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 [[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.)
 See also [[pergen|pergen names]].
 =One period per octave=
-father [&lt;1, 2, 2], &lt;0, -1, 1]&gt;
+* father [&lt;1 2 2], &lt;0 -1 1]&gt;
+** mother [&lt;1 2 2 2], &lt;0 -1 1 2]&gt;
-<ul><li>mother [&lt;1, 2, 2, 2], &lt;0, -1, 1, 2]&gt;</li><li>father [&lt;1, 2, 2, 4], &lt;0, -1, 1, -3]&gt;</li></ul>mavila [&lt;1, 2, 1], &lt;0, -1, 3]&gt;
+** father [&lt;1 2 2 4], &lt;0 -1 1 -3]&gt;
+* mavila [&lt;1 2 1], &lt;0 -1 3]&gt;
-<ul><li>pelogic [&lt;1, 2, 1, 1], &lt;0, -1, 3, 4]&gt;</li><li>armodue [&lt;1, 2, 1, 5], &lt;0, -1, 3
+** pelogic [&lt;1 2 1 1], &lt;0 -1 3 4]&gt;
+** armodue [&lt;1 2 1 5], &lt;0 -1 3 -5]&gt;
+** mavila [&lt;1 2 1 -2], &lt;0 -1 3 11]&gt;
+** hornbostel [&lt;1 2 1 8], &lt;0 -1 3 -12]&gt;
+* [[Meantone_family|
 =Two periods per octave=
-[[Diaschismic_family|srutal]] [&lt;2, 3, 5], &lt;0, 1, -2]&gt;
+* [[Diaschismic_family|srutal]] [&lt;2 3 5], &lt;0 1 -2]&gt;
+** pajara [&lt;2 3 5 6], &lt;0 1 -2 -2]&gt;
-<ul><li>pajara [&lt;2, 3, 5, 6], &lt;0, 1, -2, -2]&gt;<ul><li>pajaric [&lt;2, 3, 5, 6, 7], &lt;0, 1, -2, -2, 0]&gt;</li><li>pajarous [&lt;2, 3, 5, 6, 6], &lt;0, 1, -2, -2, 5]&gt;</li><li>pajara [&lt;2, 3, 5, 6, 8], &lt;0, 1, -2, -2, -6]&gt;</li></ul></li><li>diaschismic [&lt;2, 3, 5, 7], &lt;0, 1, -2, -8]&gt;<ul><li>diaschismic [&lt;2, 3, 5, 7, 9, 10], &lt;0, 1, -2, -8, -12, -15]&gt;</li></ul></li><li>keen [&lt;2, 3, 5, 4], &lt;0, 1, -2, 9]&gt;</li></ul>supersharp [&lt;2, 3, 4], &lt;0, 1, 3]&gt;
+*** pajaric [&lt;2 3 5 6 7], &lt;0 1 -2 -2 0]&gt;
+*** pajarous [&lt;2 3 5 6 6], &lt;0 1 -2 -2 5]&gt;
-<ul><li>octokaidecal [&lt;2, 3, 4, 5], &lt;0, 1, 3, 3]&gt;</li></ul>bipelog [&lt;2, 3, 5, 6], &lt;0, 1, -3, -3]&gt;
+*** pajara [&lt;2 3 5 6 8], &lt;0 1 -2 -2 -6]&gt;
+** diaschismic [&lt;2 3 5 7], &lt;0 1 -2 -8]&gt;
-[[Meantone_family|injera]] [&lt;2, 3, 4, 5], &lt;0, 1, 4, 4]&gt;
+*** diaschismic [&lt;2 3 5 7 9 10], &lt;0 1 -2 -8 -12 -15]&gt;
+** keen [&lt;2 3 5 4], &lt;0 1 -2 9]&gt;
-<ul><li>injera [&lt;2, 3, 4, 5, 6], &lt;0, 1, 4, 4, 6]&gt;</li></ul>[[Schismatic_family|bischismic]] [&lt;2, 3, 6, 9], &lt;0, 1, -8, -20]&gt;
+* supersharp [&lt;2 3 4], &lt;0 1 3]&gt;
+** octokaidecal [&lt;2 3 4 5], &lt;0 1 3 3]&gt;
-[[Diaschismic_family|shrutar]] [&lt;2, 3, 5, 5], &lt;0, 2, -4, 7]&gt;
+* bipelog [&lt;2 3 5 6], &lt;0 1 -3 -3]&gt;
+* [[Meantone_family|injera]] [&lt;2 3 4 5], &lt;0 1 4 4]&gt;
-<ul><li>shrutar [&lt;2, 3, 5, 5, 7], &lt;0, 2, -4, 7, -1]&gt;<ul><li>srutar [&lt;2, 3, 5, 5, 7, 8], &lt;0, 2, -4, 7, -1, -7]&gt;</li><li>shrutar [&lt;2, 3, 5, 5, 7, 6], &lt;0, 2, -4, 7, -1, 16]&gt;</li></ul></li></ul>[[Diaschismic_family|echidna]] [&lt;2, 1, 9, 2], &lt;0, 3, -6, 5]&gt;
+** injera [&lt;2 3 4 5 6], &lt;0 1 4 4 6]&gt;
+* [[Schismatic_family|bischismic]] [&lt;2 3 6 9], &lt;0 1 -8 -20]&gt;
-<ul><li>echidna [&lt;2, 1, 9, 2, 12], &lt;0, 3, -6, 5, -7]&gt;</li></ul>[[Dicot_family|decimal]] [&lt;2, 4, 5, 6], &lt;0, -2, -1, -1]&gt;
+* [[Diaschismic_family|shrutar]] [&lt;2 3 5 5], &lt;0 2 -4 7]&gt;
+** shrutar [&lt;2 3 5 5 7], &lt;0 2 -4 7 -1]&gt;
-[[Breedsmic_temperaments#Semihemi|Semihemi]] [&lt;2, 4, 15, 11, 21], &lt;0, -2, -25, -13, -34]&gt;
+*** srutar [&lt;2 3 5 5 7 8], &lt;0 2 -4 7 -1 -7]&gt;
+*** shrutar [&lt;2 3 5 5 7 6], &lt;0 2 -4 7 -1 16]&gt;
-[[Gamelismic_clan#Lemba|lemba]] [&lt;2, 2, 5, 6], &lt;0, 3, -1, -1]&gt;
+* [[Diaschismic_family|echidna]] [&lt;2 1 9 2], &lt;0 3 -6 5]&gt;
+** echidna [&lt;2 1 9 2 12], &lt;0 3 -6 5 -7]&gt;
-[[Porcupine_family|hedgehog]] [&lt;2, 4, 6, 7], &lt;0, -3, -5, -5]&gt;
+* [[Dicot_family|decimal]] [&lt;2 4 5 6], &lt;0 -2 -1 -1]&gt;
+* [[Breedsmic_temperaments#Semihemi|semihemi]] [&lt;2 4 15 11 21], &lt;0 -2 -25 -13 -34]&gt;
-doublewide [&lt;2, 5, 6], &lt;0, -4, -3]&gt;
+* [[Gamelismic_clan#Lemba|lemba]] [&lt;2 2 5 6], &lt;0 3 -1 -1]&gt;
+* [[Porcupine_family|hedgehog]] [&lt;2 4 6 7], &lt;0 -3 -5 -5]&gt;
-<ul><li>[[Jubilismic_clan|doublewide]][&lt;2, 5, 6, 7], &lt;0, -4, -3, -3]&gt;<ul><li>[[Jubilismic_clan|doublewide]] [&lt;2, 5, 6, 7, 6], &lt;0, -4, -3, -3, 2]&gt;</li></ul></li></ul>[[Schismatic_family|sesquiquartififths]] [&lt;2, 2, 14, 10], &lt;0, 4, -32, -15]&gt;
+* doublewide [&lt;2 5 6], &lt;0 -4 -3]&gt;
+** [[Jubilismic_clan|doublewide]][&lt;2 5 6 7], &lt;0 -4 -3 -3]&gt;
-hemiamity [&lt;2, 1, -1, 13, 13], &lt;0, 5, 13, -17, -14]&gt;
+*** [[Jubilismic_clan|doublewide]] [&lt;2 5 6 7 6], &lt;0 -4 -3 -3 2]&gt;
+* [[Schismatic_family|sesquiquartififths]] [&lt;2 2 14 10], &lt;0 4 -32 -15]&gt;
-wizard [&lt;2, 1, 5, 2], &lt;0, 6, -1, 10]&gt;
+* hemiamity [&lt;2 1 -1 13 13], &lt;0 5 13 -17 -14]&gt;
+* wizard [&lt;2 1 5 2], &lt;0 6 -1 10]&gt;
-<ul><li>wizard [&lt;2, 1, 5, 2, 8], &lt;0, 6, -1, 10, -3]&gt;</li></ul>[[Gamelismic_clan#Unidec|unidec]] [&lt;2, 5, 8, 5], &lt;0, -6, -11, 2]&gt;
+** wizard [&lt;2 1 5 2 8], &lt;0 6 -1 10 -3]&gt;
+* [[Gamelismic_clan#Unidec|unidec]] [&lt;2 5 8 5], &lt;0 -6 -11 2]&gt;
-<ul><li>unidec [&lt;2, 5, 8, 5, 6], &lt;0, -6, -11, 2, 3]&gt;<ul><li>hendec [&lt;2, 5, 8, 5, 6, 8], &lt;0, -6, -11, 2, 3, -2]&gt;</li></ul></li></ul>[[Breedsmic_temperaments|harry]] [&lt;2, 4, 7, 7], &lt;0, -6, -17, -10]&gt;
+** unidec [&lt;2 5 8 5 6], &lt;0 -6 -11 2 3]&gt;
+*** hendec [&lt;2 5 8 5 6 8], &lt;0 -6 -11 2 3 -2]&gt;
-vishnu [&lt;2, 4, 5], &lt;0, -7, -3]&gt;
+* [[Breedsmic_temperaments|harry]] [&lt;2 4 7 7], &lt;0 -6 -17 -10]&gt;
+* vishnu [&lt;2 4 5], &lt;0 -7 -3]&gt;
-<ul><li>vishnu [&lt;2, 4, 5, 10], &lt;0, -7, -3, -37]&gt;</li></ul>kwazy [&lt;2, 1, 6], &lt;0, 8, -5]&gt;
+** vishnu [&lt;2 4 5 10], &lt;0 -7 -3 -37]&gt;
+* kwazy [&lt;2 1 6], &lt;0 8 -5]&gt;
-<ul><li>bisupermajor [&lt;2, 1, 6, 1, 8], &lt;0, 8, -5, 17, -4]&gt;</li></ul>semiparakleismic [&lt;2, -3, -2, -11, -4], &lt;0, 13, 14, 35, 23]&gt;
+** bisupermajor [&lt;2 1 6 1 8], &lt;0 8 -5 17 -4]&gt;
+* semiparakleismic [&lt;2 -3 -2 -11 -4], &lt;0 13 14 35 23]&gt;
-hemigamera [&lt;2, 12, 20, 6], &lt;0, -23, -40, -1]&gt;
+* hemigamera [&lt;2 12 20 6], &lt;0 -23 -40 -1]&gt;
+** hemigamera [&lt;2 12 20 6 5], &lt;0 -23 -40 -1 5]&gt;
-<ul><li>hemigamera [&lt;2, 12, 20, 6, 5], &lt;0, -23, -40, -1, 5]&gt;</li></ul>abigail [&lt;2, 7, 13, -1, 1, -2], &lt;0, -11, -24, 19, 17, 27]&gt;
+* abigail [&lt;2 7 13 -1 1 -2], &lt;0 -11 -24 19 17 27]&gt;
 =Three periods per octave=
-[[Augmented_family|augmented]] [&lt;3, 5, 7], &lt;0, -1, 0]&gt;
+* [[Augmented_family|augmented]] [&lt;3 5 7], &lt;0 -1 0]&gt;
+** augene, tripletone [&lt;3 5 7 8], &lt;0 -1 0 2]&gt;
-<ul><li>augene, tripletone [&lt;3, 5, 7, 8], &lt;0, -1, 0, 2]&gt;<ul><li>augene, tripletone [&lt;3, 5, 7, 8, 10], &lt;0, -1, 0, 2, 2]&gt;</li></ul></li><li>august [&lt;3, 5, 7, 9], &lt;0, -1, 0, -2]&gt;</li></ul>misty [&lt;3, 5, 6], &lt;0, -1, 4]&gt;
+*** augene, tripletone [&lt;3 5 7 8 10], &lt;0 -1 0 2 2]&gt;
+** august [&lt;3 5 7 9], &lt;0 -1 0 -2]&gt;
-<ul><li>misty [&lt;3, 5, 6, 6], &lt;0, -1, 4, 10]&gt;</li></ul>term [&lt;3, 5, 5, 4], &lt;0, -1, 8, 18]&gt;
+* misty [&lt;3 5 6], &lt;0 -1 4]&gt;
+** misty [&lt;3 5 6 6], &lt;0 -1 4 10]&gt;
-semiaug [&lt;3, 5, 7, 9], &lt;0, -2, 0, -5]&gt;
+* term [&lt;3 5 5 4], &lt;0 -1 8 18]&gt;
+* semiaug [&lt;3 5 7 9], &lt;0 -2 0 -5]&gt;
-[[Kleismic_family|tritikleismic]] [&lt;3, 6, 8, 8], &lt;0, -6, -5, 2]&gt;
+* [[Kleismic_family|tritikleismic]] [&lt;3 6 8 8], &lt;0 -6 -5 2]&gt;
+* [[Mutt_family|mutt]] [&lt;3 5 7 8], &lt;0 -7 -1 12]&gt;
-[[Mutt_family|mutt]] [&lt;3, 5, 7, 8], &lt;0, -7, -1, 12]&gt;
+* ternary [&lt;3 5 7 8], &lt;3 5 7 9]&gt;
-ternary [&lt;3, 5, 7, 8], &lt;3, 5, 7, 9]&gt;
 =Four or more periods per octave=
-diminished [&lt;4, 6, 9], &lt;0, 1, 1]&gt;
+* diminished [&lt;4 6 9], &lt;0 1 1]&gt;
+** diminished [&lt;4 6 9 11], &lt;0 1 1 1]&gt;
-<ul><li>diminished [&lt;4, 6, 9, 11], &lt;0, 1, 1, 1]&gt;<ul><li>diminished [&lt;4, 6, 9, 11, 14], &lt;0, 1, 1, 1, 0]&gt;</li><li>demolished [&lt;4, 6, 9, 11, 13], &lt;0, 1, 1, 1, 3]&gt;</li></ul></li></ul>blackwood [&lt;5, 8, 12], &lt;0, 0, -1]&gt;
+*** diminished [&lt;4 6 9 11 14], &lt;0 1 1 1 0]&gt;
+*** demolished [&lt;4 6 9 11 13], &lt;0 1 1 1 3]&gt;
-<ul><li>blacksmith [&lt;5, 8, 12, 14], &lt;0, 0, -1, 0]&gt;</li></ul>hexe [&lt;6, 10, 14, 17], &lt;0, -1, 0, 0]&gt;
+* blackwood [&lt;5 8 12], &lt;0 0 -1]&gt;
+** blacksmith [&lt;5 8 12 14], &lt;0 0 -1 0]&gt;
-jamesbond [&lt;7, 11, 16, 20], &lt;0, 0, 0, -1]&gt;
+* hexe [&lt;6 10 14 17], &lt;0 -1 0 0]&gt;
+* jamesbond [&lt;7 11 16 20], &lt;0 0 0 -1]&gt;
-<ul><li>jamesbond [&lt;7, 11, 16, 20, 24], &lt;0, 0, 0, -1, 0]&gt;</li></ul>whitewood [&lt;7, 11, 16], &lt;0, 0, 1]&gt;
+** jamesbond [&lt;7 11 16 20 24], &lt;0 0 0 -1 0]&gt;
+* whitewood [&lt;7 11 16], &lt;0 0 1]&gt;
-octoid [&lt;8, 13, 19, 23, 28], &lt;0, -3, -4, -5, -3]&gt;
+* octoid [&lt;8 13 19 23 28], &lt;0 -3 -4 -5 -3]&gt;
+* [[Ragismic_microtemperaments|ennealimmal]] [&lt;9 15 22], &lt;0 -2 -3]&gt;
-[[Ragismic_microtemperaments|ennealimmal]] [&lt;9, 15, 22], &lt;0, -2, -3]&gt;
+** ennealimmal [&lt;9 15 22 26], &lt;0 -2 -3 -2]&gt;
+*** ennealimmal [&lt;9 15 22 26 37], &lt;0 -2 -3 -2 -16]&gt;
-<ul><li>ennealimmal [&lt;9, 15, 22, 26], &lt;0, -2, -3, -2]&gt;<ul><li>ennealimmal [&lt;9, 15, 22, 26, 37], &lt;0, -2, -3, -2, -16]&gt;</li></ul></li></ul>[[Breedsmic_temperaments|decoid]] [&lt;10 0 47 36|, &lt;0 2 -3 -1|]
+* [[Breedsmic_temperaments|decoid]] [&lt;10 0 47 36| &lt;0 2 -3 -1|]
+** decoid [&lt;10 0 47 36 98| &lt;0 2 -3 -1 -8|]
-<ul><li>decoid [&lt;10 0 47 36 98|, &lt;0 2 -3 -1 -8|]<ul><li>decoid [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]</li></ul></li></ul>hendecatonic [&lt;11, 17, 26, 30], &lt;0, 1, -1, 2]&gt;
+*** decoid [&lt;10 0 47 36 98 37| &lt;0 2 -3 -1 -8 0|]
+* hendecatonic [&lt;11 17 26 30], &lt;0 1 -1 2]&gt;
-[[Pythagorean_family|catler]] [&lt;12, 19, 28, 34], &lt;0, 0, 0, -1]&gt;
+* [[Pythagorean_family|catler]] [&lt;12 19 28 34], &lt;0 0 0 -1]&gt;
+* [[Pythagorean_family|compton]] [&lt;12 19 28], &lt;0 0 -1]&gt;
-[[Pythagorean_family|compton]] [&lt;12, 19, 28], &lt;0, 0, -1]&gt;
+** compton, waage [&lt;12 19 28 34], &lt;0 0 -1 -2]&gt;
+*** compton, duodecimal [&lt;12 19 28 34 42], &lt;0 0 -1 -2 -3]&gt;
-<ul><li>compton, waage [&lt;12, 19, 28, 34], &lt;0, 0, -1, -2]&gt;<ul><li>compton, duodecimal [&lt;12, 19, 28, 34, 42], &lt;0, 0, -1, -2, -3]&gt;</li></ul></li></ul>duodecim <span style="background-color: #ffffff;">[&lt;12, 19, 28, 34, 42], &lt;0, 0, 0, 0, -1]&gt;</span>
+* duodecim [&lt;12 19 28 34 42], &lt;0 0 0 0 -1]&gt;
+* atomic [&lt;12 19 28], &lt;0 1 -7]&gt;
-atomic [&lt;12, 19, 28], &lt;0, 1, -7]&gt;
+* hemiennealimmal [&lt;18 28 41 50 62], &lt;0 2 3 2 1]&gt;
+* [[Ragismic_microtemperaments|enneadecal]] [&lt;19 30 44], &lt;0 1 1]&gt;
-hemiennealimmal [&lt;18, 28, 41, 50, 62], &lt;0, 2, 3, 2, 1]&gt;
+** enneadecal [&lt;19 30 44 53], &lt;0 1 1 3]&gt;
+* undevigintone [&lt;19 30 44 53 66], &lt;0 0 0 0 -1]&gt;
-[[Ragismic_microtemperaments|enneadecal]] [&lt;19, 30, 44], &lt;0, 1, 1]&gt;
+* icosidillic [&lt;22 35 51 62 76], &lt;0 -1 1 -2 1]&gt;
+* vigintiduo [&lt;22 35 51 62 76], &lt;0 0 0 0 1]&gt;
-<ul><li>enneadecal [&lt;19, 30, 44, 53], &lt;0, 1, 1, 3]&gt;</li></ul>undevigintone <span style="background-color: #ffffff;">[&lt;19, 30, 44, 53, 66], &lt;0, 0, 0, 0, -1]&gt;</span>
+* mystery [&lt;29 46 67 81 100 107], &lt;0 0 1 1 1 1]&gt;
+* hemienneadecal [&lt;38 60 88 106 131], &lt;0 1 1 3 2]&gt;
-icosidillic [&lt;22, 35, 51, 62, 76], &lt;0, -1, 1, -2, 1]&gt;
-<span style="background-color: #ffffff;">vigintiduo [&lt;22, 35, 51, 62, 76], &lt;0, 0, 0, 0, 1]&gt;</span>
-mystery [&lt;29, 46, 67, 81, 100, 107], &lt;0, 0, 1, 1, 1, 1]&gt;
-hemienneadecal [&lt;38, 60, 88, 106, 131], &lt;0, 1, 1, 3, 2]&gt;
 [[Category:list]]
@@ Line 309: / Line 312: @@
 [[Category:proposal]]
 [[Category:rank_2]]
-[[Category:temperaments]]
+[[Category:temperament]]
 [[Category:theory]]