Proposed names for rank-2 temperaments: Difference between revisions

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Here is a list of some names that have been proposed for rank 2 [[temperaments|temperaments]]. The name or names of the temperament is followed by the generator mapping, which represents the number of periods and [[generator|generator]]s of the temperament for each of the [[prime_interval|prime interval]]s (2 3 5 etc.)
Here is a list of some names that have been proposed for [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]]. The name or names of the temperament is followed by the generator mapping, which represents the number of periods and [[generator]]s of the temperament for each of the [[prime interval]]s (2 3 5 etc.)


See also [[pergen|pergen names]].
{{Todo|inline=1| update }}


=One period per octave=
== One period per octave ==
* father [<1 2 2], <0 -1 1]>
* [[father]] [{{val| 1 0 4 }}, {{val| 0 1 -1}}];
** mother [<1 2 2 2], <0 -1 1 2]>
** mother [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2}}];
** father [<1 2 2 4], <0 -1 1 -3]>
** father [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3}}];
* mavila [<1 2 1], <0 -1 3]>
* [[mavila]] [{{val| 1 0 7 }}, {{val| 0 1 -3}}];
** pelogic [<1 2 1 1], <0 -1 3 4]>
** [[pelogic]] [{{val| 1 0 7 9 }}, {{val| 0 1 -3 -4}}];
** armodue [<1 2 1 5], <0 -1 3 -5]>
** [[armodue (temperament)|armodue]] [{{val| 1 0 7 -5 }}, {{val| 0 1 -3 5}}];
** mavila [<1 2 1 -2], <0 -1 3 11]>
** mavila [{{val| 1 0 7 20 }}, {{val| 0 1 -3 -11}}];
** hornbostel [<1 2 1 8], <0 -1 3 -12]>
** hornbostel [{{val| 1 0 7 -16 }}, {{val| 0 1 -3 12}}];
* [[Meantone_family|meantone]] [<1 2 4], <0 -1 -4]>
* [[meantone]] [{{val| 1 0 -4 }}, {{val| 0 1 4}}];
** dominant [<1 2 4 2], <0 -1 -4 2]>
** [[dominant (temperament)|dominant]] [{{val| 1 0 -4 6 }}, {{val| 0 1 4 -2}}];
*** arnold [<1 2 4 2 3], <0 -1 -4 2 1]>
*** arnold [{{val| 1 0 -4 6 5 }}, {{val| 0 1 4 -2 -1}}];
*** dominant [<1 2 4 2 1], <0 -1 -4 2 6]>
*** dominant [{{val| 1 0 -4 6 13 }}, {{val| 0 1 4 -2 -6}}];
*** domineering [<1 2 4 2 6], <0 -1 -4 2 -6]>
*** domineering [{{val| 1 0 -4 6 -6 }}, {{val| 0 1 4 -2 6}}];
**** dominatrix [<1 2 4 2 6 5], <0 -1 -4 2 -6 -3]>
** [[sharptone]] [{{val| 1 0 -4 -2 }}, {{val| 0 1 4 3}}];
** sharptone [<1 2 4 4], <0 -1 -4 -3]>
*** meanertone [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1}}];
*** meanertone [<1 2 4 4 3], <0 -1 -4 -3 1]>
** [[flattone]] [{{val| 1 0 -4 17 }}, {{val| 0 1 4 -9}}];
** flattone [<1 2 4 -1], <0 -1 -4 9]>
*** flattone [{{val| 1 0 -4 17 -6 }}, {{val| 0 1 4 -9 6}}];
*** flattone [<1 2 4 -1 6], <0 -1 -4 9 -6]>
** meantone [{{val| 1 0 -4 -13 }}, {{val| 0 1 4 10}}];
** meantone [<1 2 4 7], <0 -1 -4 -10]>
*** meanenneadecal [{{val| 1 0 -4 -13 -6 }}, {{val| 0 1 4 10 6}}];
*** meanenneadecal [<1 2 4 7 6], <0 -1 -4 -10 -6]>
*** meanpop [{{val| 1 0 -4 -13 24 }}, {{val| 0 1 4 10 -13}}];
*** meanpop [<1 2 4 7 -2], <0 -1 -4 -10 13]>
*** meantone [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18}}];
*** meantone [<1 2 4 7 11], <0 -1 -4 -10 -18]>
* [[avila]] [{{val| 1 0 -7 }}, {{val| 0 1 6}}];
* [[Schismatic_family|helmholtz]] [<1 2 -1], <0 -1 8]>
* [[helmholtz (temperament)|helmholtz]] [{{val| 1 0 15 }}, {{val| 0 1 -8}}];
** schism [<1 2 -1 2], <0 -1 8 2]>
** schism [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2}}];
** garibaldi [<1 2 -1 -3], <0 -1 8 14]>
** garibaldi [{{val| 1 0 15 25 }}, {{val| 0 1 -8 -14}}];
*** garibaldi [<1 2 -1 -3 13], <0 -1 8 14 -23]>
*** cassandra [{{val| 1 0 15 25 -33 }}, {{val| 0 1 -8 -14 23}}];
**** garibaldi [<1 2 -1 -3 13 12], <0 -1 8 14 -23 -20]>
**** cassandra [{{val| 1 0 15 25 -33 -28 }}, {{val| 0 1 -8 -14 23 20}}];
*** cassandra [<1 2 -1 -3 -4], <0 -1 8 14 18]>
*** andromeda [{{val| 1 0 15 25 32 }}, {{val| 0 1 -8 -14 -18}}];
**** cassandra [<1 2 -1 -3 -4 -5], <0 -1 8 14 18 21]>
**** andromeda [{{val| 1 0 15 25 32 37 }}, {{val| 0 1 -8 -14 -18 -21}}];
** grackle [<1 2 -1 -8], <0 -1 8 26]>
** grackle [{{val| 1 0 15 44 }}, {{val| 0 1 -8 -26}}];
** pontiac, infraschismic [<1 2 -1 19], <0 -1 8 -39]>
** [[pontiac]], infraschismic [{{val| 1 0 15 -59 }}, {{val| 0 1 -8 39}}];
* superpyth [<1 2 6], <0 -1 -9]>
* [[superpyth]] [{{val| 1 0 -12 }}, {{val| 0 1 9}}];
** superpyth [<1 2 6 2], <0 -1 -9 2]>
** superpyth [{{val| 1 0 -12 6 }}, {{val| 0 1 9 -2}}];
*** superpyth [<1 2 6 2 10], <0 -1 -9 2 -16]>
*** superpyth [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16}}];
*** suprapyth [<1 2 6 2 1], <0 -1 -9 2 6]>
*** suprapyth [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6}}];
* quasisuper [<1 2 -3 2], <0 -1 13 2]>
* [[quasisuper]] [{{val| 1 0 23 6 }}, {{val| 0 1 -13 -2}}];
* leapday [<1 2 11 9 8 7], <0 -1 -21 -15 -11 -8]>
* [[leapday]] [{{val| 1 0 -31 -21 -14 -9 }}, {{val| 0 1 21 15 11 8}}];
* kwai [<1 2 16 14], <0 -1 -33 -27]>
* [[kwai]] [{{val| 1 0 -50 -40 }}, {{val| 0 1 33 27}}];
** kwai [<1 2 16 14 -4], <0 -1 -33 -27 18]>
** kwai [{{val| 1 0 -50 -40 32 }}, {{val| 0 1 33 27 -18}}];
* undecental [<1 2 -13 -15], <0 -1 37 43]>
* [[undecental]] [{{val| 1 0 61 71 }}, {{val| 0 1 -37 -43}}];
* counterschismic [<1 2 21], <0 -1 -45]>
* [[counterschismic]] [{{val| 1 0 -69 }}, {{val| 0 1 45}}];
* [[Dicot_family|dicot]] [<1 1 2], <0 2 1]>
* [[dicot]] [{{val| 1 1 2 }}, {{val| 0 2 1}}];
** dicot [<1 1 2 2], <0 2 1 3]>
** [[mujannabic]] [{{val| 1 1 2 2 }}, {{val| 0 2 1 3}}];
** sharp [<1 1 2 1], <0 2 1 6]>
** [[sharpie]] [{{val| 1 1 2 1 }}, {{val| 0 2 1 6}}];
* [[Meantone_family#Mohajira|mohajira]], semififths [<1 1 0 6], <0 2 8 -11]>
* [[mohajira]], semififths [{{val| 1 1 0 6 }}, {{val| 0 2 8 -11}}];
** mohajira <1 1 0 6 2], <0 2 8 -11 5]>
** mohajira [{{val| 1 1 0 6 2 }}, {{val| 0 2 8 -11 5}}];
** [[Meantone_family|maqamic]] [<1 1 0 4 2], <0 2 8 -4 5]>
** [[neutrominant]] [{{val| 1 1 0 4 2 }}, {{val| 0 2 8 -4 5}}];
*** maqamic <1 1 0 4 2 4], <0 2 8 -4 5 -1]>
*** neutrominant [{{val| 1 1 0 4 2 4 }}, {{val| 0 2 8 -4 5 -1}}];
* beatles [<1 1 5 4], <0 2 -9 -4]>
* [[beatles]] [{{val| 1 1 5 4 }}, {{val| 0 2 -9 -4}}];
* [[Turkish_maqam_music_temperaments|karadeniz]] [<1 1 7 11 2], <0 2 -16 -28 5]>
* [[karadeniz]] [{{val| 1 1 7 11 2 }}, {{val| 0 2 -16 -28 5}}];
* [[Breedsmic_temperaments#Hemififths|hemififths]] [<1 1 -5 -1], <0 2 25 13]>
* [[hemififths]] [{{val| 1 1 -5 -1 }}, {{val| 0 2 25 13}}];
* [[Bug_family|bug]] [<1 2 3], <0 -2 -3]>
* [[bug]] [{{val| 1 0 0 }}, {{val| 0 2 3}}];
** beep [<1 2 3 3], <0 -2 -3 -1]>
** [[beep]] [{{val| 1 0 0 2 }}, {{val| 0 2 3 1}}];
*** pentoid [<1 2 3 3 3], <0 -2 -3 -1 2]>
*** pentoid [{{val| 1 0 0 2 5 }}, {{val| 0 2 3 1 -2}}];
* superpelog [<1 2 1 3], <0 -2 6 -1]>
* [[superpelog]] [{{val| 1 0 7 2 }}, {{val| 0 2 -6 1}}];
* [[Meantone_family#Godzilla|godzilla]] [<1 2 4 3], <0 -2 -8 -1]>
* [[godzilla]] [{{val| 1 0 -4 2 }}, {{val| 0 2 8 1}}];
* monzismic [<1 2 10], <0 -2 -37]>
* [[monzismic]] [{{val| 1 0 -27 }}, {{val| 0 2 37}}];
* [[Gamelismic_clan#Gidorah|gidorah]] [<1 1 2 3], <0 3 2 -1]>
* [[gidorah]] [{{val| 1 1 2 3 }}, {{val| 0 3 2 -1}}];
* penta [<1 1 2 2], <0 3 2 4]>
* [[enipucrop]] [{{val| 1 2 2 }}, {{val| 0 3 -2}}];
* [[Laconic_Family|laconic]] [<1 1 1], <0 3 7]>
* [[penta]] [{{val| 1 1 2 2 }}, {{val| 0 3 2 4}}];
** [[Gamelismic_clan#Gorgo|gorgo]] [<1 1 1 3], <0 3 7 -1]
* [[laconic]] [{{val| 1 1 1 }}, {{val| 0 3 7}}];
*** gorgo [<1 1 1 3 1| <0 3 7 -1 13|>
** [[gorgo]] [{{val| 1 1 1 3 }}, {{val| 0 3 7 -1}}];
**** gorgo [<1 1 1 3 1 2| <0 3 7 -1 13 9|>
*** gorgo [{{val| 1 1 1 3 1 }}, {{val| 0 3 7 -1 13}}];
*** spartan [<1 1 1 3 5| <0 3 7 -1 -8|>
**** gorgo [{{val| 1 1 1 3 1 2 }}, {{val| 0 3 7 -1 13 9}}];
* [[Meantone_family#Mothra|mothra]], cynder [<1 1 0 3], <0 3 12 -1]>
*** spartan [{{val| 1 1 1 3 5 }}, {{val| 0 3 7 -1 -8}}];
** mothra, cynder [<1 1 0 3 5], <0 3 12 -1 -8]>
* [[pycnic]] [{{val| 1 0 6 -3 }}, {{val| 0 3 -7 11}}];
* [[Gamelismic_clan#Rodan|rodan]] [<1 1 -1 3], <0 3 17 -1]>
* [[mothra]], cynder [{{val| 1 1 0 3 }}, {{val| 0 3 12 -1}}];
** [[Gamelismic_clan#Rodan|rodan]][<1 1 -1 3 6], <0 3 17 -1 -13]>
** mothra, cynder [{{val| 1 1 0 3 5 }}, {{val| 0 3 12 -1 -8}}];
*** [[Gamelismic_clan#Rodan|rodan]] [<1 1 -1 3 6 8], <0 3 17 -1 -13 -22]>
* [[rodan]] [{{val| 1 1 -1 3 }}, {{val| 0 3 17 -1}}];
*** [[Gamelismic_clan#Rodan|aerodactyl]] [<1 1 -1 3 6 -1], <0 3 17 -1 -13 24]>
** rodan [{{val| 1 1 -1 3 6 }}, {{val| 0 3 17 -1 -13}}];
* [[Schismatic_family#Guiron|guiron]] [<1 1 7 3], <0 3 -24 -1]>
*** rodan [{{val| 1 1 -1 3 6 8 }}, {{val| 0 3 17 -1 -13 -22}}];
* [[Porcupine_family|porcupine]] [<1 2 3], <0 -3 -5]>
*** aerodactyl [{{val| 1 1 -1 3 6 -1 }}, {{val| 0 3 17 -1 -13 24}}];
** hystrix [<1 2 3 3], <0 -3 -5 -1]>
* [[guiron]] [{{val| 1 1 7 3 }}, {{val| 0 3 -24 -1}}];
** porcupine [<1 2 3 2], <0 -3 -5 6]>
* [[porcupine]] [{{val| 1 2 3 }}, {{val| 0 3 5}}];
*** porcupine [<1 2 3 2 4], <0 -3 -5 6 -4]>
** [[hystrix]] [{{val| 1 2 3 3 }}, {{val| 0 3 5 1}}];
** opossum, pentadecimal [<1 2 3 4], <0 -3 -5 -9]>
** porcupine [{{val| 1 2 3 2 }}, {{val| 0 3 5 -6}}];
*** opossum [<1 2 3 4 4], <0 -3 -5 -9 -4]>
*** porcupine [{{val| 1 2 3 2 4 }}, {{val| 0 3 5 -6 4}}];
*** coendou [<1 2 3 1 4 3], <0 -3 -5 13 -4 5]>
** [[opossum]], pentadecimal [{{val| 1 2 3 4 }}, {{val| 0 3 5 9}}];
*** porcupinefish [<1 2 3 2 4 6], <0 -3 -5 6 -4 -17]>
*** opossum [{{val| 1 2 3 4 4 }}, {{val| 0 3 5 9 4}}];
* ammonite [<1 5 8 10], <0 -9 -15 -19]>
*** coendou [{{val| 1 2 3 1 4 3 }}, {{val| 0 3 5 -13 4 -5}}];
* triton [<1 3 -1 -1], <0 -3 7 8]>
*** porcupinefish [{{val| 1 2 3 2 4 6 }}, {{val| 0 3 5 -6 4 17}}];
* [[Meantone_family#liese|liese]], gawel [<1 3 8 8], <0 -3 -12 -11]>
* [[ammonite]] [{{val| 1 5 8 10 }}, {{val| 0 9 15 19}}];
* tricot [<1 3 16], <0 -3 -29]>
* [[triton]] [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8}}];
* [[Tetracot_family|tetracot]] [<1 1 1], <0 4 9]>
* [[liese]], gawel [{{val| 1 0 -4 -3 }}, {{val| 0 3 12 11}}];
** monkey [<1 1 1 5], <0 4 9 -15]>
* [[alphatricot]] [{{val| 1 0 -13 }}, {{val| 0 3 29}}];
** bunya [<1 1 1 -1], <0 4 9 26]>
* [[tetracot]] [{{val| 1 1 1 }}, {{val| 0 4 9}}];
* vulture [<1 0 -6], <0 4 21]>
** [[monkey]] [{{val| 1 1 1 5 }}, {{val| 0 4 9 -15}}];
** buzzard [<1 0 -6 4], <0 4 21 -3]>
** [[bunya]] [{{val| 1 1 1 -1 }}, {{val| 0 4 9 26}}];
*** buzzard [<1 0 -6 4 -12 -7], <0 4 21 -3 39 27]>
* [[vulture]] [{{val| 1 0 -6 }}, {{val| 0 4 21}}];
* [[Schismatic_family|sesquiquartififths]] [<1 1 7 5], <0 4 -32 -15]>
** [[buzzard]] [{{val| 1 0 -6 4 }}, {{val| 0 4 21 -3}}];
* semihemififths [<1 1 -5 -1 8], <0 4 50 26 -31]>
*** buzzard [{{val| 1 0 -6 4 -12 -7 }}, {{val| 0 4 21 -3 39 27}}];
* [[Dicot_family|sidi]] [<1 3 3 6], <0 -4 -2 -9]>
* [[sesquiquartififths]] [{{val| 1 1 7 5 }}, {{val| 0 4 -32 -15}}];
* negri [<1 2 2], <0 -4 3]>
* semihemififths [{{val| 1 1 -5 -1 8 }}, {{val| 0 4 50 26 -31}}];
** negri [<1 2 2 3], <0 -4 3 -2]>
* [[sidi]] [{{val| 1 3 3 6 }}, {{val| 0 4 2 9}}];
*** negri [<1 2 2 3 4| <0 -4 3 -2 -5|]
* [[negri]] [{{val| 1 2 2 }}, {{val| 0 4 -3}}];
**** negri [<1 2 2 3 4 4| <0 -4 3 -2 -5 -3|]
** negri [{{val| 1 2 2 3 }}, {{val| 0 4 -3 2}}];
*** negril [<1 2 2 3 2| <0 -4 3 -2 14|]
*** negri [{{val| 1 2 2 3 4 }}, {{val| 0 4 -3 2 5}}];
**** negril [<1 2 2 3 2 4], <0 -4 3 -2 14 -3]>
**** negri [{{val| 1 2 2 3 4 4 }}, {{val| 0 4 -3 2 5 3}}];
* sentinel [<1 3 -3 6], <0 -4 15 -9]>
*** negril [{{val| 1 2 2 3 2 }}, {{val| 0 4 -3 2 -14}}];
* [[Meantone_family#Squares|squares]] [<1 3 8 6], <0 -4 -16 -9]>
**** negril [{{val| 1 2 2 3 2 4 }}, {{val| 0 4 -3 2 -14 3}}];
* [[Magic_family|magic]] [<1 0 2], <0 5 1]>
* [[sentinel]] [{{val| 1 3 -3 6 }}, {{val| 0 4 -15 9}}];
** muggles [<1 0 2 5], <0 5 1 -7]>
* [[squares]] [{{val| 1 3 8 6 }}, {{val| 0 4 16 9}}];
** magic [<1 0 2 -1], <0 5 1 12]>
* [[magic]] [{{val| 1 0 2 }}, {{val| 0 5 1}}];
*** magic [<1 0 2 -1 6], <0 5 1 12 -8]>
** [[muggles]] [{{val| 1 0 2 5 }}, {{val| 0 5 1 -7}}];
* passion [<1 2 2], <0 -5 4]>
** magic [{{val| 1 0 2 -1 }}, {{val| 0 5 1 12}}];
** passion [<1 2 2 2], <0 -5 4 10]>
*** magic [{{val| 1 0 2 -1 6 }}, {{val| 0 5 1 12 -8}}];
* ripple [<1 2 3], <0 -5 -8]>
* [[passion]] [{{val| 1 2 2 }}, {{val| 0 5 -4}}];
** ripple [<1 2 3 3], <0 -5 -8 -2]>
** passion [{{val| 1 2 2 2 }}, {{val| 0 5 -4 -10}}];
* tritonic [<1 4 -3 -3], <0 -5 11 12]>
* [[ripple]] [{{val| 1 2 3 }}, {{val| 0 5 8}}];
** tritonic [<1 4 -3 -3 2], <0 -5 11 12 3]>
** ripple [{{val| 1 2 3 3 }}, {{val| 0 5 8 2}}];
* [[Ragismic_microtemperaments|amity]] [<1 3 6], <0 -5 -13]>
* [[tritonic]] [{{val| 1 4 -3 -3 }}, {{val| 0 5 -11 -12}}];
** amity [<1 3 6 -2], <0 -5 -13 17]>
** tritonic [{{val| 1 4 -3 -3 2 }}, {{val| 0 5 -11 -12 -3}}];
*** hitchcock, amity [<1 3 6 -2 6], <0 -5 -13 17 -9]>
* [[amity]] [{{val| 1 3 6 }}, {{val| 0 5 13}}];
**** hitchcock [<1 3 6 -2 6 2], <0 -5 -13 17 -9 6]>
** amity [{{val| 1 3 6 -2 }}, {{val| 0 5 13 -17}}];
* gravity [<1 5 12], <0 -6 -17]>
*** hitchcock, amity [{{val| 1 3 6 -2 6 }}, {{val| 0 5 13 -17 9}}];
* [[Kleismic_family|hanson]] [<1 0 1], <0 6 5]>
**** hitchcock [{{val| 1 3 6 -2 6 2 }}, {{val| 0 5 13 -17 9 -6}}];
** keemun [<1 0 1 2], <0 6 5 3]>
* [[gravity]] [{{val| 1 5 12 }}, {{val| 0 6 17}}];
*** keemun [<1 0 1 2 4], <0 6 5 3 -2]>
** [[marvo]] [{{val| 1 5 12 29 }}, {{val| 0 6 17 46}}];
** catakleismic [<1 0 1 -3], <0 6 5 22]>
* [[hanson]] [{{val| 1 0 1 }}, {{val| 0 6 5}}];
*** catakleismic [<1 0 1 -3 9], <0 6 5 22 -21]>
** [[keemun]] [{{val| 1 0 1 2 }}, {{val| 0 6 5 3}}];
**** catakleismic [<1 0 1 -3 9 0], <0 6 5 22 -21 14]>
*** keemun [{{val| 1 0 1 2 4 }}, {{val| 0 6 5 3 -2}}];
** countercata [<1 0 1 11], <0 6 5 -31]>
** [[catakleismic]] [{{val| 1 0 1 -3 }}, {{val| 0 6 5 22}}];
* ampersand [<1 1 3], <0 6 -7]>
*** catakleismic [{{val| 1 0 1 -3 9 }}, {{val| 0 6 5 22 -21}}];
** [[Gamelismic_clan#Miracle|miracle]][<1 1 3 3], <0 6 -7 -2]>
**** catakleismic [{{val| 1 0 1 -3 9 0 }}, {{val| 0 6 5 22 -21 14}}];
*** miracle [<1 1 3 3 2], <0 6 -7 -2 15]>
** [[countercata]] [{{val| 1 0 1 11 }}, {{val| 0 6 5 -31}}];
* marvo [<1 -1 -5 -17], <0 6 17 46]>
* [[ampersand]] [{{val| 1 1 3 }}, {{val| 0 6 -7}}];
* [[Porcupine_family|nautilus]] [<1 2 3 3], <0 -6 -10 -3]>
** [[miracle]] [{{val| 1 1 3 3 }}, {{val| 0 6 -7 -2}}];
* [[Semicomma_family|orson]] [<1 0 3], <0 7 -3]>
*** miracle [{{val| 1 1 3 3 2 }}, {{val| 0 6 -7 -2 15}}];
** orwell [<1 0 3 1], <0 7 -3 8]>
* [[nautilus]] [{{val| 1 2 3 3 }}, {{val| 0 6 10 3}}];
*** orwell [<1 0 3 1 3], <0 7 -3 8 2]>
* [[orson]] [{{val| 1 0 3 }}, {{val| 0 7 -3}}];
**** orwell [<1 0 3 1 3 8], <0 7 -3 8 2 -19]>
** [[orwell]] [{{val| 1 0 3 1 }}, {{val| 0 7 -3 8}}];
**** blair [<1 0 3 1 3 3], <0 7 -3 8 2 3]>
*** orwell [{{val| 1 0 3 1 3 }}, {{val| 0 7 -3 8 2}}];
**** winston [<1 0 3 1 3 1], <0 7 -3 8 2 12]>
**** orwell [{{val| 1 0 3 1 3 8 }}, {{val| 0 7 -3 8 2 -19}}];
**** doublethink [<1 0 3 1 3 2], <0 14 -6 16 4 15]>
**** blair [{{val| 1 0 3 1 3 3 }}, {{val| 0 7 -3 8 2 3}}];
* sensi [<1 -1 -1], <0 7 9]>
**** winston [{{val| 1 0 3 1 3 1 }}, {{val| 0 7 -3 8 2 12}}];
** [[Starling_temperaments#Sensi temperament|sensi]] [<1 -1 -1 -2], <0 7 9 13]>
* [[sensi]] [{{val| 1 6 8 }}, {{val| 0 7 9}}];
*** [[Starling_temperaments#Sensi temperament-Sensor|sensor]] [<1 -1 -1 -2 9], <0 7 9 13 -15]>
** sensi [{{val| 1 6 8 11 }}, {{val| 0 7 9 13}}];
**** sensor [<1 -1 -1 -2 9 0], <0 7 9 13 -15 10]>
*** [[sensor]] [{{val| 1 6 8 11 -6 }}, {{val| 0 7 9 13 -15}}];
* [[Starling_temperaments#Sensi temperament-Sensis|sensis]] [<1 6 8 11 6| <0 -7 -9 -13 -4|] ?
**** sensor [{{val| 1 6 8 11 -6 10 }}, {{val| 0 7 9 13 -15 10}}];
** sensis [<1 6 8 11 6 10| <0 -7 -9 -13 -4 -10|] ?
*** [[sensis]] [{{val| 1 6 8 11 6 }}, {{val| 0 7 9 13 4}}];
* [[Starling_temperaments#Sensi temperament-Sensus|sensus]] [<1 6 8 11 23| <0 -7 -9 -13 -31|] ?
**** sensis [{{val| 1 6 8 11 6 10 }}, {{val| 0 7 9 13 4 10}}];
** sensus [<1 6 8 11 23 10| <0 -7 -9 -13 -31 -10|] ?
*** [[sensus]] [{{val| 1 6 8 11 23 }}, {{val| 0 7 9 13 31}}];
* roman [<1 4 3 -1 0 3], <0 -7 -2 11 10 2]>
**** sensus [{{val| 1 6 8 11 23 10 }}, {{val| 0 7 9 13 31 10}}];
* [[Tetracot_family#Octacot|octacot]] [<1 1 1 2], <0 8 18 11]>
* [[roman]] [{{val| 1 4 3 -1 0 3 }}, {{val| 0 7 2 -11 -10 -2}}];
* [[Würschmidt_family|würschmidt]] [<1 -1 2], <0 8 1]>
* [[octacot]] [{{val| 1 1 1 2 }}, {{val| 0 8 18 11}}];
** worschmidt [<1 -1 2 7], <0 8 1 -13]>
* [[würschmidt]] [{{val| 1 7 3 }}, {{val| 0 8 1}}];
** wurschmidt [<1 -1 2 -3], <0 8 1 18]>
** [[worschmidt]] [{{val| 1 7 3 -6 }}, {{val| 0 8 1 -13}}];
** whirrschmidt [<1 7 3 38], <0 -8 -1 -52]>
** [[wurschmidt]] [{{val| 1 7 3 15 }}, {{val| 0 8 1 18}}];
* valentine [<1 1 2], <0 9 5]>
** [[whirrschmidt]] [{{val| 1 7 3 38 }}, {{val| 0 8 1 52}}];
** [[Starling_temperaments#Valentine temperament|valentine]][<1 1 2 3], <0 9 5 -3]>
* [[valentine]] [{{val| 1 1 2 }}, {{val| 0 9 5}}];
*** valentine [<1 1 2 3 3], <0 9 5 -3 7]>
** valentine [{{val| 1 1 2 3 }}, {{val| 0 9 5 -3}}];
**** [[Starling_temperaments#Valentine temperament-Valentino|valentino]] [<1 1 2 3 3 5], <0 9 5 -3 7 -20]>
*** valentine [{{val| 1 1 2 3 3 }}, {{val| 0 9 5 -3 7}}];
**** [[Starling_temperaments#Valentine temperament-Dwynwen|dwynwen]] [<1 1 2 3 3 2], <0 9 5 -3 7 26]>
**** valentino [{{val| 1 1 2 3 3 5 }}, {{val| 0 9 5 -3 7 -20}}];
**** [[Starling_temperaments#Valentine temperament-Lupercalia|lupercalia]] [<1 1 2 3 3 3| <0 9 5 -3 7 11|]
**** dwynwen [{{val| 1 1 2 3 3 2 }}, {{val| 0 9 5 -3 7 26}}];
* escapade [<1 2 2], <0 -9 7]>
**** lupercalia [{{val| 1 1 2 3 3 3 }}, {{val| 0 9 5 -3 7 11}}];
** escapade [<1 2 2 3], <0 -9 7 -4]>
* [[escapade]] [{{val| 1 2 2 }}, {{val| 0 9 -7}}];
** escaped [<1 2 2 4], <0 -9 7 -26]>
** escapade [{{val| 1 2 2 3 }}, {{val| 0 9 -7 4}}];
* [[Gamelismic_clan#Superkleismic|superkleismic]] [<1 4 5 2], <0 -9 -10 3]>
** [[escaped]] [{{val| 1 2 2 4 }}, {{val| 0 9 -7 26}}];
** superkleismic [<1 4 5 2 4], <0 -9 -10 3 -2]>
* [[superkleismic]] [{{val| 1 4 5 2 }}, {{val| 0 9 10 -3}}];
* [[Starling_temperaments#Myna temperament|myna]] [<1 -1 0 1], <0 10 9 7]>
** superkleismic [{{val| 1 4 5 2 4 }}, {{val| 0 9 10 -3 2}}];
** myna [<1 -1 0 1 -3], <0 10 9 7 25]>
* [[mabila]] [{{val| 1 6 1 }}, {{val| 0 10 -3}}];
*** myna [<1 -1 0 1 -3 5], <0 10 9 7 25 -5]>
* [[myna]] [{{val| 1 9 9 8 }}, {{val| 0 10 9 7}}];
* [[Sycamore_family|sycamore]] [<1 1 2], <0 11 6]>
** myna [{{val| 1 9 9 8 22 }}, {{val| 0 10 9 7 25}}];
** sycamore [<1 1 2 2], <0 11 6 15]>
*** myna [{{val| 1 9 9 8 22 0 }}, {{val| 0 10 9 7 25 -5}}];
* septimin [<1 4 1 5], <0 -11 6 -10]>
* [[sycamore]] [{{val| 1 1 2 }}, {{val| 0 11 6}}];
* [[Starling_temperaments#Nusecond temperament|nusecond]] [<1 3 4 5], <0 -11 -13 -17]>
** sycamore [{{val| 1 1 2 2 }}, {{val| 0 11 6 15}}];
* quartonic [<1 2 3 3], <0 -11 -18 -5]>
* [[septimin]] [{{val| 1 4 1 5 }}, {{val| 0 11 -6 10}}];
* [[Kleismic_family|hemikleismic]] [<1 0 1 4], <0 12 10 -9]>
* [[nusecond]] [{{val| 1 3 4 5 }}, {{val| 0 11 13 17}}];
* [[Kleismic_family|clyde]] [<1 6 6 12], <0 -12 -10 -25]>
* [[quartonic]] [{{val| 1 2 3 3 }}, {{val| 0 11 18 5}}];
* bohpier [<1 0 0 0], <0 13 19 23]>
* [[hemikleismic]] [{{val| 1 0 1 4 }}, {{val| 0 12 10 -9}}];
* [[Gammic_family|gammic]] [<1 1 2], <0 20 11]>
* [[clyde]] [{{val| 1 6 6 12 }}, {{val| 0 12 10 25}}];
** gammic [<1 1 2 0], <0 20 11 96]>
* [[bohpier]] [{{val| 1 0 0 0 }}, {{val| 0 13 19 23}}];
* [[Gammic_family|neptune]] [<1 21 13 13], <0 -40 -22 -21]>
* doublethink [{{val| 1 0 3 1 3 2 }}, {{val| 0 14 -6 16 4 15}}];
* pluto [<1 5 15 15 2], <0 7 26 25 -3]>
* [[gammic]] [{{val| 1 1 2 }}, {{val| 0 20 11}}];
* twothirdtonic [<1 3 2 4 4], <0 -13 3 -11 -5]>
** gammic [{{val| 1 1 2 0 }}, {{val| 0 20 11 96}}];
** twothirdtonic [<1 3 2 4 4 5], <0 -13 3 -11 -5 -12]>
* [[Neptune (temperament)|neptune]] [{{val| 1 21 13 13 }}, {{val| 0 40 22 21}}];
* slender [<1 2 2 3], <0 -13 10 -6]>
* [[pluto]] [{{val| 1 5 15 15 2 }}, {{val| 0 7 26 25 -3}}];
** slender [<1 2 2 3 4], <0 -13 10 -6 -17]>
* [[twothirdtonic]] [{{val| 1 3 2 4 4 }}, {{val| 0 13 -3 11 5}}];
* [[Ragismic_microtemperaments|parakleismic]] [<1 5 6], <0 -13 -14]>
** twothirdtonic [{{val| 1 3 2 4 4 5 }}, {{val| 0 13 -3 11 5 12}}];
** parakleismic [<1 5 6 12], <0 -13 -14 -35]>
* [[slender]] [{{val| 1 2 2 3 }}, {{val| 0 13 -10 6}}];
* fortune [<1 -1 11], <0 14 -47]>
** slender [{{val| 1 2 2 3 4 }}, {{val| 0 13 -10 6 17}}];
* hemithirds, luna [<1 4 2], <0 -15 2]>
* [[parakleismic]] [{{val| 1 5 6 }}, {{val| 0 13 14}}];
** [[Gamelismic_clan#Hemithirds|hemithirds]][<1 4 2 2], <0 -15 2 5]>
** parakleismic [{{val| 1 5 6 12 }}, {{val| 0 13 14 35}}];
*** [[Gamelismic_clan#Hemithirds|hemithirds]] [<1 4 2 2 7], <0 -15 2 5 -22]>
* [[fortune]] [{{val| 1 13 -36 }}, {{val| 0 14 -47}}];
* [[Wuerschmidt_family|hemiwürschmidt]] [<1 -1 2 2], <0 16 2 5]>
* [[hemithirds]], [[luna]] [{{val| 1 4 2 }}, {{val| 0 15 -2}}];
** hemiwürschmidt [<1 -1 2 2 -3], <0 16 2 5 40]>
** hemithirds [{{val| 1 4 2 2 }}, {{val| 0 15 -2 -5}}];
* semisept [<1 -5 0 -3], <0 17 6 15]>
*** hemithirds [{{val| 1 4 2 2 7 }}, {{val| 0 15 -2 -5 22}}];
* vavoom [<1 0 4], <0 17 -18]>
* [[hemiwürschmidt]] [{{val| 1 15 4 7 }}, {{val| 0 16 2 5}}];
* [[Minortonic_family|minortone]] [<1 -1 -3], <0 17 35]>
** hemiwürschmidt [{{val| 1 15 4 7 37 }}, {{val| 0 16 2 5 40}}];
** [[Minortonic_family#Mitonic|mitonic]] [<1 -1 -3 6], <0 17 35 -21]>
* [[semisept]] [{{val| 1 12 6 12 }}, {{val| 0 17 6 15}}];
* [[Starling_temperaments|casablanca]] [<1 -7 -4 1], <0 19 14 4]>
* [[vavoom]] [{{val| 1 0 4 }}, {{val| 0 17 -18}}];
** [[Starling_temperaments#Casablanca temperament|casablanca]] [<1 -7 -4 1 3], <0 19 14 4 1]>
* [[minortone]] [{{val| 1 16 32 }}, {{val| 0 17 35}}];
* [[Breedsmic_temperaments|tertiaseptal]] [<1 3 2 3], <0 -22 5 -3]>
** [[mitonic]] [{{val| 1 16 32 -15 }}, {{val| 0 17 35 -21}}];
* grendel, voodoo [<1 9 2 7], <0 -23 1 -13]>
* [[casablanca]] [{{val| 1 12 10 5 }}, {{val| 0 19 14 4}}];
* gamera [<1 6 10 3], <0 -23 -40 -1]>
** casablanca [{{val| 1 12 10 5 4 }}, {{val| 0 19 14 4 1}}];
* astro [<1 5 1], <0 -31 12]>
* [[tertiaseptal]] [{{val| 1 3 2 3 }}, {{val| 0 22 -5 3}}];
* semihemiwürschmidt [<1 15 4 7 24], <0 -32 -4 -10 -49]>
* [[grendel]], voodoo [{{val| 1 9 2 7 }}, {{val| 0 23 -1 13}}];
* whoosh [<1 17 14], <0 -33 -25]>
* [[gamera]] [{{val| 1 6 10 3 }}, {{val| 0 23 40 1}}];
* [[Turkish_maqam_music_temperaments|yarman]] [<1 2 3 4 4], <0 -33 -54 -95 -43]>
* [[astro]] [{{val| 1 5 1 }}, {{val| 0 31 -12}}];
* senior [<1 11 19], <0 -35 -62]>
* semihemiwürschmidt [{{val| 1 15 4 7 24 }}, {{val| 0 32 4 10 49}}];
* raider [<1 -9 -26], <0 37 99]>
* [[whoosh]] [{{val| 1 17 14 }}, {{val| 0 33 25}}];
* supermajor [<1 15 19 30], <0 -37 -46 -75]>
* [[yarman]] [{{val| 1 2 3 4 4 }}, {{val| 0 33 54 95 43}}];
* [[Breedsmic_temperaments|quasiorwell]] [<1 -7 3 1], <0 38 -3 8]>
* [[senior]] [{{val| 1 11 19 }}, {{val| 0 35 62}}];
* semigamera [<1 6 10 3 12], <0 -46 -80 -2 -89]>
* [[raider]] [{{val| 1 28 73 }}, {{val| 0 37 99}}];
* gross [<1 -2 4], <0 47 -22]>
* [[supermajor (temperament)|supermajor]] [{{val| 1 15 19 30 }}, {{val| 0 37 46 75}}];
* pirate [<1 -6 0], <0 49 15]>
* [[quasiorwell]] [{{val| 1 31 0 9 }}, {{val| 0 38 -3 8}}];
* egads [<1 15 16], <0 -51 -52]>
* semigamera [{{val| 1 6 10 3 12 }}, {{val| 0 46 80 2 89}}];
* avila [<1 1 -1], <0 1 6]>
* [[gross]] [{{val| 1 45 -18 }}, {{val| 0 47 -22}}];
* mabila [<1 6 1], <0 -10 3]>
* [[pirate]] [{{val| 1 43 15 }}, {{val| 0 49 15}}];
* pycnic [<1 3 -1 8], <0 -3 7 -11]>
* [[egads]] [{{val| 1 15 16 }}, {{val| 0 51 52}}];
* enipucrop [<1 2 2], <0 -3 2]>


=Two periods per octave=
== Two periods per octave ==
* [[Diaschismic_family|srutal]] [<2 3 5], <0 1 -2]>
* [[srutal]] [{{val| 2 0 11 }}, {{val| 0 1 -2}}];
** pajara [<2 3 5 6], <0 1 -2 -2]>
** [[pajara]] [{{val| 2 0 11 12 }}, {{val| 0 1 -2 -2}}];
*** pajaric [<2 3 5 6 7], <0 1 -2 -2 0]>
*** pajaric [{{val| 2 0 11 12 7 }}, {{val| 0 1 -2 -2 0}}];
*** pajarous [<2 3 5 6 6], <0 1 -2 -2 5]>
*** pajarous [{{val| 2 0 11 12 -9 }}, {{val| 0 1 -2 -2 5}}];
*** pajara [<2 3 5 6 8], <0 1 -2 -2 -6]>
*** pajara [{{val| 2 0 11 12 26 }}, {{val| 0 1 -2 -2 -6}}];
** diaschismic [<2 3 5 7], <0 1 -2 -8]>
** [[diaschismic]] [{{val| 2 0 11 31 }}, {{val| 0 1 -2 -8}}];
*** diaschismic [<2 3 5 7 9 10], <0 1 -2 -8 -12 -15]>
*** diaschismic [{{val| 2 0 11 31 45 55 }}, {{val| 0 1 -2 -8 -12 -15}}];
** keen [<2 3 5 4], <0 1 -2 9]>
** [[keen]] [{{val| 2 0 11 -23 }}, {{val| 0 1 -2 9}}];
* supersharp [<2 3 4], <0 1 3]>
* [[supersharp]] [{{val| 2 0 -5 }}, {{val| 0 1 3}}];
** octokaidecal [<2 3 4 5], <0 1 3 3]>
** [[octokaidecal]] [{{val| 2 0 -5 -4 }}, {{val| 0 1 3 3}}];
* bipelog [<2 3 5 6], <0 1 -3 -3]>
* [[bipelog]] [{{val| 2 0 14 15 }}, {{val| 0 1 -3 -3}}];
* [[Meantone_family|injera]] [<2 3 4 5], <0 1 4 4]>
* [[injera]] [{{val| 2 0 -8 -7 }}, {{val| 0 1 4 4}}];
** injera [<2 3 4 5 6], <0 1 4 4 6]>
** injera [{{val| 2 0 -8 -7 -12 }}, {{val| 0 1 4 4 6}}];
* [[Schismatic_family|bischismic]] [<2 3 6 9], <0 1 -8 -20]>
* [[bischismic]] [{{val| 2 0 30 69 }}, {{val| 0 1 -8 -20}}];
* [[Diaschismic_family|shrutar]] [<2 3 5 5], <0 2 -4 7]>
* [[shrutar]] [{{val| 2 1 9 -2 }}, {{val| 0 2 -4 7}}];
** shrutar [<2 3 5 5 7], <0 2 -4 7 -1]>
** shrutar [{{val| 2 1 9 -2 8 }}, {{val| 0 2 -4 7 -1}}];
*** srutar [<2 3 5 5 7 8], <0 2 -4 7 -1 -7]>
*** srutar [{{val| 2 1 9 -2 8 15 }}, {{val| 0 2 -4 7 -1 -7}}];
*** shrutar [<2 3 5 5 7 6], <0 2 -4 7 -1 16]>
*** shrutar [{{val| 2 1 9 -2 8 -10 }}, {{val| 0 2 -4 7 -1 16}}];
* [[Diaschismic_family|echidna]] [<2 1 9 2], <0 3 -6 5]>
* [[echidna]] [{{val| 2 1 9 2 }}, {{val| 0 3 -6 5}}];
** echidna [<2 1 9 2 12], <0 3 -6 5 -7]>
** echidna [{{val| 2 1 9 2 12 }}, {{val| 0 3 -6 5 -7}}];
* [[Dicot_family|decimal]] [<2 4 5 6], <0 -2 -1 -1]>
* [[decimal]] [{{val| 2 0 3 4 }}, {{val| 0 2 1 1}}];
* [[Breedsmic_temperaments#Semihemi|semihemi]] [<2 4 15 11 21], <0 -2 -25 -13 -34]>
* semihemi [{{val| 2 0 -35 -15 -47 }}, {{val| 0 2 25 13 34}}];
* [[Gamelismic_clan#Lemba|lemba]] [<2 2 5 6], <0 3 -1 -1]>
* [[lemba]] [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1}}];
* [[Porcupine_family|hedgehog]] [<2 4 6 7], <0 -3 -5 -5]>
* [[hedgehog]] [{{val| 2 1 1 2 }}, {{val| 0 3 5 5}}];
* doublewide [<2 5 6], <0 -4 -3]>
* [[doublewide]] [{{val| 2 1 3 }}, {{val| 0 4 3}}];
** [[Jubilismic_clan|doublewide]][<2 5 6 7], <0 -4 -3 -3]>
** doublewide [{{val| 2 1 3 4 }}, {{val| 0 4 3 3}}];
*** [[Jubilismic_clan|doublewide]] [<2 5 6 7 6], <0 -4 -3 -3 2]>
*** doublewide [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2}}];
* [[Schismatic_family|sesquiquartififths]] [<2 2 14 10], <0 4 -32 -15]>
* [[sesquiquartififths]] [{{val| 1 1 7 5 }}, {{val| 0 4 -32 -15}}];
* hemiamity [<2 1 -1 13 13], <0 5 13 -17 -14]>
* hemiamity [{{val| 2 1 -1 13 13 }}, {{val| 0 5 13 -17 -14}}];
* wizard [<2 1 5 2], <0 6 -1 10]>
* [[wizard]] [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10}}];
** wizard [<2 1 5 2 8], <0 6 -1 10 -3]>
** wizard [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3}}];
* [[Gamelismic_clan#Unidec|unidec]] [<2 5 8 5], <0 -6 -11 2]>
* [[unidec]] [{{val| 2 5 8 5 }}, {{val| 0 6 11 -2}}];
** unidec [<2 5 8 5 6], <0 -6 -11 2 3]>
** unidec [{{val| 2 5 8 5 6 }}, {{val| 0 6 11 -2 -3}}];
*** hendec [<2 5 8 5 6 8], <0 -6 -11 2 3 -2]>
*** hendec [{{val| 2 5 8 5 6 8 }}, {{val| 0 6 11 -2 -3 2}}];
* [[Breedsmic_temperaments|harry]] [<2 4 7 7], <0 -6 -17 -10]>
* [[harry]] [{{val| 2 4 7 7 }}, {{val| 0 6 17 10}}];
* vishnu [<2 4 5], <0 -7 -3]>
* [[vishnu]] [{{val| 2 4 5 }}, {{val| 0 7 3}}];
** vishnu [<2 4 5 10], <0 -7 -3 -37]>
** vishnu [{{val| 2 4 5 10 }}, {{val| 0 7 3 37}}];
* kwazy [<2 1 6], <0 8 -5]>
* [[kwazy]] [{{val| 2 1 6 }}, {{val| 0 8 -5}}];
** bisupermajor [<2 1 6 1 8], <0 8 -5 17 -4]>
** [[bisupermajor]] [{{val| 2 1 6 1 8 }}, {{val| 0 8 -5 17 -4}}];
* semiparakleismic [<2 -3 -2 -11 -4], <0 13 14 35 23]>
* [[abigail]] [{{val| 2 7 13 -1 1 -2 }}, {{val| 0 11 24 -19 -17 -27}}];
* hemigamera [<2 12 20 6], <0 -23 -40 -1]>
* semiparakleismic [{{val| 2 10 12 24 19 }}, {{val| 0 13 14 35 23}}];
** hemigamera [<2 12 20 6 5], <0 -23 -40 -1 5]>
* hemigamera [{{val| 2 12 20 6 5 }}, {{val| 0 23 40 1 -5}}];
* abigail [<2 7 13 -1 1 -2], <0 -11 -24 19 17 27]>


=Three periods per octave=
== Three periods per octave ==
* [[Augmented_family|augmented]] [<3 5 7], <0 -1 0]>
* [[augmented (temperament)|augmented]] [{{val| 3 0 7 }}, {{val| 0 1 0}}];
** augene, tripletone [<3 5 7 8], <0 -1 0 2]>
** [[augene]], tripletone [{{val| 3 0 7 18 }}, {{val| 0 1 0 -2}}];
*** augene, tripletone [<3 5 7 8 10], <0 -1 0 2 2]>
*** augene, tripletone [{{val| 3 0 7 18 20 }}, {{val| 0 1 0 -2 -2}}];
** august [<3 5 7 9], <0 -1 0 -2]>
** [[august]] [{{val| 3 0 7 -1 }}, {{val| 0 1 0 2}}];
* misty [<3 5 6], <0 -1 4]>
* [[misty]] [{{val| 3 0 26 }}, {{val| 0 1 -4}}];
** misty [<3 5 6 6], <0 -1 4 10]>
** misty [{{val| 3 0 26 56 }}, {{val| 0 1 -4 -10}}];
* term [<3 5 5 4], <0 -1 8 18]>
* [[term (temperament)|term]] [{{val| 3 0 45 94 }}, {{val| 0 1 -8 -18}}];
* semiaug [<3 5 7 9], <0 -2 0 -5]>
* semiaug [{{val| 3 1 7 -1 }}, {{val| 0 2 0 5}}];
* [[Kleismic_family|tritikleismic]] [<3 6 8 8], <0 -6 -5 2]>
* [[tritikleismic]] [{{val| 3 0 3 10 }}, {{val| 0 6 5 -2}}];
* [[Mutt_family|mutt]] [<3 5 7 8], <0 -7 -1 12]>
* [[mutt]] [{{val| 3 5 7 8 }}, {{val| 0 7 1 -12}}];
* ternary [<3 5 7 8], <3 5 7 9]>
* [[ternary (temperament)|ternary]] [{{val| 3 5 7 0 }}, {{val| 0 0 0 1}}];


=Four or more periods per octave=
== Four or more periods per octave ==
* diminished [<4 6 9], <0 1 1]>
* [[diminished (temperament)|diminished]] [{{val| 4 0 3 }}, {{val| 0 1 1}}];
** diminished [<4 6 9 11], <0 1 1 1]>
** diminished [{{val| 4 0 3 5 }}, {{val| 0 1 1 1}}];
*** diminished [<4 6 9 11 14], <0 1 1 1 0]>
*** diminished [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0}}];
*** demolished [<4 6 9 11 13], <0 1 1 1 3]>
*** demolished [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3}}];
* blackwood [<5 8 12], <0 0 -1]>
* [[blackwood]] [{{val| 5 8 0 }}, {{val| 0 0 1}}];
** blacksmith [<5 8 12 14], <0 0 -1 0]>
** blackwood [{{val| 5 8 0 14 }}, {{val| 0 0 1 0}}];
* hexe [<6 10 14 17], <0 -1 0 0]>
* [[hexe]] [{{val| 6 0 14 17 }}, {{val| 0 1 0 0}}];
* jamesbond [<7 11 16 20], <0 0 0 -1]>
* [[jamesbond]] [{{val| 7 11 16 0 }}, {{val| 0 0 0 1}}];
** jamesbond [<7 11 16 20 24], <0 0 0 -1 0]>
** jamesbond [{{val| 7 11 16 0 24 }}, {{val| 0 0 0 1 0}}];
* whitewood [<7 11 16], <0 0 1]>
* [[whitewood]] [{{val| 7 11 0 }}, {{val| 0 0 1}}];
* octoid [<8 13 19 23 28], <0 -3 -4 -5 -3]>
* [[octoid]] [{{val| 8 1 3 3 16 }}, {{val| 0 3 4 5 3}}];
* [[Ragismic_microtemperaments|ennealimmal]] [<9 15 22], <0 -2 -3]>
* [[ennealimmal]] [{{val| 9 1 1 }}, {{val| 0 2 3}}];
** ennealimmal [<9 15 22 26], <0 -2 -3 -2]>
** ennealimmal [{{val| 9 1 1 12 }}, {{val| 0 2 3 2}}];
*** ennealimmal [<9 15 22 26 37], <0 -2 -3 -2 -16]>
*** ennealimmal [{{val| 9 1 1 12 -75 }}, {{val| 0 2 3 2 16}}];
* [[Breedsmic_temperaments|decoid]] [<10 0 47 36| <0 2 -3 -1|]
* [[decoid]] [{{val| 10 0 47 36 }}, {{val| 0 2 -3 -1}}];
** decoid [<10 0 47 36 98| <0 2 -3 -1 -8|]
** decoid [{{val| 10 0 47 36 98 }}, {{val| 0 2 -3 -1 -8}}];
*** decoid [<10 0 47 36 98 37| <0 2 -3 -1 -8 0|]
*** decoid [{{val| 10 0 47 36 98 37 }}, {{val| 0 2 -3 -1 -8 0}}];
* hendecatonic [<11 17 26 30], <0 1 -1 2]>
* [[hendecatonic (temperament)|hendecatonic]] [{{val| 11 0 43 -4 }}, {{val| 0 1 -1 2}}];
* [[Pythagorean_family|catler]] [<12 19 28 34], <0 0 0 -1]>
* [[catler]] [{{val| 12 19 28 0 }}, {{val| 0 0 0 1}}];
* [[Pythagorean_family|compton]] [<12 19 28], <0 0 -1]>
* [[compton]] [{{val| 12 19 0 }}, {{val| 0 0 1}}];
** compton, waage [<12 19 28 34], <0 0 -1 -2]>
** compton, waage [{{val| 12 19 0 -22 }}, {{val| 0 0 1 2}}];
*** compton, duodecimal [<12 19 28 34 42], <0 0 -1 -2 -3]>
*** compton, duodecimal [{{val| 12 19 0 -22 -42 }}, {{val| 0 0 1 2 3}}];
* duodecim [<12 19 28 34 42], <0 0 0 0 -1]>
* duodecim [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1}}];
* atomic [<12 19 28], <0 1 -7]>
* [[atomic]] [{{val| 12 0 161 }}, {{val| 0 1 -7}}];
* hemiennealimmal [<18 28 41 50 62], <0 2 3 2 1]>
* hemiennealimmal [{{val| 18 0 -1 22 48 }}, {{val| 0 2 3 2 1}}];
* [[Ragismic_microtemperaments|enneadecal]] [<19 30 44], <0 1 1]>
* [[enneadecal]] [{{val| 19 0 14 }}, {{val| 0 1 1}}];
** enneadecal [<19 30 44 53], <0 1 1 3]>
** enneadecal [{{val| 19 0 14 -37 }}, {{val| 0 1 1 3}}];
* undevigintone [<19 30 44 53 66], <0 0 0 0 -1]>
* undevigintone [{{val| 19 30 44 53 0 }}, {{val| 0 0 0 0 1}}];
* icosidillic [<22 35 51 62 76], <0 -1 1 -2 1]>
* icosidillic [{{val| 22 0 86 -8 111 }}, {{val| 0 1 -1 2 -1}}];
* vigintiduo [<22 35 51 62 76], <0 0 0 0 1]>
* vigintiduo [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1}}];
* mystery [<29 46 67 81 100 107], <0 0 1 1 1 1]>
* [[mystery]] [{{val| 29 46 0 14 33 40 }}, {{val| 0 0 1 1 1 1}}];
* hemienneadecal [<38 60 88 106 131], <0 1 1 3 2]>
* hemienneadecal [{{val| 38 0 28 -74 11 }}, {{val| 0 1 1 3 2}}];


[[Category:list]]
== See also ==
[[Category:project]]
* [[Kite's thoughts on pergens]]
[[Category:proposal]]
* [[Temperament naming]]
[[Category:rank_2]]
 
[[Category:temperament]]
[[Category:Lists of temperaments]]
[[Category:theory]]
[[Category:Temperament naming]]
[[Category:Regular temperament theory]]

Latest revision as of 04:05, 8 July 2026

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.)

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]];
    • 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]];
  • 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]];
  • alphatricot [⟨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]];
    • blackwood [⟨5 8 0 14], ⟨0 0 1 0]];
  • 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]];

See also

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