Polaris: Difference between revisions
Jump to navigation
Jump to search
CompactStar (talk | contribs) No edit summary |
CompactStar (talk | contribs) No edit summary |
||
| Line 1: | Line 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 [[5/3]]'s fall short of [[15/11]]. Polaris temperament is to [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. 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 smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option. | '''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 temperament is to [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. 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 heptatonic scale is usually too lopsided to use so the nonatonic scale is the smallest usable option. 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 02:06, 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 5/3's fall short of 15/11. Polaris temperament is to Arcturus as meantone temperament is to Pythagorean tuning. It contains MOS scales of the families 2L 5s<3/1>, 2L 7s<3/1>, and 2L 9s<3/1>. The heptatonic scale is usually too lopsided to use so the nonatonic scale is the smallest usable option. 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 chord and its "minor" version 99:135:165.