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 [[ | '''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]] | |||