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. 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.
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.