46th-octave temperaments

Fractional-octave temperaments

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For information on the wheel and its hinges, see 46edo.

Palladium (5-limit)

In the 5-limit, palladium tempers out the comma by which 46 10/9 minor tones fall short of 7 octaves. For the canonical 7-limit extension, see Ragismic microtemperaments#Palladium.

Subgroup: 2.3.5

Comma list: [-39 92 -46⟩

Mapping: [⟨46 73 107], ⟨0 -1 -2]]

mapping generators: ~2541865828329/2500000000000 = 1\46, ~3/2 = 701.888

Optimal tuning (CTE): ~3/2 = 701.888

Supporting ETs: 46, 414, 460, 506, 552, 966, 1012, 1426

Quadrapalladium

Quadrapalladium can be described as the 414 & 1012 temperament.

Subgroup: 2.3.5.7

Comma list: 2401/2400, [-29 94 -42 -8⟩

Mapping: [⟨46 0 -39 38], ⟨0 4 8 5]]

mapping generators: ~7625597484987/7503125000000 = 1\46, ~282429536481/214375000000 = 475.477

Optimal tuning (CTE): ~282429536481/214375000000 = 475.477

Optimal ET sequence: 414, 1012, 1426, 2438