Dual-fifth tuning: Difference between revisions
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A '''dual-fifth system''' is a(n octave-equivalent) tuning system with two sizes of fifths, '''major fifth''' and '''minor fifth''' instead of a single perfect fifth, and accordingly two sizes fourths, '''major fourth''' and '''minor fourth''' instead of a single perfect fourth. | A '''dual-fifth system''' is a(n octave-equivalent) tuning system with two sizes of fifths, '''major fifth''' and '''minor fifth''' instead of a single perfect fifth, and accordingly two sizes fourths, '''major fourth''' and '''minor fourth''' instead of a single perfect fourth. | ||
== Dual-fifth edos == | == Dual-fifth edos == | ||
[[18edo]] is usually considered the quintessential dual-fifth edo by people who work in dual-fifth systems, which has a 733.3c sharp fifth 31.4c sharp from pure [[3/2], and a 666.7c flat fifth 35.3 cents flat. | [[18edo]] is usually considered the quintessential dual-fifth edo by people who work in dual-fifth systems (which are admittedly few), which has a 733.3c sharp fifth 31.4c sharp from pure [[3/2]], and a 666.7c flat fifth 35.3 cents flat. | ||
== Dual-fifth temperaments == | == Dual-fifth temperaments == | ||
Unlike conventional temperaments, "[[dual-fifth temperaments]]" do not attempt to optimize every interval to low-limit JI, but usually 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⁻.9.5" and 2.3⁺.3⁻.5 are equivalent subgroups. | Unlike conventional temperaments, "[[dual-fifth temperaments]]" do not attempt to optimize every interval to low-limit JI, but usually 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⁻.9.5" and 2.3⁺.3⁻.5 are equivalent subgroups. | ||