Proposed names for rank-2 temperaments

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Here is a list of some names that have been proposed for rank 2 temperaments. The name or names of the temperament is followed by the generator mapping, which represents the number of periods and generators of the temperament for each of the prime intervals (2 3 5 etc.)

See also pergen names.

One period per octave

  • father [<1 2 2], <0 -1 1]>
    • mother [<1 2 2 2], <0 -1 1 2]>
    • father [<1 2 2 4], <0 -1 1 -3]>
  • mavila [<1 2 1], <0 -1 3]>
    • pelogic [<1 2 1 1], <0 -1 3 4]>
    • armodue [<1 2 1 5], <0 -1 3 -5]>
    • mavila [<1 2 1 -2], <0 -1 3 11]>
    • hornbostel [<1 2 1 8], <0 -1 3 -12]>
  • meantone [<1 2 4], <0 -1 -4]>
    • dominant [<1 2 4 2], <0 -1 -4 2]>
      • arnold [<1 2 4 2 3], <0 -1 -4 2 1]>
      • dominant [<1 2 4 2 1], <0 -1 -4 2 6]>
      • domineering [<1 2 4 2 6], <0 -1 -4 2 -6]>
        • dominatrix [<1 2 4 2 6 5], <0 -1 -4 2 -6 -3]>
    • sharptone [<1 2 4 4], <0 -1 -4 -3]>
      • meanertone [<1 2 4 4 3], <0 -1 -4 -3 1]>
    • flattone [<1 2 4 -1], <0 -1 -4 9]>
      • flattone [<1 2 4 -1 6], <0 -1 -4 9 -6]>
    • meantone [<1 2 4 7], <0 -1 -4 -10]>
      • meanenneadecal [<1 2 4 7 6], <0 -1 -4 -10 -6]>
      • meanpop [<1 2 4 7 -2], <0 -1 -4 -10 13]>
      • meantone [<1 2 4 7 11], <0 -1 -4 -10 -18]>
  • helmholtz [<1 2 -1], <0 -1 8]>
    • schism [<1 2 -1 2], <0 -1 8 2]>
    • garibaldi [<1 2 -1 -3], <0 -1 8 14]>
      • garibaldi [<1 2 -1 -3 13], <0 -1 8 14 -23]>
        • garibaldi [<1 2 -1 -3 13 12], <0 -1 8 14 -23 -20]>
      • cassandra [<1 2 -1 -3 -4], <0 -1 8 14 18]>
        • cassandra [<1 2 -1 -3 -4 -5], <0 -1 8 14 18 21]>
    • grackle [<1 2 -1 -8], <0 -1 8 26]>
    • pontiac, infraschismic [<1 2 -1 19], <0 -1 8 -39]>
  • superpyth [<1 2 6], <0 -1 -9]>
    • superpyth [<1 2 6 2], <0 -1 -9 2]>
      • superpyth [<1 2 6 2 10], <0 -1 -9 2 -16]>
      • suprapyth [<1 2 6 2 1], <0 -1 -9 2 6]>
  • quasisuper [<1 2 -3 2], <0 -1 13 2]>
  • leapday [<1 2 11 9 8 7], <0 -1 -21 -15 -11 -8]>
  • kwai [<1 2 16 14], <0 -1 -33 -27]>
    • kwai [<1 2 16 14 -4], <0 -1 -33 -27 18]>
  • undecental [<1 2 -13 -15], <0 -1 37 43]>
  • counterschismic [<1 2 21], <0 -1 -45]>
  • dicot [<1 1 2], <0 2 1]>
    • dicot [<1 1 2 2], <0 2 1 3]>
    • sharp [<1 1 2 1], <0 2 1 6]>
  • mohajira, semififths [<1 1 0 6], <0 2 8 -11]>
    • mohajira <1 1 0 6 2], <0 2 8 -11 5]>
    • maqamic [<1 1 0 4 2], <0 2 8 -4 5]>
      • maqamic <1 1 0 4 2 4], <0 2 8 -4 5 -1]>
  • beatles [<1 1 5 4], <0 2 -9 -4]>
  • karadeniz [<1 1 7 11 2], <0 2 -16 -28 5]>
  • hemififths [<1 1 -5 -1], <0 2 25 13]>
  • bug [<1 2 3], <0 -2 -3]>
    • beep [<1 2 3 3], <0 -2 -3 -1]>
      • pentoid [<1 2 3 3 3], <0 -2 -3 -1 2]>
  • superpelog [<1 2 1 3], <0 -2 6 -1]>
  • godzilla [<1 2 4 3], <0 -2 -8 -1]>
  • monzismic [<1 2 10], <0 -2 -37]>
  • gidorah [<1 1 2 3], <0 3 2 -1]>
  • penta [<1 1 2 2], <0 3 2 4]>
  • laconic [<1 1 1], <0 3 7]>
    • gorgo [<1 1 1 3], <0 3 7 -1]
      • gorgo [<1 1 1 3 1| <0 3 7 -1 13|>
        • gorgo [<1 1 1 3 1 2| <0 3 7 -1 13 9|>
      • spartan [<1 1 1 3 5| <0 3 7 -1 -8|>
  • mothra, cynder [<1 1 0 3], <0 3 12 -1]>
    • mothra, cynder [<1 1 0 3 5], <0 3 12 -1 -8]>
  • rodan [<1 1 -1 3], <0 3 17 -1]>
    • rodan[<1 1 -1 3 6], <0 3 17 -1 -13]>
      • rodan [<1 1 -1 3 6 8], <0 3 17 -1 -13 -22]>
      • aerodactyl [<1 1 -1 3 6 -1], <0 3 17 -1 -13 24]>
  • guiron [<1 1 7 3], <0 3 -24 -1]>
  • porcupine [<1 2 3], <0 -3 -5]>
    • hystrix [<1 2 3 3], <0 -3 -5 -1]>
    • porcupine [<1 2 3 2], <0 -3 -5 6]>
      • porcupine [<1 2 3 2 4], <0 -3 -5 6 -4]>
    • opossum, pentadecimal [<1 2 3 4], <0 -3 -5 -9]>
      • opossum [<1 2 3 4 4], <0 -3 -5 -9 -4]>
      • coendou [<1 2 3 1 4 3], <0 -3 -5 13 -4 5]>
      • porcupinefish [<1 2 3 2 4 6], <0 -3 -5 6 -4 -17]>
  • ammonite [<1 5 8 10], <0 -9 -15 -19]>
  • triton [<1 3 -1 -1], <0 -3 7 8]>
  • liese, gawel [<1 3 8 8], <0 -3 -12 -11]>
  • tricot [<1 3 16], <0 -3 -29]>
  • tetracot [<1 1 1], <0 4 9]>
    • monkey [<1 1 1 5], <0 4 9 -15]>
    • bunya [<1 1 1 -1], <0 4 9 26]>
  • vulture [<1 0 -6], <0 4 21]>
    • buzzard [<1 0 -6 4], <0 4 21 -3]>
      • buzzard [<1 0 -6 4 -12 -7], <0 4 21 -3 39 27]>
  • sesquiquartififths [<1 1 7 5], <0 4 -32 -15]>
  • semihemififths [<1 1 -5 -1 8], <0 4 50 26 -31]>
  • sidi [<1 3 3 6], <0 -4 -2 -9]>
  • negri [<1 2 2], <0 -4 3]>
    • negri [<1 2 2 3], <0 -4 3 -2]>
      • negri [<1 2 2 3 4| <0 -4 3 -2 -5|]
        • negri [<1 2 2 3 4 4| <0 -4 3 -2 -5 -3|]
      • negril [<1 2 2 3 2| <0 -4 3 -2 14|]
        • negril [<1 2 2 3 2 4], <0 -4 3 -2 14 -3]>
  • sentinel [<1 3 -3 6], <0 -4 15 -9]>
  • squares [<1 3 8 6], <0 -4 -16 -9]>
  • magic [<1 0 2], <0 5 1]>
    • muggles [<1 0 2 5], <0 5 1 -7]>
    • magic [<1 0 2 -1], <0 5 1 12]>
      • magic [<1 0 2 -1 6], <0 5 1 12 -8]>
  • passion [<1 2 2], <0 -5 4]>
    • passion [<1 2 2 2], <0 -5 4 10]>
  • ripple [<1 2 3], <0 -5 -8]>
    • ripple [<1 2 3 3], <0 -5 -8 -2]>
  • tritonic [<1 4 -3 -3], <0 -5 11 12]>
    • tritonic [<1 4 -3 -3 2], <0 -5 11 12 3]>
  • amity [<1 3 6], <0 -5 -13]>
    • amity [<1 3 6 -2], <0 -5 -13 17]>
      • hitchcock, amity [<1 3 6 -2 6], <0 -5 -13 17 -9]>
        • hitchcock [<1 3 6 -2 6 2], <0 -5 -13 17 -9 6]>
  • gravity [<1 5 12], <0 -6 -17]>
  • hanson [<1 0 1], <0 6 5]>
    • keemun [<1 0 1 2], <0 6 5 3]>
      • keemun [<1 0 1 2 4], <0 6 5 3 -2]>
    • catakleismic [<1 0 1 -3], <0 6 5 22]>
      • catakleismic [<1 0 1 -3 9], <0 6 5 22 -21]>
        • catakleismic [<1 0 1 -3 9 0], <0 6 5 22 -21 14]>
    • countercata [<1 0 1 11], <0 6 5 -31]>
  • ampersand [<1 1 3], <0 6 -7]>
    • miracle[<1 1 3 3], <0 6 -7 -2]>
      • miracle [<1 1 3 3 2], <0 6 -7 -2 15]>
  • marvo [<1 -1 -5 -17], <0 6 17 46]>
  • nautilus [<1 2 3 3], <0 -6 -10 -3]>
  • orson [<1 0 3], <0 7 -3]>
    • orwell [<1 0 3 1], <0 7 -3 8]>
      • orwell [<1 0 3 1 3], <0 7 -3 8 2]>
        • orwell [<1 0 3 1 3 8], <0 7 -3 8 2 -19]>
        • blair [<1 0 3 1 3 3], <0 7 -3 8 2 3]>
        • winston [<1 0 3 1 3 1], <0 7 -3 8 2 12]>
        • doublethink [<1 0 3 1 3 2], <0 14 -6 16 4 15]>
  • sensi [<1 -1 -1], <0 7 9]>
    • sensi [<1 -1 -1 -2], <0 7 9 13]>
      • sensor [<1 -1 -1 -2 9], <0 7 9 13 -15]>
        • sensor [<1 -1 -1 -2 9 0], <0 7 9 13 -15 10]>
  • sensis [<1 6 8 11 6| <0 -7 -9 -13 -4|] ?
    • sensis [<1 6 8 11 6 10| <0 -7 -9 -13 -4 -10|] ?
  • sensus [<1 6 8 11 23| <0 -7 -9 -13 -31|] ?
    • sensus [<1 6 8 11 23 10| <0 -7 -9 -13 -31 -10|] ?
  • roman [<1 4 3 -1 0 3], <0 -7 -2 11 10 2]>
  • octacot [<1 1 1 2], <0 8 18 11]>
  • würschmidt [<1 -1 2], <0 8 1]>
    • worschmidt [<1 -1 2 7], <0 8 1 -13]>
    • wurschmidt [<1 -1 2 -3], <0 8 1 18]>
    • whirrschmidt [<1 7 3 38], <0 -8 -1 -52]>
  • valentine [<1 1 2], <0 9 5]>
    • valentine[<1 1 2 3], <0 9 5 -3]>
      • valentine [<1 1 2 3 3], <0 9 5 -3 7]>
  • escapade [<1 2 2], <0 -9 7]>
    • escapade [<1 2 2 3], <0 -9 7 -4]>
    • escaped [<1 2 2 4], <0 -9 7 -26]>
  • superkleismic [<1 4 5 2], <0 -9 -10 3]>
    • superkleismic [<1 4 5 2 4], <0 -9 -10 3 -2]>
  • myna [<1 -1 0 1], <0 10 9 7]>
    • myna [<1 -1 0 1 -3], <0 10 9 7 25]>
      • myna [<1 -1 0 1 -3 5], <0 10 9 7 25 -5]>
  • sycamore [<1 1 2], <0 11 6]>
    • sycamore [<1 1 2 2], <0 11 6 15]>
  • septimin [<1 4 1 5], <0 -11 6 -10]>
  • nusecond [<1 3 4 5], <0 -11 -13 -17]>
  • quartonic [<1 2 3 3], <0 -11 -18 -5]>
  • hemikleismic [<1 0 1 4], <0 12 10 -9]>
  • clyde [<1 6 6 12], <0 -12 -10 -25]>
  • bohpier [<1 0 0 0], <0 13 19 23]>
  • gammic [<1 1 2], <0 20 11]>
    • gammic [<1 1 2 0], <0 20 11 96]>
  • neptune [<1 21 13 13], <0 -40 -22 -21]>
  • pluto [<1 5 15 15 2], <0 7 26 25 -3]>
  • twothirdtonic [<1 3 2 4 4], <0 -13 3 -11 -5]>
    • twothirdtonic [<1 3 2 4 4 5], <0 -13 3 -11 -5 -12]>
  • slender [<1 2 2 3], <0 -13 10 -6]>
    • slender [<1 2 2 3 4], <0 -13 10 -6 -17]>
  • parakleismic [<1 5 6], <0 -13 -14]>
    • parakleismic [<1 5 6 12], <0 -13 -14 -35]>
  • fortune [<1 -1 11], <0 14 -47]>
  • hemithirds, luna [<1 4 2], <0 -15 2]>
  • hemiwürschmidt [<1 -1 2 2], <0 16 2 5]>
    • hemiwürschmidt [<1 -1 2 2 -3], <0 16 2 5 40]>
  • semisept [<1 -5 0 -3], <0 17 6 15]>
  • vavoom [<1 0 4], <0 17 -18]>
  • minortone [<1 -1 -3], <0 17 35]>
    • mitonic [<1 -1 -3 6], <0 17 35 -21]>
  • casablanca [<1 -7 -4 1], <0 19 14 4]>
  • tertiaseptal [<1 3 2 3], <0 -22 5 -3]>
  • grendel, voodoo [<1 9 2 7], <0 -23 1 -13]>
  • gamera [<1 6 10 3], <0 -23 -40 -1]>
  • astro [<1 5 1], <0 -31 12]>
  • semihemiwürschmidt [<1 15 4 7 24], <0 -32 -4 -10 -49]>
  • whoosh [<1 17 14], <0 -33 -25]>
  • yarman [<1 2 3 4 4], <0 -33 -54 -95 -43]>
  • senior [<1 11 19], <0 -35 -62]>
  • raider [<1 -9 -26], <0 37 99]>
  • supermajor [<1 15 19 30], <0 -37 -46 -75]>
  • quasiorwell [<1 -7 3 1], <0 38 -3 8]>
  • semigamera [<1 6 10 3 12], <0 -46 -80 -2 -89]>
  • gross [<1 -2 4], <0 47 -22]>
  • pirate [<1 -6 0], <0 49 15]>
  • egads [<1 15 16], <0 -51 -52]>
  • avila [<1 1 -1], <0 1 6]>
  • mabila [<1 6 1], <0 -10 3]>
  • pycnic [<1 3 -1 8], <0 -3 7 -11]>
  • enipucrop [<1 2 2], <0 -3 2]>

Two periods per octave

  • srutal [<2 3 5], <0 1 -2]>
    • pajara [<2 3 5 6], <0 1 -2 -2]>
      • pajaric [<2 3 5 6 7], <0 1 -2 -2 0]>
      • pajarous [<2 3 5 6 6], <0 1 -2 -2 5]>
      • pajara [<2 3 5 6 8], <0 1 -2 -2 -6]>
    • diaschismic [<2 3 5 7], <0 1 -2 -8]>
      • diaschismic [<2 3 5 7 9 10], <0 1 -2 -8 -12 -15]>
    • keen [<2 3 5 4], <0 1 -2 9]>
  • supersharp [<2 3 4], <0 1 3]>
    • octokaidecal [<2 3 4 5], <0 1 3 3]>
  • bipelog [<2 3 5 6], <0 1 -3 -3]>
  • injera [<2 3 4 5], <0 1 4 4]>
    • injera [<2 3 4 5 6], <0 1 4 4 6]>
  • bischismic [<2 3 6 9], <0 1 -8 -20]>
  • shrutar [<2 3 5 5], <0 2 -4 7]>
    • shrutar [<2 3 5 5 7], <0 2 -4 7 -1]>
      • srutar [<2 3 5 5 7 8], <0 2 -4 7 -1 -7]>
      • shrutar [<2 3 5 5 7 6], <0 2 -4 7 -1 16]>
  • echidna [<2 1 9 2], <0 3 -6 5]>
    • echidna [<2 1 9 2 12], <0 3 -6 5 -7]>
  • decimal [<2 4 5 6], <0 -2 -1 -1]>
  • semihemi [<2 4 15 11 21], <0 -2 -25 -13 -34]>
  • lemba [<2 2 5 6], <0 3 -1 -1]>
  • hedgehog [<2 4 6 7], <0 -3 -5 -5]>
  • doublewide [<2 5 6], <0 -4 -3]>
  • sesquiquartififths [<2 2 14 10], <0 4 -32 -15]>
  • hemiamity [<2 1 -1 13 13], <0 5 13 -17 -14]>
  • wizard [<2 1 5 2], <0 6 -1 10]>
    • wizard [<2 1 5 2 8], <0 6 -1 10 -3]>
  • unidec [<2 5 8 5], <0 -6 -11 2]>
    • unidec [<2 5 8 5 6], <0 -6 -11 2 3]>
      • hendec [<2 5 8 5 6 8], <0 -6 -11 2 3 -2]>
  • harry [<2 4 7 7], <0 -6 -17 -10]>
  • vishnu [<2 4 5], <0 -7 -3]>
    • vishnu [<2 4 5 10], <0 -7 -3 -37]>
  • kwazy [<2 1 6], <0 8 -5]>
    • bisupermajor [<2 1 6 1 8], <0 8 -5 17 -4]>
  • semiparakleismic [<2 -3 -2 -11 -4], <0 13 14 35 23]>
  • hemigamera [<2 12 20 6], <0 -23 -40 -1]>
    • hemigamera [<2 12 20 6 5], <0 -23 -40 -1 5]>
  • abigail [<2 7 13 -1 1 -2], <0 -11 -24 19 17 27]>

Three periods per octave

  • augmented [<3 5 7], <0 -1 0]>
    • augene, tripletone [<3 5 7 8], <0 -1 0 2]>
      • augene, tripletone [<3 5 7 8 10], <0 -1 0 2 2]>
    • august [<3 5 7 9], <0 -1 0 -2]>
  • misty [<3 5 6], <0 -1 4]>
    • misty [<3 5 6 6], <0 -1 4 10]>
  • term [<3 5 5 4], <0 -1 8 18]>
  • semiaug [<3 5 7 9], <0 -2 0 -5]>
  • tritikleismic [<3 6 8 8], <0 -6 -5 2]>
  • mutt [<3 5 7 8], <0 -7 -1 12]>
  • ternary [<3 5 7 8], <3 5 7 9]>

Four or more periods per octave

  • diminished [<4 6 9], <0 1 1]>
    • diminished [<4 6 9 11], <0 1 1 1]>
      • diminished [<4 6 9 11 14], <0 1 1 1 0]>
      • demolished [<4 6 9 11 13], <0 1 1 1 3]>
  • blackwood [<5 8 12], <0 0 -1]>
    • blacksmith [<5 8 12 14], <0 0 -1 0]>
  • hexe [<6 10 14 17], <0 -1 0 0]>
  • jamesbond [<7 11 16 20], <0 0 0 -1]>
    • jamesbond [<7 11 16 20 24], <0 0 0 -1 0]>
  • whitewood [<7 11 16], <0 0 1]>
  • octoid [<8 13 19 23 28], <0 -3 -4 -5 -3]>
  • ennealimmal [<9 15 22], <0 -2 -3]>
    • ennealimmal [<9 15 22 26], <0 -2 -3 -2]>
      • ennealimmal [<9 15 22 26 37], <0 -2 -3 -2 -16]>
  • decoid [<10 0 47 36| <0 2 -3 -1|]
    • decoid [<10 0 47 36 98| <0 2 -3 -1 -8|]
      • decoid [<10 0 47 36 98 37| <0 2 -3 -1 -8 0|]
  • hendecatonic [<11 17 26 30], <0 1 -1 2]>
  • catler [<12 19 28 34], <0 0 0 -1]>
  • compton [<12 19 28], <0 0 -1]>
    • compton, waage [<12 19 28 34], <0 0 -1 -2]>
      • compton, duodecimal [<12 19 28 34 42], <0 0 -1 -2 -3]>
  • duodecim [<12 19 28 34 42], <0 0 0 0 -1]>
  • atomic [<12 19 28], <0 1 -7]>
  • hemiennealimmal [<18 28 41 50 62], <0 2 3 2 1]>
  • enneadecal [<19 30 44], <0 1 1]>
    • enneadecal [<19 30 44 53], <0 1 1 3]>
  • undevigintone [<19 30 44 53 66], <0 0 0 0 -1]>
  • icosidillic [<22 35 51 62 76], <0 -1 1 -2 1]>
  • vigintiduo [<22 35 51 62 76], <0 0 0 0 1]>
  • mystery [<29 46 67 81 100 107], <0 0 1 1 1 1]>
  • hemienneadecal [<38 60 88 106 131], <0 1 1 3 2]>
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