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. 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 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]]. Due to the fifth being reached at the extremely divisible number of 210 steps, 359edo turns out to be important as an accurate supporting edo of various temperaments that divide the fifth into multiple parts.

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{{citation needed}}; the 678.495{{c}} [[262144/177147|Pythagorean diminished sixth]]; in 359edo this is reached using 203 steps, or 678.55153{{c}}.

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=== 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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* "This Madness Won't Stop!" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/50O9nTxeMafR8AyBtsPSKa Spotify] | [https://francium223.bandcamp.com/track/this-madness-wont-stop Bandcamp] | [https://www.youtube.com/watch?v=UJyIKzgLVQU YouTube]

[[Category:3-limit record edos|###]]

[[Category:Hera]]

[[Category:Listen]]

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 {{Infobox ET}}
-{{EDO intro|359}}
+{{ED intro}}
 == 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. 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 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]]. Due to the fifth being reached at the extremely divisible number of 210 steps, 359edo turns out to be important as an accurate supporting edo of various temperaments that divide the fifth into multiple parts.
 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{{citation needed}}; the 678.495{{c}} [[262144/177147|Pythagorean diminished sixth]]; in 359edo this is reached using 203 steps, or 678.55153{{c}}.
@@ Line 15: / Line 15: @@
 === 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 99: / Line 99: @@
 * "This Madness Won't Stop!" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/50O9nTxeMafR8AyBtsPSKa Spotify] | [https://francium223.bandcamp.com/track/this-madness-wont-stop Bandcamp] | [https://www.youtube.com/watch?v=UJyIKzgLVQU YouTube]
+[[Category:3-limit record edos|###]] <!-- 3-digit number -->
 [[Category:Hera]]
 [[Category:Listen]]