Ed7/3 - Revision history

Lériendil: removed redlink

2026-05-13T21:27:22Z

removed redlink

← Older revision		Revision as of 21:27, 13 May 2026
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	== Chords and harmonies ==		== Chords and harmonies ==
	~~{{main\|Pseudo-traditional harmonic functions of enneatonic scale degrees}}~~
	[[:Category:9-tone scales\|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.		[[:Category:9-tone scales\|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.

Lériendil: 7/2 shouldn't occur in a 7/3.5/3.4/3 context so this is just wrong RTT

2026-05-13T21:26:48Z

7/2 shouldn't occur in a 7/3.5/3.4/3 context so this is just wrong RTT

← Older revision		Revision as of 21:26, 13 May 2026
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	[[:Category:9-tone scales\|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.		[[:Category:9-tone scales\|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.

	Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) 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 two [[28/15]] to get to [[7/2]] (tempering out the comma [[225/224]]). So, doing this yields 15-, 19-, and 34-note [[mos]] 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. [[Joseph Ruhf]] named this scheme "macrobichromatic".		Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].

	== Individual pages for ed7/3's ==		== Individual pages for ed7/3's ==

Lériendil: ed7/3s in the 100s are all deleted now

2026-05-13T21:21:25Z

ed7/3s in the 100s are all deleted now

@@ Line 126: / Line 126: @@
 | [[98ed7/3|98]]
 | [[99ed7/3|99]]
 |}

Lériendil: removed middletown stuff, archived it on mmtm's userpage

2026-05-13T21:21:03Z

removed middletown stuff, archived it on mmtm's userpage

← Older revision		Revision as of 21:21, 13 May 2026
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	Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) 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 two [[28/15]] to get to [[7/2]] (tempering out the comma [[225/224]]). So, doing this yields 15-, 19-, and 34-note [[mos]] 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. [[Joseph Ruhf]] named this scheme "macrobichromatic".		Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) 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 two [[28/15]] to get to [[7/2]] (tempering out the comma [[225/224]]). So, doing this yields 15-, 19-, and 34-note [[mos]] 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. [[Joseph Ruhf]] named this scheme "macrobichromatic".

	~~== Middletown ==~~
	~~{{idiosyncratic terms}}~~
	7/3 provides a fairly trivial point to split the difference between the [[octave]] and the [[tritave]], which is why Ruhf has named the region of intervals between 6 and 7 degrees of [[5edo]] the "[[Middletown valley]]".

	The proper [[Middletown family\|Middletown temperament family]] is based on an [[enneatonic]] scale [[generator\|generated]] by a third or a fifth optionally with a [[period]] of a [[Wolf interval\|wolf]] fourth at most 560 [[cents]] wide) and, as is the twelfth (tritave), an alternative interval where {{w\|Inversion (music) #Counterpoint\|invertible counterpoint}} has classically occurred.

	~~The branches of the Middletown family are named thus:~~
	* 3&6: Tritetrachordal
	* 4&5: Montrose (between 5\4edo and 4\3edo in particular, MOS generated by [pseudo] octaves belong to this branch)
	* 2&7: Terra Rubra

	~~The family of interlaced [[octatonic scale]]-based temperaments in the "Middletown valley" is called Vesuvius (i.e. the volcano east of Naples).~~

	~~The Middlebury temperament falls in the "Middletown valley", but its enneatonic scales are "[[generator-remainder]]".~~

	~~The temperaments neighboring Middletown proper are named thus:~~
	* 5&6: Rosablanca
	* 4&7: Saptimpun (10 1/2)
	* 5&7: 8bittone (Old Middetown)

	~~The [[pyrite]] tuning of [[edX]]s will turn out to divide a barely mistuned [[5/2]] of almost exactly 45\[[34edo]].~~

	== Individual pages for ed7/3's ==		== Individual pages for ed7/3's ==

Sintel: move the warning to the top

2026-05-13T00:34:51Z

move the warning to the top

← Older revision		Revision as of 00:34, 13 May 2026
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			{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}

	The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3\|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps.		The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3\|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps.

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	<!-- main article -->		<!-- main article -->
	[[Category:Lists of scales]]		[[Category:Lists of scales]]


	{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:39:42Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:39, 1 August 2025
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	[[Category:Ed7/3's\| ]]		[[Category:Ed7/3's\| ]]
	<!-- main article -->		<!-- main article -->
	~~[[Category:Edonoi]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]


	{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}		{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}

Fredg999 category edits: Moving from Category:Ed7/3 to Category:Ed7/3's using Cat-a-lot

2025-08-01T18:41:49Z

Moving from Category:Ed7/3 to Category:Ed7/3's using Cat-a-lot

← Older revision		Revision as of 18:41, 1 August 2025
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	\|}		\|}

	[[Category:Ed7/3\| ]] <!-- main article -->		[[Category:Ed7/3's\| ]]
			<!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

Lériendil at 20:13, 22 May 2025

2025-05-22T20:13:25Z

← Older revision		Revision as of 20:13, 22 May 2025
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	== Chords and harmonies ==		== Chords and harmonies ==
	{{main\|Pseudo-traditional harmonic functions of enneatonic ~~scale_degrees~~}}		{{main\|Pseudo-traditional harmonic functions of enneatonic scale degrees}}
	[[:Category:9-tone scales\|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.		[[:Category:9-tone scales\|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.

BudjarnLambeth: Todo

2025-05-22T03:14:45Z

Todo

← Older revision		Revision as of 03:14, 22 May 2025
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	{{todo\|inline=1\|~~review~~\|cleanup~~\|improve layout~~}}		{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}

BudjarnLambeth at 00:56, 19 May 2025

2025-05-19T00:56:14Z

← Older revision		Revision as of 00:56, 19 May 2025
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	~~{{Editable user page}}~~
	The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3\|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps.		The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3\|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps.