Ed5/2 - Revision history

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

2025-08-01T19:39:43Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:39, 1 August 2025
Line 129:		Line 129:
	[[Category:Ed5/2's\| ]]		[[Category:Ed5/2'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 5/2 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 5/2 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:Ed5/2 to Category:Ed5/2's using Cat-a-lot

2025-08-01T18:40:44Z

Moving from Category:Ed5/2 to Category:Ed5/2's using Cat-a-lot

← Older revision		Revision as of 18:40, 1 August 2025
Line 127:		Line 127:
	\|}		\|}

	[[Category:Ed5/2\| ]] <!-- main article -->		[[Category:Ed5/2's\| ]]
			<!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth: Todo

2025-05-22T03:15:08Z

Todo

← Older revision		Revision as of 03:15, 22 May 2025
Line 132:		Line 132:


	{{todo\|inline=1\|~~improve synopsis~~}}		{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 5/2 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: {{todo|inline=1|improve synopsis}}

2025-04-25T02:29:41Z

← Older revision		Revision as of 02:29, 25 April 2025
Line 130:		Line 130:
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]


			{{todo\|inline=1\|improve synopsis}}

BudjarnLambeth: /* Properties */ adapted wording from ed16/15 (someone help me, I'm going to have an aneurysm)

2025-04-25T02:02:18Z

Properties: adapted wording from ed16/15 (someone help me, I'm going to have an aneurysm)

← Older revision		Revision as of 02:02, 25 April 2025
Line 2:		Line 2:

	== Properties ==		== Properties ==
	Division of 5/2 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 5/2, (or another tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, 5/2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, ~~of these~~ scales have a perceptually important false octave, with various degrees of accuracy.		Division of 5/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/2 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way to treat~~ 5/2 ~~as an equivalence~~ is the ~~use~~ of ~~the 2:3:4:(5) 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 3~~/2 ~~to get to 6/5 (tempering out~~ the ~~comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the mos formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.		The structural utility of 5/2 (or another tenth) is apparent by its being the base of so much common practice tonal harmony{{clarify}}, and by 5/2 being the best option for “no-threes” harmony excluding the octave{{clarify}}.

	Another option is to treat ed5/2's as "no-threes" systems (like how [[edt]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.		One way to approach ed5/2 tunings is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). So, doing this yields 5-, 7-, and 12-note [[mos]], just like meantone. While the notes are rather closer together, the scheme shares the scale shape of meantone.

			[[Joseph Ruhf]] proposes the term "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]"{{idiosyncratic}} for the above approach because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the [[MOS]] scales formerly known as Middletown{{idiosyncratic}} because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

			Another option is to treat ed5/2's as "no-threes" systems (like how [[edt]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of [[jubilic]] temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.

	== Individual pages for ed5/2's ==		== Individual pages for ed5/2's ==

BudjarnLambeth: /* Individual pages for ed5/2's */ Expand table to match similar ETs with similar numbers of pages

2024-10-01T02:16:17Z

Individual pages for ed5/2's: Expand table to match similar ETs with similar numbers of pages

@@ Line 9: / Line 9: @@
 == Individual pages for ed5/2's ==
 {| class="wikitable center-all"
-|+ style=white-space:nowrap | 0…49
+|+ style=white-space:nowrap | 0…99
 | [[0ed5/2|0]]
 | [[1ed5/2|1]]
@@ Line 41: / Line 42: @@
 | [[26ed5/2|26]]
 | [[27ed5/2|27]]
-| [[28ed5/|28]]
+| [[28ed5/2|28]]
 | [[29ed5/2|29]]
 |-
@@ Line 65: / Line 66: @@
 | [[48ed5/2|48]]
 | [[49ed5/2|49]]
 |}

FloraC: Recategorize; misc. cleanup

2024-05-19T09:10:47Z

Recategorize; misc. cleanup

← Older revision		Revision as of 09:10, 19 May 2024
Line 6:		Line 6:
	Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the mos formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.		Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the mos formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

	Another option is to treat ~~ED5~~/2s as "no-threes" systems (like how [[~~EDT~~]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.		Another option is to treat ed5/2's as "no-threes" systems (like how [[edt]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.

	== Individual pages for ed5/2's ==		== Individual pages for ed5/2's ==
Line 68:		Line 68:

	[[Category:Ed5/2\| ]] <!-- main article -->		[[Category:Ed5/2\| ]] <!-- main article -->
	[[Category:~~Equal-step tuning~~]]		[[Category:Edonoi]]
			[[Category:Lists of scales]]

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

2024-05-18T16:15:22Z

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

← Older revision		Revision as of 16:15, 18 May 2024
Line 1:		Line 1:
	'''~~Ed5~~/2''' ~~means~~ '''~~Division of~~ the classic major tenth ([[5/2]]~~) into n~~ equal ~~parts'''~~.		The '''equal division of 5/2''' ('''ed5/2''') is a [[tuning]] obtained by dividing the [[5/2\|classic major tenth (5/2)]] in a certain number of [[equal]] steps.

	== Properties ==		== Properties ==
	Division of 5/2 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 5:2, (or another tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, 5:2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, of these scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.		Division of 5/2 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 5/2, (or another tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, 5/2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

	Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the ~~MOS~~ formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.		Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the mos formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

	Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, 13, and 21 note ~~MOS~~.		Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.

	== Individual pages for ~~ED5~~/2s ==		== Individual pages for ed5/2's ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+ style=white-space:nowrap \| 0…49		\|+ style=white-space:nowrap \| 0…49
Line 66:		Line 66:
	\| [[49ed5/2\|49]]		\| [[49ed5/2\|49]]
	\|}		\|}


	[[Category:Ed5/2\| ]] <!-- main article -->		[[Category:Ed5/2\| ]] <!-- main article -->
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

Francium: /* Individual pages for ED5/2s */ +table

2024-02-27T19:41:11Z

Individual pages for ED5/2s: +table

← Older revision		Revision as of 19:41, 27 February 2024
Line 9:		Line 9:

	== Individual pages for ED5/2s ==		== Individual pages for ED5/2s ==
	* [[1ed5/2]]		{\| class="wikitable center-all"
	* [[2ed5/2]]		\|+ style=white-space:nowrap \| 0…49
	* [[3ed5/2]]		\| [[0ed5/2\|0]]
	* [[4ed5/2]]		\| [[1ed5/2\|1]]
	* [[5ed5/2]]		\| [[2ed5/2\|2]]
	* [[6ed5/2]]		\| [[3ed5/2\|3]]
	* [[7ed5/2]]		\| [[4ed5/2\|4]]
	* [[8ed5/2]]		\| [[5ed5/2\|5]]
	* [[9ed5/2]]		\| [[6ed5/2\|6]]
	* [[10ed5/2]]		\| [[7ed5/2\|7]]
	* [[11ed5/2]]		\| [[8ed5/2\|8]]
	* [[12ed5/2]]		\| [[9ed5/2\|9]]
	* [[13ed5/2]]		\|-
	* [[14ed5/2]]		\| [[10ed5/2\|10]]
	* [[15ed5/2]]		\| [[11ed5/2\|11]]
	* [[16ed5/2]]		\| [[12ed5/2\|12]]
	* [[18ed5/2]]		\| [[13ed5/2\|13]]
	* [[25ed5/2]]		\| [[14ed5/2\|14]]
	* [[45ed5/2]]		\| [[15ed5/2\|15]]
			\| [[16ed5/2\|16]]
			\| [[17ed5/2\|17]]
			\| [[18ed5/2\|18]]
			\| [[19ed5/2\|19]]
			\|-
			\| [[20ed5/2\|20]]
			\| [[21ed5/2\|21]]
			\| [[22ed5/2\|22]]
			\| [[23ed5/2\|23]]
			\| [[24ed5/2\|24]]
			\| [[25ed5/2\|25]]
			\| [[26ed5/2\|26]]
			\| [[27ed5/2\|27]]
			\| [[28ed5/\|28]]
			\| [[29ed5/2\|29]]
			\|-
			\| [[30ed5/2\|30]]
			\| [[31ed5/2\|31]]
			\| [[32ed5/2\|32]]
			\| [[33ed5/2\|33]]
			\| [[34ed5/2\|34]]
			\| [[35ed5/2\|35]]
			\| [[36ed5/2\|36]]
			\| [[37ed5/2\|37]]
			\| [[38ed5/2\|38]]
			\| [[39ed5/2\|39]]
			\|-
			\| [[40ed5/2\|40]]
			\| [[41ed5/2\|41]]
			\| [[42ed5/2\|42]]
			\| [[43ed5/2\|43]]
			\| [[44ed5/2\|44]]
			\| [[45ed5/2\|45]]
			\| [[46ed5/2\|46]]
			\| [[47ed5/2\|47]]
			\| [[48ed5/2\|48]]
			\| [[49ed5/2\|49]]
			\|}


	[[Category:Ed5/2\| ]] <!-- main article -->		[[Category:Ed5/2\| ]] <!-- main article -->
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

CompactStar at 01:03, 25 June 2023

2023-06-25T01:03:52Z

← Older revision		Revision as of 01:03, 25 June 2023
Line 6:		Line 6:
	Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the MOS formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.		Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "[[Macrodiatonic and microdiatonic scales\|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the MOS formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

	Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, and ~~either 11 or 13~~ note MOS.		Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, 13, and 21 note MOS.

	== Individual pages for ED5/2s ==		== Individual pages for ED5/2s ==

← Older revision		Revision as of 19:41, 27 February 2024
Line 9:		Line 9:

	== Individual pages for ED5/2s ==		== Individual pages for ED5/2s ==
	* [[1ed5/2]]		{\| class="wikitable center-all"
	* [[2ed5/2]]		\|+ style=white-space:nowrap \| 0…49
	* [[3ed5/2]]		\| [[0ed5/2\|0]]
	* [[4ed5/2]]		\| [[1ed5/2\|1]]
	* [[5ed5/2]]		\| [[2ed5/2\|2]]
	* [[6ed5/2]]		\| [[3ed5/2\|3]]
	* [[7ed5/2]]		\| [[4ed5/2\|4]]
	* [[8ed5/2]]		\| [[5ed5/2\|5]]
	* [[9ed5/2]]		\| [[6ed5/2\|6]]
	* [[10ed5/2]]		\| [[7ed5/2\|7]]
	* [[11ed5/2]]		\| [[8ed5/2\|8]]
	* [[12ed5/2]]		\| [[9ed5/2\|9]]
	* [[13ed5/2]]		\|-
	* [[14ed5/2]]		\| [[10ed5/2\|10]]
	* [[15ed5/2]]		\| [[11ed5/2\|11]]
	* [[16ed5/2]]		\| [[12ed5/2\|12]]
	* [[18ed5/2]]		\| [[13ed5/2\|13]]
	* [[25ed5/2]]		\| [[14ed5/2\|14]]
	* [[45ed5/2]]		\| [[15ed5/2\|15]]
			\| [[16ed5/2\|16]]
			\| [[17ed5/2\|17]]
			\| [[18ed5/2\|18]]
			\| [[19ed5/2\|19]]
			\|-
			\| [[20ed5/2\|20]]
			\| [[21ed5/2\|21]]
			\| [[22ed5/2\|22]]
			\| [[23ed5/2\|23]]
			\| [[24ed5/2\|24]]
			\| [[25ed5/2\|25]]
			\| [[26ed5/2\|26]]
			\| [[27ed5/2\|27]]
			\| [[28ed5/\|28]]
			\| [[29ed5/2\|29]]
			\|-
			\| [[30ed5/2\|30]]
			\| [[31ed5/2\|31]]
			\| [[32ed5/2\|32]]
			\| [[33ed5/2\|33]]
			\| [[34ed5/2\|34]]
			\| [[35ed5/2\|35]]
			\| [[36ed5/2\|36]]
			\| [[37ed5/2\|37]]
			\| [[38ed5/2\|38]]
			\| [[39ed5/2\|39]]
			\|-
			\| [[40ed5/2\|40]]
			\| [[41ed5/2\|41]]
			\| [[42ed5/2\|42]]
			\| [[43ed5/2\|43]]
			\| [[44ed5/2\|44]]
			\| [[45ed5/2\|45]]
			\| [[46ed5/2\|46]]
			\| [[47ed5/2\|47]]
			\| [[48ed5/2\|48]]
			\| [[49ed5/2\|49]]
			\|}


	[[Category:Ed5/2\| ]] <!-- main article -->		[[Category:Ed5/2\| ]] <!-- main article -->
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]