46th-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|46}} | ||
For information on the wheel and its hinges, see [[46edo]]. | For information on the wheel and its hinges, see [[46edo]]. | ||
== Palladium (5-limit) == | == 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]]. | 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]]. | ||
Revision as of 03:54, 14 February 2025
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
]