69th-octave temperaments
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Fractional-octave temperaments
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Ptolemi-nicemic (rank-4)
A highly precise temperament derived from the proximity of 100/99 to the step of 1\69.
Subgroup: 2.3.5.7.11
Comma list: [137 -138 138 0 -69⟩
Mapping: [⟨69 0 0 0 137], ⟨0 1 0 0 -2], ⟨0 0 1 0 2], ⟨0 0 0 1 0]]
- mapping generators: ~100/99 = 1\69, ~3, ~5, ~7
Supporting ETs: 69, 414, 552, 897, 966, 1311, 1380, 3243, 7797, 8763, 11040, 12006, 20769, 31395