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
 
(33 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"
|-
|-
! colspan="10" | Generator
! colspan="10" | Generator
! | Cents
! Cents
! | Comments
! Comments
|-
|-
| | 0\3
| 0\3
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 0.000
| 0.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\30
| 1\30
|
|  
|
|  
|
|  
| | 40.000
| 40.000
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\27
| 1\27
| |  
|  
|
|  
|
|  
|
|  
| | 44.444
| 44.444
| | [[Semiaug|Semiaug]]
| [[Hemiaug]]
|-
| |
| |
| |
| |
| |
| |
| | 2\51
|
|
|
| | 47.059
| | Semiaug
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 1\24
|  
| |  
|  
| |
| 2\51
|
|  
|
|  
|
|  
| | 50.000
| 47.059
| | Semiaug/[[Augmented family#Hemiug|Hemiug]]
| Hemiaug
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\24
|2\45
|  
|
|  
|
|  
|
|  
|
|  
|53.333
| 50.000
|Hemiug
| Hemiaug/[[Hemiug]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 1\21
|  
| |  
|  
| |
| 2\45
| |  
|  
|
|  
|
|  
|
|  
| | 57.143
| 53.333
| | Hemiug
| Hemiug
|-
|-
| |  
|  
| |  
|  
| | 1\18
|  
| |  
| 1\21
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 66.667
| 57.143
| |
| Hemiug
|-
|-
| |  
|  
| | 1\15
|  
| |  
| 1\18
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 80.000
| 66.667
| |  
|  
|-
|-
| |  
|  
| |
| 1\15
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 6\87
|  
|
|  
|
|  
|
|  
| | 82.759
| 80.000
| |  
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 6\87
|11\159
|  
|
|  
|
|  
|83.019
| 82.759
|[[Tritikleismic]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 11\159
|16\231
|  
|
|  
|83.117
| 83.019
|Tritikleismic
| [[Tritikleismic]]
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\72
|  
| |  
|  
|
|  
|
| 16\231
|
|  
| | 83.333
| 83.117
| | Tritikleismic
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 4\57
|  
| |  
| 5\72
| |  
|  
|
|  
|
|  
|
|  
| | 84.211
| 83.333
| | Tritikleismic
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 3\42
|  
| |  
| 4\57
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 85.714
| 84.211
| |
| Tritikleismic
|-
|-
| |  
|  
| |  
|  
| | 2\27
|  
| |  
| 3\42
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 88.889
| 85.714
| |[[Augmented]]/[[Augene]]
|  
|-
|-
|
|  
|
|  
|
| 2\27
|3\39
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 88.889
|Augmented/Augene/[[Fog]]
| | [[Augmented (temperament)|Augmented]]/[[Augene]]
|-
|-
|
|  
|
|  
|
|  
|
| 3\39
|4\51
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|94.118
| 92.308
|Augmented/Augene/Fog
| Augmented/Augene/[[Fog]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 4\51
|5\63
|  
|
|  
|
|  
|
|  
|
|  
|95.238
| 94.118
|Augmented/Augene/Fog
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 5\63
|
|  
|11\138
|  
|
|  
|
|  
|95.652
| 95.238
|Augmented Augene/Fog
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|6\75
|  
|
| 11\138
|
|  
|
|  
|96
| 95.652
|Augmented/Augene/Fog
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 6\75
|7\87
|  
|
|  
|
|  
|96.552
| 96
|Augmented/Augene/[[Misty]]
| Augmented/Augene/Fog
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\87
|
|  
|15\186
|  
|96.774
| 96.552
|Augmented/Augene/Misty
| Augmented/Augene/[[Misty]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\99
|  
|
| 15\186
|96.97
| 96.774
|Augmented/Augene/Misty
| Augmented/Augene/Misty
|-
|-
| | 1\12
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
| 8\99
|
|  
| | 100.000
| 96.97
| | Augmented/Augene/[[August]]
| Augmented/Augene/Misty
|-
|-
| |
| 1\12
| |  
|  
| | 3\33
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 109.091
| 100.000
| | August
| Augmented/Augene/[[August]]
|-
|-
| |  
|  
| | 2\21
|  
| |  
| 3\33
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 114.286
| 109.091
| | August
| August
|-
|-
| |  
|  
| |
| 2\21
| | 3\30
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 120.000
| 114.286
| |
| August
|-
|-
| | 1\9
|  
| |  
|  
| |
| 3\30
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|
|  
|
|  
|
|  
| | 133.333
| 120.000
| |  
|  
|-
|-
| |
| 1\9
| |
|  
| | 4\33
|  
| |
|  
| |
|  
| |
|  
| |
|  
|
|  
|
|  
|
|  
| | 145.455
| 133.333
| |  
|  
|-
| |  
| | 3\24
| |  
| |  
| |  
| |  
| |
|
|
|
| | 150.000
| |[[Triforce]]
|-
|-
|
|  
|
|  
|5\39
| 4\33
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|153.846
| 145.455
|Triforce
|  
|-
|-
| | 2\15
|  
| |  
| 3\24
| |  
|  
| |  
|  
| |  
|  
| |
|  
| |  
|  
|
|  
|
|  
|
|  
| | 160.000
| 150.000
| | Triforce
| [[Triforce]]/[[Augment]]
|-
| |
| | 3\21
| |
| |
| |
| |
| |
|
|
|
| | 171.429
| |[[Oodako]]
|-
|-
|
|  
|
|  
|
| 5\39
|7\48
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|175
| 153.846
|Oodako
| Triforce/Augment
|-
|-
|
| 2\15
|
|  
|
|  
|
|  
|11\75
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|176
| 160.000
|Oodako
| Triforce/Augment
|-
|-
|
|  
|
| 3\21
|
|  
|
|  
|
|  
|15\102
|  
|
|  
|
|  
|
|  
|
|  
|176.471
| 171.429
|Oodako
| [[Oodako]]/Augment
|-
|-
|
|  
|
|  
|
|  
|
| 7\48
|
|  
|
|  
|19\129
|  
|
|  
|
|  
|
|  
|176.744
| 175
|Oodako
| Oodako/Augment
|-
|-
|
|  
|
|  
|4\27
|  
|
|  
|
| 11\75
|
|  
|
|  
|
|  
|
|  
|
|  
|177.778
| 176
|Oodako
| Oodako
|-
|-
| | 1\6
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |
| 15\102
| |  
|  
|
|  
|
|  
|
|  
| | 200.000
| 176.471
| |
| Oodako
|}
 
==Four periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator !! Cents !! Comments
|-
|-
| 0\4 ||  ||  ||  ||  ||  || 0 ||  
|  
|-
|  
| ||  ||  || 1\76 ||  ||  || 15.789 ||
|  
|-
|  
|  ||  ||  || 1\72 ||  ||  || 16.667 || [[Quadritikleismic]]
|  
|-
|  
|
| 19\129
|
|  
|
|  
|
|  
|
| 176.744
|3\212
| Oodako
|16.981
|Quadritikleismic
|-
|-
| || || || || 2\140 || || 17.143 || Quadritikleismic
|  
|  
| 4\27
|  
|  
|  
|  
|  
|  
|  
| 177.778
| Oodako
|-
|-
| || || || 1\68 || || || 17.647 || Quadritikleismic
| 1\6
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 200.000
|  
|}
 
== Four periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="6" | Generator
! Cents
! Comments
|-
|-
| ||  ||  || 1\64 || ||  || 18.75 ||  
| 0\4
|-
|  
|  ||  ||  || 1\60 ||  ||  || 20 ||  
|  
|-
|  
|  ||  ||  || ... ||  ||  || ... ||  
|  
|  
| 0
|  
|-
|-
| || ||  || 1\36 || ||  || 33.333 ||  
|  
|  
|  
| 1\76
|  
|  
| 15.789
|  
|-
|-
| || ||  || 1\32 || ||  || 37.5 ||  
|  
|  
|  
| 1\72
|  
|  
| 16.667
| [[Quadritikleismic]]
|-
|-
| || || || 1\28 ||  ||  || 42.857 ||  
|  
|  
|  
|  
|  
| 3\212
| 16.981
| Quadritikleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\52
| 2\140
|
|  
|46.154
| 17.143
|[[Hemidim]]
| Quadritikleismic
|-
|-
|
|  
|
|  
|
|  
|
| 1\68
|
|  
|3\76
|  
|47.368
| 17.647
|Hemidim
| Quadritikleismic
|-
|-
| || || 1\24 ||  ||  ||  || 50 || Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|  
|  
|  
| 1\64
|  
|  
| 18.75
|  
|-
|-
| || 1\20 || ||  ||  ||  || 60 ||  
|  
|  
|
| 1\60
|  
|  
| 20
|  
|-
|-
| 1\16 || || || ||  ||  || 75 ||  
|  
|  
|  
| ...
|  
|  
| ...
|  
|-
|-
|
|  
|2\28
|  
|
|  
|
| 1\36
|
|  
|
|  
|85.714
| 33.333
|[[Demolished]]
|  
|-
|-
|
|  
|
|  
|3\40
|  
|
| 1\32
|
|  
|
|  
|90
| 37.5
|Demolished
|  
|-
|-
| 1\12 || || ||  ||  ||  || 100 || Demolished/[[Diminished]]
|  
|  
|  
| 1\28
|  
|  
| 42.857
|  
|-
|-
|
|  
|
|  
|
|  
|14\164
|  
|
| 2\52
|
|  
|102.439
| 46.154
|Diminished
| [[Hemidim]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|27\316
|  
|
| 3\76
|102.532
| 47.368
|Diminished/[[Unlit]]
| Hemidim
|-
|-
|
|  
|
|  
|
| 1\24
|
|  
|
|  
|40\468
|  
|102.564
| 50
|Diminished/Unlit
| Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|-
|-
|
|  
|
| 1\20
|
|  
|13\152
|  
|
|  
|
|  
|102.632
| 60
|Diminished/Unlit/[[Undim]]
|  
|-
|-
|
| 1\16
|
|  
|
|  
|
|  
|
|  
|38\444
|  
|102.703
| 75
|Diminished/Undim
|  
|-
|-
|
|  
|
| 2\28
|
|  
|
|  
|25\292
|  
|
|  
|102.740
| 85.714
|Diminished/Undim
| [[Demolished]]
|-
|-
|
|  
|
|  
|
| 3\40
|12\140
|  
|
|  
|
|  
|102.857
| 90
|Diminished/Undim
| Demolished
|-
|-
|
| 1\12
|
|  
|
|  
|11\128
|  
|
|  
|
|  
|103.125
| 100
|Diminished
| Demolished/[[Diminished (temperament)|Diminished]]
|-
|-
|
|  
|
|  
|
|  
|10\116
| 14\164
|
|  
|
|  
|103.448
| 102.439
|Diminished
| Diminished
|-
|-
|
|  
|
|  
|
|  
|9\104
|  
|
| 27\316
|
|  
|103.846
| 102.532
|Diminished
| Diminished/[[Unlit]]
|-
|-
|
|  
|
|  
|
|  
|8\92
|  
|
|  
|
| 40\468
|104.348
| 102.564
|Diminished
| Diminished/Unlit
|-
|-
| || ||  || 7\80 ||  ||  || 105 || Diminished/[[Bidia]]
|  
|  
|  
| 13\152
|  
|  
| 102.632
| Diminished/Unlit/[[Undim]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|20\228
| 38\444
|105.263
| 102.703
|Diminished/Bidia
| Diminished/Undim
|-
|-
|
|
|
|
|13\148
|
|105.405
|Diminished/Bidia
|-
|  ||  ||  || 6\68 ||  ||  || 105.882 || Diminished/Bidia
|-
|  ||  ||  || 5\56 ||  ||  || 107.143 || Diminished/Bidia
|-
|  ||  || 4\44 ||  ||  ||  || 109.091 || Diminished
|-
|  || 3\32 ||  ||  ||  ||  || 112.5 || Diminished
|-
| 2\20 ||  ||  ||  ||  ||  || 120 || Diminished
|-
|
|3\28
|
|
|
|
|128.571
|
|-
| 1\8 ||  ||  ||  ||  ||  || 150 ||
|}
==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 ||  || ||
|
|  
|  
|  
|  
|  
|  
| || 0||
|  
| 25\292
|  
| 102.740
| Diminished/Undim
|-
|-
|
|  
|
|  
|
|  
|
| 12\140
|
|  
|1\140
|  
|
| 102.857
|
| Diminished/Undim
|
|8.571
|
|-
|-
|
|  
|
|  
|
|  
|
| 11\128
|
|  
|1\135
|  
|
| 103.125
|
| Diminished
|
|8.889
|[[5th-octave temperaments#Slendrismic|Slendrismic]]
|-
|-
|
|  
|
|  
|
|  
|
| 10\116
|
|  
|
|  
|
| 103.448
|3\400
| Diminished
|
|9
|Slendrismic
|-
|-
|
|  
|
|  
|
|  
|
| 9\104
|
|  
|
|  
|
| 103.846
|
| Diminished
|5\665
|9.023
|Slendrismic
|-
|-
|
|  
|
|  
|
|  
|
| 8\92
|
|  
|
|  
|2\265
| 104.348
|
| Diminished
|
|9.057
|Slendrismic
|-
|-
|
|  
|
|  
|
|  
|
| 7\80
|
|  
|1\130
|  
|
| 105
|
| Diminished/[[Bidia]]
|
|9.231
|Slendrismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 20\228
|
| 105.263
|
| Diminished/Bidia
|4\515
|9.32
|Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 13\148
|
|  
|
| 105.405
|3\385
| Diminished/Bidia
|
|9.351
|Hemipental
|-
|-
|
|  
|
|  
|
|  
|
| 6\68
|
|  
|
|  
|
| 105.882
|
| Diminished/Bidia
|5\640
|9.375
|Hemipental
|-
|-
|
|  
|
|  
|
|  
|
| 5\56
|
|  
|
|  
|2\255
| 107.143
|
| Diminished/Bidia
|
|9.412
|Hemipental
|-
|-
|
|  
|
|  
|
| 4\44
|
|  
|
|  
|1\125
|  
|
| 109.091
|
| Diminished
|
|9.6
|Hemipental
|-
|-
|
|  
|
| 3\32
|
|  
|
|  
|
|  
|1\120
|  
|
| 112.5
|
| Diminished
|
|10
|
|-
|-
|
| 2\20
|
|  
|
|  
|
|  
|
|  
|1\115
|  
|
| 120
|
| Diminished
|
|10.435
|
|-
|-
|
|  
|
| 3\28
|
|  
|
|  
|
|  
|...
|  
|
| 128.571
|
|  
|
|...
|
|-
|-
|
| 1\8
|
|  
|
|  
|
|  
|
|  
|1\70
|  
|
| 150
|
|  
|
|}
|17.143
 
|
== 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
|
|  
|
|  
|
|  
|
|  
|1\65
|  
|
|  
|
|  
|
|  
|18.462
| 0
|[[Pental (temperament)|Pental]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\140
|
|  
|
|  
|4\255
|  
|18.824
| 8.571
|Pental
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\135
|
|  
|3\190
|  
|
|  
|18.947
| 8.889
|Pental
| [[5th-octave temperaments#Slendroschismic| Slendroschismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\400
|5\315
|  
|19.048
| 9
|Pental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|2\125
|  
|
|  
|
| 5\665
|19.2
| 9.023
|Pental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\265
|3\185
|  
|
|  
|19.459
| 9.057
|Pental
| Slendroschismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\60
| 1\130
|
|  
|
|  
|
|  
|20
| 9.231
|Pental
| Slendroschismic/[[Hemipental]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\55
|  
|
|  
|
|  
|
| 4\515
|21.818
| 9.32
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\50
|  
|
|  
|
| 3\385
|
|  
|24
| 9.351
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|1\45
|  
|
|  
|
|  
|
| 5\640
|26.67
| 9.375
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\40
|  
|
|  
|
| 2\255
|
|  
|
|  
|30
| 9.412
|
| Hemipental
|-
|-
|
|  
|
|  
|
|  
|1\35
|  
|
|  
|
| 1\125
|
|  
|
|  
|
|  
|34.286
| 9.6
|
| Hemipental
|-
|-
|
|  
|
|  
|1\30
|  
|
|  
|
|  
|
| 1\120
|
|  
|
|  
|
|  
|40
| 10
|
|  
|-
|-
|
|  
|1\25
|  
|
|  
|
|  
|
|  
|
| 1\115
|
|  
|
|  
|
|  
|48
| 10.435
|
|  
|-
|-
|1\20
|  
|
|  
|
|  
|
|  
|
|  
|
| 1\70
|
|  
|
|  
|
|  
|60
| 17.143
|
|  
|-
|-
|
|  
|2\35
|  
|
|  
|
|  
|
|  
|
| 1\65
|
|  
|
|  
|
|  
|68.571
| 18.462
|[[Coblack]]
| [[Pental (temperament)| Pental]]
|-
|-
|
|  
|
|  
|
|  
|5\85
|  
|
|  
|
|  
|
|  
|
|  
|
| 4\255
|70.588
| 18.824
|Coblack
| Pental
|-
|-
|
|  
|
|  
|3\50
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\190
|
|  
|72
| 18.947
|Coblack
| Pental
|-
|-
|
|  
|
|  
|
|  
|
|  
|7\115
|  
|
|  
|
|  
|
|  
|
| 5\315
|73.043
| 19.048
|Coblack
| Pental
|-
|-
|
|  
|
|  
|
|  
|4\65
|  
|
|  
|
|  
|
| 2\125
|
|  
|
|  
|73.846
| 19.2
|Coblack
| Pental
|-
|-
| 1\15 ||  ||  ||
|
|  
|  
|  
|  
|  
|  
| || 80||[[Blackwood]]/[[Blacksmith]]
|  
|  
|  
|  
| 3\185
|
| 19.459
| Pental
|-
|-
|
|  
|
|  
|
|  
|5\70
|  
|
|  
|
| 1\60
|
|  
|
|  
|
|  
|85.714
| 20
|Blackwood/Blacksmith
| Pental
|-
|-
|
|  
|
|  
|4\55
|  
|
|  
|
|  
|
| 1\55
|
|  
|
|  
|
|  
|87.273
| 21.818
|Blackwood/Blacksmith
|  
|-
|-
|
|  
|
|  
|
|  
|7\95
|  
|
|  
|
| 1\50
|
|  
|
|  
|
|  
|88.421
| 24
|Blackwood/Blacksmith
| [[Cloudtone]]
|-
|-
|
|  
|3\40
|  
|
|  
|
|  
|
|  
|
| 1\45
|
|  
|
|  
|
|  
|90
| 26.67
|Blackwood/Blacksmith
| Cloudtone
|-
|-
|
|  
|
|  
|
|  
|8\105
|  
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|91.429
| 30
|Blackwood/Blacksmith
| Cloudtone
|-
|-
|
|  
|
|  
|5\65
|  
|
| 1\35
|
|  
|
|  
|
|  
|
|  
|
|  
|92.308
| 34.286
|Blackwood/Blacksmith
|  
|-
|-
|
|  
|
|  
|
| 1\30
|7\90
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|93.333
| 40
|Blackwood/Blacksmith
|  
|-
|-
|2\25
|  
|
| 1\25
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|96
| 48
|Blackwood/Blacksmith
|  
|-
|-
|
| 1\20
|
|  
|5\60
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|100
| 60
|Blackwood
|  
|-
|-
|
|  
|
| 2\35
|
|  
|8\95
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|101.053
| 68.571
|Blackwood
| [[Coblack]]
|-
|-
|
|  
|3\35
|  
|
|  
|
| 5\85
|
|  
|
|  
|
|  
|
|  
|
|  
|102.857
| 70.588
|Blackwood
| Coblack
|-
|-
|
|  
|
|  
|
| 3\50
|7\80
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|105
| 72
|Blackwood
| Coblack
|-
|-
|
|  
|
|  
|4\45
|  
|
|  
|
| 7\115
|
|  
|
|  
|
|  
|
|  
|106.667
| 73.043
|Blackwood
| Coblack
|-
|-
|
|  
|
|  
|
|  
|5\55
| 4\65
|
|  
|
|  
|
|  
|
|  
|
|  
|109.091
| 73.846
|Blackwood
| Coblack
|-
|-
|
| 1\15
|
|  
|
|  
|
|  
|6\65
|  
|
|  
|
|  
|
|  
|
|  
|110.769
| 80
|Blackwood/[[Quintosec]]/[[Sengasec]]
| [[Blackwood]]
|-
|-
|
|  
|
|  
|
|  
|
| 5\70
|
|  
|
|  
|
|  
|
|  
|25\270
|  
|111.111
| 85.714
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
| Blackwood
|-
|-
|
|  
|
|  
|
| 4\55
|
|  
|
|  
|
|  
|
|  
|19\205
|  
|
|  
|111.220
| 87.273
|Blackwood/Quintosec/SengasecQintosec
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 7\95
|
|  
|
|  
|13\140
|  
|
|  
|
|  
|111.429
| 88.421
|Blackwood/Quintosec/Sengasec/Qintosec
| Blackwood
|-
|-
|
|  
|
| 3\40
|
|  
|
|  
|
|  
|
|  
|
|  
|20\215
|  
|
|  
|111.628
| 90
|Blackwood/Qintosec
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 8\105
|
|  
|7\75
|  
|
|  
|
|  
|
|  
|112
| 91.429
|Blackwood/[[Qinto]]
| Blackwood
|-
|-
|
|  
|
|  
|
| 5\65
|
|  
|
|  
|
|  
|
|  
|15\160
|  
|
|  
|112.5
| 92.308
|Blackwood/Qinto
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
| 7\90
|
|  
|
|  
|8\85
|  
|
|  
|
|  
|112.941
| 93.333
|Blackwood/[[Phi as a Generator|Elderthing]]
| Blackwood
|-
|-
|
| 2\25
|
|  
|
|  
|
|  
|
|  
|
|  
|9\95
|  
|
|  
|
|  
|113.684
| 96
|Blackwood
| Blackwood
|-
|-
|
|  
|
|  
|
| 5\60
|
|  
|
|  
|
|  
|10\105
|  
|
|  
|
|  
|114.286
| 100
|Blackwood
| Blackwood
|-
|-
|1\10
|  
|
|  
|
|  
|
| 8\95
|
|  
|
|  
|
|  
|
|  
|
|  
|120
| 101.053
|Blackwood
| Blackwood
|}
 
==Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" |Generator!!Cents !!Comments
|-
|-
|0\6|| || ||  
|  
|
| 3\35
|
|  
|||0||
|  
|  
|  
|  
|  
|  
| 102.857
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|1\288
| 7\80
|
|  
|
|  
|
|  
|4.167
|  
|
|  
| 105
| Blackwood
|-
|-
|
|  
|
|
|
| 4\45
|1\282
|  
|
|  
|
|  
|
|  
|4.255
|  
|
|  
| 106.667
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|1\276
| 5\55
|2\552
|
|
|
|
|  
|4.348
|  
|[[Sextile]]
|  
| 109.091
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
|
|
| 6\65
|3\822
|  
|
|  
|4.380
|  
|Sextile
|  
| 110.769
| Blackwood/[[Quintosec]]/[[Sengasec]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\1092
|  
|4.396
|
|Sextile
| 25\270
| 111.111
| Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
|
|  
|
|  
|
|  
|1\270
|  
|
|  
|
|  
|
|  
|4.444
| 19\205
|Sextile
|
| 111.220
| Blackwood/Quintosec/SengasecQintosec
|-
|-
|
|  
|
|  
|
|  
|1\264
|  
|
|  
|
|
|
| 13\140
|4.545
|  
|
|  
| 111.429
| Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
|
|  
|
|  
|
|  
|...
|  
|
|  
|
|  
|
|  
|...
| 20\215
|
|
| 111.628
| Blackwood/Qintosec
|-
|-
|
|  
|
|  
|
|  
|1\90
|  
|
|
|
| 7\75
|
|  
|13.333
|  
|
|  
| 112
| Blackwood/[[Qinto]]
|-
|-
|
|  
|
|  
|
|  
|1\84
|  
|
|  
|
|  
|
|  
|14.286
| 15\160
|
|
| 112.5
| Blackwood/Qinto
|-
|-
|
|  
|
|  
|
|  
|1\78
|  
|
|  
|
|
|
| 8\85
|15.385
|  
|
|  
| 112.941
| Blackwood/[[Phi as a Generator|Elderthing]]
|-
|-
|
|  
|
|  
|
|  
|1\72
|  
|
|  
|
|
|
| 9\95
|16.667
|  
|[[Stearnscape]]
|  
| 113.684
| Blackwood
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|4\282
| 10\105
|17.021
|  
|Stearnscape
|
| 114.286
| Blackwood
|-
|-
|
| 1\10
|
|
|
|
|
|
|
|
|3\210
|  
|
|  
|17.143
|  
|Stearnscape
|  
| 120
| Blackwood
|}
 
== Six periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\6
|
|  
|
|  
|
|  
|2\138
|  
|
|  
|
|  
|17.391
| 0
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\66
| 1\288
|
|  
|
|  
|
|  
|18.182
| 4.167
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\60
| 1\282
|
|  
|
|  
|
|  
|20
| 4.255
|
|  
|-
|-
|
|  
|
|  
|
|  
|1\54
| 1\276
|
| 2\552
|
|  
|
|  
|22.222
| 4.348
|
| [[Sextile]]
|-
|-
|
|  
|
|  
|
|  
|1\48
|  
|
|  
|
| 3\822
|
|  
|25
| 4.380
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\42
|  
|
|  
|
|  
|
| 4\1092
|28.571
| 4.396
|
| Sextile
|-
|-
|
|  
|
|  
|
|  
|1\36
| 1\270
|
|  
|
|  
|
|  
|33.333
| 4.444
|
| Sextile
|-
|-
|
|
|
|  
|1\30
|  
|
| 1\264
|
|  
|
|  
|
|  
|40
| 4.545
|
|  
|-
|-
|
|  
|1\24
|  
|
|  
|
| ...
|
|  
|
|  
|
|  
|50
| ...
|  
|  
|-
|-
|1\18
|  
|
|  
|
|  
|
| 1\90
|
|  
|
|  
|
|  
| 66.667
| 13.333
|
|  
|-
|-
|
|  
|2\30
|  
|
|  
|
| 1\84
|
|  
|
|  
|
|  
| 80
| 14.286
|[[Hexe]]
|  
|-
|-
|
|  
|
|  
|
|  
|5\72
| 1\78
|
|  
|
|  
|
|  
|83.333
| 15.385
|Hexe
|  
|-
|-
|
|  
|
|  
|3\42
|  
|
| 1\72
|
|  
|
|  
|
|  
|85.714
| 16.667
| Hexe
| [[Stearnscape]]
|-
|-
|
|  
|
|  
|
|  
|4\54
|  
|
|  
|
|  
|
| 4\282
|88.889
| 17.021
|Hexe
| Stearnscape
|-
|-
|1\12
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\210
|
|  
| 100
| 17.143
|Hexe
| Stearnscape
|}
==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"
! colspan="8" |Generator!! Cents!!Comments
|-
|-
| 0\7||  || ||
|  
|
|  
|
|  
|
|  
| ||0||
| 2\138
|  
|  
| 17.391
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\66
|1\91
|  
|
|  
|
|  
|
| 18.182
|13.187
|  
|
|-
|-
|
|  
|
|  
|
|  
|
| 1\60
|1\84
|  
|
|  
|
|  
|
| 20
|14.286
|  
|[[Absurdity]]
|-
|-
|
|  
|
|  
|
|  
|
| 1\54
|
|  
|
|  
|
|  
|4\329
| 22.222
|14.59
|  
|Absurdity
|-
|-
|
|  
|
|  
|
|  
|
| 1\48
|
|  
|
|  
|3\245
|  
|
| 25
|14.69
|  
|
|-
|-
|
|  
|
|  
|
|  
|
| 1\42
|
|  
|2\161
|  
|
|  
|
| 28.571
|14.907
|  
|
|-
|-
|
|  
|
|  
|
|  
|
| 1\36
|1\77
|
|
|
|
|
|
| 33.333
|15.584
|
|[[Septant]]
|-
|
|
| 1\30
|
|
|
|
| 40
|
|-
|  
| 1\24
|  
|  
|  
|  
|
| 50
| [[Hemisemiaug]]
|-
|-
|
|
|
|
|2\42
|
|
|
|
|
|
|
|
|
|57.143
|4\301
|Hemisemiaug
|15.947
|Septant
|-
|-
| 1\18
|
|
|
|
Line 2,808: Line 2,836:
|
|
|
|
|3\224
| 66.667
|
| Hemisemiaug
|16.071
|Septant
|-
|-
|
|  
|
| 2\30
|
|  
|
|  
|
|  
|2\147
|  
|
|  
|
| 80
|16.327
| [[Hexe]]
|Septant
|-
|-
|
|  
|
|  
|
|  
|
| 5\72
|1\70
|  
|
|  
|
|  
|
| 83.333
|17.143
| Hexe
|
|-
|-
|
|  
|
|  
|
| 3\42
|
|  
|1\63
|  
|
|  
|
|  
|
| 85.714
|19.048
| Hexe
|[[Sevond]]
|-
|-
|
|  
|
|  
|
|  
|
| 4\54
|
|  
|2\119
|  
|
|  
|
| 88.889
|20.168
| Hexe
|Sevond
|-
|-
|
| 1\12
|
|
|
|
|
|  
|1\56
|  
|
|  
|
|  
|
| 100
|21.429
| Hexe
|Sevond
|}
 
== 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"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\7
|
|  
|
|  
|
|  
|1\49
|  
|
|  
|
|  
|
|  
|24.49
| 0
|
|  
|-
|-
|
|
|
|  
|
|  
|1\42
|  
|
| 1\91
|
|  
|
|  
|
|  
|28.571
| 13.187
|[[Mistismic temperaments#Neutron|Neutron]]
|  
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\84
|3\119
|  
|
|  
|
|  
|30.252
| 14.286
|Neutron
| [[Absurdity]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\196
|  
|
| 4\329
|30.612
| 14.59
|Neutron
| Absurdity
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\245
|7\273
|  
|30.769
| 14.69
|Neutron
|  
|-
|-
|
|
|
|  
|
|  
|
|  
|2\77
|  
|
| 2\161
|
|  
|
|  
|31.169
| 14.907
|Neutron
|  
|-
|-
|
|  
|
|  
|1\35
|  
|
|  
|
| 1\77
|
|  
|
|  
|
|  
|34.286
| 15.584
|[[Whitewood family#Redwood|Redwood]]
| [[Septant]]
|-
|-
|
|  
|
|  
|
|  
| 2\63
|  
|
|  
|
|  
|
|  
|
| 4\301
|38.095
| 15.947
|Redwood
| Septant
|-
|-
|
|  
| 1\28
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\224
|
|  
|42.857
| 16.071
|Redwood/[[Whitewood]]
| Septant
|-
|-
|
|  
|
|  
|
|  
| 3\77
|  
|
|  
|
| 2\147
|
|  
|
|  
| 46.753
| 16.327
|Whitewood
| Septant
|-
|-
|
|  
|
|  
|2\49
|  
|
|  
|
| 1\70
|
|  
|
|  
|
|  
|48.980
| 17.143
|Whitewood
|  
|-
|-
|
|  
|
|  
|
|  
|3\70
|  
|
| 1\63
|
|  
|
|  
|
|  
| 51.429
| 19.048
|Whitewood
| [[Sevond]]
|-
|-
|1\21
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\119
|
|  
|
|  
|57.143
| 20.168
|Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
| Sevond
|-
|-
|
|  
|
|  
|
|  
| 4\77
|  
|
| 1\56
|
|  
|
|  
|
|  
|62.338
| 21.429
|Jamesbond/Septimal
| Sevond
|-
|-
|
|  
|
|  
|3\56
|  
|
|  
|
| 1\49
|
|  
|
|  
|
|  
|64.286
| 24.49
| Jamesbond/Septimal
|  
|-
|-
|
|  
|
|  
|
|  
|5\91
| 1\42
|
|  
|
|  
|
|  
|
|  
|65.934
| 28.571
|Jamesbond/Septimal
| [[Mistismic temperaments#Neutron| Neutron]]
|-
|-
|
|  
|2\35
|  
|
|  
|
|  
|
|  
|
| 3\119
|
|  
|
|  
| 68.571
| 30.252
|Jamesbond/Septimal/[[Greenwood]]
| Neutron
|-
|-
|
|  
|
|  
|
|  
|5\84
|  
|
|  
|
|  
|
| 5\196
|
|  
|71.429
| 30.612
|Jamesbond/Septimal/Greenwood
| Neutron
|-
|-
|
|  
|
|  
|3\49
|  
|
|  
|
|  
|
|  
|
|  
|
| 7\273
| 73.469
| 30.769
|Jamesbond/Septimal/Greenwood
| Neutron
|-
|-
|
|  
|
|  
|
|  
|4\63
|  
|
| 2\77
|
|  
|
|  
|
|  
|76.190
| 31.169
|Jamesbond/Septimal/Greenwood
| Neutron
|-
|-
| 1\14
|  
|
|  
|
| 1\35
|
|  
|
|  
|
|  
|
|  
|
|  
|85.714
| 34.286
|Jamesbond/Septimal/Greenwood
| [[Whitewood family#Redwood| Redwood]]
|}
 
==Eight periods per octave==
{{todo|complete table|comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable sortable mw-collapsible"
! colspan="9" |Generator!!Cents!!Comments
|-
|-
|0\8|| ||
|  
|
|  
|
|  
|
| 2\63
|
|  
|
|  
| ||0||
|  
|  
| 38.095
| Redwood
|-
|-
|
|  
|
| 1\28
|
|  
|
|  
|
|  
|
|  
|1\80
|  
|
|  
|
| 42.857
|15
| Redwood/[[Whitewood]]
|
|-
|-
|
|  
|
|  
|
|  
|
| 3\77
|
|  
|
|  
|
|  
|2\152
|  
|
| 46.753
|15.789
| Whitewood
|[[Octoid]]
|-
|-
|
|  
|
|  
|
| 2\49
|
|  
|
|  
|
|  
|
|  
|
|  
|3\224
| 48.980
|16.071
| Whitewood
|Octoid
|-
|-
|
|  
|
|  
|
|  
|
| 3\70
|
|  
|1\72
|  
|
|  
|
|  
|
| 51.429
|16.667
| Whitewood
|Octoid
|-
|-
|
| 1\21
|
|  
|
|  
|
|  
|1\64
|  
|
|  
|
|  
|
|  
|
| 57.143
|18.75
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Austinpowers|Austinpowers]]
|
|-
|-
|
|  
|
|  
|
|  
|1\56
| 4\77
|
|  
|
|  
|
|  
|
|  
|
| 62.338
|21.429
| Jamesbond/Austinpowers
|
|-
|-
|
|  
|
|  
|1\48
| 3\56
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 64.286
|25
| Jamesbond/Austinpowers
|
|-
|-
|
|  
| 1\40
|  
|
|  
|
| 5\91
|
|  
|
|  
|
|  
|
|  
|
| 65.934
|30
| Jamesbond/Austinpowers
|
|-
|-
|
|  
|
| 2\35
|2\72
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 68.571
|33.333
| Jamesbond/Austinpowers/[[Greenwood]]
|
|-
|-
|1\32
|  
|
|  
|
|  
|
| 5\84
|
|  
|
|  
|
|  
|
|  
|
| 71.429
|37.5
| Jamesbond/Austinpowers/Greenwood
|[[Semidim]]
|-
|-
|
|  
|
|  
|3\88
| 3\49
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 73.469
|40.909
| Jamesbond/Austinpowers/Greenwood
|Semidim
|-
|-
|
|  
|2\56
|  
|
|  
|
| 4\63
|
|  
|
|  
|
|  
|
|  
|
| 76.190
|42.857
| Jamesbond/Austinpowers/Greenwood
|Semidim
|-
|-
|
| 1\14
|
|
|3\80
|
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 85.714
|45
| Jamesbond/Austinpowers/Greenwood
|Semidim
|}
 
== Eight periods per octave ==
{{todo| complete table| comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|
| 0\8
|
|  
|
|  
|4\104
|  
|
|  
|
|  
|
|  
|
|  
|
| 0
|46.154
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|5\128
| 1\480
|
|  
|
|  
|
|  
|
| 2.5
|46.875
|  
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\472
|6\152
|  
|
|  
|
|  
|
| 2.542
|47.368
| [[Octium]]
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\176
| 4\1872
|
|  
|
| 2.564
|47.727
| Octium
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\200
|  
|
| 7\3272
|
| 2.567
|48
| Octium
|Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 3\1400
|9\224
|  
|
|  
|
| 2.571
|48.214
| Octium
|Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\464
|
|  
|
|  
|
|  
|28\696
| 2.586
|48.276
|  
|Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| …
|
|  
|
|  
|19\472
|  
|
|  
|48.305
|  
|Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\96
|
|  
|10\248
|  
|
|  
|
| 12.5
|48.387
|  
|Semidim
|-
|-
|1\24
|  
|
|  
|
|  
|
|  
|
| 1\88
|
|  
|
|  
|
|  
|
| 13.635
|50
|  
|Semidim
|-
|-
|2\40
|  
|
|  
|
|  
|
|  
|
| 1\80
|
|  
|
|  
|
|  
|
| 15
| 60
|  
|
|-
|-
|1\16
|  
|
|  
|
|  
|
|  
|
|  
|
| 2\152
|
|  
|
|  
|
| 15.789
|75
| [[Octoid]]
|
|}
 
==Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!! Comments
|-
|-
|0\9||  || ||
|  
|  
|
|  
|
|  
| ||0||
|  
|  
|  
| 3\224
|  
| 16.071
| Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|1\72
| 1\72
|
|  
|
|  
|
|  
|16.667
| 16.667
|[[Enneaportent]]
| Octoid
|-
|-
|
|  
|
|  
|
|  
|
|  
|
| 1\64
|
|  
|
|  
|4\279
|  
|17.204
| 18.75
|Enneaportent
|  
|-
|-
|
|  
|
|  
|
|  
|
| 1\56
|
|  
|
|  
|3\207
|  
|
|  
|17.391
| 21.429
|Enneaportent
|  
|-
|-
|
|  
|
|  
|
| 1\48
|
|  
|
|  
|2\135
|  
|
|  
|
|  
|17.778
| 25
|Enneaportent
|  
|-
|-
|
|  
|
| 1\40
|
|  
|1\63
|  
|
|  
|
|  
|
|  
|
|  
|19.048
| 30
|Enneaportent
|  
|-
|-
|
|  
|
|  
|1\54
| 2\72
|
|  
|
|  
|
|  
|
|  
|
|  
|22.222
| 33.333
|
|  
|-
|-
|
| 1\32
|1\45
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|26.667
| 37.5
|
| [[Semidim]]
|-
|-
|1\36
|  
|
|  
|
| 3\88
|
|  
|
|  
|
|  
|
|  
|
|  
|33.333
| 40.909
|[[Tritrizo clan#No-five tritrizo|No-five tritrizo]]
| Semidim
|-
|-
|
|  
|
| 2\56
|
|  
|4\135
|  
|
|  
|
|  
|
|  
|
|  
|35.556
| 42.857
|No-five tritrizo
| Semidim
|-
|-
|
|  
|
|  
|3\99
| 3\80
|
|  
|
|  
|
|  
|
|  
|
|  
|36.364
| 45
|No-five tritrizo
| Semidim
|-
|-
|
|  
|2\63
|  
|
|  
|
| 4\104
|
|  
|
|  
|
|  
|
|  
|38.095
| 46.154
|[[Niner]]
| Semidim
|-
|-
|
|
|3\90
|  
|  
|
|  
|
|  
|
|  
|
| 5\128
|40
|  
|Niner
|  
|-
|  
|1\27
| 46.875
|
| Semidim
|
|
|
|
|
|
| 44.444
|Niner
|-
|-
|
|  
|
|  
|4\99
|  
|
|  
|
| 6\152
|
|  
|
|  
|
|  
|48.485
| 47.368
|[[Ennealimmal]]
| Semidim
|-
|-
|
|  
|
|  
|
|  
|7\171
|  
|
|  
|
| 7\176
|
|  
|
|  
|49.123
| 47.727
|Ennealimmal
| Semidim
|-
|-
|
|3\72
|  
|  
|
|  
|
|  
|
|  
|
|  
|
| 8\200
| 50
|  
|Ennealimmal
|  
| 48
| Semidim
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 9\224
|
|  
|20\477
|  
|50.314
| 48.214
|[[Novemkleismic]]
| Semidim/[[Octant]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|17\405
|  
|
| 28\696
|50.370
| 48.276
|Novemkleismic
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|14\333
|  
|
| 19\472
|
|  
|50.451
| 48.305
|Novemkleismic
| Semidim/Octant
|-
|-
|
|  
|
|  
|
|  
|
|  
|11\261
|  
|
| 10\248
|
|  
|
|  
|50.575
| 48.387
|Novemkleismic
| Semidim
|-
|-
|
| 1\24
|
|  
|
|  
|8\189
|  
|
|  
|
|  
|
|  
|
|  
|50.794
| 50
|Novemkleismic
| Semidim
|-
|-
|
| 2\40
|
|  
|5\117
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|51.282
| 60
|
|  
|-
|-
|2\45
| 1\16
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|53.333
| 75
|  
|  
|}
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
|1\18
| 0\9
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
| 66.667
| 0
|
|  
|}
 
==Twelve periods per octave==
See also: [[Compton family]]
 
{| class="wikitable sortable mw-collapsible"
! colspan="8" |Generator!!Cents!!Comments
|-
|-
|0\12||  || ||
|
|  
|  
|
|  
|||0||
|  
|  
| 1\72
|  
|  
|
| 16.667
| [[Enneaportent]]
|-
|-
|
|  
|
|  
|
|  
|1\636
|  
|
|  
|
|  
|
|  
|
| 4\279
|1.887
| 17.204
|
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|1\624
|  
|
|  
|
|  
|
| 3\207
|
|  
|1.923
| 17.391
|
| Enneaportent
|-
|-
|
|
|
|  
|
|  
|
|  
|2\1236
|  
|
| 2\135
|
|  
|
|  
|1.942
| 17.778
|[[Atomic]]
| Enneaportent
|-
|-
|
|  
|
|  
|
|  
|
| 1\63
|
|  
|3\1848
|  
|
|  
|
|  
|1.948
| 19.048
|Atomic
| Enneaportent
|-
|-
|
|  
|
|  
|
| 1\54
|
|  
|
|  
|
|  
|4\2460
|  
|
|  
|1.951
| 22.222
|Atomic
|  
|-
|-
|
|  
|
| 1\45
|
|  
|
|  
|
|  
|
|  
|
|  
|5\3072
|  
|1.953
| 26.667
|Atomic
|  
|-
|-
|
| 1\36
|
|  
|
|  
|1\612
|  
|
|  
|
|  
|
|  
|
|  
|1.961
| 33.333
|Atomic
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|-
|-
|
|  
|
|  
|
|  
|1\600
| 4\135
|
|  
|
|  
|
|  
|
|  
|2
| 35.556
|
| No-five tritrizo
|-
|-
|
|  
|
|  
|
| 3\99
|1\588
|  
|
|  
|
|  
|
|  
|
|  
|2.041
| 36.364
|
| No-five tritrizo
|-
|-
|
|  
|
| 2\63
|
|  
|1\576
|  
|
|  
|
|  
|
|  
|
|  
|2.083
| 38.095
|
| [[Niner]]
|-
|-
|
|  
|
|  
|
| 3\90
|...
|  
|
|  
|
|  
|
|  
|
|  
|...
| 40
|
| Niner
|-
|-
|
| 1\27
|
|  
|
|  
|1\108
|  
|
|  
|
|  
|
|  
|
|  
|11.111
| 44.444
|
| Niner
|-
|-
|
|  
|
|  
|
| 4\99
|1\96
|  
|
|  
|
|  
|
|  
|
|  
|12.5
| 48.485
|[[Compton]]
| [[Ennealimmal]]
|-
|-
|
|  
|
|  
|
|  
|1\84
| 7\171
|
|  
|
|  
|
|  
|
|  
|14.286
| 49.123
|Compton
| Ennealimmal
|-
|-
|
|  
|
| 3\72
|
|  
|
|  
|
|  
|3\240
|  
|
|  
|
|  
|15
| 50
|Compton
| Ennealimmal
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\636
| 20\477
|15.094
| 50.314
|Compton
| [[Novemkleismic]]
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|5\396
| 17\405
|
|  
|15.152
| 50.370
|Compton
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 14\333
|
|  
|7\552
|  
|15.217
| 50.451
|Compton
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
|  
|2\156
| 11\261
|
|  
|
|  
|
|  
|15.385
| 50.575
|Compton
| Novemkleismic
|-
|-
|
|  
|
|  
|
|  
|
| 8\189
|
|  
|
|  
|
|  
|7\540
|  
|15.556
| 50.794
|Compton
| Novemkleismic
|-
|-
|
|  
|
|  
|
| 5\117
|
|  
|
|  
|
|  
|5\384
|  
|
|  
|15.625
| 51.282
|Compton
|  
|-
|-
|
| 2\45
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|8\612
|  
|15.686
| 53.333
|Compton
|  
|-
|-
|
| 1\18
|
|  
|
|  
|
|  
|
|  
|3\228
|  
|
|  
|
|  
|15.789
| 66.667
|Compton
|
|}
 
== Ten periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
|
| 0\10
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|7\528
| 0
|15.909
|  
|Compton
|-
|-
|1\140
|
|
|
|
Line 3,971: Line 3,981:
|
|
|
|
|4\300
|8.571
|
|[[Decoid]]
|16
|Compton
|-
|-
|
|
|2\270
|
|
|
|
Line 3,982: Line 3,991:
|
|
|
|
|
|8.888
|5\372
|Decoid
|16.129
|Compton
|-
|-
|1\130
|
|
|
|
|
|
|1\72
|
|
|
|
|
|
|
|9.231
|16.667
|Decoid
|Compton
|-
|-
|1\120
|
|
|
|
|1\60
|
|
|
|
|
|
|
|
|10
|
|
|20
|Compton
|-
|-
|
| 1\110
|
|  
|
|  
|2\108
|  
|
|  
|
|  
|
|  
|
| 10.909
|22.222
|  
|
|-
|-
|
| 1\100
|1\48
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 12
|25
|  
|[[Catler]]
|-
|-
|
|  
|
| 2\190
|
|  
|3\132
|  
|
|  
|
|  
|
|  
|
| 12.632
| 27.273
| [[Deca]]
|Catler
|-
|-
|
| 1\90
|
|  
| 2\84
|  
|
|  
|
|  
|
|  
|
|  
|
| 13.333
|28.571
| Deca
|Catler
|-
|-
|
| 1\80
|
|  
|
|  
|3\120
|  
|
|  
|
|  
|
|  
|
| 15
|30
| Deca
|Catler
|-
|-
|1\36
| 1\70
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 17.143
|33.333
|  
|Catler/[[Catnip]]
|-
|-
|
| 1\60
|
|  
|
|  
|4\132
|  
|
|  
|
|  
|
|  
|
| 20
|36.364
|  
|Catnip
|-
|-
|
| 1\50
|
|  
|3\96
|  
|
|  
|
|  
|
|  
|
|  
|
| 24
|37.5
| [[Decimetra]]
| Catnip
|-
|-
|
|  
|
|  
|
|  
|5\156
| 4\190
|
|  
|
|  
|
|  
|
| 25.263
|38.462
| Decimetra
|Catnip
|-
|-
|
|  
|2\60
|  
|
|  
|
|  
|
| 7\330
|
|  
|
|  
|
| 25.455
|40
| Decimetra
|Catnip
|-
|-
|
|  
|
|  
|
|  
|5\144
|  
|
|  
|
|  
|
| 17\800
|
| 25.5
|41.667
| Decimetra
|
|-
|-
|
|
|
|
|3\84
|
|
|
|
|
|
| 10\470
|
|
|
| 25.532
| 42.857
| Decimetra
| [[Magnesium]]
|-
|  
|  
| 3\140
|
|
|
|
| 25.714
| Decimetra
|-
|
| 2\90
|  
|  
|  
|  
|  
| 26.667
| Decimetra
|-
|-
|
| 1\40
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|16\444
| 30
|43.243
| [[Decic]]
|Magnesium
|-
|-
|
|
| 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
|
|
|
|-
|
| 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"