359edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:46Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Counterschismic]]		\| [[Counterschismic]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: + category

2025-07-12T12:47:48Z

+ category

← Older revision		Revision as of 12:47, 12 July 2025
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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]		* "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:Hera]]
	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294 at 14:46, 20 February 2025

2025-02-20T14:46:16Z

← Older revision		Revision as of 14:46, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|359~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Lériendil at 14:09, 12 February 2025

2025-02-12T14:09:23Z

← Older revision		Revision as of 14:09, 12 February 2025
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	== Theory ==		== 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]]. 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 ~~dividing~~ the fifth into multiple parts.		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}}.		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}}.

Lériendil at 04:21, 5 February 2025

2025-02-05T04:21:22Z

← Older revision		Revision as of 04:21, 5 February 2025
Line 3:		Line 3:

	== Theory ==		== 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]]. 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 dividing the fifth into parts.		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 dividing 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}}.		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}}.

Lériendil: /* Theory */

2025-01-31T18:34:06Z

Theory

← Older revision		Revision as of 18:34, 31 January 2025
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	== Theory ==		== 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 dividing the fifth into 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}}.		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 ===		=== 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.		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 ==		== Regular temperament properties ==

ArrowHead294 at 19:35, 15 January 2025

2025-01-15T19:35:55Z

← Older revision		Revision as of 19:35, 15 January 2025
Line 5:		Line 5:
	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]].

	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 ~~Pythagorean fifth (701~~.~~955¢) minus the~~ Pythagorean ~~comma (23.46¢) = 678.495¢~~; in 359edo this is ~~the step~~ 203~~\359 of~~ 678.~~55153¢~~.		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}}.

	Pythagorean diatonic scale: 61 61 27 61 61 61 27		Pythagorean diatonic scale: 61 61 27 61 61 61 27
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	\| 393216/390625, {{monzo\| -69 45 -1 }}		\| 393216/390625, {{monzo\| -69 45 -1 }}
	\| {{mapping\| 359 569 834 }}		\| {{mapping\| 359 569 834 }}
	\| ~~−0~~.2042		\| −0.2042
	\| 0.2910		\| 0.2910
	\| 8.71		\| 8.71
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	\| 2401/2400, 3136/3125, {{monzo\| -18 24 -5 -3 }}		\| 2401/2400, 3136/3125, {{monzo\| -18 24 -5 -3 }}
	\| {{mapping\| 359 569 834 1008 }}		\| {{mapping\| 359 569 834 1008 }}
	\| ~~−0~~.2007		\| −0.2007
	\| 0.2521		\| 0.2521
	\| 7.54		\| 7.54
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	\| 2401/2400, 3136/3125, 8019/8000, 42592/42525		\| 2401/2400, 3136/3125, 8019/8000, 42592/42525
	\| {{mapping\| 359 569 834 1008 1242 }}		\| {{mapping\| 359 569 834 1008 1242 }}
	\| ~~−0~~.1729		\| −0.1729
	\| 0.2322		\| 0.2322
	\| 6.95		\| 6.95
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	\| 729/728, 847/845, 1001/1000, 1716/1715, 3136/3125		\| 729/728, 847/845, 1001/1000, 1716/1715, 3136/3125
	\| {{mapping\| 359 569 834 1008 1242 1328 }} (359f)		\| {{mapping\| 359 569 834 1008 1242 1328 }} (359f)
	\| ~~−0~~.2257		\| −0.2257
	\| 0.2426		\| 0.2426
	\| 7.26		\| 7.26
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	\| [[Counterschismic]]		\| [[Counterschismic]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "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]		* "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:Hera]]		[[Category:Hera]]
	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:37:14Z

Partial undo

← Older revision		Revision as of 12:37, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 0.2426		\| 0.2426
	\| 7.26		\| 7.26
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 4/3		\| 4/3
	\| [[Counterschismic]]		\| [[Counterschismic]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==

ArrowHead294 at 04:17, 16 November 2024

2024-11-16T04:17:15Z

← Older revision		Revision as of 04:17, 16 November 2024
Line 18:		Line 18:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 393216/390625, {{monzo\| -69 45 -1 }}		\| 393216/390625, {{monzo\| -69 45 -1 }}
	\| {{mapping\| 359 569 834 }}		\| {{mapping\| 359 569 834 }}
	\| -0.2042		\| −0.2042
	\| 0.2910		\| 0.2910
	\| 8.71		\| 8.71
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	\| 2401/2400, 3136/3125, {{monzo\| -18 24 -5 -3 }}		\| 2401/2400, 3136/3125, {{monzo\| -18 24 -5 -3 }}
	\| {{mapping\| 359 569 834 1008 }}		\| {{mapping\| 359 569 834 1008 }}
	\| -0.2007		\| −0.2007
	\| 0.2521		\| 0.2521
	\| 7.54		\| 7.54
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	\| 2401/2400, 3136/3125, 8019/8000, 42592/42525		\| 2401/2400, 3136/3125, 8019/8000, 42592/42525
	\| {{mapping\| 359 569 834 1008 1242 }}		\| {{mapping\| 359 569 834 1008 1242 }}
	\| -0.1729		\| −0.1729
	\| 0.2322		\| 0.2322
	\| 6.95		\| 6.95
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	\| 729/728, 847/845, 1001/1000, 1716/1715, 3136/3125		\| 729/728, 847/845, 1001/1000, 1716/1715, 3136/3125
	\| {{mapping\| 359 569 834 1008 1242 1328 }} (359f)		\| {{mapping\| 359 569 834 1008 1242 1328 }} (359f)
	\| -0.2257		\| −0.2257
	\| 0.2426		\| 0.2426
	\| 7.26		\| 7.26
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 4/3		\| 4/3
	\| [[Counterschismic]]		\| [[Counterschismic]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "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]		* "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:Hera]]		[[Category:Hera]]
	[[Category:Listen]]		[[Category:Listen]]

Francium: +music

2024-02-20T12:00:53Z

+music

← Older revision		Revision as of 12:00, 20 February 2024
Line 92:		Line 92:
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Music ==
			; [[Francium]]
			* "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:Hera]]		[[Category:Hera]]
			[[Category:Listen]]