15th-octave temperaments
15edo has some close approximations including 22/21 to one step and 77/64 to four steps.
Temperaments discussed elsewhere include quindecic, pentadecal, slendscape, and phosphorus.
Pentadecoid
In pentadecoid, the period (1\15) is given an interpretation of 22/21, and four of them represent the keenanismic minor third, 77/64 = (147/128)⋅(22/21). The temperament is named for an analog of its relating temperaments, decoid (130 & 140) and triacontoid (120 & 150). Triacontoid is a weak extension of pentadecoid, as well as slendscape (255 & 270).
Subgroup: 2.3.7.11
Comma list: 1362944/1361367, 1771561/1769472
Mapping: [⟨15 108 0 94], ⟨0 -2 1 -1]]
- mapping generators: ~22/21, ~7
Optimal tuning (CTE): ~22/21 = 80.0000, ~8/7 = 231.0071 (~1029/1024 = 8.9929)
Optimal ET sequence: 120, 135, 660, 795, 930, 1065, 1200, 1335, 2535e
Badness (Sintel): 0.951