament)|Hendecatonic]]
|-
|-
|
|  
|
| 3\77
|
|  
|5\121
|  
|
|  
|
|  
|
|  
|49.587
| 46.753
|Cohendecatonic
| Hendecatonic
|-
|-
|
|  
|
|  
|
|  
|
| 7\176
|6\143
|  
|
|  
|
|  
|50.350
| 47.727
|
| Hendecatonic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 11\275
|7\165
|  
|
|  
|50.909
| 48
|
| Hendecatonic
|-
|-
|
|  
|
|  
|
| 4\99
|
|  
|
|  
|
|  
|8\187
|  
|51.337
| 48.485
|[[Undeka]]
| Hendecatonic / [[cohendecatonic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 9\220
|
|  
|9\209
|  
|51.675
| 49.091
|Undeka
| Cohendecatonic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 14\341
|10\231
|  
|51.948
| 49.267
|Undeka
| Cohendecatonic
|-
|-
|
|  
|
|  
|
|  
|
| 5\121
|
|  
|
|  
|11\253
|  
|52.174
| 49.587
|Undeka
| Cohendecatonic
|-
|-
|1\22
|  
|
|  
|
|  
|
|  
|
| 6\143
|
|  
|
|  
|54.545
| 50.350
|Undeka
|  
|}
 
==Twelve periods per octave==
{{See also|Compton family}}
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator
!Cents
!Comments
|-
|-
|0\12
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\165
|
|  
|
| 50.909
|0
|  
|
|-
|-
|
|  
|
|  
|
|  
|1\636
|  
|
|  
|
|  
|
| 8\187
|
| 51.337
|1.887
| [[Undeka]]
|
|-
|-
|
|  
|
|  
|
|  
|1\624
|  
|
|  
|
|  
|
| 9\209
|
| 51.675
|1.923
| Undeka
|
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\1236
|  
|
|  
|
| 10\231
|
| 51.948
|1.942
| Undeka
|[[Atomic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\1848
|  
|
| 11\253
|
| 52.174
|1.948
| Undeka
|Atomic
|-
|-
|
| 1\22
|
|
|
|
|
|  
|
|  
|
|  
|4\2460
|  
|
| 54.545
|1.951
| Undeka
|Atomic
|}
 
==Twelve periods per octave==
{{See also| Compton family}}
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\12
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\3072
|  
|1.953
| 0
|Atomic
|  
|-
|-
|
|  
|
|  
|
|  
|1\612
| 1\636
|
|  
|
|  
|
|  
|
|  
|1.961
| 1.887
|Atomic
|  
|-
|-
|
|  
|
|  
|
|  
|1\600
| 1\624
|
|  
|
|  
|
|  
|
|  
|2
| 1.923
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\588
|  
|
| 2\1236
|
|  
|
|  
|
|  
|2.041
| 1.942
|
| [[Atomic]]
|-
|-
|
|  
|
|  
|
|  
|1\576
|  
|
|  
|
| 3\1848
|
|  
|
|  
|2.083
| 1.948
|
| Atomic
|-
|-
|
|  
|
|  
|
|  
|...
|  
|
|  
|
|  
|
| 4\2460
|
|  
|...
| 1.951
|
| Atomic
|-
|-
|
|  
|
|  
|
|  
|1\108
|  
|
|  
|
|  
|
|  
|
| 5\3072
|11.111
| 1.953
|
| Atomic
|-
|-
|
|  
|
|  
|
|  
|1\96
| 1\612
|
|  
|
|  
|
|  
|
|  
|12.5
| 1.961
|[[Compton]]
| Atomic
|-
|-
|
|  
|
|  
|
|  
|1\84
| 1\600
|
|  
|
|  
|
|  
|
|  
|14.286
| 2
|Compton
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\588
|
|  
|3\240
|  
|
|  
|
|  
|15
| 2.041
|Compton
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\576
|
|  
|
|  
|
|  
|8\636
|  
|15.094
| 2.083
|Compton
|  
|-
|-
|
|  
|
|  
|
|  
|
| ...
|
|  
|
|  
|5\396
|  
|
|  
|15.152
| ...
|Compton
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\108
|
|  
|
|  
|
|  
|7\552
|  
|15.217
| 11.111
|Compton
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\96
|2\156
|  
|
|  
|
|  
|
|  
|15.385
| 12.5
|Compton
| [[Compton]]
|-
|-
|
|  
|
|  
|
|  
|
| 1\84
|
|  
|
|  
|
|  
|7\540
|  
|15.556
| 14.286
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\240
|5\384
|  
|
|  
|15.625
| 15
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\612
| 8\636
|15.686
| 15.094
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\228
|  
|
| 5\396
|
|  
|15.789
| 15.152
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
| 7\552
|15.909
| 15.217
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 2\156
|
|  
|4\300
|  
|
|  
|16
| 15.385
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\372
| 7\540
|16.129
| 15.556
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|  
|
| 5\384
|
|  
|16.667
| 15.625
|Compton
| Compton
|-
|-
|
|  
|
|  
|1\60
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\612
|20
| 15.686
|Compton
| Compton
|-
|-
|
|  
|
|  
|
|  
|2\108
|  
|
|  
|
| 3\228
|
|  
|
|  
|22.222
| 15.789
|
| Compton
|-
|-
|
|  
|1\48
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\528
|25
| 15.909
|[[Catler]]
| Compton
|-
|-
|
|  
|
|  
|
|  
|3\132
|  
|
|  
|
|  
|
| 4\300
|
|  
|27.273
| 16
|Catler
| Compton
|-
|-
|
|  
|
|  
|2\84
|  
|
|  
|
|  
|
|  
|
|  
|
| 5\372
|28.571
| 16.129
|Catler
| Compton
|-
|-
|
|  
|
|  
|
|  
|3\120
| 1\72
|
|  
|
|  
|
|  
|
|  
|30
| 16.667
|Catler
| Compton
|-
|-
|1\36
|  
|
|  
|
| 1\60
|
|  
|
|  
|
|  
|
|  
|
|  
|33.333
| 20
|Catler/[[Catnip]]
| Compton
|-
|-
|
|  
|
|  
|
|  
|4\132
| 2\108
|
|  
|
|  
|
|  
|
|  
|36.364
| 22.222
|Catnip
|  
|-
|-
|
|  
|
| 1\48
|3\96
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|37.5
| 25
|Catnip
| [[Catler]]
|-
|-
|
|  
|
|  
|
|  
|5\156
| 3\132
|
|  
|
|  
|
|  
|
|  
|38.462
| 27.273
|Catnip
| Catler
|-
|-
|
|
|2\60
|  
|
| 2\84
|
|  
|
|  
|
|  
|
|  
|
|  
|40
| 28.571
|Catnip
| Catler
|-
|-
|
|  
|
|  
|
|  
|5\144
| 3\120
|
|  
|
|  
|
|  
|
|  
|41.667
| 30
|
| Catler
|-
|-
|
| 1\36
|
|  
|3\84
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|42.857
| 33.333
|[[Magnesium]]
| Catler/[[Catnip]]
|-
|-
|
|  
|
|  
|
|  
|
| 4\132
|
|  
|
|  
|
|  
|16\444
|  
|43.243
| 36.364
|Magnesium
| Catnip
|-
|-
|
|  
|
|  
|
| 3\96
|
|  
|
|  
|
|  
|13\360
|  
|
|  
|43.333
| 37.5
|Magnesium
| Catnip
|-
|-
|
|  
|
|  
|
|  
|
| 5\156
|
|  
|10\276
|  
|
|  
|
|  
|43.378
| 38.462
|
| Catnip
|-
|-
|
|  
|
| 2\60
|
|  
|
|  
|7\192
|  
|
|  
|
|  
|
|  
|43.75
| 40
|
| Catnip
|-
|-
|
|  
|
|  
|
|  
|4\108
| 5\144
|
|  
|
|  
|
|  
|
|  
|44.444
| 41.667
|
|  
|-
|-
|1\24
|
|
|
|
| 3\84
|
|
|
|
|
|
|
|
|
|
|50
| 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"