User:CompactStar/Ed11/4 - Revision history

BudjarnLambeth at 12:04, 18 May 2025

2025-05-18T12:04:07Z

← Older revision		Revision as of 12:04, 18 May 2025
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			{{Editable user page}}
	The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4\|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps.		The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4\|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed11/4 to User:CompactStar/Ed11/4

2025-05-18T12:03:57Z

BudjarnLambeth moved page Ed11/4 to User:CompactStar/Ed11/4

← Older revision	Revision as of 12:03, 18 May 2025
(No difference)

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

2025-04-25T02:07:08Z

Properties: adapted wording from ed16/15

← Older revision		Revision as of 02:07, 25 April 2025
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	== Properties ==		== Properties ==
	Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]]. Many, though not all, ~~of these~~ scales have a perceptually important false octave, with various degrees of accuracy.		Division of 11/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed11/4 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way to treat~~ 11/4 as ~~an equivalence in~~ a ~~temperament~~ is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note [[mos scale]]s, coincidentally similar to [[Pythagorean tuning]].		The structural utility of 11/4 is apparent by being central to much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]].

			One approach to ed11/4 tunings is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note [[mos scale]]s, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Ed11/4\| ]] <!-- main article -->		[[Category:Ed11/4\| ]] <!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

FloraC: Recategorize

2024-05-19T09:13:48Z

Recategorize

← Older revision		Revision as of 09:13, 19 May 2024
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	Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note [[mos scale]]s, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note [[mos scale]]s, coincidentally similar to [[Pythagorean tuning]].

	[[Category:~~Equal~~-~~step tuning~~]]		[[Category:Ed11/4\| ]] <!-- main article -->
			[[Category:Edonoi]]
			[[Category:Lists of scales]]

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

2024-05-18T16:23:45Z

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

← Older revision		Revision as of 16:23, 18 May 2024
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	'''~~Ed11~~/4''' is ~~division of~~ [[11/4]] ~~into~~ equal ~~parts~~.		The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4\|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps.

	== Properties ==		== Properties ==
	Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.		Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]]. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

	Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note ~~MOS~~, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note [[mos scale]]s, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 04:11, 21 April 2023

2023-04-21T04:11:47Z

← Older revision		Revision as of 04:11, 21 April 2023
Line 2:		Line 2:

	== Properties ==		== Properties ==
	Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 04:09, 21 April 2023

2023-04-21T04:09:50Z

← Older revision		Revision as of 04:09, 21 April 2023
Line 2:		Line 2:

	== Properties ==		== Properties ==
	Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of [[11-limit]] harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 04:09, 21 April 2023

2023-04-21T04:09:15Z

← Older revision		Revision as of 04:09, 21 April 2023
Line 2:		Line 2:

	== Properties ==		== Properties ==
	Division of 11/4 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 11/4 ~~or another eleventh~~ as a base though, is apparent by being used at the base of ~~so much modern tonal~~ harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of [[11-limit]] harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 04:06, 21 April 2023

2023-04-21T04:06:22Z

← Older revision		Revision as of 04:06, 21 April 2023
Line 4:		Line 4:
	Division of 11/4 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 11/4 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 11/4 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 11/4 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat ~~8/3 or~~ 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 04:05, 21 April 2023

2023-04-21T04:05:32Z

← Older revision		Revision as of 04:05, 21 April 2023
Line 2:		Line 2:

	== Properties ==		== Properties ==
	Division of 11/4 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 11/4 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.		Division of 11/4 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 11/4 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 8/3 or 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].		Incidentally, one way to treat 8/3 or 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]