Polaris
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 extremely lopsided (with L:s often exceeding 5:1) 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.