Xenharmonic Wiki

Map of rank-2 temperaments: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,282 edits
→Six periods per octave: add hemisemiaug
 
(5 intermediate revisions by 3 users not shown)
Line 2: Line 2:


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 1,335: 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 3,282: Line 3,284:


== 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 3,303: Line 3,306:
|  
|  
|  
|  
| 1\480
| 1\80
|  
|  
|  
|  
|  
|  
| 2.5
| 15
|  
|  
|-
|-
Line 3,314: Line 3,317:
|  
|  
|  
|  
| 1\472
|  
|  
| 2\152
|  
|  
|  
|  
| 2.542
| 15.789
| [[Octium]]
| [[Octoid]]
|-
|-
|  
|  
Line 3,327: Line 3,330:
|  
|  
|  
|  
| 4\1872
| 3\224
|  
|  
| 2.564
| 16.071
| Octium
| Octoid
|-
|-
|  
|  
Line 3,336: Line 3,339:
|  
|  
|  
|  
| 1\72
|  
|  
|  
|  
|  
|  
| 7\3272
| 16.667
| 2.567
| Octoid
| Octium
|-
|-
|  
|  
Line 3,347: 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 3,426: 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 3,503: Line 3,505:
|  
|  
|  
|  
| 9\224
|  
|  
|  
|  
| 37.5
| 48.214
| [[Semidim]]
| Semidim/[[Octant]]
|-
|-
|  
|  
|  
|  
| 3\88
|  
|  
|  
|  
Line 3,516: Line 3,518:
|  
|  
|  
|  
| 40.909
| 28\696
| Semidim
| 48.276
| Semidim/Octant
|-
|-
|  
|  
| 2\56
|  
|  
|  
|  
Line 3,526: 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
|  
|  
|  
|  
| 60
|  
|  
| 46.875
| Semidim
|-
|-
| 1\16
|
|  
|  
|  
|  
|  
|  
|  
|  
| 6\152
|  
|  
|  
|  
| 75
|  
|  
| 47.368
|}
| Semidim
 
== Nine periods per octave ==
{| class="wikitable sortable mw-collapsible"
! colspan="8" | Generator
! Cents
! Comments
|-
|-
| 0\9
|  
|  
|  
|  
Line 3,579: Line 3,590:
|  
|  
|  
|  
| 7\176
|  
|  
|  
|  
| 47.727
| 0
| Semidim
|  
|-
|-
|  
|  
Line 3,589: Line 3,599:
|  
|  
|  
|  
| 1\72
|  
|  
| 8\200
|  
|  
|  
|  
| 48
| 16.667
| Semidim
| [[Enneaportent]]
|-
|-
|  
|  
Line 3,601: Line 3,611:
|  
|  
|  
|  
| 9\224
|  
|  
|  
|  
| 48.214
| 4\279
| Semidim/[[Octant]]
| 17.204
| Enneaportent
|-
|-
|  
|  
Line 3,613: Line 3,623:
|  
|  
|  
|  
| 3\207
|  
|  
| 28\696
| 17.391
| 48.276
| Enneaportent
| Semidim/Octant
|-
|-
|  
|  
Line 3,623: 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 3,647: Line 3,658:
|  
|  
|  
|  
| 22.222
|  
|  
| 50
| Semidim
|-
|-
| 2\40
|  
|  
| 1\45
|  
|  
|  
|  
Line 3,659: Line 3,669:
|  
|  
|  
|  
| 60
| 26.667
|  
|  
|-
|-
| 1\16
| 1\36
|  
|  
|  
|  
Line 3,670: 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 3,709: Line 3,713:
|  
|  
|  
|  
| 4\279
| 38.095
| 17.204
| [[Niner]]
| Enneaportent
|-
|-
|  
|  
|  
|  
| 3\90
|  
|  
|  
|  
|  
|  
|  
|  
| 3\207
|  
|  
| 17.391
| 40
| Enneaportent
| Niner
|-
|-
| 1\27
|  
|  
|  
|  
Line 3,729: 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 3,765: Line 3,768:
|  
|  
|  
|  
| 26.667
| 50
|  
| Ennealimmal
|-
|-
| 1\36
|  
|  
|  
|  
Line 3,776: 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 3,831: Line 3,834:
|  
|  
|  
|  
| 44.444
| 51.282
| Niner
|  
|-
|-
| 2\45
|
|  
|  
|  
|  
| 4\99
|  
|  
|  
|  
|  
|  
|  
|  
| 53.333
|  
|  
| 48.485
| [[Ennealimmal]]
|-
|-
| 1\18
|  
|  
|  
|  
|  
|  
| 7\171
|  
|  
|  
|  
|  
|  
|  
|  
| 49.123
| 66.667
| Ennealimmal
|-
|  
|  
| 3\72
|}
|
 
|
== Ten periods per octave==
|
{| class="wikitable sortable mw-collapsible"
|
! colspan="7" | Generator
|  
! Cents
|  
! Comments
| 50
| Ennealimmal
|-
|-
| 0\10
|  
|  
|  
|  
Line 3,873: Line 3,873:
|  
|  
|  
|  
| 0
|  
|  
| 20\477
| 50.314
| [[Novemkleismic]]
|-
|-
|1\140
|
|
|
|
|
|
|8.571
|[[Decoid]]
|-
|
|2\270
|
|
|
|
|
|8.888
|Decoid
|-
|1\130
|
|
|
|
|
|
|9.231
|Decoid
|-
|1\120
|
|
|
|
|
|
|10
|
|-
| 1\110
|  
|  
|  
|  
Line 3,884: Line 3,923:
|  
|  
|  
|  
| 17\405
| 10.909
|  
|  
| 50.370
| Novemkleismic
|-
|-
| 1\100
|  
|  
|  
|  
Line 3,894: Line 3,932:
|  
|  
|  
|  
| 14\333
|  
|  
| 12
|  
|  
| 50.451
| Novemkleismic
|-
|-
|  
|  
| 2\190
|  
|  
|  
|  
|  
|  
| 11\261
|  
|  
|  
|  
|  
| 12.632
| 50.575
| [[Deca]]
| Novemkleismic
|-
|-
| 1\90
|  
|  
|  
|  
|  
|  
| 8\189
|  
|  
|  
|  
|  
|  
|  
| 13.333
| 50.794
| Deca
| Novemkleismic
|-
|-
| 1\80
|  
|  
|  
|  
| 5\117
|  
|  
|  
|  
|  
|  
|  
|  
|  
| 15
| 51.282
| Deca
|
|-
|-
| 2\45
| 1\70
|  
|  
|  
|  
Line 3,940: Line 3,973:
|  
|  
|  
|  
|  
| 17.143
| 53.333
|  
|  
|-
|-
| 1\18
| 1\60
|  
|  
|  
|  
Line 3,951: Line 3,983:
|  
|  
|  
|  
| 20
|  
|  
| 66.667
|
|}
== Ten periods per octave==
{| class="wikitable sortable mw-collapsible"
! colspan="7" | Generator
! Cents
! Comments
|-
|-
| 0\10
| 1\50
|  
|  
|  
|  
Line 3,969: Line 3,993:
|  
|  
|  
|  
| 0
| 24
|  
| [[Decimetra]]
|-
|-
| 1\110
|  
|  
|  
|  
|  
|  
| 4\190
|  
|  
|  
|  
|  
|  
| 10.909
| 25.263
|
|-
| 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
| Decimetra
|-
|-
Line 4,320: Line 4,264:
|  
|  
| 55.385
| 55.385
| [[Decoid]]
|
|-
|-
| 1\20
| 1\20
Line 4,407: Line 4,351:
|  
|  
| 42.636
| 42.636
| [[Hendecatonic]]
| [[Hendecatonic (temperament)|Hendecatonic]]
|-
|-
|  
|  
Line 4,447: Line 4,391:
|  
|  
| 48.485
| 48.485
| Hendecatonic/[[Cohendecatonic]]
| Hendecatonic / [[cohendecatonic]]
|-
|-
|  
|  
Retrieved from "https://en.xen.wiki/w/Map_of_rank-2_temperaments"