Polaris: Difference between revisions

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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]].
'''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
! 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 contains an accurate tuning of the chord 33:45:55.
 
== Scales ==
* [[Polaris9]]
* [[Polaris11]]
 
[[Category:Polaris| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Non-octave temperaments]]