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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 [[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. | '''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) == | == Interval chain (CTE tuning) == | ||
{|class="wikitable" | {|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 == | == Chords == | ||
Due to equating 7 5/3's with 15/11, Polaris | Due to equating 7 5/3's with 15/11, Polaris contains an accurate tuning of the chord 33:45:55. | ||
== Scales == | == Scales == | ||
* [[Polaris9]] | * [[Polaris9]] | ||
* [[Polaris11]] | * [[Polaris11]] | ||
[[Category: | [[Category:Polaris| ]] <!-- main article --> | ||
[[Category: | [[Category:Rank-2 temperaments]] | ||
[[Category: | [[Category:Non-octave temperaments]] | ||
Latest revision as of 09:27, 29 April 2025
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 scales of the families 2L 5s<3/1>, 2L 7s<3/1>, and 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)
| 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.