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 [[5/3]]'s fall short of [[15/11 | '''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. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option. | ||
== Interval chain (CTE tuning) == | == Interval chain (CTE tuning) == | ||
{|class="wikitable" | {|class="wikitable" | ||
Revision as of 02:46, 31 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 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. The smallest EDT that can seriously claim to support Polaris temperament is 15edt, with 32edt also being a good option.
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 enables the 9:11:15 no-twos otonal chord and its "minor" utonal counterpart 99:135:165.