|
|
| (12 intermediate revisions by 4 users not shown) |
| Line 1: |
Line 1: |
| '''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 hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. 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) ==
| |
| {|class="wikitable"
| |
| |-
| |
| !Generators up
| |
| !Cents
| |
| |-
| |
| |0
| |
| |0.0
| |
| |-
| |
| |1
| |
| |892.6
| |
| |-
| |
| |2
| |
| |1785.2
| |
| |-
| |
| |3
| |
| |775.8
| |
| |-
| |
| |4
| |
| |1668.4
| |
| |-
| |
| |5
| |
| |659.0
| |
| |-
| |
| |6
| |
| |1551.6
| |
| |-
| |
| |7
| |
| |542.2
| |
| |-
| |
| |8
| |
| |1434.8
| |
| |-
| |
| |9
| |
| |425.4
| |
| |-
| |
| |10
| |
| |1318.0
| |
| |}
| |
| == Chords ==
| |
| 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.
| |
| == Scales ==
| |
| * [[Polaris9]]
| |
| * [[Polaris11]]
| |
|
| |
|
| [[Category:Temperaments]] | | [[Category:Rank-2 temperaments]] |
| [[Category:Nonoctave]] | | [[Category:Non-octave temperaments]] |
| [[Category:Tritave]]
| |