Map of rank-2 temperaments: Difference between revisions

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Revision as of 02:42, 18 January 2026

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 of the ones directly above and below.

One period per octave

Since this is the largest subset, it has its own page: map of linear temperaments.

Two periods per octave

Generator Cents Comments
0\2 0.000
1\26 46.154
1\24 50.000 Shrutar
2\46 52.174 Shrutar
1\22 54.545 Shrutar
1\20 60.000
1\18 66.667
2\34 70.588 Vishnu
7\118 71.186 Vishnu
5\84 71.429 Vishnu
3\50 72.000
1\16 75.000
2\30 80.000
3\44 81.818
4\58 82.759 Harry
9\130 83.077 Harry
5\72 83.333 Harry
1\14 85.714
2\26 92.308 Injera
3\38 94.737 Injera
1\12 100.000 Injera/Diaschismic
5\58 103.448 Diaschismic
4\46 104.348 Diaschismic/Srutal
7\80 105.000 Srutal
3\34 105.882 Srutal/Pajara
5\56 107.143 Pajara
2\22 109.091 Pajara
3\32 112.500
1\10 120.000 Octokaidecal
3\28 128.571 Octokaidecal
2\18 133.333 Octokaidecal
3\26 138.462
6\60 140.000
11\94 140.126 Fifive
15\128 140.625 Fifive
4\34 141.176 Fifive
5\42 142.857
1\8 150.000
4\30 160.000
3\22 163.636 Hedgehog/Echidna
11\80 165.000 Hedgehog/Echidna
8\58 165.517 Hedgehog/Echidna
5\36 166.667
2\14 171.429
3\20 180.000
7\46 182.609 Unidec/Hendec
11\72 183.333 Unidec/Hendec
4\26 184.615 Unidec/Hendec
5\32 187.500
1\6 200.000
6\34 211.765
5\28 214.286 Antikythera
9\50 216.000 Antikythera/Wizard
13\72 216.667 Antikythera/Wizard
4\22 218.182 Antikythera/Wizard/Astrology
15\82 219.512 Astrology
11\60 220.000 Astrology
7\38 221.053
225.000 Lemba
5\26 230.769 Lemba
12\62 232.258 Lemba
7\36 233.333
9\46 234.783 Echidnic
29\148 235.135 Echidnic
20\102 235.294 Echidnic
11\56 235.714
2\10 240.000 Decimal
5\24 250.000 Decimal
8\38 252.632 Decimal
257.143 Decimal
4\18 266.667
5\22 272.727 Doublewide
16\70 274.286 Doublewide
11\48 275.000 Doublewide
6\26 276.923
1\4 300.000

Three periods per octave

Generator Cents Comments
0\3 0.000
1\30 40.000
1\27 44.444 Hemiaug
2\51 47.059 Hemiaug
1\24 50.000 Hemiaug/Hemiug
2\45 53.333 Hemiug
1\21 57.143 Hemiug
1\18 66.667
1\15 80.000
6\87 82.759
11\159 83.019 Tritikleismic
16\231 83.117 Tritikleismic
5\72 83.333 Tritikleismic
4\57 84.211 Tritikleismic
3\42 85.714
2\27 88.889 Augmented/Augene
3\39 92.308 Augmented/Augene/Fog
4\51 94.118 Augmented/Augene/Fog
5\63 95.238 Augmented/Augene/Fog
11\138 95.652 Augmented/Augene/Fog
6\75 96 Augmented/Augene/Fog
7\87 96.552 Augmented/Augene/Misty
15\186 96.774 Augmented/Augene/Misty
8\99 96.97 Augmented/Augene/Misty
1\12 100.000 Augmented/Augene/August
3\33 109.091 August
2\21 114.286 August
3\30 120.000
1\9 133.333
4\33 145.455
3\24 150.000 Triforce
5\39 153.846 Triforce
2\15 160.000 Triforce
3\21 171.429 Oodako
7\48 175 Oodako
11\75 176 Oodako
15\102 176.471 Oodako
19\129 176.744 Oodako
4\27 177.778 Oodako
1\6 200.000

Four periods per octave

Generator Cents Comments
0\4 0
1\76 15.789
1\72 16.667 Quadritikleismic
3\212 16.981 Quadritikleismic
2\140 17.143 Quadritikleismic
1\68 17.647 Quadritikleismic
1\64 18.75
1\60 20
... ...
1\36 33.333
1\32 37.5
1\28 42.857
2\52 46.154 Hemidim
3\76 47.368 Hemidim
1\24 50 Hemidim/Darian calendar
1\20 60
1\16 75
2\28 85.714 Demolished
3\40 90 Demolished
1\12 100 Demolished/Diminished
14\164 102.439 Diminished
27\316 102.532 Diminished/Unlit
40\468 102.564 Diminished/Unlit
13\152 102.632 Diminished/Unlit/Undim
38\444 102.703 Diminished/Undim
25\292 102.740 Diminished/Undim
12\140 102.857 Diminished/Undim
11\128 103.125 Diminished
10\116 103.448 Diminished
9\104 103.846 Diminished
8\92 104.348 Diminished
7\80 105 Diminished/Bidia
20\228 105.263 Diminished/Bidia
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

Generator Cents Comments
0\5 0
1\140 8.571
1\135 8.889 Slendroschismic
3\400 9 Slendroschismic
5\665 9.023 Slendroschismic
2\265 9.057 Slendroschismic
1\130 9.231 Slendroschismic/Hemipental
4\515 9.32 Hemipental
3\385 9.351 Hemipental
5\640 9.375 Hemipental
2\255 9.412 Hemipental
1\125 9.6 Hemipental
1\120 10
1\115 10.435
1\70 17.143
1\65 18.462 Pental
4\255 18.824 Pental
3\190 18.947 Pental
5\315 19.048 Pental
2\125 19.2 Pental
3\185 19.459 Pental
1\60 20 Pental
1\55 21.818
1\50 24 Cloudtone
1\45 26.67 Cloudtone
1\40 30 Cloudtone
1\35 34.286
1\30 40
1\25 48
1\20 60
2\35 68.571 Coblack
5\85 70.588 Coblack
3\50 72 Coblack
7\115 73.043 Coblack
4\65 73.846 Coblack
1\15 80 Blackwood
5\70 85.714 Blackwood
4\55 87.273 Blackwood
7\95 88.421 Blackwood
3\40 90 Blackwood
8\105 91.429 Blackwood
5\65 92.308 Blackwood
7\90 93.333 Blackwood
2\25 96 Blackwood
5\60 100 Blackwood
8\95 101.053 Blackwood
3\35 102.857 Blackwood
7\80 105 Blackwood
4\45 106.667 Blackwood
5\55 109.091 Blackwood
6\65 110.769 Blackwood/Quintosec/Sengasec
25\270 111.111 Blackwood/Quintosec/Sengasec/Qintosec
19\205 111.220 Blackwood/Quintosec/SengasecQintosec
13\140 111.429 Blackwood/Quintosec/Sengasec/Qintosec
20\215 111.628 Blackwood/Qintosec
7\75 112 Blackwood/Qinto
15\160 112.5 Blackwood/Qinto
8\85 112.941 Blackwood/Elderthing
9\95 113.684 Blackwood
10\105 114.286 Blackwood
1\10 120 Blackwood

Six periods per octave

Generator Cents Comments
0\6 0
1\288 4.167
1\282 4.255
1\276 2\552 4.348 Sextile
3\822 4.380 Sextile
4\1092 4.396 Sextile
1\270 4.444 Sextile
1\264 4.545
... ...
1\90 13.333
1\84 14.286
1\78 15.385
1\72 16.667 Stearnscape
4\282 17.021 Stearnscape
3\210 17.143 Stearnscape
2\138 17.391
1\66 18.182
1\60 20
1\54 22.222
1\48 25
1\42 28.571
1\36 33.333
1\30 40
1\24 50 Hemisemiaug
2\42 57.143 Hemisemiaug
1\18 66.667 Hemisemiaug
2\30 80 Hexe
5\72 83.333 Hexe
3\42 85.714 Hexe
4\54 88.889 Hexe
1\12 100 Hexe

Seven periods per octave

Generator Cents Comments
0\7 0
1\91 13.187
1\84 14.286 Absurdity
4\329 14.59 Absurdity
3\245 14.69
2\161 14.907
1\77 15.584 Septant
4\301 15.947 Septant
3\224 16.071 Septant
2\147 16.327 Septant
1\70 17.143
1\63 19.048 Sevond
2\119 20.168 Sevond
1\56 21.429 Sevond
1\49 24.49
1\42 28.571 Neutron
3\119 30.252 Neutron
5\196 30.612 Neutron
7\273 30.769 Neutron
2\77 31.169 Neutron
1\35 34.286 Redwood
2\63 38.095 Redwood
1\28 42.857 Redwood/Whitewood
3\77 46.753 Whitewood
2\49 48.980 Whitewood
3\70 51.429 Whitewood
1\21 57.143 Whitewood/Jamesbond/Austinpowers
4\77 62.338 Jamesbond/Austinpowers
3\56 64.286 Jamesbond/Austinpowers
5\91 65.934 Jamesbond/Austinpowers
2\35 68.571 Jamesbond/Austinpowers/Greenwood
5\84 71.429 Jamesbond/Austinpowers/Greenwood
3\49 73.469 Jamesbond/Austinpowers/Greenwood
4\63 76.190 Jamesbond/Austinpowers/Greenwood
1\14 85.714 Jamesbond/Austinpowers/Greenwood

Eight periods per octave

Generator Cents Comments
0\8 0
1\480 2.5
1\472 2.542 Octium
4\1872 2.564 Octium
7\3272 2.567 Octium
3\1400 2.571 Octium
1\464 2.586
…
1\96 12.5
1\88 13.635
1\80 15
2\152 15.789 Octoid
3\224 16.071 Octoid
1\72 16.667 Octoid
1\64 18.75
1\56 21.429
1\48 25
1\40 30
2\72 33.333
1\32 37.5 Semidim
3\88 40.909 Semidim
2\56 42.857 Semidim
3\80 45 Semidim
4\104 46.154 Semidim
5\128 46.875 Semidim
6\152 47.368 Semidim
7\176 47.727 Semidim
8\200 48 Semidim
9\224 48.214 Semidim/Octant
28\696 48.276 Semidim/Octant
19\472 48.305 Semidim/Octant
10\248 48.387 Semidim
1\24 50 Semidim
2\40 60
1\16 75

Nine periods per octave

Generator Cents Comments
0\9 0
1\72 16.667 Enneaportent
4\279 17.204 Enneaportent
3\207 17.391 Enneaportent
2\135 17.778 Enneaportent
1\63 19.048 Enneaportent
1\54 22.222
1\45 26.667
1\36 33.333 No-five tritrizo
4\135 35.556 No-five tritrizo
3\99 36.364 No-five tritrizo
2\63 38.095 Niner
3\90 40 Niner
1\27 44.444 Niner
4\99 48.485 Ennealimmal
7\171 49.123 Ennealimmal
3\72 50 Ennealimmal
20\477 50.314 Novemkleismic
17\405 50.370 Novemkleismic
14\333 50.451 Novemkleismic
11\261 50.575 Novemkleismic
8\189 50.794 Novemkleismic
5\117 51.282
2\45 53.333
1\18 66.667

Ten periods per octave

Generator Cents Comments
0\10 0
1\140 8.571 Decoid
2\270 8.888 Decoid
1\130 9.231 Decoid
1\120 10
1\110 10.909
1\100 12
2\190 12.632 Deca
1\90 13.333 Deca
1\80 15 Deca
1\70 17.143
1\60 20
1\50 24 Decimetra
4\190 25.263 Decimetra
7\330 25.455 Decimetra
17\800 25.5 Decimetra
10\470 25.532 Decimetra
3\140 25.714 Decimetra
2\90 26.667 Decimetra
1\40 30 Decic
3\110 32.727 Decic
2\70 34.286 Decic
4\170 28.235 Decic
3\100 36 Decic
1\30 40 Decic/Decal
3\80 45 Decal/Decistearn
8\210 45.714 Decal/Decistearn
13\340 45.882 Decal/Decistearn
18\470 45.957 Decal/Decistearn
23\600 46 Decal/Decistearn
5\130 46.154 Decal/Decistearn
2\50 48 Decistearn/Decavish
11\270 48.889 Decavish
9\220 49.091 Decavish
7\170 49.412 Decavish
5\120 50 Decavish
3\70 51.429 Decavish
4\90 53.333
5\110 54.545
6\130 55.385
1\20 60

Eleven periods per octave

Generator Cents Comments
0\11 0
1\55 21.818
1\44 27.273
2\77 31.169
1\33 36.364
3\88 40.909
2\55 42.636 Hendecatonic
3\77 46.753 Hendecatonic
7\176 47.727 Hendecatonic
11\275 48 Hendecatonic
4\99 48.485 Hendecatonic/Cohendecatonic
9\220 49.091 Cohendecatonic
14\341 49.267 Cohendecatonic
5\121 49.587 Cohendecatonic
6\143 50.350
7\165 50.909
8\187 51.337 Undeka
9\209 51.675 Undeka
10\231 51.948 Undeka
11\253 52.174 Undeka
1\22 54.545 Undeka

Twelve periods per octave

See also: Compton family
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

Retrieved from "https://en.xen.wiki/index.php?title=Map_of_rank-2_temperaments&oldid=221861"