509edo - Revision history

Overthink: /* Theory */ specify "optimal"; explanation; fix link

2026-04-22T01:27:53Z

Theory: specify "optimal"; explanation; fix link

← Older revision		Revision as of 01:27, 22 April 2026
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	== Theory ==		== Theory ==
	509edo has a sharp tendency in lower [[harmonic]]s. ~~The~~ [[13-limit]] [[TE ~~tuning\|optimal~~ tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.		509edo has a sharp tendency in lower [[harmonic]]s. It is only consistent to the [[7-odd-limit]] due to harmonic [[3/1\|3]] being too sharp, causing harmonic [[9/1\|9]] to become inconsistent, but the [[13-limit]] [[TE tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave stretch\|octave compression]] tight.

	As an equal temperament, it [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].		As an equal temperament, it [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].

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"

2026-03-13T13:31:40Z

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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	\| [[Amity]]		\| [[Amity]]
	\|}		\|}
	<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 ==

Francium: changed EDO intro to ED intro

2025-02-21T06:17:25Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:17, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|509~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:23:31Z

Theory: cleanup

← Older revision		Revision as of 16:23, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	509edo has a sharp tendency in lower [[harmonic]]s. The 13-limit [[TE tuning\|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.		509edo has a sharp tendency in lower [[harmonic]]s. The [[13-limit]] [[TE tuning\|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.

	It [[tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].		As an equal temperament, it [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 19:38, 15 January 2025

2025-01-15T19:38:09Z

← Older revision		Revision as of 19:38, 15 January 2025
Line 5:		Line 5:
	509edo has a sharp tendency in lower [[harmonic]]s. The 13-limit [[TE tuning\|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.		509edo has a sharp tendency in lower [[harmonic]]s. The 13-limit [[TE tuning\|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.

	~~The equal temperament~~ [[~~tempering out\|~~tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].		It [[tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	\| {{monzo\| 807 -509 }}		\| {{monzo\| 807 -509 }}
	\| {{mapping\| 509 807 }}		\| {{mapping\| 509 807 }}
	\| ~~−0~~.1890		\| −0.1890
	\| 0.1889		\| 0.1889
	\| 8.01		\| 8.01
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	\| {{monzo\| 9 -13 5 }}, {{monzo\| 93 -3 -38 }}		\| {{monzo\| 9 -13 5 }}, {{monzo\| 93 -3 -38 }}
	\| {{mapping\| 509 807 1182 }}		\| {{mapping\| 509 807 1182 }}
	\| ~~−0~~.1729		\| −0.1729
	\| 0.1559		\| 0.1559
	\| 6.61		\| 6.61
Line 42:		Line 42:
	\| 2401/2400, 1600000/1594323, 29360128/29296875		\| 2401/2400, 1600000/1594323, 29360128/29296875
	\| {{mapping\| 509 807 1182 1429 }}		\| {{mapping\| 509 807 1182 1429 }}
	\| ~~−0~~.1415		\| −0.1415
	\| 0.1456		\| 0.1456
	\| 6.18		\| 6.18
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	\| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323		\| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323
	\| {{mapping\| 509 807 1182 1429 1761 }}		\| {{mapping\| 509 807 1182 1429 1761 }}
	\| ~~−0~~.1335		\| −0.1335
	\| 0.1312		\| 0.1312
	\| 5.57		\| 5.57
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	\| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625		\| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625
	\| {{mapping\| 509 807 1182 1429 1761 1884 }}		\| {{mapping\| 509 807 1182 1429 1761 1884 }}
	\| ~~−0~~.1618		\| −0.1618
	\| 0.1354		\| 0.1354
	\| 5.74		\| 5.74
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	\| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913		\| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913
	\| {{mapping\| 509 807 1182 1429 1761 1884 2081 }}		\| {{mapping\| 509 807 1182 1429 1761 1884 2081 }}
	\| ~~−0~~.1784		\| −0.1784
	\| 0.1318		\| 0.1318
	\| 5.59		\| 5.59
Line 102:		Line 102:
	\| [[Amity]]		\| [[Amity]]
	\|}		\|}
	<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 ==

ArrowHead294: Partial undo

2024-11-16T12:55:44Z

Partial undo

← Older revision		Revision as of 12:55, 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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	\| 0.1318		\| 0.1318
	\| 5.59		\| 5.59
	~~{{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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	\| 243/200		\| 243/200
	\| [[Amity]]		\| [[Amity]]
	~~{{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 03:15, 16 November 2024

2024-11-16T03:15:09Z

← Older revision		Revision as of 03:15, 16 November 2024
Line 14:		Line 14:

	== 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
	\| {{monzo\| 807 -509 }}		\| {{monzo\| 807 -509 }}
	\| {{mapping\| 509 807 }}		\| {{mapping\| 509 807 }}
	\| -0.1890		\| −0.1890
	\| 0.1889		\| 0.1889
	\| 8.01		\| 8.01
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	\| {{monzo\| 9 -13 5 }}, {{monzo\| 93 -3 -38 }}		\| {{monzo\| 9 -13 5 }}, {{monzo\| 93 -3 -38 }}
	\| {{mapping\| 509 807 1182 }}		\| {{mapping\| 509 807 1182 }}
	\| -0.1729		\| −0.1729
	\| 0.1559		\| 0.1559
	\| 6.61		\| 6.61
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	\| 2401/2400, 1600000/1594323, 29360128/29296875		\| 2401/2400, 1600000/1594323, 29360128/29296875
	\| {{mapping\| 509 807 1182 1429 }}		\| {{mapping\| 509 807 1182 1429 }}
	\| -0.1415		\| −0.1415
	\| 0.1456		\| 0.1456
	\| 6.18		\| 6.18
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	\| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323		\| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323
	\| {{mapping\| 509 807 1182 1429 1761 }}		\| {{mapping\| 509 807 1182 1429 1761 }}
	\| -0.1335		\| −0.1335
	\| 0.1312		\| 0.1312
	\| 5.57		\| 5.57
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	\| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625		\| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625
	\| {{mapping\| 509 807 1182 1429 1761 1884 }}		\| {{mapping\| 509 807 1182 1429 1761 1884 }}
	\| -0.1618		\| −0.1618
	\| 0.1354		\| 0.1354
	\| 5.74		\| 5.74
Line 62:		Line 54:
	\| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913		\| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913
	\| {{mapping\| 509 807 1182 1429 1761 1884 2081 }}		\| {{mapping\| 509 807 1182 1429 1761 1884 2081 }}
	\| -0.1784		\| −0.1784
	\| 0.1318		\| 0.1318
	\| 5.59		\| 5.59
	\|}		{{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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	\| 243/200		\| 243/200
	\| [[Amity]]		\| [[Amity]]
	\|}		{{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: +categories

2024-02-13T18:15:31Z

+categories

← Older revision		Revision as of 18:15, 13 February 2024
Line 105:		Line 105:
	; [[Francium]]		; [[Francium]]
	* "Modern Legends" from ''Mysteries'' (2023) [https://open.spotify.com/track/6GnnrqfYkIcf4xYTivAgRA Spotify] \| [https://francium223.bandcamp.com/track/modern-legends Bandcamp] \| [https://www.youtube.com/watch?v=A0-37NwYBFM YouTube]		* "Modern Legends" from ''Mysteries'' (2023) [https://open.spotify.com/track/6GnnrqfYkIcf4xYTivAgRA Spotify] \| [https://francium223.bandcamp.com/track/modern-legends Bandcamp] \| [https://www.youtube.com/watch?v=A0-37NwYBFM YouTube]

			[[Category:Listen]]

Francium: /* Music */

2023-11-20T05:42:27Z

Music

← Older revision		Revision as of 05:42, 20 November 2023
Line 104:		Line 104:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Modern Legends" from ''Mysteries'' (2023) [https://open.spotify.com/~~intl-de~~/6GnnrqfYkIcf4xYTivAgRA Spotify] \| [https://francium223.bandcamp.com/track/modern-legends Bandcamp] \| [https://www.youtube.com/watch?v=A0-37NwYBFM YouTube]		* "Modern Legends" from ''Mysteries'' (2023) [https://open.spotify.com/track/6GnnrqfYkIcf4xYTivAgRA Spotify] \| [https://francium223.bandcamp.com/track/modern-legends Bandcamp] \| [https://www.youtube.com/watch?v=A0-37NwYBFM YouTube]

Francium: +music

2023-11-20T05:35:08Z

+music

← Older revision		Revision as of 05:35, 20 November 2023
Line 101:		Line 101:
	\|}		\|}
	<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]]
			* "Modern Legends" from ''Mysteries'' (2023) [https://open.spotify.com/intl-de/6GnnrqfYkIcf4xYTivAgRA Spotify] \| [https://francium223.bandcamp.com/track/modern-legends Bandcamp] \| [https://www.youtube.com/watch?v=A0-37NwYBFM YouTube]