69th-octave temperaments

Fractional-octave temperaments

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← 71st-octave • 72nd-octave • 73rd-octave →

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← 68th-octave • 69th-octave • 70th-octave →

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← 65th-octave • 66th-octave • 67th-octave →

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