Xenharmonic Wiki

Map of rank-2 temperaments: Difference between revisions

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m Septimal blackwood is now canon
 
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Please make sure each fraction of an octave is always the [[mediant]] of the ones directly above and below.
Please make sure each fraction of an octave is always the [[mediant]] of the ones directly above and below.
Interactive maps of ''all'' linear temperaments with octave, half-octave, third-octave, or tritave period that are logged on the wiki are available [https://hkm2685.github.io/temperament-map/rank2/viewer/ here].


== One period per octave ==
== One period per octave ==
Line 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/[[Hemiug]]
| Hemiaug/[[Hemiug]]
|-
|-
|  
|  
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 1,594: Line 1,596:
|  
|  
| 50  
| 50  
| Hemidim/[[4th-octave temperaments#Darian calendar| Darian calendar]]
| Hemidim/[[4th-octave temperaments#Darian calendar|Darian calendar]]
|-
|-
|  
|  
Line 2,124: Line 2,126:
|  
|  
| 24
| 24
|  
| [[Cloudtone]]
|-
|-
|  
|  
Line 2,136: Line 2,138:
|  
|  
| 26.67
| 26.67
|  
| Cloudtone
|-
|-
|  
|  
Line 2,148: Line 2,150:
|  
|  
| 30
| 30
|  
| Cloudtone
|-
|-
|  
|  
Line 2,532: Line 2,534:
|  
|  
| 112.941
| 112.941
| Blackwood/[[Phi as a Generator| Elderthing]]
| Blackwood/[[Phi as a Generator|Elderthing]]
|-
|-
|  
|  
Line 2,815: Line 2,817:
|  
|  
| 50
| 50
|  
| [[Hemisemiaug]]
|-
|
|
|2\42
|
|
|
|
|57.143
|Hemisemiaug
|-
|-
| 1\18
| 1\18
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 66.667
| 66.667
|  
| Hemisemiaug
|-
|-
|  
|  
Line 3,180: Line 3,192:
|  
|  
| 57.143
| 57.143
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal| Septimal]]
| Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Austinpowers|Austinpowers]]
|-
|-
|  
|  
Line 3,191: Line 3,203:
|  
|  
| 62.338
| 62.338
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|  
|  
Line 3,202: Line 3,214:
|  
|  
| 64.286
| 64.286
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|  
|  
Line 3,213: Line 3,225:
|  
|  
| 65.934
| 65.934
| Jamesbond/Septimal
| Jamesbond/Austinpowers
|-
|-
|  
|  
Line 3,224: Line 3,236:
|  
|  
| 68.571
| 68.571
| Jamesbond/Septimal/[[Greenwood]]
| Jamesbond/Austinpowers/[[Greenwood]]
|-
|-
|  
|  
Line 3,235: Line 3,247:
|  
|  
| 71.429
| 71.429
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
|  
|  
Line 3,246: Line 3,258:
|  
|  
| 73.469
| 73.469
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
|  
|  
Line 3,257: Line 3,269:
|  
|  
| 76.190
| 76.190
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|-
|-
| 1\14
| 1\14
Line 3,268: Line 3,280:
|  
|  
| 85.714
| 85.714
| Jamesbond/Septimal/Greenwood
| Jamesbond/Austinpowers/Greenwood
|}
|}


== Eight periods per octave ==
== Eight periods per octave ==
{{todo| complete table| comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{{Todo| complete table |comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808)}}
 
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! colspan="8" | Generator
Line 3,293: Line 3,306:
|  
|  
|  
|  
| 1\480
| 1\80
|  
|  
|  
|  
|  
|  
| 2.5
| 15
|  
|  
|-
|-
Line 3,304: Line 3,317:
|  
|  
|  
|  
| 1\472
|  
|  
| 2\152
|  
|  
|  
|  
| 2.542
| 15.789
| [[Octium]]
| [[Octoid]]
|-
|-
|  
|  
Line 3,317: Line 3,330:
|  
|  
|  
|  
| 4\1872
| 3\224
|  
|  
| 2.564
| 16.071
| Octium
| Octoid
|-
|-
|  
|  
Line 3,326: Line 3,339:
|  
|  
|  
|  
| 1\72
|  
|  
|  
|  
|  
|  
| 7\3272
| 16.667
| 2.567
| Octoid
| Octium
|-
|-
|  
|  
Line 3,337: Line 3,350:
|  
|  
|  
|  
| 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
|  
|  
|  
|  
Line 3,416: Line 3,430:
|  
|  
|  
|  
| 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
|  
|  
|  
|  
Line 3,493: Line 3,505:
|  
|  
|  
|  
| 9\224
|  
|  
|  
|  
| 37.5
| 48.214
| [[Semidim]]
| Semidim/[[Octant]]
|-
|-
|  
|  
|  
|  
| 3\88
|  
|  
|  
|  
Line 3,506: Line 3,518:
|  
|  
|  
|  
| 40.909
| 28\696
| Semidim
| 48.276
| Semidim/Octant
|-
|-
|  
|  
| 2\56
|  
|  
|  
|  
Line 3,516: Line 3,528:
|  
|  
|  
|  
| 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
|
|  
|  
|  
|  
Line 3,569: Line 3,591:
|  
|  
|  
|  
| 7\176
|  
|  
| 0
|  
|  
| 47.727
| Semidim
|-
|-
|  
|  
Line 3,579: Line 3,599:
|  
|  
|  
|  
| 1\72
|  
|  
| 8\200
|  
|  
|  
|  
| 48
| 16.667
| Semidim
| [[Enneaportent]]
|-
|-
|  
|  
Line 3,591: Line 3,611:
|  
|  
|  
|  
| 9\224
|  
|  
|  
|  
| 48.214
| 4\279
| Semidim/[[Octant]]
| 17.204
| Enneaportent
|-
|-
|  
|  
Line 3,603: Line 3,623:
|  
|  
|  
|  
| 3\207
|  
|  
| 28\696
| 17.391
| 48.276
| Enneaportent
| Semidim/Octant
|-
|-
|  
|  
Line 3,613: Line 3,633:
|  
|  
|  
|  
| 2\135
|  
|  
| 19\472
|  
|  
| 48.305
| 17.778
| Semidim/Octant
| Enneaportent
|-
|-
|  
|  
|  
|  
|  
|  
| 1\63
|  
|  
|  
|  
| 10\248
|  
|  
|  
|  
| 48.387
| 19.048
| Semidim
| Enneaportent
|-
|-
| 1\24
|  
|  
|
| 1\54
|  
|  
|  
|  
Line 3,637: Line 3,658:
|  
|  
|  
|  
| 22.222
|  
|  
| 50
| Semidim
|-
|-
| 2\40
|  
|  
| 1\45
|  
|  
|  
|  
Line 3,649: Line 3,669:
|  
|  
|  
|  
| 60
| 26.667
|  
|  
|-
|-
| 1\16
| 1\36
|  
|  
|  
|  
Line 3,660: Line 3,680:
|  
|  
|  
|  
| 75
| 33.333
|  
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
|}
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
| 0\9
|  
|  
|  
|  
|  
|  
| 4\135
|  
|  
|  
|  
|  
|  
|  
|  
| 0
| 35.556
|  
| No-five tritrizo
|-
|-
|  
|  
|  
|  
| 3\99
|  
|  
|  
|  
| 1\72
|  
|  
|  
|  
|  
|  
| 16.667
| 36.364
| [[Enneaportent]]
| No-five tritrizo
|-
|-
|  
|  
| 2\63
|  
|  
|  
|  
Line 3,699: Line 3,713:
|  
|  
|  
|  
| 4\279
| 38.095
| 17.204
| [[Niner]]
| Enneaportent
|-
|-
|  
|  
|  
|  
| 3\90
|  
|  
|  
|  
|  
|  
|  
|  
| 3\207
|  
|  
| 17.391
| 40
| Enneaportent
| Niner
|-
|-
| 1\27
|  
|  
|  
|  
Line 3,719: Line 3,733:
|  
|  
|  
|  
| 2\135
|  
|  
|  
|  
| 17.778
| 44.444
| Enneaportent
| Niner
|-
|-
|  
|  
|  
|  
| 4\99
|  
|  
| 1\63
|  
|  
|  
|  
|  
|  
|  
|  
| 19.048
| 48.485
| Enneaportent
| [[Ennealimmal]]
|-
|-
|  
|  
|  
|  
| 1\54
|  
|  
| 7\171
|  
|  
|  
|  
|  
|  
|  
|  
| 22.222
| 49.123
|  
| Ennealimmal
|-
|-
|  
|  
| 1\45
| 3\72
|  
|  
|  
|  
Line 3,755: Line 3,768:
|  
|  
|  
|  
| 26.667
| 50
|  
| Ennealimmal
|-
|-
| 1\36
|  
|  
|  
|  
Line 3,766: Line 3,778:
|  
|  
|  
|  
| 33.333
| 20\477
| [[Tritrizo clan#No-five tritrizo| No-five tritrizo]]
| 50.314
| [[Novemkleismic]]
|-
|-
|  
|  
|  
|  
|  
|  
| 4\135
|  
|  
|  
|  
|  
|  
| 17\405
|  
|  
| 35.556
| 50.370
| No-five tritrizo
| Novemkleismic
|-
|-
|  
|  
|  
|  
| 3\99
|  
|  
|  
|  
|  
|  
| 14\333
|  
|  
|  
|  
| 36.364
| 50.451
| No-five tritrizo
| Novemkleismic
|-
|-
|  
|  
| 2\63
|  
|  
|  
|  
|  
|  
| 11\261
|  
|  
|  
|  
|  
|  
| 38.095
| 50.575
| [[Niner]]
| Novemkleismic
|-
|-
|  
|  
|  
|  
| 3\90
|  
|  
| 8\189
|  
|  
|  
|  
|  
|  
|  
|  
| 40
| 50.794
| Niner
| Novemkleismic
|-
|-
| 1\27
|  
|  
|  
|  
| 5\117
|  
|  
|  
|  
Line 3,821: Line 3,834:
|  
|  
|  
|  
| 44.444
| 51.282
| Niner
|  
|-
|-
| 2\45
|
|  
|  
|  
|  
| 4\99
|  
|  
|  
|  
|  
|  
|  
|  
| 53.333
|  
|  
| 48.485
| [[Ennealimmal]]
|-
|-
| 1\18
|
|  
|  
|  
|  
|  
|  
| 7\171
|  
|  
|  
|  
|  
|  
| 66.667
|  
|  
| 49.123
|}
| Ennealimmal
 
== Ten periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
| 0\10
|  
|  
| 3\72
|  
|  
|  
|  
Line 3,853: Line 3,873:
|  
|  
|  
|  
| 0
|  
|  
| 50
| Ennealimmal
|-
|-
|  
|1\140
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
| 20\477
|8.571
| 50.314
|[[Decoid]]
| [[Novemkleismic]]
|-
|-
|  
|
|  
|2\270
|  
|
|  
|
|  
|
|  
|
| 17\405
|
|  
|8.888
| 50.370
|Decoid
| Novemkleismic
|-
|-
|  
|1\130
|  
|
|  
|
|  
|
|  
|
| 14\333
|
|  
|
|  
|9.231
| 50.451
|Decoid
| Novemkleismic
|-
|-
|
|1\120
|
|
|
|
|
|
| 11\261
|
|
|
|
|
|
|10
| 50.575
|
| Novemkleismic
|-
|
|
|
| 8\189
|
|
|
|
| 50.794
| Novemkleismic
|-
|
|
| 5\117
|
|
|
|
|
| 51.282
|
|-
| 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\110
| 1\110
Line 4,310: Line 4,264:
|  
|  
| 55.385
| 55.385
| [[Decoid]]
|
|-
|-
| 1\20
| 1\20
Line 4,397: Line 4,351:
|  
|  
| 42.636
| 42.636
| [[Hendecatonic]]
| [[Hendecatonic (temperament)|Hendecatonic]]
|-
|-
|  
|  
Line 4,437: Line 4,391:
|  
|  
| 48.485
| 48.485
| Hendecatonic/[[Cohendecatonic]]
| Hendecatonic / [[cohendecatonic]]
|-
|-
|  
|  
Retrieved from "https://en.xen.wiki/w/Map_of_rank-2_temperaments"