User:Xenllium/Ed7/4 - Revision history

Fredg999 category edits: Categories

2025-08-01T18:44:19Z

BudjarnLambeth at 02:40, 19 May 2025

2025-05-19T02:40:14Z

← Older revision		Revision as of 02:40, 19 May 2025
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			{{Editable user page}}
	The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4\|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.		The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4\|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed7/4 to User:Xenllium/Ed7/4 over redirect

2025-05-19T02:40:04Z

BudjarnLambeth moved page Ed7/4 to User:Xenllium/Ed7/4 over redirect

← Older revision	Revision as of 02:40, 19 May 2025
(No difference)

BudjarnLambeth at 00:55, 19 May 2025

2025-05-19T00:55:07Z

← Older revision		Revision as of 00:55, 19 May 2025
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	~~{{Editable user page}}~~
	The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4\|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.		The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4\|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page User:Xenllium/Ed7/4 to Ed7/4 over redirect: Discussion in Discord

2025-05-19T00:54:53Z

BudjarnLambeth moved page User:Xenllium/Ed7/4 to Ed7/4 over redirect: Discussion in Discord

← Older revision	Revision as of 00:54, 19 May 2025
(No difference)

BudjarnLambeth at 11:57, 18 May 2025

2025-05-18T11:57:33Z

← Older revision		Revision as of 11:57, 18 May 2025
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			{{Editable user page}}
	The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4\|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.		The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4\|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed7/4 to User:Xenllium/Ed7/4

2025-05-18T11:57:23Z

BudjarnLambeth moved page Ed7/4 to User:Xenllium/Ed7/4

← Older revision	Revision as of 11:57, 18 May 2025
(No difference)

BudjarnLambeth: /* Properties */

2025-04-25T02:21:10Z

Properties

← Older revision		Revision as of 02:21, 25 April 2025
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	The structural importance of 16/9 is suggested by its being the most common width for a [[tetrad]] in Western harmony, though it could be argued that this distinction belongs instead to [[16/9]] or [[9/5]] depending how one converts [[12edo\|10\12]] into [[JI]].		The structural importance of 16/9 is suggested by its being the most common width for a [[tetrad]] in Western harmony, though it could be argued that this distinction belongs instead to [[16/9]] or [[9/5]] depending how one converts [[12edo\|10\12]] into [[JI]].

	One approach to ed7/4 tunings is the use of the 4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic" for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.		One approach to ed7/4 tunings is the use of the 4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic"{{idiosyncratic}} for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

	== Individual pages for ed7/4's ==		== Individual pages for ed7/4's ==

BudjarnLambeth: /* Properties */

2025-04-25T01:42:38Z

Properties

← Older revision		Revision as of 01:42, 25 April 2025
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	Division of 7/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/4 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.		Division of 7/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/4 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	The structural importance of 7/4 is ~~hinted~~ by its being the most common width for a [[tetrad]] in Western harmony.		The structural importance of 16/9 is suggested by its being the most common width for a [[tetrad]] in Western harmony, though it could be argued that this distinction belongs instead to [[16/9]] or [[9/5]] depending how one converts [[12edo\|10\12]] into [[JI]].

	One approach to ed7/4 tunings is the use of the 4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic" for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.		One approach to ed7/4 tunings is the use of the 4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic" for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

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

2025-04-25T01:37:48Z

Properties: adapted wording from ed16/15

← Older revision		Revision as of 01:37, 25 April 2025
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	== Properties ==		== Properties ==
	Division of 7/4 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 7/4 (or another seventh) 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 false octave, with various degrees of accuracy.		Division of 7/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/4 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way to treat~~ 7/4 ~~as an equivalence~~ is the ~~use of the 4:5:6:(7) chord as the fundamental complete sonority in~~ a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[~~mos scale~~]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Microdiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely compressed.		The structural importance of 7/4 is hinted by its being the most common width for a [[tetrad]] in Western harmony.

	~~Where examples~~ of this ~~particular temperament in use are concerned~~, ~~they are already everywhere~~, just ~~with~~ notes ~~which~~ are rather ~~farther apart~~.		One approach to ed7/4 tunings is the use of the 4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic" for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

	== Individual pages for ed7/4's ==		== Individual pages for ed7/4's ==

← Older revision		Revision as of 18:44, 1 August 2025
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	\|}		\|}

	[[Category:Ed7/4\| ]] <!-- main article -->		[[Category:Ed7/4's\| ]] <!-- main article -->
	~~[[Category:Edonoi]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]