359edo: Difference between revisions

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== Theory ==

359edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. ~~It provides~~ the [[optimal patent val]] for ~~the~~ 11-limit [[hera]] ~~temperament~~.

359edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. In the 5-limit it tempers out the [[würschmidt comma]] and the [[counterschisma]]; in the 7-limit [[2401/2400]] and [[3136/3125]], supporting [[hemiwürschmidt]]; in the 11-limit, [[8019/8000]], providing the [[optimal patent val]] for 11-limit [[hera]].

359edo [[support]]s a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359edo this is the step 203\359 of 678.55153¢.

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Exaggerated Hornbostel superdiatonic scale: 47 47 47 15 47 47 47 47 15 (fails in the position of Phi and the square root of Pi [+1\359 step of each one]{{clarify}}).

~~359edo is the 72nd [[prime edo]].~~

=== Prime harmonics ===

=== Subsets and supersets ===

359edo is the 72nd [[prime edo]]. [[718edo]], which doubles it, provides a good correction to the harmonics 5, 13, 17, and 31.

== Regular temperament properties ==

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~~[[Category:Equal divisions of the octave|###]] ~~

~~[[Category:Prime EDO]]~~

[[Category:Hera]]

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 == Theory ==
-edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. It provides the [[optimal patent val]] for the 11-limit [[hera]] temperament.
+edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. In the 5-limit it tempers out the [[würschmidt comma]] and the [[counterschisma]]; in the 7-limit [[2401/2400]] and [[3136/3125]], supporting [[hemiwürschmidt]]; in the 11-limit, [[8019/8000]], providing the [[optimal patent val]] for 11-limit [[hera]].
 edo [[support]]s a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359edo this is the step 203\359 of 678.55153¢.
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 Exaggerated Hornbostel superdiatonic scale: 47 47 47 15 47 47 47 47 15 (fails in the position of Phi and the square root of Pi [+1\359 step of each one]{{clarify}}).
-edo is the 72nd [[prime edo]].
 === Prime harmonics ===
 {{Harmonics in equal|359|columns=11}}
+=== Subsets and supersets ===
+edo is the 72nd [[prime edo]]. [[718edo]], which doubles it, provides a good correction to the harmonics 5, 13, 17, and 31.
 == Regular temperament properties ==
@@ Line 91: / Line 92: @@
 |}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-[[Category:Prime EDO]]
 [[Category:Hera]]