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| '''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. Polaris temperament is to [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)|2L 9s<3/1>]]. The heptatonic scale is usually too lopsided so the nonatonic scale is the smallest usable option , although even then, L:s > 3:1. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.
| | #redirect [[No-twos subgroup temperaments #Polaris]] |
| == Interval chain (CTE tuning) ==
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| {|class="wikitable"
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| |-
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| !Generators up
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| !Cents
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| |-
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| |0
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| |0.0
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| |-
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| |1
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| |892.6
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| |-
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| |2
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| |1785.2
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| |-
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| |3
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| |775.8
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| |-
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| |4
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| |1668.4
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| |-
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| |5
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| |659.0
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| |-
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| |6
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| |1551.6
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| |-
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| |7
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| |542.2
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| |-
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| |8
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| |1434.8
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| |-
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| |9
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| |425.4
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| |-
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| |10
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| |1318.0
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| |}
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| == Chords ==
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| Due to equating 7 5/3's with 15/11, Polaris enables the 9:11:15 no-twos chord and its "minor" version 99:135:165.
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| == Scales ==
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| * [[Polaris9]]
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| * [[Polaris11]]
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| [[Category:Temperaments]] | | [[Category:Rank-2 temperaments]] |
| [[Category:Nonoctave]] | | [[Category:Non-octave temperaments]] |