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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












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










3\50


72.000







1\16





75.000








2\30




80.000









3\44



81.818










4\58


82.759
Harry










5\72

83.333
Harry





1\14






85.714







2\26





92.308
Injera







3\38




94.737
Injera




1\12







100.000
Srutal/pajara/injera







4\46




104.348
Srutal/pajara/diaschismic






3\34





105.882
Srutal/pajara/diaschismic





2\22






109.091
Srutal/pajara



1\10








120.000





2\18







133.333
Octokaidecal





3\26






138.462







4\34





141.176
Fifive


1\8









150.000






4\30






160.000





3\22







163.636
Hedgehog/echidna






8\58





165.517
Hedgehog/echidna





5\36






166.667
Hedgehog/echidna



2\14








171.429





3\20







180.000







7\46





182.609
Unidec/hendec







11\72




183.333
Unidec/hendec





4\26






184.615







5\32





187.500








6\38




189.474









7\44



190.909










8\50


192.000











9\56

192.857












10\62
193.544


1\6










200.000












11\64
206.250











10\58

206.897










9\52


207.692









8\46



208.696








7\40




210.000







6\34





211.765






5\28






214.286







9\50





216.000








13\72




216.667
Antikythera/astrology/wizard




4\22







218.182
Antikythera/astrology



3\16








225.000






8\42






228.571





5\26







230.769
Lemba





7\36






233.333
Lemba






9\46





234.783
Echidnic


2\10









240.000
Decimal





7\34






247.059
Decimal




5\24







250.000
Decimal



3\14








257.143





4\18







266.667






5\22






272.727
Doublewide







11\48




275.000
Doublewide






6\26





276.923
Doublewide







7\30




280.000









8/34



282.353










9/38


284.2105











10/42

285.714












11\46
286.9565

1\4











300.000

Three periods per octave

Generator
Cents
Comments
0\3








0









1\30
40.000








1\27

44.444
Semiaug








2\51
47.059
Semiaug






1\24


50.000
Semiaug





1\21



57.143





1\18




66.667




1\15





80.000









6\87
82.759
Tritikleismic







5\72

83.333
Tritikleismic






4\57


84.2105






3\42



85.714





2\27




88.889
Augmented/augene


1\12






100.000
Augmented/augene/august




3\33




109.091
Augmented/august



2\21





114.286





3\30




120.000






4\39



123.077







5\48


125.000








6\57

126.316









7\66
127.273


1\9







133.333









8\69
139.134








7\60

140.000







6\51


141.176






5\42



142.857





4\33




145.4545




3\24





150.000
Triforce


2\15






160.000




3/21





171.429





4/27




177.778






5/33



181.818







6\39


184.615








7\45

186.667









8\51
118.235

1\6








200.000

Four periods per octave

Generator
Cents
Comments
0\4

















0


















1\76
15.78947

















1\72

16.6
Quadritikleismic

















2\140
17.14286
















1\68


17.64706















1\64



18.75














1\60




20













1\56





21.42857












1\52






23.06792











1\48







25










1\44








27.27









1\40









30








1\36










33.3







1\32











37.5






1\28












42.85714





1\24













50




1\20














60



1\16















75
Diminished



2\28














85.714285





3\40













90






4\52












92.30769







5\64











93.75








6\76










94.73684









7\88









95.45










8\100








96











9\112







96.42857












10\124






96.77419













11\136





97.08852














12\148




97.297















13\160



97.5
















14\172


97.67442

















15\184

97.82609


















16\196
97.95918


1\12
















100
Diminished

















17\200
102

















16\188

102.12766
















15\176


102.27















14\164



102.43902














13\152




102.63158













12\140





102.85714












11\128






103.125











10\116







103.448275










9\104








103.84615









8\92









104.34783








7\80










105







6\68











105.88235
Bidia





5\56












107.14286





4\44













109.09




3\32














112.5



2\20















120




3\28














128.57143





4\36













133.3






5\44












136.36







6\52











138.46154








7\60










140









8\68









141.17646










9\76








142.10526











10\84







142.85714












11\92






143.47826













12\100





144














13\108




144.4















14\116



144.82759
















15\124


145.16129

















16\132

145.45


















17\140
145.714285

1\8

















150

Five periods per octave

  • Blackwood/blacksmith - The prime 3, and in blacksmith also 7, is represented using 5edo. The generator gets you to all intervals of 5.
  • Elderthing - generator of phi. Two generators up to 3, two down to 7, other primes are more complex. (One generator up or one down are ambiguous 13.)

Six periods per octave

  • Hexe - The 2.5.7 subgroup is represented using 6edo, and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to 12edo.

Seven periods per octave

  • Whitewood - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5.
  • Jamesbond/septimal - The 5-limit (and in septimal the prime 11) is represented using 7edo, and the generator is only used for intervals of 7.
  • Sevond - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.
  • Absurdity - A complex temperament (perhaps "absurdly" so).

Eight periods per octave

  • Octoid - 16-cent generator, sub-cent accuracy.

Nine periods per octave

  • Ennealimmal - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate.

Twelve periods per octave

See also: Pythagorean family
Temperaments in this family are interesting because they can be thought of as 12edo with microtonal alterations.
  • Compton - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called waage), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of 72edo might make this more concrete.
  • Catler - 5-limit as in 12edo; intervals of 7 are off by one generator.
  • Atomic - Does not temper out the schisma, so 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.