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Map of rank-2 temperaments: Difference between revisions

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


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


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


== 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 997: Line 997:
|  
|  
| 50.000
| 50.000
| Semiaug/[[Augmented family#Hemiug|Hemiug]]
| Semiaug/[[Augmented family#Hemiug| Hemiug]]
|-
|-
|  
|  
Line 1,497: Line 1,497:
| 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 1,587:
| 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 1,633:
|-
|-
| 1\12  
| 1\12  
|
|  
|
|  
|
|  
|
|  
|
|  
| 100  
| 100  
| Demolished/[[Diminished]]
| Demolished/[[Diminished]]
Line 1,740: Line 1,740:
| Diminished
| Diminished
|-
|-
|
|  
|
|  
|
|  
| 7\80  
| 7\80  
|
|  
|
|  
| 105  
| 105  
| Diminished/[[Bidia]]
| Diminished/[[Bidia]]
Line 1,767: Line 1,767:
| 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 1,822:
|-
|-
| 1\8  
| 1\8  
|
|  
|
|  
|
|  
|
|  
|
|  
| 150  
| 150  
|  
|  
Line 1,832: Line 1,832:


== 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 1,839:
|-
|-
| 0\5  
| 0\5  
|
|  
|  
|  
|  
|  
Line 1,872: Line 1,872:
|  
|  
| 8.889
| 8.889
| [[5th-octave temperaments#Slendrismic|Slendrismic]]
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|  
|  
Line 1,884: Line 1,884:
|  
|  
| 9
| 9
| Slendrismic
| Slendroschismic
|-
|-
|  
|  
Line 1,896: Line 1,896:
| 5\665
| 5\665
| 9.023
| 9.023
| Slendrismic
| Slendroschismic
|-
|-
|  
|  
Line 1,908: Line 1,908:
|  
|  
| 9.057
| 9.057
| Slendrismic
| Slendroschismic
|-
|-
|  
|  
Line 1,920: Line 1,920:
|  
|  
| 9.231
| 9.231
| Slendrismic/[[Hemipental]]
| Slendroschismic/[[Hemipental]]
|-
|-
|  
|  
Line 2,028: Line 2,028:
|  
|  
| 18.462
| 18.462
| [[Pental (temperament)|Pental]]
| [[Pental (temperament)| Pental]]
|-
|-
|  
|  
Line 2,259: Line 2,259:
|-
|-
| 1\15  
| 1\15  
|
|  
|
|  
|  
|  
|  
|  
Line 2,532: Line 2,532:
|  
|  
| 112.941
| 112.941
| Blackwood/[[Phi as a Generator|Elderthing]]
| Blackwood/[[Phi as a Generator| Elderthing]]
|-
|-
|  
|  
Line 2,578: Line 2,578:
|-
|-
| 0\6
| 0\6
|
|  
|  
|  
|  
|  
Line 2,879: Line 2,879:


== 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 2,886:
|-
|-
| 0\7
| 0\7
|
|  
|  
|  
|  
|  
Line 3,059: Line 3,059:
|  
|  
| 28.571
| 28.571
| [[Mistismic temperaments#Neutron|Neutron]]
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|  
|  
Line 3,114: Line 3,114:
|  
|  
| 34.286
| 34.286
| [[Whitewood family#Redwood|Redwood]]
| [[Whitewood family#Redwood| Redwood]]
|-
|-
|  
|  
Line 3,180: Line 3,180:
|  
|  
| 57.143
| 57.143
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal| Septimal]]
|-
|-
|  
|  
Line 3,272: Line 3,272:


== 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 3,279:
|-
|-
| 0\8
| 0\8
|
|  
|  
|  
|  
|  
Line 3,288: Line 3,288:
| 0
| 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
|
|-
|-
|  
|  
Line 3,392: Line 3,293:
|  
|  
|  
|  
| 1\80
| 1\480
|  
|  
|  
|  
|  
|  
| 15
| 2.5
|  
|  
|-
|-
Line 3,403: Line 3,304:
|  
|  
|  
|  
| 1\472
|  
|  
| 2\152
|  
|  
|  
|  
| 15.789
| 2.542
|[[Octoid]]
| [[Octium]]
|-
|-
|  
|  
Line 3,416: Line 3,317:
|  
|  
|  
|  
| 3\224
| 4\1872
|  
|  
| 16.071
| 2.564
| Octoid
| Octium
|-
|-
|  
|  
Line 3,425: Line 3,326:
|  
|  
|  
|  
| 1\72
|  
|  
|  
|  
|  
|  
| 16.667
| 7\3272
| Octoid
| 2.567
| Octium
|-
|-
|  
|  
Line 3,436: Line 3,337:
|  
|  
|  
|  
| 1\64
|  
|  
| 3\1400
|  
|  
|  
|  
| 18.75
| 2.571
|  
| Octium
|-
|-
|  
|  
|  
|  
|  
|  
| 1\56
|  
|  
| 1\464
|  
|  
|  
|  
|  
|  
| 21.429
| 2.586
|  
|  
|-
|-
|  
|  
|  
|  
| 1\48
|  
|  
|
| …
|  
|  
|  
|  
|  
|  
|  
|  
| 25
|  
|  
|-
|-
|  
|  
| 1\40
|  
|  
|  
|  
|  
|  
| 1\96
|  
|  
|  
|  
|  
|  
| 30
| 12.5
|  
|  
|-
|-
|  
|  
|  
|  
| 2\72
|  
|  
|  
|  
| 1\88
|  
|  
|  
|  
|  
|  
| 33.333
| 13.635
|  
|  
|-
|-
| 1\32
|  
|  
|  
|  
|  
|  
|  
|  
| 1\80
|  
|  
|  
|  
|  
|  
| 37.5
| 15
| [[Semidim]]
|  
|-
|-
|  
|  
|  
|  
| 3\88
|  
|  
|  
|  
|  
|  
| 2\152
|  
|  
|  
|  
| 40.909
| 15.789
| Semidim
| [[Octoid]]
|-
|-
|  
|  
| 2\56
|  
|  
|  
|  
Line 3,516: Line 3,416:
|  
|  
|  
|  
| 3\224
|  
|  
| 42.857
| 16.071
| Semidim
| Octoid
|-
|-
|  
|  
|  
|  
| 3\80
|  
|  
|  
|  
| 1\72
|  
|  
|  
|  
|  
|  
| 45
| 16.667
| Semidim
| Octoid
|-
|-
|  
|  
|  
|  
|  
|  
| 4\104
|  
| 1\64
|  
|  
|  
|  
|  
|  
| 18.75
|  
|  
| 46.154
| Semidim
|-
|-
|  
|  
|  
|  
|  
|  
| 1\56
|  
|  
| 5\128
|  
|  
|  
|  
|  
|  
| 46.875
| 21.429
| Semidim
|  
|-
|-
|  
|  
|  
|  
| 1\48
|  
|  
|  
|  
| 6\152
|  
|  
|  
|  
|  
|  
| 47.368
| 25
| Semidim
|  
|-
|-
|
| 1\40
|  
|  
|  
|  
Line 3,569: Line 3,472:
|  
|  
|  
|  
| 7\176
|  
|  
| 30
|  
|  
| 47.727
| Semidim
|-
|-
|  
|  
|
| 2\72
|  
|  
|  
|  
|  
|  
|  
|  
| 8\200
|  
|  
| 33.333
|  
|  
| 48
| Semidim
|-
|-
| 1\32
|  
|  
|  
|  
Line 3,591: Line 3,493:
|  
|  
|  
|  
| 9\224
|  
|  
|  
|  
| 48.214
| 37.5
| Semidim/[[Octant]]
| [[Semidim]]
|-
|-
|  
|  
|  
|  
| 3\88
|  
|  
|  
|  
Line 3,604: Line 3,506:
|  
|  
|  
|  
| 28\696
| 40.909
| 48.276
| Semidim
| Semidim/Octant
|-
|-
|  
|  
| 2\56
|  
|  
|  
|  
Line 3,614: Line 3,516:
|  
|  
|  
|  
| 19\472
|  
|  
| 48.305
| 42.857
| Semidim/Octant
| Semidim
|-
|-
|  
|  
|  
|  
| 3\80
|  
|  
|  
|  
|  
|  
| 10\248
|  
|  
|  
|  
| 48.387
| 45
| Semidim
| Semidim
|-
|-
| 1\24
|  
|  
|  
|  
|  
|  
| 4\104
|  
|  
|  
|  
|  
|  
|  
|  
| 50
| 46.154
| Semidim
| Semidim
|-
|-
| 2\40
|  
|  
|  
|  
|  
|  
|  
|  
| 5\128
|  
|  
|  
|  
|  
|  
| 60
| 46.875
|  
| Semidim
|-
|-
| 1\16
|  
|  
|  
|  
|  
|  
|  
|  
| 6\152
|  
|  
|  
|  
|  
|  
| 75
| 47.368
|  
| Semidim
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
| 0\9
| 
|  
|  
|  
|  
Line 3,677: Line 3,569:
|  
|  
|  
|  
| 7\176
|  
|  
| 0
|  
|  
| 47.727
| Semidim
|-
|-
|  
|  
Line 3,685: Line 3,579:
|  
|  
|  
|  
| 1\72
|  
|  
| 8\200
|  
|  
|  
|  
| 16.667
| 48
| [[Enneaportent]]
| Semidim
|-
|-
|  
|  
Line 3,697: Line 3,591:
|  
|  
|  
|  
| 9\224
|  
|  
|  
|  
| 4\279
| 48.214
| 17.204
| Semidim/[[Octant]]
| Enneaportent
|-
|-
|  
|  
Line 3,709: Line 3,603:
|  
|  
|  
|  
| 3\207
|  
|  
| 17.391
| 28\696
| Enneaportent
| 48.276
| Semidim/Octant
|-
|-
|  
|  
Line 3,719: Line 3,613:
|  
|  
|  
|  
| 2\135
|  
|  
| 19\472
|  
|  
| 17.778
| 48.305
| Enneaportent
| Semidim/Octant
|-
|-
|  
|  
|  
|  
|  
|  
| 1\63
|  
|  
|  
|  
| 10\248
|  
|  
|  
|  
| 19.048
| 48.387
| Enneaportent
| Semidim
|-
|-
| 1\24
|  
|  
|  
|  
| 1\54
|  
|  
|  
|  
Line 3,744: Line 3,638:
|  
|  
|  
|  
| 22.222
| 50
|  
| Semidim
|-
|-
| 2\40
|  
|  
| 1\45
|  
|  
|  
|  
Line 3,755: Line 3,649:
|  
|  
|  
|  
| 26.667
| 60
|  
|  
|-
|-
| 1\36
| 1\16
|  
|  
|  
|  
Line 3,766: Line 3,660:
|  
|  
|  
|  
| 33.333
| 75
| [[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
|  
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
| 0\9
|
|  
|  
|  
|  
|  
|  
| 4\135
|  
|  
|  
|  
|  
|  
| 0
|  
|  
| 35.556
| No-five tritrizo
|-
|-
|  
|  
|  
|  
| 3\99
|  
|  
|  
|  
| 1\72
|  
|  
|  
|  
|  
|  
| 36.364
| 16.667
| No-five tritrizo
| [[Enneaportent]]
|-
|-
|  
|  
| 2\63
|  
|  
|  
|  
Line 3,799: Line 3,699:
|  
|  
|  
|  
| 38.095
| 4\279
| [[Niner]]
| 17.204
| Enneaportent
|-
|-
|  
|  
|  
|  
| 3\90
|  
|  
|  
|  
|  
|  
|  
|  
| 3\207
|  
|  
| 40
| 17.391
| Niner
| Enneaportent
|-
|-
| 1\27
|  
|  
|  
|  
Line 3,819: Line 3,719:
|  
|  
|  
|  
| 2\135
|  
|  
|  
|  
| 44.444
| 17.778
| Niner
| Enneaportent
|-
|-
|  
|  
|  
|  
| 4\99
|  
|  
| 1\63
|  
|  
|  
|  
|  
|  
|  
|  
| 48.485
| 19.048
| [[Ennealimmal]]
| Enneaportent
|-
|-
|  
|  
|
| 1\54
|  
|  
|  
|  
| 7\171
|  
|  
|  
|  
|  
|  
| 22.222
|  
|  
| 49.123
| Ennealimmal
|-
|-
|  
|  
| 3\72
| 1\45
|  
|  
|  
|  
Line 3,854: Line 3,755:
|  
|  
|  
|  
| 50
| 26.667
| Ennealimmal
|  
|-
|-
| 1\36
|  
|  
|  
|  
Line 3,864: Line 3,766:
|  
|  
|  
|  
| 20\477
| 33.333
| 50.314
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
| [[Novemkleismic]]
|-
|-
|  
|  
|  
|  
|  
|  
| 4\135
|  
|  
|  
|  
|  
|  
| 17\405
|  
|  
| 50.370
| 35.556
| Novemkleismic
| No-five tritrizo
|-
|-
|  
|  
|  
|  
| 3\99
|  
|  
|  
|  
|  
|  
| 14\333
|  
|  
|  
|  
| 50.451
| 36.364
| Novemkleismic
| No-five tritrizo
|-
|-
|  
|  
| 2\63
|  
|  
|  
|  
|  
|  
| 11\261
|  
|  
|  
|  
|  
|  
| 50.575
| 38.095
| Novemkleismic
| [[Niner]]
|-
|-
|  
|  
|  
|  
| 3\90
|  
|  
| 8\189
|  
|  
|  
|  
|  
|  
|  
|  
| 50.794
| 40
| Novemkleismic
| Niner
|-
|-
| 1\27
|  
|  
|  
|  
| 5\117
|  
|  
|  
|  
Line 3,920: Line 3,821:
|  
|  
|  
|  
| 51.282
| 44.444
|  
| Niner
|-
|-
| 2\45
|  
|  
|  
|  
| 4\99
|  
|  
|  
|  
Line 3,931: Line 3,832:
|  
|  
|  
|  
| 53.333
| 48.485
| [[Ennealimmal]]
|-
|
|  
|  
|-
| 1\18
|  
|  
| 7\171
|  
|  
|  
|  
|  
|  
|  
|  
| 49.123
| Ennealimmal
|-
|  
|  
| 3\72
|  
|  
| 66.667
|  
|  
|}
|  
 
|
== Ten periods per octave==
|
{| class="wikitable sortable mw-collapsible"
|  
! colspan="7" |Generator
| 50
!Cents
| Ennealimmal
!Comments
|-
|-
|0\10
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|0
| 20\477
|
| 50.314
|-
| [[Novemkleismic]]
|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
|
|
| 17\405
|
| 50.370
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|4\170
|  
|
|  
|
| 14\333
|
|  
|28.235
|  
|Decic
| 50.451
| Novemkleismic
|-
|-
|
|
|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
|
|  
|  
|  
|  
|  
|  
|
|  
|
| 11\261
|0
|  
|
|  
|
| 50.575
| Novemkleismic
|-
|-
|
|1\55
|
|
|
|
|
|21.818
|
|-
|1\44
|
|
|
|
|
|
|27.273
|
|-
|
|2\77
|
|
|
|  
|  
|
| 31.169
|  
|  
|
| 8\189
|
|
|
|
| 50.794
| Novemkleismic
|-
|-
|1\33
|  
|
|  
|
| 5\117
|
|  
|
|  
|
|  
|
|  
|36.364
|  
|
| 51.282
|-
|  
|
|3\88
|
|
|
|
|
|40.909
|
|-
|2\55
|
|
|
|
|
|
|42.636
|[[Hendecatonic]]
|-
|-
|
| 2\45
|3\77
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|46.753
|  
|Hendecatonic
| 53.333
|  
|-
|-
|
| 1\18
|
|  
|
|  
|7\176
|  
|
|  
|
|  
|
|  
|47.727
|  
|Hendecatonic
| 66.667
|-
|  
|
|
|
|
|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==
== Ten periods per octave==
{{See also|Compton family}}
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator
! colspan="7" | Generator
!Cents
! Cents
!Comments
! Comments
|-
|-
|0\12
| 0\10
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 0
|0
|  
|
|-
|-
|
| 1\110
|
|  
|
|  
|1\636
|  
|
|  
|
|  
|
|  
|
| 10.909
|1.887
|  
|
|-
|-
|
| 1\100
|
|  
|
|  
|1\624
|  
|
|  
|
|  
|
|  
|
| 12
|1.923
|  
|
|-
|-
|
|  
|
| 2\190
|
|  
|
|  
|2\1236
|  
|
|  
|
|  
|
| 12.632
|1.942
| [[Deca]]
|[[Atomic]]
|-
|-
|
| 1\90
|
|  
|
|  
|
|  
|
|  
|3\1848
|  
|
|  
|
| 13.333
|1.948
| Deca
|Atomic
|-
|
|
|
|
|
|
|4\2460
|
|1.951
|Atomic
|-
|
|
|
|
|
|
|
|5\3072
|1.953
|Atomic
|-
|-
|
| 1\80
|
|  
|
|  
|1\612
|  
|
|  
|
|  
|
|  
|
| 15
|1.961
| Deca
|Atomic
|-
|-
|
| 1\70
|
|  
|
|  
|1\600
|  
|
|  
|
|  
|
|  
|
| 17.143
|2
|  
|
|-
|-
|
| 1\60
|
|  
|
|  
|1\588
|  
|
|  
|
|  
|
|  
|
| 20
|2.041
|  
|
|-
|-
|
| 1\50
|
|  
|
|  
|1\576
|  
|
|  
|
|  
|
|  
|
| 24
|2.083
| [[Decimetra]]
|
|-
|-
|
|  
|
|  
|
|  
|...
| 4\190
|
|  
|
|  
|
|  
|
| 25.263
|...
| Decimetra
|
|-
|
|
|
|1\108
|
|
|
|
|11.111
|
|-
|-
|
|  
|
|  
|
|  
|1\96
|  
|
| 7\330
|
|  
|
|  
|
| 25.455
|12.5
| Decimetra
|[[Compton]]
|-
|-
|
|  
|
|  
|
|  
|1\84
|  
|
|  
|
|  
|
| 17\800
|
| 25.5
|14.286
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\240
| 10\470
|
|  
|
| 25.532
|15
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
| 3\140
|
|  
|
|  
|
|  
|
|  
|8\636
| 25.714
|15.094
| Decimetra
|Compton
|-
|-
|
|  
|
| 2\90
|
|  
|
|  
|
|  
|
|  
|5\396
|  
|
| 26.667
|15.152
| Decimetra
|Compton
|-
|-
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
| 30
|15.217
| [[Decic]]
|Compton
|-
|-
|
|  
|
|  
|
| 3\110
|
|  
|2\156
|  
|
|  
|
|  
|
| 32.727
|15.385
| Decic
|Compton
|-
|-
|
|  
|
| 2\70
|
|  
|
|  
|
|  
|
|  
|
|  
|7\540
| 34.286
|15.556
| Decic
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 4\170
|
|  
|
|  
|5\384
|  
|
| 28.235
|15.625
| Decic
|Compton
|-
|-
|
|  
|
|  
|
| 3\100
|
|  
|
|  
|
|  
|
|  
|8\612
| 36
|15.686
| Decic
|Compton
|-
|-
|
| 1\30
|
|  
|
|  
|
|  
|
|  
|3\228
|  
|
|  
|
| 40
|15.789
| Decic/[[Decal]]
|Compton
|-
|-
|
|  
|
| 3\80
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
| 45
|15.909
| Decal/[[Decistearn]]
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 8\210
|
|  
|
|  
|4\300
|  
|
| 45.714
|16
| Decal/Decistearn
|Compton
|-
|
|
|
|
|
|
|
|5\372
|16.129
|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
| [[Decoid]]
|
|-
|-
|
| 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
|  
|
|-
|-
|1\24
|
|
| 3\88
|
|
|
|
|
|
|
|
|
|
|
| 40.909
|50
|
|
|-
| 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==
== 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"