Polaris

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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 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.

Scales