User:CompactStar/Ed10/3 - Revision history

BudjarnLambeth: BudjarnLambeth moved page Ed10/3 to User:CompactStar/Ed10/3 over redirect

2025-05-21T03:12:22Z

BudjarnLambeth moved page Ed10/3 to User:CompactStar/Ed10/3 over redirect

← Older revision	Revision as of 03:12, 21 May 2025
(No difference)

BudjarnLambeth: BudjarnLambeth moved page User:CompactStar/Ed10/3 to Ed10/3 over redirect

2025-05-19T13:25:33Z

BudjarnLambeth moved page User:CompactStar/Ed10/3 to Ed10/3 over redirect

← Older revision	Revision as of 13:25, 19 May 2025
(No difference)

BudjarnLambeth at 12:04, 18 May 2025

2025-05-18T12:04:39Z

← Older revision		Revision as of 12:04, 18 May 2025
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			{{Editable user page}}
	The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3\|just major thirteenth (10/3)]] into a number of [[equal]] steps.		The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3\|just major thirteenth (10/3)]] into a number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed10/3 to User:CompactStar/Ed10/3

2025-05-18T12:04:30Z

BudjarnLambeth moved page Ed10/3 to User:CompactStar/Ed10/3

← Older revision	Revision as of 12:04, 18 May 2025
(No difference)

2^67-1 at 23:43, 4 May 2025

2025-05-04T23:43:14Z

← Older revision		Revision as of 23:43, 4 May 2025
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	The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3\|just major thirteenth (10/3)]] into a number of [[equal]] steps.		The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3\|just major thirteenth (10/3)]] into a number of [[equal]] steps.

	== ~~Joseph Ruhf's approach~~ ==		== Properties ==
	Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.		Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

2^67-1 at 23:42, 4 May 2025

2025-05-04T23:42:09Z

← Older revision		Revision as of 23:42, 4 May 2025
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	The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3\|just major thirteenth (10/3)]] into a number of [[equal]] steps.		The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3\|just major thirteenth (10/3)]] into a number of [[equal]] steps.

	== ~~Properties~~ ==		== Joseph Ruhf's approach ==
	Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.		Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

BudjarnLambeth: /* Properties */ adapted wording from ed16/15

2025-04-25T02:08:55Z

Properties: adapted wording from ed16/15

← Older revision		Revision as of 02:08, 25 April 2025
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	== Properties ==		== Properties ==
	Division of 10/3 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 10/3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes{{clarify}}. Many, though not all, ~~of these~~ scales have a perceptually important false octave, with various degrees of accuracy.		Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally~~, ~~one way~~ to ~~treat~~ 10/3 ~~as an equivalence~~ is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] mos.		The structural significance of 10/3 or another thirteenth is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes{{clarify}}.

			One approach to ed10/3 tunings is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] mos.

	[[Category:Ed10/3\| ]] <!-- main article -->		[[Category:Ed10/3\| ]] <!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

FloraC: Recategorize

2024-05-19T09:14:28Z

Recategorize

← Older revision		Revision as of 09:14, 19 May 2024
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	Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] mos.		Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] mos.

			[[Category:Ed10/3\| ]] <!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
			[[Category:Lists of scales]]

FloraC: Rework the trivial statement into something more informative; improve linking and style; request clarification

2024-05-19T08:18:31Z

Rework the trivial statement into something more informative; improve linking and style; request clarification

← Older revision		Revision as of 08:18, 19 May 2024
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	== Properties ==		== Properties ==
	Division of 10:3 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 10:3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[~~EDT~~\|tritave]] and the [[~~Ed4~~\|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes. Many, though not all, of these scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.		Division of 10/3 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 10/3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes{{clarify}}. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

	Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in ~~10/3.3.~~5 ~~subgroup~~). This [[regular temperament]] yields monolarge ~~MOS~~ with ~~1-12~~ notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] ~~MOS~~.		Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] mos.

	[[Category:Edonoi]]		[[Category:Edonoi]]

CompactStar at 03:07, 6 July 2023

2023-07-06T03:07:28Z

← Older revision		Revision as of 03:07, 6 July 2023
Line 4:		Line 4:
	Division of 10:3 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 10:3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[EDT\|tritave]] and the [[Ed4\|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 10:3 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 10:3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[EDT\|tritave]] and the [[Ed4\|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in 10/3.3.5 subgroup). This [[regular temperament]] yields monolarge MOS with 1-12 notes, followed by a 13-note [[12L 1s]] MOS.		Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in 10/3.3.5 subgroup). This [[regular temperament]] yields monolarge MOS with 1-12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)\|12L 1s&lang;10/3&rang;]] MOS.

	[[Category:Edonoi]]		[[Category:Edonoi]]