Polaris: Difference between revisions

Revision as of 01:51, 16 March 2023

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 11/5's fall short of 15/11. It enables 9:11:15 no-twos chords. Polaris temperament is to Arcturus as meantone temperament is to Pythagorean tuning. Similar to Arcturus, It contains MOS scales of the families 2L 5s<3/1>, 2L 7s<3/1>, and 2L 9s<3/1>.

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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 [[11/5]]'s fall short of [[15/11]]. It enables 9:11:15 no-twos chords. Polaris temperament is to [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. Similar to Arcturus, 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>]], although it differs from Arcturus in having a  [[2L 11s (tritave-equivalent)|2L 11s<3/1>]] triskaidecatonic scale rather than [[11L 2ss (tritave-equivalent)|11L 2s<3/1>]] .
+'''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 [[11/5]]'s fall short of [[15/11]]. It enables 9:11:15 no-twos chords. Polaris temperament is to [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. Similar to Arcturus, 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>]].
 == Interval chain (CTE tuning) ==
 {|class="wikitable"