Ed4/3 - Revision history

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

2025-08-01T19:39:41Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:39, 1 August 2025
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	[[Category:Ed4/3's\| ]]		[[Category:Ed4/3's\| ]]
	<!-- main article -->		<!-- main article -->
	~~[[Category:Edonoi]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]


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

Fredg999 category edits: Moving from Category:Ed4/3 to Category:Ed4/3's using Cat-a-lot

2025-08-01T18:37:43Z

Moving from Category:Ed4/3 to Category:Ed4/3's using Cat-a-lot

← Older revision		Revision as of 18:37, 1 August 2025
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	* [[Square root of 13 over 10]] (previously listed here as an "edIV")		* [[Square root of 13 over 10]] (previously listed here as an "edIV")

	[[Category:Ed4/3\| ]] <!-- main article -->		[[Category:Ed4/3's\| ]]
			<!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth at 03:10, 22 May 2025

2025-05-22T03:10:50Z

← Older revision		Revision as of 03:10, 22 May 2025
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	{{todo\|inline=1~~\|review~~\|cleanup\|improve layout}}		{{todo\|inline=1\|cleanup\|improve layout}}

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

2025-04-25T02:19:48Z

← Older revision		Revision as of 02:19, 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: Adapt wording from ed16/15

2025-04-25T01:20:08Z

Adapt wording from ed16/15

← Older revision		Revision as of 01:20, 25 April 2025
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	An '''equal division of the fourth''' ('''ed4/3''') is an [[equal-step tuning]] in which the perfect fourth ([[4/3]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps~~. The fourth can be treated as an [[equave]], but it is not necessary and, more importantly, it is not well known whether most listeners can hear it as such~~.		An '''equal division of the fourth''' ('''ed4/3''') is an [[equal-step tuning]] in which the perfect fourth ([[4/3]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps.

	The expression ''equal division of the fourth'' could be interpreted as applying to other [[interval]]s in the region of the fourth (see [[:Category: Fourth]]), such as [[15/11]]. However, these should be named more specifically and be treated on other pages to avoid any confusion.		The expression ''equal division of the fourth'' could be interpreted as applying to other [[interval]]s in the region of the fourth (see [[:Category: Fourth]]), such as [[15/11]]. However, these should be named more specifically and be treated on other pages to avoid any confusion.

	The utility of the fourth as ~~a base~~ is apparent by being used at the base of so much Neo-Medieval harmony. Many, though not all, ~~of these~~ scales have a ~~pseudo (~~false) octave, with various degrees of accuracy~~, but which context(s), if any, it is very perceptually important in is as yet an open question~~.		The utility of the fourth as structural scaffolding is apparent by being used at the base of so much Neo-Medieval harmony (see [[tetrachord]]). Division of 4/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed4/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way~~ to ~~treat 4~~/3 ~~as an equivalence~~ is the use of the 12:13:14:(16) 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 (an octave-reduced stack of) four [[3/2]] to get to [[5/4]], here it takes (a fourth-reduced stack of) eight [[7/6]] to get to [[13/12]] (tempering out the comma [[5764801/5750784]]). So, doing this yields 13-, 15-, and 28-note [[mos scale]]s for ed4/3's. While the notes are rather closer together, the scheme is uncannily similar to meantone.		One approach to some ed4/3 tunings is the use of the 12:13:14:(16) 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 (an octave-reduced stack of) four [[3/2]] to get to [[5/4]], here it takes (a fourth-reduced stack of) eight [[7/6]] to get to [[13/12]] (tempering out the comma [[5764801/5750784]]). So, doing this yields 13-, 15-, and 28-note [[mos scale]]s for ed4/3's. While the notes are rather closer together, the scheme is uncannily similar to meantone.

	== 7-limit, analogy with equal divisions of (3/2) ==		== 7-limit, analogy with equal divisions of (3/2) ==

BudjarnLambeth: /* Individual pages for ed4/3s */

2024-12-21T21:51:30Z

Individual pages for ed4/3s

← Older revision		Revision as of 21:51, 21 December 2024
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	\|-		\|-
	\| [[5ed4/3]]		\| [[5ed4/3]]
	\| Quintilipyth scale <br>{{citation needed\|date=December 2021\|reason=Who used that term?}})		\| Quintilipyth scale <br>{{citation needed\|date=December 2021\|reason=Who used that term?}}
	\|-		\|-
	\| [[6ed4/3]]		\| [[6ed4/3]]
	\| Sextilipyth scale <br>{{citation needed\|date=December 2021\|reason=Who used that term?}})		\| Sextilipyth scale <br>{{citation needed\|date=December 2021\|reason=Who used that term?}}
	\|-		\|-
	\| [[7ed4/3]]		\| [[7ed4/3]]

BudjarnLambeth: /* Individual pages for ed4/3s */ Make neater using tables

2024-12-21T21:50:41Z

Individual pages for ed4/3s: Make neater using tables

@@ Line 15: / Line 15: @@
 == Individual pages for ed4/3s ==
-* [[Cube Root of P4|3ed4/3]] (aka Cube Root of P4)
-* [[4ed4/3]]
+{| class="wikitable center-all"
-* [[5ed4/3]] (aka Quintilipyth scale{{citation needed|date=December 2021|reason=Who used that term?}})
+|+ 0…9
-* [[6ed4/3]] (aka Sextilipyth scale{{citation needed|date=December 2021|reason=Who used that term?}})
+|-
-* [[7ed4/3]]
+! Standard name
-* [[8ed4/3]]
+! Common name
-* [[Noleta|9ed4/3]] (aka Noleta scale)
+|-
 == See also ==

BudjarnLambeth at 03:32, 5 October 2024

2024-10-05T03:32:15Z

← Older revision		Revision as of 03:32, 5 October 2024
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	* [[Cube Root of P4\|3ed4/3]] (aka Cube Root of P4)		* [[Cube Root of P4\|3ed4/3]] (aka Cube Root of P4)
	* [[4ed4/3]]		* [[4ed4/3]]
	* [[~~5ed4/3\|~~5ed4/3]] (aka Quintilipyth scale{{citation needed\|date=December 2021\|reason=Who used that term?}})		* [[5ed4/3]] (aka Quintilipyth scale{{citation needed\|date=December 2021\|reason=Who used that term?}})
	* [[6ed4/3]] (aka Sextilipyth scale{{citation needed\|date=December 2021\|reason=Who used that term?}})		* [[6ed4/3]] (aka Sextilipyth scale{{citation needed\|date=December 2021\|reason=Who used that term?}})
	* [[7ed4/3]]		* [[7ed4/3]]

Contribution at 16:41, 29 August 2024

2024-08-29T16:41:14Z

← Older revision		Revision as of 16:41, 29 August 2024
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	ED4/3 tuning systems that accurately represent the intervals 8/7 and 7/6 include: [[13ed4/3]] (1.31 cent error), [[15ed4/3]] (1.25 cent error), and [[28ed4/3]] (0.06 cent error).		ED4/3 tuning systems that accurately represent the intervals 8/7 and 7/6 include: [[13ed4/3]] (1.31 cent error), [[15ed4/3]] (1.25 cent error), and [[28ed4/3]] (0.06 cent error).

	In this sense, [[13ed4/3]], [[15ed4/3]], and [[28ed4/3]] are to the division of the fourth what [[9edf\|9ed3/2]], [[11edf\|11ed3/2,]] and [[20edf\|20ed3/2]] are to the division of the fifth, and what [[5edo]], [[7edo]], and [[12edo]] are to the division of the octave.		In this sense, [[13ed4/3]], [[15ed4/3]], and [[28ed4/3]] are to the division of the fourth what [[9edf\|9ed3/2]], [[11edf\|11ed3/2]], and [[20edf\|20ed3/2]] are to the division of the fifth, and what [[5edo]], [[7edo]], and [[12edo]] are to the division of the octave.

	== Individual pages for ed4/3s ==		== Individual pages for ed4/3s ==

Lériendil at 19:37, 27 August 2024

2024-08-27T19:37:18Z

← Older revision		Revision as of 19:37, 27 August 2024
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	ED4/3 tuning systems that accurately represent the intervals 8/7 and 7/6 include: [[13ed4/3]] (1.31 cent error), [[15ed4/3]] (1.25 cent error), and [[28ed4/3]] (0.06 cent error).		ED4/3 tuning systems that accurately represent the intervals 8/7 and 7/6 include: [[13ed4/3]] (1.31 cent error), [[15ed4/3]] (1.25 cent error), and [[28ed4/3]] (0.06 cent error).

	In this sense, [[13ed4/3]], [[15ed4/3]], and [[28ed4/3]] are to the division of the fourth what [[9edf\|9ed3/2]], [[11edf\|11ed3/2,]] and [[20edf\|20ed3/2]] are to the division of the fifth.		In this sense, [[13ed4/3]], [[15ed4/3]], and [[28ed4/3]] are to the division of the fourth what [[9edf\|9ed3/2]], [[11edf\|11ed3/2,]] and [[20edf\|20ed3/2]] are to the division of the fifth, and what [[5edo]], [[7edo]], and [[12edo]] are to the division of the octave.

	== Individual pages for ed4/3s ==		== Individual pages for ed4/3s ==