Dual-fifth temperaments: Difference between revisions
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Unlike conventional temperaments, [[dual-fifth]] temperaments do not attempt to optimize every [[interval]] to low-limit [[JI]], but treat the "sharp 3" (3⁺) and the "flat 3" (3⁻) as distinct dimensions. The sharp 3 and the flat 3 are not meant to represent JI intervals by themselves, but satisfy 3⁺ × 3⁻ = 9 (representing [[9/1]] in JI); hence 2.3⁻.9 and 2.3⁻.3⁺ are the same [[subgroup]]. | Unlike conventional temperaments, [[dual-fifth]] temperaments do not attempt to optimize every [[interval]] to low-limit [[JI]], but treat the "sharp 3" (3⁺) and the "flat 3" (3⁻) as distinct dimensions. The sharp 3 and the flat 3 are not meant to represent JI intervals by themselves, but satisfy 3⁺ × 3⁻ = 9 (representing [[9/1]] in JI); hence 2.3⁻.9 and 2.3⁻.3⁺ are the same [[subgroup]]. | ||