Xenharmonic Wiki

Map of rank-2 temperaments: Difference between revisions

← Older edit
VisualWikitext
ArrowHead294 (talk | contribs)
15,215 edits
Hkm (talk | contribs)
autopatrolled
1,038 edits
No edit summary
 
(32 intermediate revisions by 5 users not shown)
Line 1: Line 1:
This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only rank-2 temperaments not appearing here should be ones like [[Bohlen-Pierce|Bohlen-Pierce]] that completely lack octaves.
This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only rank-2 temperaments not appearing here should be ones like [[Bohlen–Pierce]] that completely lack octaves.


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


==One period per octave==
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 !! Cents !! Comments
! colspan="6" | Generator
! Cents
! Comments
|-
|-
| 0\4 || || ||  ||  ||  || 0 ||  
| 0\4
|  
|  
|  
|  
|  
| 0
|  
|-
|-
| || ||  || 1\76 || ||  || 15.789 ||  
|  
|  
|  
| 1\76
|  
|  
| 15.789
|  
|-
|-
| || ||  || 1\72 || ||  || 16.667 || [[Quadritikleismic]]
|  
|  
|  
| 1\72
|  
|  
| 16.667
| [[Quadritikleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\212
| 3\212
|16.981
| 16.981
|Quadritikleismic
| Quadritikleismic
|-
|-
| || ||  ||  || 2\140 ||  || 17.143 || Quadritikleismic
|  
|  
|  
|  
| 2\140  
|  
| 17.143  
| Quadritikleismic
|-
|-
| || ||  || 1\68 || ||  || 17.647 || Quadritikleismic
|  
|-
|  
|  ||  ||  || 1\64 ||  ||  || 18.75 ||
|  
|-
| 1\68  
|  ||  ||  || 1\60 ||  ||  || 20 ||
|  
|  
| 17.647  
| Quadritikleismic
|-
|-
| || || || ... ||  ||  || ... ||  
|  
|  
|  
| 1\64
|  
|  
| 18.75
|  
|-
|-
| || ||  || 1\36 ||  ||  || 33.333 ||  
|  
|  
|  
| 1\60
|  
|  
| 20
|  
|-
|-
| || || || 1\32 ||  ||  || 37.5 ||  
|  
|  
|  
| ...
|  
|  
| ...
|  
|-
|-
| || ||  || 1\28 || ||  || 42.857 ||  
|  
|  
|  
| 1\36
|  
|  
| 33.333
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\32
|2\52
|  
|
|  
|46.154
| 37.5
|[[Hemidim]]
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\28
|
|  
|3\76
|  
|47.368
| 42.857
|Hemidim
|  
|-
|-
| || || 1\24 || ||  ||  || 50 || Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|  
|  
|  
|  
| 2\52
|  
| 46.154
| [[Hemidim]]
|-
|-
| || 1\20 || || ||  ||  || 60 ||  
|  
|  
|  
|  
|  
| 3\76
| 47.368
| Hemidim
|-
|-
| 1\16 ||  ||  ||  ||  || || 75 ||  
|
|
| 1\24
|  
|  
|  
| 50
| Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|-
|-
|
|  
|2\28
| 1\20
|
|  
|
|  
|
|  
|
|  
|85.714
| 60
|[[Demolished]]
|  
|-
|-
|
| 1\16
|
|  
|3\40
|  
|
|  
|
|  
|
|  
|90
| 75
|Demolished
|  
|-
|-
| 1\12 ||  || || || ||  || 100 || Demolished/[[Diminished]]
|  
| 2\28
|  
|  
|  
|  
| 85.714
| [[Demolished]]
|-
|-
|
|  
|
|  
|
| 3\40
|14\164
|  
|
|  
|
|  
|102.439
| 90
|Diminished
| Demolished
|-
|-
|
| 1\12
|
|  
|
|  
|
|  
|27\316
|  
|
|  
|102.532
| 100
|Diminished/[[Unlit]]
| Demolished/[[Diminished (temperament)|Diminished]]
|-
|-
|
|  
|
|  
|
|  
|
| 14\164
|
|  
|40\468
|  
|102.564
| 102.439
|Diminished/Unlit
| Diminished
|-
|-
|
|  
|
|  
|
|  
|13\152
|  
|
| 27\316
|
|  
|102.632
| 102.532
|Diminished/Unlit/[[Undim]]
| Diminished/[[Unlit]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|38\444
| 40\468
|102.703
| 102.564
|Diminished/Undim
| Diminished/Unlit
|-
|-
|
|  
|
|  
|
|  
|
| 13\152
|25\292
|  
|
|  
|102.740
| 102.632
|Diminished/Undim
| Diminished/Unlit/[[Undim]]
|-
|-
|
|  
|
|  
|
|  
|12\140
|  
|
|  
|
| 38\444
|102.857
| 102.703
|Diminished/Undim
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|11\128
|  
|
| 25\292
|
|  
|103.125
| 102.740
|Diminished
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|10\116
| 12\140
|
|  
|
|  
|103.448
| 102.857
|Diminished
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|9\104
| 11\128
|
|  
|
|  
|103.846
| 103.125
|Diminished
| Diminished
|-
|-
|
|  
|
|  
|
|  
|8\92
| 10\116
|
|  
|
|  
|104.348
| 103.448
|Diminished
| Diminished
|-
|-
| || ||  || 7\80 ||  ||  || 105 || Diminished/[[Bidia]]
|  
|  
|  
| 9\104
|  
|  
| 103.846
| Diminished
|-
|-
|
|  
|
|  
|
|  
|
| 8\92
|
|  
|20\228
|  
|105.263
| 104.348
|Diminished/Bidia
| Diminished
|-
|-
|
|  
|
|  
|
|  
|
| 7\80
|13\148
|  
|
|  
|105.405
| 105  
|Diminished/Bidia
| Diminished/[[Bidia]]
|-
|-
| || || || 6\68 ||  ||  || 105.882 || Diminished/Bidia
|  
|  
|  
|  
|  
| 20\228
| 105.263
| Diminished/Bidia
|-
|-
| || || || 5\56 || ||  || 107.143 || Diminished/Bidia
|  
|  
|  
|  
| 13\148
|  
| 105.405
| Diminished/Bidia
|-
|-
| || || 4\44 ||  || ||  || 109.091 || Diminished
|  
|  
|  
| 6\68
|  
|  
| 105.882
| Diminished/Bidia
|-
|-
| || 3\32 ||  ||  ||  ||  || 112.5 || Diminished
|  
|-
|  
| 2\20 ||  ||  ||  ||  ||  || 120 || Diminished
|  
| 5\56
|  
|  
| 107.143
| Diminished/Bidia
|-
|-
|
|  
|3\28
|  
|
| 4\44
|
|  
|
|  
|
|  
|128.571
| 109.091
|
| Diminished
|-
|-
| 1\8 ||  ||  ||  ||  ||  || 150 ||  
|  
|}
| 3\32
 
|  
==Five periods per octave==
|  
{{todo|complete table|comment=add trisedodge (optimal ETs 15, 50, 65, 80, 340, 405) and countdown (15, 35, 50, 65, 210, 275, 340)}}
|  
{| class="wikitable sortable mw-collapsible"
|  
! colspan="9" |Generator!!Cents !!Comments
| 112.5
| Diminished
|-
|-
|0\5 ||  || ||
| 2\20
|
|  
|  
|  
|  
|  
|  
|  
|  
| || 0||
| 120
| Diminished
|-
|-
|
|  
|
| 3\28
|
|  
|
|  
|
|  
|1\140
|  
|
| 128.571
|
|  
|
|8.571
|
|-
|-
|
| 1\8
|
|  
|
|  
|
|  
|
|  
|1\135
|  
|
| 150
|
|  
|
|}
|8.889
 
|[[5th-octave temperaments#Slendrismic|Slendrismic]]
== Five periods per octave ==
{{todo| complete table| comment=add trisedodge (optimal ETs 15, 50, 65, 80, 340, 405) and countdown (15, 35, 50, 65, 210, 275, 340)}}
{| class="wikitable sortable mw-collapsible"
! colspan="9" | Generator
! Cents
! Comments
|-
|-
|
| 0\5
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\400
|  
|
|  
|9
| 0
|Slendrismic
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\140
|
|  
|
|  
|5\665
|  
|9.023
| 8.571
|Slendrismic
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\135
|2\265
|  
|
|  
|
|  
|9.057
| 8.889
|Slendrismic
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\130
|  
|
|  
|
| 3\400
|
|  
|9.231
| 9
|Slendrismic/[[Hemipental]]
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\515
| 5\665
|9.32
| 9.023
|Hemipental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\265
|3\385
|  
|
|  
|9.351
| 9.057
|Hemipental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\130
|
|  
|
|  
|5\640
|  
|9.375
| 9.231
|Hemipental
| Slendroschismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\255
|  
|
|  
|
| 4\515
|9.412
| 9.32
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\125
|  
|
|  
|
| 3\385
|
|  
|9.6
| 9.351
|Hemipental
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\120
|  
|
|  
|
|  
|
| 5\640
|10
| 9.375
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\115
|  
|
| 2\255
|
|  
|
|  
|10.435
| 9.412
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|...
| 1\125
|
|  
|
|  
|
|  
|...
| 9.6
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\70
| 1\120
|
|  
|
|  
|
|  
|17.143
| 10
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\65
| 1\115
|
|  
|
|  
|
|  
|18.462
| 10.435
|[[Pental (temperament)|Pental]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\70
|
|  
|
|  
|4\255
|  
|18.824
| 17.143
|Pental
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\65
|
|  
|3\190
|  
|
|  
|18.947
| 18.462
|Pental
| [[Pental (temperament)| Pental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\315
| 4\255
|19.048
| 18.824
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\125
|  
|
| 3\190
|
|  
|19.2
| 18.947
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\185
|  
|
| 5\315
|19.459
| 19.048
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\60
|  
|
| 2\125
|
|  
|
|  
|20
| 19.2
|Pental
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\55
|  
|
|  
|
| 3\185
|
|  
|21.818
| 19.459
|
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\50
| 1\60
|
|  
|
|  
|
|  
|24
| 20
|
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\45
| 1\55
|
|  
|
|  
|
|  
|26.67
| 21.818
|
|  
|-
|-
|
|
|
|  
|
|  
|
|  
|1\40
|  
|
| 1\50
|
|  
|
|  
|
|  
|30
| 24
|
| [[Cloudtone]]
|-
|-
|
|  
|
|  
|
|  
|1\35
|  
|
|  
|
| 1\45
|
|  
|
|  
|
|  
|34.286
| 26.67
|
| Cloudtone
|-
|-
|
|  
|
|  
|1\30
|  
|
|  
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|40
| 30
|
| Cloudtone
|-
|-
|
|  
|1\25
|  
|
|  
|
| 1\35
|
|  
|
|  
|
|  
|
|  
|
|  
|48
| 34.286
|
|  
|-
|-
|1\20
|  
|
|  
|
| 1\30
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|60
| 40
|
|  
|-
|-
|
|  
|2\35
| 1\25
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|68.571
| 48
|[[Coblack]]
|  
|-
|-
|
| 1\20
|
|  
|
|  
|5\85
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|70.588
| 60
|Coblack
|  
|-
|-
|
|  
|
| 2\35
|3\50
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|72
| 68.571
|Coblack
| [[Coblack]]
|-
|-
|
|
|
|
|7\115
|
|
|
|
|73.043
|Coblack
|-
|
|
|
|4\65
|
|
|
|
|
|73.846
|Coblack
|-
| 1\15 ||  ||  ||
|
|  
|  
|  
|  
|  
|  
| || 80||[[Blackwood]]/[[Blacksmith]]
| 5\85
|-
|  
|
|  
|
|  
|
|  
|5\70
|  
|
| 70.588
|
| Coblack
|
|
|
|85.714
|Blackwood/Blacksmith
|-
|-
|
|  
|
|  
|4\55
| 3\50
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|87.273
| 72
|Blackwood/Blacksmith
| Coblack
|-
|-
|
|
|
|  
|
|  
|7\95
|  
|
| 7\115
|
|  
|
|  
|
|  
|
|  
|88.421
| 73.043
|Blackwood/Blacksmith
| Coblack
|-
|-
|
|  
|3\40
|  
|
|  
|
| 4\65
|
|  
|
|  
|
|  
|
|  
|
|  
|90
| 73.846
|Blackwood/Blacksmith
| Coblack
|-
|-
|
| 1\15
|
|  
|
|  
|8\105
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|91.429
| 80
|Blackwood/Blacksmith
| [[Blackwood]]
|-
|-
|
|
|
|  
|5\65
|  
|
| 5\70
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 85.714
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|
|  
|
| 4\55
|7\90
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|93.333
| 87.273
|Blackwood/Blacksmith
| Blackwood
|-
|-
|2\25
|  
|
|  
|
|  
|
| 7\95
|
|  
|
|  
|
|  
|
|  
|
|  
|96
| 88.421
|Blackwood/Blacksmith
| Blackwood
|-
|-
|
|  
|
| 3\40
|5\60
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|100
| 90
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|8\95
| 8\105
|
|  
|
|  
|
|  
|
|  
|
|  
|101.053
| 91.429
|Blackwood
| Blackwood
|-
|-
|
|  
|3\35
|  
|
| 5\65
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|102.857
| 92.308
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|7\80
| 7\90
|
|  
|
|  
|
|  
|
|  
|
|  
|105
| 93.333
|Blackwood
| Blackwood
|-
|-
|
| 2\25
|
|  
|4\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|106.667
| 96
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
| 5\60
|5\55
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|109.091
| 100
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 8\95
|6\65
|  
|
|  
|
|  
|
|  
|
|  
|110.769
| 101.053
|Blackwood/[[Quintosec]]/[[Sengasec]]
| Blackwood
|-
|-
|
|  
|
| 3\35
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|25\270
|  
|111.111
| 102.857
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 7\80
|
|  
|
|  
|
|  
|19\205
|  
|
|  
|111.220
| 105
|Blackwood/Quintosec/SengasecQintosec
| Blackwood
|-
|-
|
|  
|
|  
|
| 4\45
|
|  
|
|  
|
|  
|13\140
|  
|
|  
|
|  
|111.429
| 106.667
|Blackwood/Quintosec/Sengasec/Qintosec
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 5\55
|
|  
|
|  
|
|  
|20\215
|  
|
|  
|111.628
| 109.091
|Blackwood/Qintosec
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 6\65
|7\75
|  
|
|  
|
|  
|
|  
|112
| 110.769
|Blackwood/[[Qinto]]
| Blackwood/[[Quintosec]]/[[Sengasec]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|15\160
|  
|
| 25\270
|112.5
| 111.111
|Blackwood/Qinto
| Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\85
|  
|
| 19\205
|
|  
|112.941
| 111.220
|Blackwood/[[Phi as a Generator|Elderthing]]
| Blackwood/Quintosec/SengasecQintosec
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|9\95
| 13\140
|
|  
|
|  
|113.684
| 111.429
|Blackwood
| Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|10\105
|  
|
| 20\215
|
|  
|114.286
| 111.628
|Blackwood
| Blackwood/Qintosec
|-
|-
|1\10
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\75
|
|  
|
|  
|
|  
|120
| 112
|Blackwood
| Blackwood/[[Qinto]]
|}
 
==Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" |Generator!!Cents !!Comments
|-
|-
|0\6|| || ||  
|  
|
|  
|
|  
|||0||
|  
|  
|  
|  
| 15\160
|  
| 112.5
| Blackwood/Qinto
|-
|-
|
|  
|
|  
|
|  
|1\288
|  
|
|  
|
|
|
| 8\85
|4.167
|  
|
|  
| 112.941
| Blackwood/[[Phi as a Generator|Elderthing]]
|-
|-
|
|  
|
|  
|
|  
|1\282
|  
|
|  
|
|
|
| 9\95
|4.255
|  
|
|  
| 113.684
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|1\276
|  
|2\552
|  
|
|
|
| 10\105
|4.348
|  
|[[Sextile]]
|  
| 114.286
| Blackwood
|-
|-
|
| 1\10
|
|
|
|
|
|
|
|
|3\822
|  
|
|  
|4.380
|  
|Sextile
|  
| 120
| Blackwood
|}
 
== Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\6
|
|  
|
|  
|
|  
|
|  
|
|  
|4\1092
|  
|4.396
| 0
|Sextile
|  
|-
|-
|
|  
|
|  
|
|  
|1\270
| 1\288
|
|  
|
|  
|
|  
|4.444
| 4.167
|Sextile
|  
|-
|-
|
|  
|
|  
|
|  
|1\264
| 1\282
|
|  
|
|  
|
|  
|4.545
| 4.255
|
|  
|-
|-
|
|  
|
|  
|
|  
|...
| 1\276
|
| 2\552
|
|  
|
|  
|...
| 4.348
|
| [[Sextile]]
|-
|-
|
|  
|
|  
|
|  
|1\90
|  
|
|  
|
| 3\822
|
|  
|13.333
| 4.380
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\84
|  
|
|  
|
|  
|
| 4\1092
|14.286
| 4.396
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\78
| 1\270
|
|  
|
|  
|
|  
|15.385
| 4.444
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\72
| 1\264
|
|  
|
|  
|
|  
|16.667
| 4.545
|[[Stearnscape]]
|  
|-
|-
|
|  
|
|  
|
|  
|
| ...
|
|  
|
|  
|4\282
|  
|17.021
| ...
|Stearnscape
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\90
|
|  
|3\210
|  
|
|  
|17.143
| 13.333
|Stearnscape
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\84
|2\138
|  
|
|  
|
|  
|17.391
| 14.286
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\66
| 1\78
|
|  
|
|  
|
|  
|18.182
| 15.385
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\60
| 1\72
|
|  
|
|  
|
|  
|20
| 16.667
|
| [[Stearnscape]]
|-
|-
|
|  
|
|  
|
|  
|1\54
|  
|
|  
|
|  
|
| 4\282
|22.222
| 17.021
|
| Stearnscape
|-
|-
|
|  
|
|  
|
|  
|1\48
|  
|
|  
|
| 3\210
|
|  
|25
| 17.143
|
| Stearnscape
|-
|-
|
|  
|
|  
|
|  
|1\42
|  
|
| 2\138
|
|  
|
|  
|28.571
| 17.391
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\36
| 1\66
|
|  
|
|  
|
|  
|33.333
| 18.182
|
|  
|-
|-
|
|
|
|  
|1\30
|  
|
| 1\60
|
|  
|
|  
|
|  
|40
| 20
|
|  
|-
|-
|
|  
|1\24
|  
|
|  
|
| 1\54
|
|  
|
|  
|
|  
|50
| 22.222
|  
|  
|-
|-
|1\18
|
|
|
|
|
|
| 1\48
|
|
|
| 25
|
|-
|
|
|
| 1\42
|
|
|
| 28.571
|
|-
|
|
|
| 1\36
|
|
|
| 33.333
|
|-
|
|
| 1\30
|
|
|
|
| 40
|
|-
|
| 1\24
|
|
|
|
|
| 50
| [[Hemisemiaug]]
|-
|
|
|
|
|2\42
|
|
| 66.667
|
|
|-
|
|
|2\30
|
|
|
|57.143
|
|Hemisemiaug
|
|
| 80
|[[Hexe]]
|-
|-
| 1\18
|
|
|
|
|
|
|5\72
|
|
|
|
|
|
|83.333
| 66.667
|Hexe
| Hemisemiaug
|-
|-
|
|
|
| 2\30
|3\42
|
|
|
|
|
|
|
|
|
|85.714
| 80
| [[Hexe]]
|-
|  
|  
|  
| 5\72
|  
|  
|  
| 83.333
| Hexe
| Hexe
|-
|-
|
|
|
|
|
| 3\42
|4\54
|
|
|
|
|
|
|
|88.889
| 85.714
|Hexe
| Hexe
|-
|  
|  
|  
| 4\54
|  
|  
|  
| 88.889
| Hexe
|-
|-
|1\12
| 1\12
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 100
| 100
|Hexe
| Hexe
|}
|}
==Seven periods per octave==
 
{{todo|complete table|comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
== Seven periods per octave ==
{{todo| complete table| comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!! Cents!!Comments
! colspan="8" | Generator
! Cents
! Comments
|-
|-
| 0\7||  || ||
| 0\7
|
|  
|
|  
|
|  
| ||0||
|  
|-
|  
|
|  
|
|  
|
| 0
|
|  
|1\91
|
|
|
|13.187
|
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\84
| 1\91
|
|  
|
|  
|
|  
|14.286
| 13.187
|[[Absurdity]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\84
|
|  
|
|  
|4\329
|  
|14.59
| 14.286
|Absurdity
| [[Absurdity]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\245
|  
|
| 4\329
|14.69
| 14.59
|
| Absurdity
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\161
|  
|
| 3\245
|
|  
|14.907
| 14.69
|
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\77
|  
|
| 2\161
|
|  
|
|  
|15.584
| 14.907
|[[Septant]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\77
|
|  
|
|  
|4\301
|  
|15.947
| 15.584
|Septant
| [[Septant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\224
|  
|
| 4\301
|16.071
| 15.947
|Septant
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|2\147
|  
|
| 3\224
|
|  
|16.327
| 16.071
|Septant
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\70
|  
|
| 2\147
|
|  
|
|  
|17.143
| 16.327
|
| Septant
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\63
| 1\70
|
|  
|
|  
|
|  
|19.048
| 17.143
|[[Sevond]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\63
|2\119
|  
|
|  
|
|  
|20.168
| 19.048
|Sevond
| [[Sevond]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\56
|  
|
| 2\119
|
|  
|
|  
|21.429
| 20.168
|Sevond
| Sevond
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\49
| 1\56
|
|  
|
|  
|
|  
|24.49
| 21.429
|
| Sevond
|-
|-
|
|
|
|  
|
|  
|1\42
|  
|
| 1\49
|
|  
|
|  
|
|  
|28.571
| 24.49
|[[Mistismic temperaments#Neutron|Neutron]]
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\42
|
|  
|3\119
|  
|
|  
|
|  
|30.252
| 28.571
|Neutron
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\119
|5\196
|  
|
|  
|30.612
| 30.252
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 5\196
|7\273
|  
|30.769
| 30.612
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\77
|  
|
|  
|
|  
|
| 7\273
|31.169
| 30.769
|Neutron
| Neutron
|-
|-
|
|  
|
|  
|1\35
|  
|
|  
|
| 2\77
|
|  
|
|  
|
|  
|34.286
| 31.169
|[[Whitewood family#Redwood|Redwood]]
| Neutron
|-
|-
|
|
|
|
|
| 1\35
|
|
|
|
|
| 34.286
| [[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) 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\480
|
|  
|1\80
|  
|
|  
|
| 2.5
|15
|  
|
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\472
|
|  
|
|  
|2\152
|  
|
| 2.542
|15.789
| [[Octium]]
|[[Octoid]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\1872
|
|  
|3\224
| 2.564
|16.071
| Octium
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
| 7\3272
|
| 2.567
|16.667
| Octium
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\64
|  
|
| 3\1400
|
|  
|
|  
|
| 2.571
|18.75
| Octium
|
|-
|-
|
|
|
|  
|
|  
|1\56
|  
|
| 1\464
|
|  
|
|  
|
|  
|
| 2.586
|21.429
|  
|
|-
|-
|
|  
|
|  
|1\48
|  
|
|  
|
| …
|
|  
|
|  
|
|  
|
|  
|25
|  
|
|-
|-
|
|  
| 1\40
|  
|
|  
|
|  
|
| 1\96
|
|  
|
|  
|
|  
|
| 12.5
|30
|  
|
|-
|-
|
|  
|
|  
|2\72
|  
|
|  
|
| 1\88
|
|  
|
|  
|
|  
|
| 13.635
|33.333
|  
|
|-
|-
|1\32
|  
|
|  
|
|  
|
|  
|
| 1\80
|
|  
|
|  
|
|  
|
| 15
|37.5
|  
|[[Semidim]]
|-
|-
|
|  
|
|  
|3\88
|  
|
|  
|
|  
|
| 2\152
|
|  
|
|  
|
| 15.789
|40.909
| [[Octoid]]
|Semidim
|-
|-
|
|  
|2\56
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\224
|
|  
|
| 16.071
|42.857
| Octoid
|Semidim
|-
|-
|
|  
|
|  
|3\80
|  
|
|  
|
| 1\72
|
|  
|
|  
|
|  
|
| 16.667
|45
| Octoid
|Semidim
|-
|-
|
|  
|
|  
|
|  
|4\104
|  
|
| 1\64
|
|  
|
|  
|
|  
|
| 18.75
|46.154
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
| 1\56
|5\128
|  
|
|  
|
|  
|
|  
|
| 21.429
|46.875
|  
|Semidim
|-
|-
|
|  
|
|  
|
| 1\48
|
|  
|
|  
|6\152
|  
|
|  
|
|  
|
| 25
|47.368
|  
|Semidim
|-
|-
|
|  
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|7\176
|  
|
|  
|
| 30
|47.727
|  
|Semidim
|-
|-
|
|  
|
|  
|
| 2\72
|
|  
|
|  
|
|  
|8\200
|  
|
|  
|
| 33.333
|48
|  
|Semidim
|-
|-
|
| 1\32
|
|  
|
|  
|
|  
|
|  
|
|  
|9\224
|  
|
|  
|
| 37.5
|48.214
| [[Semidim]]
|Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
| 3\88
|
|  
|
|  
|
|  
|
|  
|
|  
|28\696
| 40.909
|48.276
| Semidim
|Semidim/Octant
|-
|-
|
|  
|
| 2\56
|
|  
|
|  
|
|  
|
|  
|
|  
|19\472
|  
|
| 42.857
|48.305
| Semidim
|Semidim/Octant
|-
|-
|
|  
|
|  
|
| 3\80
|
|  
|
|  
|
|  
|10\248
|  
|
|  
|
| 45
|48.387
| Semidim
|Semidim
|-
|-
|1\24
|  
|
|  
|
|  
|
| 4\104
|
|  
|
|  
|
|  
|
|  
|
| 46.154
|50
| Semidim
|Semidim
|-
|-
|2\40
|  
|
|  
|
|  
|
|  
|
| 5\128
|
|  
|
|  
|
|  
|
| 46.875
| 60
| Semidim
|
|-
|-
|1\16
|  
|
|  
|
|  
|
|  
|
| 6\152
|
|  
|
|  
|
|  
|
| 47.368
|75
| Semidim
|
|}
 
==Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!! Comments
|-
|-
|0\9||  || ||
|  
|  
|
|  
|
|  
| ||0||
|  
|  
| 7\176
|  
|  
| 47.727
| Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\72
|  
|
| 8\200
|
|  
|
|  
|16.667
| 48
|[[Enneaportent]]
| Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 9\224
|
|  
|4\279
|  
|17.204
| 48.214
|Enneaportent
| Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|3\207
|  
|
| 28\696
|17.391
| 48.276
|Enneaportent
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|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
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|22.222
| 50
|
| Semidim
|-
|-
|
| 2\40
|1\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|26.667
| 60
|
|  
|-
|-
|1\36
| 1\16
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|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
|  
|
|  
|
|  
|
|  
|
|  
|35.556
| 0
|No-five tritrizo
|  
|-
|-
|
|  
|
|  
|3\99
|  
|
|  
|
| 1\72
|
|  
|
|  
|
|  
|36.364
| 16.667
|No-five tritrizo
| [[Enneaportent]]
|-
|-
|
|  
|2\63
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\279
|38.095
| 17.204
|[[Niner]]
| Enneaportent
|-
|-
|
|
|3\90
|  
|  
|
|  
|
|  
|
|  
|
|  
|40
|  
|Niner
| 3\207
|
| 17.391
| Enneaportent
|-
|-
|1\27
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\135
|
|  
|
|  
| 44.444
| 17.778
|Niner
| Enneaportent
|-
|-
|
|  
|
|  
|4\99
|  
|
| 1\63
|
|  
|
|  
|
|  
|
|  
|48.485
| 19.048
|[[Ennealimmal]]
| Enneaportent
|-
|-
|
|  
|
|  
|
| 1\54
|7\171
|  
|
|  
|
|  
|
|  
|
|  
|49.123
| 22.222
|Ennealimmal
|  
|-
|-
|
|3\72
|  
|  
|
| 1\45
|
|  
|
|  
|
|  
|
|  
| 50
|  
|Ennealimmal
|  
| 26.667
|
|-
|-
|
| 1\36
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|20\477
|  
|50.314
| 33.333
|[[Novemkleismic]]
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|-
|
|  
|
|  
|
|  
|
| 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
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|51.282
| 44.444
|
| Niner
|-
|-
|2\45
|
|
|
|
|
|
|
|53.333
|  
|  
|
| 4\99
|
|
|
|
|
| 48.485
| [[Ennealimmal]]
|-
|-
|1\18
|  
|
|  
|
|  
|
| 7\171
|
|  
|
|  
|
|  
|
|  
| 66.667
| 49.123
|
| Ennealimmal
|}
 
==Twelve periods per octave==
See also: [[Compton family]]
 
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!!Comments
|-
|-
|0\12||  || ||
|
|  
|  
|
| 3\72
|||0||
|  
|
|
|  
|  
|  
| 50
| Ennealimmal
|-
|-
|
|  
|
|  
|
|  
|1\636
|  
|
|  
|
|  
|
|  
|
| 20\477
|1.887
| 50.314
|
| [[Novemkleismic]]
|-
|-
|
|  
|
|  
|
|  
|1\624
|  
|
|  
|
|  
|
| 17\405
|
|  
|1.923
| 50.370
|
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\1236
|  
|
| 14\333
|
|  
|
|  
|1.942
| 50.451
|[[Atomic]]
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 11\261
|3\1848
|  
|
|  
|
|  
|1.948
| 50.575
|Atomic
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
| 8\189
|
|  
|
|  
|4\2460
|  
|
|  
|1.951
| 50.794
|Atomic
| Novemkleismic
|-
|-
|
|  
|
|  
|
| 5\117
|
|  
|
|  
|
|  
|
|  
|5\3072
|  
|1.953
| 51.282
|Atomic
|  
|-
|
|
|
|1\612
|
|
|
|
|1.961
|Atomic
|-
|-
| 2\45
|
|
|
|
|
|
|
| 53.333
|
|-
| 1\18
|
|
|
|
|
|
|
| 66.667
|
|}
== Ten periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
| 0\10
|
|
|
|
|
|
| 0
|
|-
|1\140
|
|
|
|
|
|
|1\600
|
|
|
|
|
|
|
|8.571
|2
|[[Decoid]]
|
|-
|-
|
|
|2\270
|
|
|
|1\588
|
|
|
|
|
|
|
|
|2.041
|8.888
|
|Decoid
|-
|-
|1\130
|
|
|
|
|
|
|1\576
|
|
|
|
|
|
|
|9.231
|2.083
|Decoid
|
|-
|-
|1\120
|
|
|
|
|
|
|...
|
|
|
|
|
|
|
|10
|...
|
|
|-
|-
|
| 1\110
|
|  
|
|  
|1\108
|  
|
|  
|
|  
|
|  
|
| 10.909
|11.111
|  
|
|-
|-
|
| 1\100
|
|  
|
|  
|1\96
|  
|
|  
|
|  
|
|  
|
| 12
|12.5
|  
|[[Compton]]
|-
|-
|
|  
|
| 2\190
|
|  
|1\84
|  
|
|  
|
|  
|
|  
|
| 12.632
|14.286
| [[Deca]]
|Compton
|-
|-
|
| 1\90
|
|  
|
|  
|
|  
|
|  
|3\240
|  
|
|  
|
| 13.333
|15
| Deca
|Compton
|-
|-
|
| 1\80
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\636
| 15
|15.094
| Deca
|Compton
|-
|-
|
| 1\70
|
|  
|
|  
|
|  
|
|  
|
|  
|5\396
|  
|
| 17.143
|15.152
|  
|Compton
|-
|-
|
| 1\60
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\552
| 20
|15.217
|  
|Compton
|-
|-
|
| 1\50
|
|  
|
|  
|
|  
|2\156
|  
|
|  
|
|  
|
| 24
|15.385
| [[Decimetra]]
|Compton
|-
|-
|
|  
|
|  
|
|  
|
| 4\190
|
|  
|
|  
|
|  
|7\540
| 25.263
|15.556
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 7\330
|
|  
|5\384
|  
|
| 25.455
|15.625
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 17\800
|8\612
| 25.5
|15.686
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|3\228
| 10\470
|
|  
|
| 25.532
|15.789
| Decimetra
|Compton
|-
|-
|
|  
|
|  
|
| 3\140
|
|  
|
|  
|
|  
|
|  
|7\528
| 25.714
|15.909
| Decimetra
|Compton
|-
|-
|
|  
|
| 2\90
|
|  
|
|  
|
|  
|
|  
|4\300
|  
|
| 26.667
|16
| Decimetra
|Compton
|-
|-
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\372
| 30
|16.129
| [[Decic]]
|Compton
|-
|-
|
|  
|
|  
|
| 3\110
|1\72
|  
|
|  
|
|  
|
|  
|
| 32.727
|16.667
| Decic
|Compton
|-
|-
|
|  
|
| 2\70
|1\60
|  
|
|  
|
|  
|
|  
|
|  
|
| 34.286
|20
| Decic
|Compton
|-
|-
|
|  
|
|  
|
|  
|2\108
| 4\170
|
|  
|
|  
|
|  
|
| 28.235
|22.222
| Decic
|
|-
|-
|
|  
|1\48
|  
|
| 3\100
|
|  
|
|  
|
|  
|
|  
|
| 36
|25
| Decic
|[[Catler]]
|-
|-
|
| 1\30
|
|  
|
|  
|3\132
|  
|
|  
|
|  
|
|  
|
| 40
| 27.273
| Decic/[[Decal]]
|Catler
|-
|-
|
|  
|
| 3\80
| 2\84
|  
|
|  
|
|  
|
|  
|
|  
|
| 45
|28.571
| Decal/[[Decistearn]]
|Catler
|-
|-
|
|  
|
|  
|
|  
|3\120
| 8\210
|
|  
|
|  
|
|  
|
| 45.714
|30
| Decal/Decistearn
|Catler
|-
|-
|1\36
|  
|
|  
|
|  
|
|  
|
| 13\340
|
|  
|
|  
|
| 45.882
|33.333
| Decal/Decistearn
|Catler/[[Catnip]]
|-
|-
|
|  
|
|  
|
|  
|4\132
|  
|
|  
|
| 18\470
|
|  
|
| 45.957
|36.364
| Decal/Decistearn
|Catnip
|-
|-
|
|  
|
|  
|3\96
|  
|
|  
|
|  
|
|  
|
| 23\600
|
| 46
|37.5
| Decal/Decistearn
| Catnip
|-
|-
|
|  
|
|  
|
| 5\130
|5\156
|  
|
|  
|
|  
|
|  
|
| 46.154
|38.462
| Decal/Decistearn
|Catnip
|-
|-
|
| 2\50
|2\60
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 48
|40
| Decistearn/[[Decavish]]
|Catnip
|-
|-
|
|  
|
|  
|
|  
|5\144
|  
|
|  
|
| 11\270
|
|  
|
| 48.889
|41.667
| Decavish
|
|-
|-
|
|  
|
|  
|3\84
|  
|
|  
|
| 9\220
|
|  
|
|  
|
| 49.091
| 42.857
| Decavish
| [[Magnesium]]
|-
|-
|
|  
|
|  
|
|  
|
| 7\170
|
|  
|
|  
|
|  
|16\444
| 49.412
|43.243
| Decavish
|Magnesium
|-
|-
|
|
| 5\120
|
|
|
|
| 50
| Decavish
|-
|
| 3\70
|
|
|
|
|
| 51.429
| Decavish
|-
|
|
| 4\90
|
|
|
|
| 53.333
|
|-
|
|
|
| 5\110
|
|
|
| 54.545
|
|-
|
|
|
|
| 6\130
|
|
| 55.385
|
|
|
|-
|
| 1\20
|
|
|
|
|
|
|13\360
|
|
|
|43.333
|
|Magnesium
| 60
|-
|
|
|}
|
 
|
== Eleven periods per octave==
|
{| class="wikitable sortable mw-collapsible"
|
! colspan="7" | Generator
|10\276
! Cents
|
! Comments
|
|-
|43.378
| 0\11
|
|
|-
|
|
|
|
|
|
|
|
|
|7\192
| 0
|
|
|
|-
|
|
|43.75
| 1\55
|
|
|-
|
|
|
|
|
|
|
|4\108
| 21.818
|
|
|
|-
|
| 1\44
|
|
|44.444
|
|
|
|-
|
|1\24
|
|
|
|
| 27.273
|
|
|
|-
|
|
|
| 2\77
|
|
| 50
|
|
|
|
|
| 31.169
|
|-
| 1\33
|
|
|
|
|
|
| 36.364
|
|-
|
| 3\88
|
|
|
|
|
| 40.909
|
|-
| 2\55
|
|
|
|
|
|
| 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"