User:Moremajorthanmajor/Ed9/5 - Revision history

Fredg999 category edits: Categories

2025-08-01T19:41:55Z

BudjarnLambeth at 11:59, 18 May 2025

2025-05-18T11:59:25Z

← Older revision		Revision as of 11:59, 18 May 2025
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			{{Editable user page}}
	The '''equal division of 9/5''' ('''ed9/5''') is a [[tuning]] obtained by dividing the [[9/5\|classic minor seventh (9/5)]] in a certain number of [[equal]] steps.		The '''equal division of 9/5''' ('''ed9/5''') is a [[tuning]] obtained by dividing the [[9/5\|classic minor seventh (9/5)]] in a certain number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed9/5 to User:Moremajorthanmajor/Ed9/5

2025-05-18T11:59:13Z

BudjarnLambeth moved page Ed9/5 to User:Moremajorthanmajor/Ed9/5

← Older revision	Revision as of 11:59, 18 May 2025
(No difference)

BudjarnLambeth: {{todo|inline=1|review|cleanup|improve layout}}

2025-04-25T02:22:32Z

← Older revision		Revision as of 02:22, 25 April 2025
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	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]


			{{todo\|inline=1\|review\|cleanup\|improve layout}}

BudjarnLambeth: /* Properties */

2025-04-25T02:22:21Z

Properties

← Older revision		Revision as of 02:22, 25 April 2025
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	The structural importance of 9/5 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 [[7/4]] or [[16/9]] depending how one converts [[12edo\|10\12]] into [[JI]].		The structural importance of 9/5 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 [[7/4]] or [[16/9]] depending how one converts [[12edo\|10\12]] into [[JI]].

	One approach to some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.		One approach to some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). 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 term "microdiatonic"{{idiosyncratic}} for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

			However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.

	== Individual pages for ed9/5's ==		== Individual pages for ed9/5's ==

BudjarnLambeth: /* Properties */

2025-04-25T01:42:56Z

Properties

← Older revision		Revision as of 01:42, 25 April 2025
Line 4:		Line 4:
	Division of 9/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed9/5 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.		Division of 9/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed9/5 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	The structural importance of 9/5 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 [[7/4]] or [[16/9]] depending how one converts [[12edo\|10\12]] into [[JI]].		The structural importance of 9/5 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 [[7/4]] or [[16/9]] depending how one converts [[12edo\|10\12]] into [[JI]].

	One approach to some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.		One approach to some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.

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

2025-04-25T01:41:29Z

Properties: adapted wording from ed16/15

← Older revision		Revision as of 01:41, 25 April 2025
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	== Properties ==		== Properties ==
	Division of 9/5 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 9/5 (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 9/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed9/5 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way to treat~~ 9/5 ~~as an equivalence~~ is the ~~use of the 5:6:7:(9) chord as the fundamental complete sonority in~~ a ~~very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas~~ in ~~meantone it takes four 3/2 to get to 5/1~~, ~~here~~ it ~~takes four 7/5 to get~~ to ~~6/5 (~~[[~~tempering out]] the comma [[2430~~/~~2401~~]]). 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. However, a just or ~~very slightly flat 9/5 leads to the just 7/5~~ [[~~generator]] converging to a scale where the '6~~/~~5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy~~]] ~~of a~~ [[~~pelogic~~]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[~~cents~~]] ~~of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously~~.		The structural importance of 9/5 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 [[7/4]] or [[16/9]] depending how one converts [[12edo\|10\12]] into [[JI]].

	~~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 some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.

	== Individual pages for ed9/5's ==		== Individual pages for ed9/5's ==

BudjarnLambeth: Add links

2024-12-26T01:19:02Z

Add links

← Older revision		Revision as of 01:19, 26 December 2024
Line 4:		Line 4:
	Division of 9/5 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 9/5 (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 9/5 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 9/5 (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.

	Incidentally, one way to treat 9/5 as an equivalence is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 (tempering out the comma 2430/2401). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 generator converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a pelogic temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 cents of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.		Incidentally, one way to treat 9/5 as an equivalence is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.

	Where examples of this particular temperament in use are concerned, they are already everywhere, just with notes which are rather farther apart.		Where examples of this particular temperament in use are concerned, they are already everywhere, just with notes which are rather farther apart.

BudjarnLambeth: /* Individual pages for ed9/5's */ Expanded list to include all existing pages

2024-10-01T02:12:56Z

Individual pages for ed9/5's: Expanded list to include all existing pages

@@ Line 9: / Line 9: @@
 == Individual pages for ed9/5's ==
-* [[5ed9/5]]
-* [[7ed9/5]]
+{| class="wikitable center-all"
-* [[12ed9/5]]
+|+ style=white-space:nowrap | 0…99
 [[Category:Ed9/5| ]] <!-- main article -->
 [[Category:Edonoi]]
 [[Category:Lists of scales]]

FloraC: Recategorize; misc. cleanup

2024-05-19T09:04:31Z

Recategorize; misc. cleanup

← Older revision		Revision as of 09:04, 19 May 2024
Line 4:		Line 4:
	Division of 9/5 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 9/5 (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 9/5 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 9/5 (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.

	Incidentally, one way to treat 9/5 as an equivalence is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 (tempering out the comma 2430/2401). So, doing this yields 5-, 7-, and 12-note [[mos]], 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. However, a just or very slightly flat 9/5 leads to the just 7/5 generator converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a pelogic temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 cents of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.		Incidentally, one way to treat 9/5 as an equivalence is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 (tempering out the comma 2430/2401). 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. However, a just or very slightly flat 9/5 leads to the just 7/5 generator converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a pelogic temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 cents of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.

	Where examples of this particular temperament in use are concerned, they are already everywhere, just with notes which are rather farther apart.		Where examples of this particular temperament in use are concerned, they are already everywhere, just with notes which are rather farther apart.
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	* [[12ed9/5]]		* [[12ed9/5]]

	~~[[Category:Equal-step tuning]]~~
	[[Category:Ed9/5\| ]] <!-- main article -->		[[Category:Ed9/5\| ]] <!-- main article -->
			[[Category:Edonoi]]
			[[Category:Lists of scales]]

← Older revision		Revision as of 19:41, 1 August 2025
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	\|}		\|}

	[[Category:Ed9/5\| ]] <!-- main article -->		[[Category:Ed9/5's\| ]] <!-- main article -->
	~~[[Category:Edonoi]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]


	~~{{todo\|inline=1\|review\|cleanup\|improve layout}}~~