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 [[temperament]] | Here is a list of some names that have been proposed for 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.) | ||
{{Todo|inline=1| update }} | {{Todo|inline=1| update }} | ||
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** hornbostel [{{val| 1 0 7 -16 }}, {{val| 0 1 -3 12}}]; | ** hornbostel [{{val| 1 0 7 -16 }}, {{val| 0 1 -3 12}}]; | ||
* [[meantone]] [{{val| 1 0 -4 }}, {{val| 0 1 4}}]; | * [[meantone]] [{{val| 1 0 -4 }}, {{val| 0 1 4}}]; | ||
** [[ | ** [[dominant (temperament)|dominant]] [{{val| 1 0 -4 6 }}, {{val| 0 1 4 -2}}]; | ||
*** arnold [{{val| 1 0 -4 6 5 }}, {{val| 0 1 4 -2 -1}}]; | *** arnold [{{val| 1 0 -4 6 5 }}, {{val| 0 1 4 -2 -1}}]; | ||
*** dominant [{{val| 1 0 -4 6 13 }}, {{val| 0 1 4 -2 -6}}]; | *** dominant [{{val| 1 0 -4 6 13 }}, {{val| 0 1 4 -2 -6}}]; | ||
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*** meantone [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18}}]; | *** meantone [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18}}]; | ||
* [[avila]] [{{val| 1 0 -7 }}, {{val| 0 1 6}}]; | * [[avila]] [{{val| 1 0 -7 }}, {{val| 0 1 6}}]; | ||
* [[helmholtz]] [{{val| 1 0 15 }}, {{val| 0 1 -8}}]; | * [[Helmholtz (temperament)|helmholtz]] [{{val| 1 0 15 }}, {{val| 0 1 -8}}]; | ||
** schism [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2}}]; | ** schism [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2}}]; | ||
** garibaldi [{{val| 1 0 15 25 }}, {{val| 0 1 -8 -14}}]; | ** garibaldi [{{val| 1 0 15 25 }}, {{val| 0 1 -8 -14}}]; | ||
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* [[triton]] [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8}}]; | * [[triton]] [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8}}]; | ||
* [[liese]], gawel [{{val| 1 0 -4 -3 }}, {{val| 0 3 12 11}}]; | * [[liese]], gawel [{{val| 1 0 -4 -3 }}, {{val| 0 3 12 11}}]; | ||
* [[ | * [[alphatricot]] [{{val| 1 0 -13 }}, {{val| 0 3 29}}]; | ||
* [[tetracot]] [{{val| 1 1 1 }}, {{val| 0 4 9}}]; | * [[tetracot]] [{{val| 1 1 1 }}, {{val| 0 4 9}}]; | ||
** [[monkey]] [{{val| 1 1 1 5 }}, {{val| 0 4 9 -15}}]; | ** [[monkey]] [{{val| 1 1 1 5 }}, {{val| 0 4 9 -15}}]; | ||
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== Three periods per octave == | == Three periods per octave == | ||
* [[augmented]] [{{val| 3 0 7 }}, {{val| 0 1 0}}]; | * [[augmented (temperament)|augmented]] [{{val| 3 0 7 }}, {{val| 0 1 0}}]; | ||
** [[augene]], tripletone [{{val| 3 0 7 18 }}, {{val| 0 1 0 -2}}]; | ** [[augene]], tripletone [{{val| 3 0 7 18 }}, {{val| 0 1 0 -2}}]; | ||
*** augene, tripletone [{{val| 3 0 7 18 20 }}, {{val| 0 1 0 -2 -2}}]; | *** augene, tripletone [{{val| 3 0 7 18 20 }}, {{val| 0 1 0 -2 -2}}]; | ||
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* [[misty]] [{{val| 3 0 26 }}, {{val| 0 1 -4}}]; | * [[misty]] [{{val| 3 0 26 }}, {{val| 0 1 -4}}]; | ||
** misty [{{val| 3 0 26 56 }}, {{val| 0 1 -4 -10}}]; | ** misty [{{val| 3 0 26 56 }}, {{val| 0 1 -4 -10}}]; | ||
* [[term]] [{{val| 3 0 45 94 }}, {{val| 0 1 -8 -18}}]; | * [[term (temperament)|term]] [{{val| 3 0 45 94 }}, {{val| 0 1 -8 -18}}]; | ||
* semiaug [{{val| 3 1 7 -1 }}, {{val| 0 2 0 5}}]; | * semiaug [{{val| 3 1 7 -1 }}, {{val| 0 2 0 5}}]; | ||
* [[tritikleismic]] [{{val| 3 0 3 10 }}, {{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 0 }}, {{val| 0 0 0 1}}]; | * [[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]] [{{val| 4 0 3 }}, {{val| 0 1 1}}]; | * [[diminished (temperament)|diminished]] [{{val| 4 0 3 }}, {{val| 0 1 1}}]; | ||
** diminished [{{val| 4 0 3 5 }}, {{val| 0 1 1 1}}]; | ** diminished [{{val| 4 0 3 5 }}, {{val| 0 1 1 1}}]; | ||
*** diminished [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0}}]; | *** diminished [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0}}]; | ||
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[[Category:Lists]] | [[Category:Lists]] | ||
[[Category:Temperament naming]] | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||