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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 ==
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"
|-
|-
Line 997: Line 997:
|  
|  
| 50.000
| 50.000
| Semiaug/[[Augmented family#Hemiug|Hemiug]]
| Semiaug/[[Augmented family#Hemiug| Hemiug]]
|-
|-
|  
|  
Line 1,455: Line 1,455:
|}
|}


==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 1,497:
| 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  
|  
|  
|}
|}


==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 2,004: Line 2,004:
|  
|  
| 10.435
| 10.435
|
|-
|
|
|
|
|
| ...
|
|
|
| ...
|  
|  
|-
|-
Line 2,040: Line 2,028:
|  
|  
| 18.462
| 18.462
| [[Pental (temperament)|Pental]]
| [[Pental (temperament)| Pental]]
|-
|-
|  
|  
Line 2,271: Line 2,259:
|-
|-
| 1\15  
| 1\15  
|
|  
|
|  
|  
|  
|  
|  
Line 2,544: Line 2,532:
|  
|  
| 112.941
| 112.941
| Blackwood/[[Phi as a Generator|Elderthing]]
| Blackwood/[[Phi as a Generator| Elderthing]]
|-
|-
|  
|  
Line 2,583: Line 2,571:
|}
|}


==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 2,578:
|-
|-
| 0\6
| 0\6
|
|  
|  
|  
|  
|  
Line 2,890: Line 2,878:
|}
|}


==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 2,898: Line 2,886:
|-
|-
| 0\7
| 0\7
|
|  
|  
|  
|  
|  
Line 3,071: Line 3,059:
|  
|  
| 28.571
| 28.571
| [[Mistismic temperaments#Neutron|Neutron]]
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|  
|  
Line 3,126: Line 3,114:
|  
|  
| 34.286
| 34.286
| [[Whitewood family#Redwood|Redwood]]
| [[Whitewood family#Redwood| Redwood]]
|-
|-
|  
|  
Line 3,192: Line 3,180:
|  
|  
| 57.143
| 57.143
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal| Septimal]]
|-
|-
|  
|  
Line 3,283: Line 3,271:
|}
|}


==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="9" |Generator!!Cents!!Comments
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|0\8||  ||
| 0\8
|
|  
|
|  
|
|  
|
|  
|
|  
| ||0||
|  
|-
|  
|
| 0
|
|  
|
|
|
|
|1\80
|
|
|15
|
|-
|
|
|
|
|
|
|
|2\152
|
|15.789
|[[Octoid]]
|-
|
|
|
|
|
|
|
|
|3\224
|16.071
|Octoid
|-
|
|
|
|
|
|1\72
|
|
|
|16.667
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\64
| 1\480
|
|  
|
|  
|
|  
|
| 2.5
|18.75
|  
|
|-
|-
|
|
|
|  
|
|  
|1\56
|  
|
| 1\472
|
|  
|
|  
|
|  
|
| 2.542
|21.429
| [[Octium]]
|
|-
|-
|
|  
|
|  
|1\48
|  
|
|  
|
|  
|
|  
|
| 4\1872
|
|  
|
| 2.564
|25
| Octium
|
|-
|-
|
|  
| 1\40
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\3272
|
| 2.567
|30
| Octium
|
|-
|-
|
|  
|
|  
|2\72
|  
|
|  
|
|  
|
| 3\1400
|
|  
|
|  
|
| 2.571
|33.333
| Octium
|
|-
|1\32
|
|
|
|
|
|
|
|
|37.5
|[[Semidim]]
|-
|
|
|3\88
|
|
|
|
|
|
|40.909
|Semidim
|-
|
|2\56
|
|
|
|
|
|
|
|42.857
|Semidim
|-
|-
|
|  
|
|  
|3\80
|  
|
|  
|
| 1\464
|
|  
|
|  
|
|  
|
| 2.586
|45
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|4\104
|  
|
| …
|
|  
|
|  
|
|  
|
|  
|46.154
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|5\128
| 1\96
|
|  
|
|  
|
|  
|
| 12.5
|46.875
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\88
|6\152
|  
|
|  
|
|  
|
| 13.635
|47.368
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\80
|
|  
|7\176
|  
|
|  
|
| 15
|47.727
|  
|Semidim
|-
|
|
|
|
|
|
|8\200
|
|
|48
|Semidim
|-
|
|
|
|
|
|
|9\224
|
|
|48.214
|Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\152
|
|  
|
|  
|28\696
| 15.789
|48.276
| [[Octoid]]
|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
|  
|  
|
|  
|
|  
|
|  
|
| 3\224
|
|  
| 50
| 16.071
|Ennealimmal
| Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\72
|
|  
|
|  
|20\477
|  
|50.314
| 16.667
|[[Novemkleismic]]
| Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\64
|
|  
|17\405
|  
|
|  
|50.370
| 18.75
|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
|
|}
==Twelve periods per octave==
See also: [[Compton family]]
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!!Comments
|-
|0\12||  || ||
|
|  
|  
|
|  
|||0||
| 1\56
|  
|  
|  
|
| 21.429
|  
|-
|-
|
|  
|
|  
|
| 1\48
|1\636
|  
|
|  
|
|  
|
|  
|
|  
|1.887
| 25
|
|  
|-
|-
|
|  
|
| 1\40
|
|  
|1\624
|  
|
|  
|
|  
|
|  
|
|  
|1.923
| 30
|
|  
|-
|-
|
|  
|
|  
|
| 2\72
|
|  
|2\1236
|  
|
|  
|
|  
|
|  
|1.942
| 33.333
|[[Atomic]]
|  
|-
|-
|
| 1\32
|
|  
|
|  
|
|  
|
|  
|3\1848
|  
|
|  
|
|  
|1.948
| 37.5
|Atomic
| [[Semidim]]
|-
|-
|
|  
|
|  
|
| 3\88
|
|  
|
|  
|
|  
|4\2460
|  
|
|  
|1.951
| 40.909
|Atomic
| Semidim
|-
|
|
|
|
|
|
|
|5\3072
|1.953
|Atomic
|-
|-
|
|  
|
| 2\56
|
|  
|1\612
|  
|
|  
|
|  
|
|  
|
|  
|1.961
| 42.857
|Atomic
| Semidim
|-
|-
|
|  
|
|  
|
| 3\80
|1\600
|  
|
|  
|
|  
|
|  
|
|  
|2
| 45
|
| Semidim
|-
|-
|
|  
|
|  
|
|  
|1\588
| 4\104
|
|  
|
|  
|
|  
|
|  
|2.041
| 46.154
|
| Semidim
|-
|-
|
|  
|
|  
|
|  
|1\576
|  
|
| 5\128
|
|  
|
|  
|
|  
|2.083
| 46.875
|
| Semidim
|-
|-
|
|  
|
|  
|
|  
|...
|  
|
| 6\152
|
|  
|
|  
|
|  
|...
| 47.368
|
| Semidim
|-
|
|
|
|1\108
|
|
|
|
|11.111
|
|-
|
|
|
|1\96
|
|
|
|
|12.5
|[[Compton]]
|-
|
|
|
|1\84
|
|
|
|
|14.286
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\240
| 7\176
|
|  
|
|  
|15
| 47.727
|Compton
| Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\200
|
|  
|8\636
|  
|15.094
| 48
|Compton
| Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 9\224
|5\396
|  
|
|  
|15.152
| 48.214
|Compton
| Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
| 28\696
|15.217
| 48.276
|Compton
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\156
|  
|
|  
|
| 19\472
|
|  
|15.385
| 48.305
|Compton
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 10\248
|
|  
|7\540
|  
|15.556
| 48.387
|Compton
| Semidim
|-
|-
|
| 1\24
|
|  
|
|  
|
|  
|
|  
|
|  
|5\384
|  
|
|  
|15.625
| 50
|Compton
| Semidim
|-
|-
|
| 2\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\612
|  
|15.686
| 60
|Compton
|  
|-
|-
|
| 1\16
|
|
|
|
|
|  
|
|  
|3\228
|  
|
|  
|
|  
|15.789
| 75
|Compton
|  
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\9
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
|  
|15.909
| 0
|Compton
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\72
|
|  
|4\300
|  
|
|  
|16
| 16.667
|Compton
| [[Enneaportent]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\372
| 4\279
|16.129
| 17.204
|Compton
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|  
|
| 3\207
|
|  
|16.667
| 17.391
|Compton
| Enneaportent
|-
|-
|
|  
|
|  
|1\60
|  
|
|  
|
|  
|
| 2\135
|
|  
|
|  
|20
| 17.778
|Compton
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|2\108
| 1\63
|
|  
|
|  
|
|  
|
|  
|22.222
| 19.048
|
| Enneaportent
|-
|
|1\48
|
|
|
|
|
|
|25
|[[Catler]]
|-
|-
|
|  
|
|  
|
| 1\54
|3\132
|  
|
|  
|
|  
|
|  
|
|  
| 27.273
| 22.222
|Catler
|  
|-
|-
|
|  
|
| 1\45
| 2\84
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|28.571
| 26.667
|Catler
|  
|-
|-
|
| 1\36
|
|  
|
|  
|3\120
|  
|
|  
|
|  
|
|  
|
|  
|30
| 33.333
|Catler
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|-
|1\36
|  
|
|  
|
|  
|
| 4\135
|
|  
|
|  
|
|  
|
|  
|33.333
| 35.556
|Catler/[[Catnip]]
| No-five tritrizo
|-
|
|
|
|4\132
|
|
|
|
|36.364
|Catnip
|-
|-
|
|  
|
|  
|3\96
| 3\99
|
|  
|
|  
|
|  
|
|  
|
|  
|37.5
| 36.364
| Catnip
| No-five tritrizo
|-
|-
|
|  
|
| 2\63
|
|  
|5\156
|  
|
|  
|
|  
|
|  
|
|  
|38.462
| 38.095
|Catnip
| [[Niner]]
|-
|-
|
|  
|2\60
|  
|
| 3\90
|
|  
|
|  
|
|  
|
|  
|
|  
|40
| 40
|Catnip
| Niner
|-
|-
|
| 1\27
|
|  
|
|  
|5\144
|  
|
|  
|
|  
|
|  
|
|  
|41.667
| 44.444
|
| Niner
|-
|-
|
|  
|
|  
|3\84
| 4\99
|
|  
|
|  
|
|  
|
|  
|
|  
| 42.857
| 48.485
| [[Magnesium]]
| [[Ennealimmal]]
|-
|-
|
|  
|
|  
|
|  
|
| 7\171
|
|  
|
|  
|
|  
|16\444
|  
|43.243
| 49.123
|Magnesium
| Ennealimmal
|-
|-
|
|  
|
| 3\72
|
|  
|
|  
|
|  
|
|  
|13\360
|  
|
|  
|43.333
| 50
|Magnesium
| Ennealimmal
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|10\276
|  
|
|  
|
| 20\477
|43.378
| 50.314
|
| [[Novemkleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|7\192
|  
|
|  
|
| 17\405
|
|  
|43.75
| 50.370
|
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|4\108
|  
|
|
|
| 14\333
|
|
|
|
|44.444
| 50.451
|
| Novemkleismic
|-
|-
|1\24
|
|
|
|
|
|
|
|
| 11\261
|
|
|
|
|
|
| 50
| 50.575
|
| Novemkleismic
|}
|-
 
|  
== See also ==
|  
|
| 8\189
|
|
|
|
| 50.794
| Novemkleismic
|-
|
|
| 5\117
|
|
|
|
|
| 51.282
|
|-
| 2\45
|
|
|
|
|
|
|
| 53.333
|  
|-
| 1\18
|  
|  
|  
|  
|  
|  
|  
| 66.667
|  
|}


*[[Fractional-octave temperaments]]: Lists dozens more temperaments beyond what can be listed here.
== 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"