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Proposed names for rank-2 temperaments: Difference between revisions

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put mappings into defactored Hermite form (canonical form)
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== One period per octave ==
== One period per octave ==
* [[father]] [{{val| 1 2 2 }}, {{val| 0 -1 1 }}];
* [[father]] [{{val| 1 0 4 }}, {{val| 0 1 -1}}];
** mother [{{val| 1 2 2 2 }}, {{val| 0 -1 1 2 }}];
** mother [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2}}];
** father [{{val| 1 2 2 4 }}, {{val| 0 -1 1 -3 }}];
** father [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3}}];
* [[mavila]] [{{val| 1 2 1 }}, {{val| 0 -1 3 }}];
* [[mavila]] [{{val| 1 0 7 }}, {{val| 0 1 -3}}];
** [[pelogic]] [{{val| 1 2 1 1 }}, {{val| 0 -1 3 4 }}];
** [[pelogic]] [{{val| 1 0 7 9 }}, {{val| 0 1 -3 -4}}];
** [[armodue]] [{{val| 1 2 1 5 }}, {{val| 0 -1 3 -5 }}];
** [[armodue]] [{{val| 1 0 7 -5 }}, {{val| 0 1 -3 5}}];
** mavila [{{val| 1 2 1 -2 }}, {{val| 0 -1 3 11
** mavila [{{val| 1 0 7 20 }}, {{val| 0 1 -3


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


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


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


[[Category:List]]
[[Category:List]]
[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Rank 2]]
[[Category:Rank 2]]
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