16th-octave temperaments
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16edo is an interesting system when it comes to fractional-octave temperaments, as it has no straightforward JI approximation on its own, but some of its multiples do.
Sulfur
Subgroup: 2.3.5
Comma list: [115 96 -16⟩
Mapping: [⟨16 0 -115], ⟨0 1 6]]
- mapping generators: ~214748364800000/205891132094649 = 1\16, ~3
Optimal tuning (CTE): ~3/2 = 701.980
Supporting ETs: 48, 176, 224, 400, 624, 848, 1024, 1072, 1296, 1472
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 936/935, 1716/1715, 2080/2079, 2376/2375, 4096/4095, 11016/11011
Mapping: [⟨16 0 -115 121 30 186 319 423], ⟨0 1 6 -3 1 -5 -10 -14]]
- mapping generators: ~117/112 = 1\16, ~3
Optimal tuning (CTE): ~3/2 = 701.950