Polaris: Difference between revisions

← Older edit

VisualWikitext

@@ 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 heptatonic scale is usually extremely lopsided in Polaris temperament (with L:s often exceeding 6:1) so the nonatonic scale is the smallest usable option, although it only slightly less lopsided with L:s > 4/1. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.
+'''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]]. 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. Good tunings for Polaris are [[15edt]] and [[32edt]].
+Technical data: [[No-twos subgroup temperaments#Polaris]]
 == Interval chain (CTE tuning) ==
 {|class="wikitable"
 |-
-!Generators up
+! Generators up
-!Cents
+! Cents
 |-
-|0
+| 0
-|0.0
+| 0.0
 |-
-|1
+| 1
-|892.6
+| 892.6
 |-
-|2
+| 2
-|1785.2
+| 1785.2
 |-
-|3
+| 3
-|775.8
+| 775.8
 |-
-|4
+| 4
-|1668.4
+| 1668.4
 |-
-|5
+| 5
-|659.0
+| 659.0
 |-
-|6
+| 6
-|1551.6
+| 1551.6
 |-
-|7
+| 7
-|542.2
+| 542.2
 |-
-|8
+| 8
-|1434.8
+| 1434.8
 |-
-|9
+| 9
-|425.4
+| 425.4
 |-
-|10
+| 10
-|1318.0
+| 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.
+Due to equating 7 5/3's with 15/11, Polaris contains an accurate tuning of the chord 33:45:55.
 == Scales ==
 * [[Polaris9]]
 * [[Polaris11]]
-[[Category:Temperaments]]
+[[Category:Polaris| ]] <!-- main article -->
-[[Category:Nonoctave]]
+[[Category:Rank-2 temperaments]]
-[[Category:Tritave]]
+[[Category:Non-octave temperaments]]