239edo: Difference between revisions

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== Theory ==

239edo excels as an [[11-limit]] system with a sharp tendency: [[prime harmonic]]s 3 through 11 are all tuned sharp. The accuracy of [[12/11]] is particularly notable, as 30\239 represents a [[convergent]] to this interval, ~~although the circle it~~ forms ~~is only~~ [[consistent circle~~|weakly consistent~~]].

239edo excels as an [[11-limit]] system with a sharp tendency: [[prime harmonic]]s 3 through 11 are all tuned sharp. The accuracy of [[12/11]] is particularly notable, as 30\239 represents a [[convergent]] to this interval, which forms a barely [[consistent circle]], with the closing error being about 45% of a step.

239 is a convergent to the [[argent temperament]], where the perfect fourth and fifth are in the logarithmic ratio of 1:√2, and with a fifth in this range, tempers out [[5120/5103]] with great accuracy. This implies that [[81/80]] and [[64/63]] are equated (to 5 steps), that three wholetones ([[9/8]]) stack to [[10/7]], and that the [[2187/2048|apotome]], the [[256/243|limma]], and the [[Pythagorean comma]] are equated with [[15/14]] (24 steps), [[21/20]] (17 steps), and [[50/49]] (7 steps) respectively.

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 == Theory ==
-edo excels as an [[11-limit]] system with a sharp tendency: [[prime harmonic]]s 3 through 11 are all tuned sharp. The accuracy of [[12/11]] is particularly notable, as 30\239 represents a [[convergent]] to this interval, although the circle it forms is only [[consistent circle|weakly consistent]].
+edo excels as an [[11-limit]] system with a sharp tendency: [[prime harmonic]]s 3 through 11 are all tuned sharp. The accuracy of [[12/11]] is particularly notable, as 30\239 represents a [[convergent]] to this interval, which forms a barely [[consistent circle]], with the closing error being about 45% of a step.
 is a convergent to the [[argent temperament]], where the perfect fourth and fifth are in the logarithmic ratio of 1:√2, and with a fifth in this range, tempers out [[5120/5103]] with great accuracy. This implies that [[81/80]] and [[64/63]] are equated (to 5 steps), that three wholetones ([[9/8]]) stack to [[10/7]], and that the [[2187/2048|apotome]], the [[256/243|limma]], and the [[Pythagorean comma]] are equated with [[15/14]] (24 steps), [[21/20]] (17 steps), and [[50/49]] (7 steps) respectively.