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.

Todo: update

One period per octave

  • father [⟨1 0 4], ⟨0 1 -1]];
    • mother [⟨1 0 4 6], ⟨0 1 -1 -2]];
    • father [⟨1 0 4 -2], ⟨0 1 -1 3]];
  • mavila [⟨1 0 7], ⟨0 1 -3]];
    • pelogic [⟨1 0 7 9], ⟨0 1 -3 -4]];
    • armodue [⟨1 0 7 -5], ⟨0 1 -3 5]];
    • mavila [⟨1 0 7 20], ⟨0 1 -3 -11]];
    • hornbostel [⟨1 0 7 -16], ⟨0 1 -3 12]];
  • meantone [⟨1 0 -4], ⟨0 1 4]];
    • dominant [⟨1 0 -4 6], ⟨0 1 4 -2]];
      • arnold [⟨1 0 -4 6 5], ⟨0 1 4 -2 -1]];
      • dominant [⟨1 0 -4 6 13], ⟨0 1 4 -2 -6]];
      • domineering [⟨1 0 -4 6 -6], ⟨0 1 4 -2 6]];
        • dominatrix [⟨1 0 -4 6 -6 -1], ⟨0 1 4 -2 6 3]];
    • sharptone [⟨1 0 -4 -2], ⟨0 1 4 3]];
      • meanertone [⟨1 0 -4 -2 5], ⟨0 1 4 3 -1]];
    • flattone [⟨1 0 -4 17], ⟨0 1 4 -9]];
      • flattone [⟨1 0 -4 17 -6], ⟨0 1 4 -9 6]];
    • meantone [⟨1 0 -4 -13], ⟨0 1 4 10]];
      • meanenneadecal [⟨1 0 -4 -13 -6], ⟨0 1 4 10 6]];
      • meanpop [⟨1 0 -4 -13 24], ⟨0 1 4 10 -13]];
      • meantone [⟨1 0 -4 -13 -25], ⟨0 1 4 10 18]];
  • avila [⟨1 0 -7], ⟨0 1 6]];
  • helmholtz [⟨1 0 15], ⟨0 1 -8]];
    • schism [⟨1 0 15 6], ⟨0 1 -8 -2]];
    • garibaldi [⟨1 0 15 25], ⟨0 1 -8 -14]];
      • cassandra [⟨1 0 15 25 -33], ⟨0 1 -8 -14 23]];
        • cassandra [⟨1 0 15 25 -33 -28], ⟨0 1 -8 -14 23 20]];
      • andromeda [⟨1 0 15 25 32], ⟨0 1 -8 -14 -18]];
        • andromeda [⟨1 0 15 25 32 37], ⟨0 1 -8 -14 -18 -21]];
    • grackle [⟨1 0 15 44], ⟨0 1 -8 -26]];
    • pontiac, infraschismic [⟨1 0 15 -59], ⟨0 1 -8 39]];
  • superpyth [⟨1 0 -12], ⟨0 1 9]];
    • superpyth [⟨1 0 -12 6], ⟨0 1 9 -2]];
      • superpyth [⟨1 0 -12 6 -22], ⟨0 1 9 -2 16]];
      • suprapyth [⟨1 0 -12 6 13], ⟨0 1 9 -2 -6]];
  • quasisuper [⟨1 0 23 6], ⟨0 1 -13 -2]];
  • leapday [⟨1 0 -31 -21 -14 -9], ⟨0 1 21 15 11 8]];
  • kwai [⟨1 0 -50 -40], ⟨0 1 33 27]];
    • kwai [⟨1 0 -50 -40 32], ⟨0 1 33 27 -18]];
  • undecental [⟨1 0 61 71], ⟨0 1 -37 -43]];
  • counterschismic [⟨1 0 -69], ⟨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]];
    • neutrominant [⟨1 1 0 4 2], ⟨0 2 8 -4 5]];
      • neutrominant [⟨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 0 0], ⟨0 2 3]];
    • beep [⟨1 0 0 2], ⟨0 2 3 1]];
      • pentoid [⟨1 0 0 2 5], ⟨0 2 3 1 -2]];
  • superpelog [⟨1 0 7 2], ⟨0 2 -6 1]];
  • godzilla [⟨1 0 -4 2], ⟨0 2 8 1]];
  • monzismic [⟨1 0 -27], ⟨0 2 37]];
  • gidorah [⟨1 1 2 3], ⟨0 3 2 -1]];
  • enipucrop [⟨1 2 2], ⟨0 3 -2]];
  • 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]];
  • pycnic [⟨1 0 6 -3], ⟨0 3 -7 11]];
  • 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 0 6 7], ⟨0 3 -7 -8]];
  • liese, gawel [⟨1 0 -4 -3], ⟨0 3 12 11]];
  • tricot [⟨1 0 -13], ⟨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]];
    • marvo [⟨1 5 12 29], ⟨0 6 17 46]];
  • 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]];
  • 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]];
  • sensi [⟨1 6 8], ⟨0 7 9]];
    • sensi [⟨1 6 8 11], ⟨0 7 9 13]];
      • sensor [⟨1 6 8 11 -6], ⟨0 7 9 13 -15]];
        • sensor [⟨1 6 8 11 -6 10], ⟨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 7 3], ⟨0 8 1]];
  • 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]];
        • valentino [⟨1 1 2 3 3 5], ⟨0 9 5 -3 7 -20]];
        • dwynwen [⟨1 1 2 3 3 2], ⟨0 9 5 -3 7 26]];
        • lupercalia [⟨1 1 2 3 3 3], ⟨0 9 5 -3 7 11]];
  • 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]];
  • mabila [⟨1 6 1], ⟨0 10 -3]];
  • myna [⟨1 9 9 8], ⟨0 10 9 7]];
    • myna [⟨1 9 9 8 22], ⟨0 10 9 7 25]];
      • myna [⟨1 9 9 8 22 0], ⟨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]];
  • doublethink [⟨1 0 3 1 3 2], ⟨0 14 -6 16 4 15]];
  • 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 13 -36], ⟨0 14 -47]];
  • hemithirds, luna [⟨1 4 2], ⟨0 15 -2]];
    • hemithirds [⟨1 4 2 2], ⟨0 15 -2 -5]];
      • hemithirds [⟨1 4 2 2 7], ⟨0 15 -2 -5 22]];
  • hemiwürschmidt [⟨1 15 4 7], ⟨0 16 2 5]];
    • hemiwürschmidt [⟨1 15 4 7 37], ⟨0 16 2 5 40]];
  • semisept [⟨1 12 6 12], ⟨0 17 6 15]];
  • vavoom [⟨1 0 4], ⟨0 17 -18]];
  • minortone [⟨1 16 32], ⟨0 17 35]];
    • mitonic [⟨1 16 32 -15], ⟨0 17 35 -21]];
  • casablanca [⟨1 12 10 5], ⟨0 19 14 4]];
    • casablanca [⟨1 12 10 5 4], ⟨0 19 14 4 1]];
  • 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 28 73], ⟨0 37 99]];
  • supermajor [⟨1 15 19 30], ⟨0 37 46 75]];
  • quasiorwell [⟨1 31 0 9], ⟨0 38 -3 8]];
  • semigamera [⟨1 6 10 3 12], ⟨0 46 80 2 89]];
  • gross [⟨1 45 -18], ⟨0 47 -22]];
  • pirate [⟨1 43 15], ⟨0 49 15]];
  • egads [⟨1 15 16], ⟨0 51 52]];

Two periods per octave

  • srutal [⟨2 0 11], ⟨0 1 -2]];
    • pajara [⟨2 0 11 12], ⟨0 1 -2 -2]];
      • pajaric [⟨2 0 11 12 7], ⟨0 1 -2 -2 0]];
      • pajarous [⟨2 0 11 12 -9], ⟨0 1 -2 -2 5]];
      • pajara [⟨2 0 11 12 26], ⟨0 1 -2 -2 -6]];
    • diaschismic [⟨2 0 11 31], ⟨0 1 -2 -8]];
      • diaschismic [⟨2 0 11 31 45 55], ⟨0 1 -2 -8 -12 -15]];
    • keen [⟨2 0 11 -23], ⟨0 1 -2 9]];
  • supersharp [⟨2 0 -5], ⟨0 1 3]];
  • bipelog [⟨2 0 14 15], ⟨0 1 -3 -3]];
  • injera [⟨2 0 -8 -7], ⟨0 1 4 4]];
    • injera [⟨2 0 -8 -7 -12], ⟨0 1 4 4 6]];
  • bischismic [⟨2 0 30 69], ⟨0 1 -8 -20]];
  • shrutar [⟨2 1 9 -2], ⟨0 2 -4 7]];
    • shrutar [⟨2 1 9 -2 8], ⟨0 2 -4 7 -1]];
      • srutar [⟨2 1 9 -2 8 15], ⟨0 2 -4 7 -1 -7]];
      • shrutar [⟨2 1 9 -2 8 -10], ⟨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 0 3 4], ⟨0 2 1 1]];
  • semihemi [⟨2 0 -35 -15 -47], ⟨0 2 25 13 34]];
  • lemba [⟨2 2 5 6], ⟨0 3 -1 -1]];
  • hedgehog [⟨2 1 1 2], ⟨0 3 5 5]];
  • doublewide [⟨2 1 3], ⟨0 4 3]];
    • doublewide [⟨2 1 3 4], ⟨0 4 3 3]];
      • doublewide [⟨2 1 3 4 8], ⟨0 4 3 3 -2]];
  • sesquiquartififths [⟨1 1 7 5], ⟨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]];
  • abigail [⟨2 7 13 -1 1 -2], ⟨0 11 24 -19 -17 -27]];
  • semiparakleismic [⟨2 10 12 24 19], ⟨0 13 14 35 23]];
  • hemigamera [⟨2 12 20 6 5], ⟨0 23 40 1 -5]];

Three periods per octave

  • augmented [⟨3 0 7], ⟨0 1 0]];
    • augene, tripletone [⟨3 0 7 18], ⟨0 1 0 -2]];
      • augene, tripletone [⟨3 0 7 18 20], ⟨0 1 0 -2 -2]];
    • august [⟨3 0 7 -1], ⟨0 1 0 2]];
  • misty [⟨3 0 26], ⟨0 1 -4]];
    • misty [⟨3 0 26 56], ⟨0 1 -4 -10]];
  • term [⟨3 0 45 94], ⟨0 1 -8 -18]];
  • semiaug [⟨3 1 7 -1], ⟨0 2 0 5]];
  • tritikleismic [⟨3 0 3 10], ⟨0 6 5 -2]];
  • mutt [⟨3 5 7 8], ⟨0 7 1 -12]];
  • ternary [⟨3 5 7 0], ⟨0 0 0 1]];

Four or more periods per octave

  • diminished [⟨4 0 3], ⟨0 1 1]];
    • diminished [⟨4 0 3 5], ⟨0 1 1 1]];
      • diminished [⟨4 0 3 5 14], ⟨0 1 1 1 0]];
      • demolished [⟨4 0 3 5 -5], ⟨0 1 1 1 3]];
  • blackwood [⟨5 8 0], ⟨0 0 1]];
  • hexe [⟨6 0 14 17], ⟨0 1 0 0]];
  • jamesbond [⟨7 11 16 0], ⟨0 0 0 1]];
    • jamesbond [⟨7 11 16 0 24], ⟨0 0 0 1 0]];
  • whitewood [⟨7 11 0], ⟨0 0 1]];
  • octoid [⟨8 1 3 3 16], ⟨0 3 4 5 3]];
  • ennealimmal [⟨9 1 1], ⟨0 2 3]];
    • ennealimmal [⟨9 1 1 12], ⟨0 2 3 2]];
      • ennealimmal [⟨9 1 1 12 -75], ⟨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 0 43 -4], ⟨0 1 -1 2]];
  • catler [⟨12 19 28 0], ⟨0 0 0 1]];
  • compton [⟨12 19 0], ⟨0 0 1]];
    • compton, waage [⟨12 19 0 -22], ⟨0 0 1 2]];
      • compton, duodecimal [⟨12 19 0 -22 -42], ⟨0 0 1 2 3]];
  • duodecim [⟨12 19 28 34 0], ⟨0 0 0 0 1]];
  • atomic [⟨12 0 161], ⟨0 1 -7]];
  • hemiennealimmal [⟨18 0 -1 22 48], ⟨0 2 3 2 1]];
  • enneadecal [⟨19 0 14], ⟨0 1 1]];
    • enneadecal [⟨19 0 14 -37], ⟨0 1 1 3]];
  • undevigintone [⟨19 30 44 53 0], ⟨0 0 0 0 1]];
  • icosidillic [⟨22 0 86 -8 111], ⟨0 1 -1 2 -1]];
  • vigintiduo [⟨22 35 51 62 0], ⟨0 0 0 0 1]];
  • mystery [⟨29 46 0 14 33 40], ⟨0 0 1 1 1 1]];
  • hemienneadecal [⟨38 0 28 -74 11], ⟨0 1 1 3 2]];
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