User:CompactStar/Ed11/5 - Revision history

Fredg999 category edits: Categories

2025-08-01T17:57:29Z

BudjarnLambeth at 12:00, 18 May 2025

2025-05-18T12:00:33Z

← Older revision		Revision as of 12:00, 18 May 2025
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			{{Editable user page}}
	The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.		The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed11/5 to User:CompactStar/Ed11/5

2025-05-18T12:00:21Z

BudjarnLambeth moved page Ed11/5 to User:CompactStar/Ed11/5

← Older revision	Revision as of 12:00, 18 May 2025
(No difference)

BudjarnLambeth: Adapted wording from ed16/15

2025-04-25T01:47:19Z

Adapted wording from ed16/15

← Older revision		Revision as of 01:47, 25 April 2025
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	The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.		The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.

	Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1\|harmonic 5]], and the awkwardly narrow [[7/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, ~~of these scales~~ have a perceptually important false octave, with various degrees of accuracy.		Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed11/5 have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it ~~can~~ be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.		The structural utility of 11/5 is apparent by it being the high ninth of a [[just]] dominant 11th chord, being the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1\|harmonic 5]] and the awkwardly narrow [[7/5\|small septimal tritone]], and being a relatively strong [[consonance]] by most metrics.

			The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it might be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.

	== Ed11/5-edo correspondence ==		== Ed11/5-edo correspondence ==

BudjarnLambeth: /* Individual pages for ed11/5's */ List did not previously show all existing articles. It now does

2024-10-01T02:07:30Z

Individual pages for ed11/5's: List did not previously show all existing articles. It now does

@@ Line 40: / Line 40: @@
 == Individual pages for ed11/5's ==
-* [[2ed11/5]]
-* [[3ed11/5]]
+{| class="wikitable center-all"
-* [[4ed11/5]]
+|+ style=white-space:nowrap | 0…99
-* [[5ed11/5]]
+| [[0ed11/5|0]]
-* [[6ed11/5]]
+| [[1ed11/5|1]]
-* [[7ed11/5]]
+| [[2ed11/5|2]]
-* [[8ed11/5]]
+| [[3ed11/5|3]]
-* [[9ed11/5]]
+| [[4ed11/5|4]]
-* [[10ed11/5]]
+| [[5ed11/5|5]]
-* [[13ed11/5]]
+| [[6ed11/5|6]]
-* [[14ed11/5]]
+| [[7ed11/5|7]]
-* [[20ed11/5]]
+| [[8ed11/5|8]]
 [[Category:Ed11/5| ]] <!-- main article -->
 [[Category:Edonoi]]
 [[Category:Lists of scales]]

FloraC: Recategorize; misc. cleanup

2024-05-19T09:05:51Z

Recategorize; misc. cleanup

← Older revision		Revision as of 09:05, 19 May 2024
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	The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.		The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.

	Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]~~, or not~~. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1\|harmonic 5]], and the awkwardly narrow [[7/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.		Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1\|harmonic 5]], and the awkwardly narrow [[7/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

	The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.		The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
Line 54:		Line 54:

	[[Category:Ed11/5\| ]] <!-- main article -->		[[Category:Ed11/5\| ]] <!-- main article -->
	[[Category:~~Nonoctave~~]]		[[Category:Edonoi]]
	[[Category:~~Equal-step tuning~~]]		[[Category:Lists of scales]]

FloraC: Rework the trivial statements into something more informative; improve linking and style

2024-05-18T15:53:22Z

Rework the trivial statements into something more informative; improve linking and style

← Older revision		Revision as of 15:53, 18 May 2024
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	'''~~ED11~~/5''' is ~~division of~~ the neutral ninth ([[11/5]]) into n equal ~~parts~~.		The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5\|neutral ninth (11/5)]] into a certain number of [[equal]] steps.

	Division of 11/5 into equal parts ~~can be conceived of as to~~ directly ~~use~~ this interval as an equivalence, or not. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[~~ed5~~\|~~pentave~~]], and the awkwardly narrow [[~~Ed7~~/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, ~~but~~ not all, of these scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.		Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]], or not. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1\|harmonic 5]], and the awkwardly narrow [[7/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

	The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses ~~MOS scales~~ of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.		The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
	== ~~ED11~~/5-~~EDO~~ correspondence ==
			== Ed11/5-edo correspondence ==
	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	!~~ED11~~/5		! Ed11/5
	!~~EDO~~		! Edo
	\|-		\|-
	\|[[8ed11/5]]		\| [[8ed11/5]]
	\|[[7edo]]		\| [[7edo]]
	\|-		\|-
	\|[[9ed11/5]]		\| [[9ed11/5]]
	\|[[8edo]]		\| [[8edo]]
	\|-		\|-
	\|[[16ed11/5]]		\| [[16ed11/5]]
	\|[[14edo]]		\| [[14edo]]
	\|-		\|-
	\|[[18ed11/5]]		\| [[18ed11/5]]
	\|[[16edo]]		\| [[16edo]]
	\|-		\|-
	\|[[24ed11/5]]		\| [[24ed11/5]]
	\|[[21edo]]		\| [[21edo]]
	\|-		\|-
	\|[[25ed11/5]]		\| [[25ed11/5]]
	\|[[22edo]]		\| [[22edo]]
	\|-		\|-
	\|[[27ed11/5]]		\| [[27ed11/5]]
	\|[[24edo]]		\| [[24edo]]
	\|-		\|-
	\|[[33ed11/5]]		\| [[33ed11/5]]
	\|[[29edo]]		\| [[29edo]]
	\|-		\|-
	\|[[50ed11/5]]		\| [[50ed11/5]]
	\|[[44edo]]		\| [[44edo]]
	\|}		\|}
	== Individual pages for ~~ED11~~/5s ==
			== Individual pages for ed11/5's ==
	* [[2ed11/5]]		* [[2ed11/5]]
	* [[3ed11/5]]		* [[3ed11/5]]
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	* [[14ed11/5]]		* [[14ed11/5]]
	* [[20ed11/5]]		* [[20ed11/5]]
	[[Category:Ed11/5]]
			[[Category:Ed11/5\| ]] <!-- main article -->
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 04:59, 11 March 2023

2023-03-11T04:59:52Z

← Older revision		Revision as of 04:59, 11 March 2023
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	[[Category:Ed11/5]]		[[Category:Ed11/5]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Equal ~~tunings~~]]		[[Category:Equal-step tuning]]

CompactStar at 04:59, 11 March 2023

2023-03-11T04:59:40Z

← Older revision		Revision as of 04:59, 11 March 2023
Line 52:		Line 52:
	[[Category:Ed11/5]]		[[Category:Ed11/5]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Equal~~-step~~ tunings]]		[[Category:Equal tunings]]

CompactStar at 04:40, 11 March 2023

2023-03-11T04:40:24Z

← Older revision		Revision as of 04:40, 11 March 2023
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	Division of 11/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[ed5\|pentave]], and the awkwardly narrow [[Ed7/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, but not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 11/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[ed5\|pentave]], and the awkwardly narrow [[Ed7/5\|small septimal tritone]]. It is also a relatively strong consonance. Many, but not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[~~salmon~~]] temperament, which can be viewed as an analog to [[meantone]]. It possesses MOS scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.		The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses MOS scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
	== ED11/5-EDO correspondence ==		== ED11/5-EDO correspondence ==
	{\|class="wikitable"		{\|class="wikitable"

← Older revision		Revision as of 17:57, 1 August 2025
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	\|}		\|}

	[[Category:Ed11/5\| ]] <!-- main article -->		[[Category:Ed11/5's\| ]] <!-- main article -->
	~~[[Category:Edonoi]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]