Ed5/3 - Revision history

Lériendil at 05:54, 14 May 2026

2026-05-14T05:54:13Z

← Older revision		Revision as of 05:54, 14 May 2026
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	Division of 5/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.		Division of 5/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	5/3 is the most consonant interval in between 1/1 and 2/1, so this suggests it could be useful either as an equivalence, or as just an important structural feature.		5/3 is the most consonant interval in between 3/2 and 2/1, so this suggests it could be useful either as an equivalence, or as just an important structural feature.

	[[Joseph Ruhf]] suggested the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone as a way to evoke 5/3-equivalence. Though it could also be used just as a useful sonority, even without equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s\|armotonic]].		[[Joseph Ruhf]] suggested the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone as a way to evoke 5/3-equivalence. Though it could also be used just as a useful sonority, even without equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s\|armotonic]].

Fredg999 category edits: Moving from Category:Ed5/3 to Category:Ed5/3's using Cat-a-lot

2025-08-01T18:40:58Z

Moving from Category:Ed5/3 to Category:Ed5/3's using Cat-a-lot

← Older revision		Revision as of 18:40, 1 August 2025
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	[[Category:Ed5/3\| ]] <!-- main article -->		[[Category:Ed5/3's\| ]]
			<!-- main article -->
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth: /* Individual pages for ed5/3's */

2025-05-22T03:13:51Z

Individual pages for ed5/3's

← Older revision		Revision as of 03:13, 22 May 2025
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	{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 5/3 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.}}		{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 5/3 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 03:13, 22 May 2025

2025-05-22T03:13:20Z

← Older revision		Revision as of 03:13, 22 May 2025
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	{{todo\|inline=1\|explain edonoi\|text=Most people do not think 5/4 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.}}		{{todo\|inline=1\|cleanup\|explain edonoi\|text=Most people do not think 5/3 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.}}

BudjarnLambeth: Todo

2025-05-22T03:13:01Z

Todo

← Older revision		Revision as of 03:13, 22 May 2025
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	{{todo\|inline=1\|~~review~~\|~~cleanup\|improve layout~~}}		{{todo\|inline=1\|explain edonoi\|text=Most people do not think 5/4 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.}}

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

2025-04-25T02:20:43Z

← Older revision		Revision as of 02:20, 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 */ adapted wording from ed16/15

2025-04-25T01:34:09Z

Properties: adapted wording from ed16/15

← Older revision		Revision as of 01:34, 25 April 2025
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	== Properties ==		== Properties ==
	Division of 5/3 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 5/3, [[11/7]] or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based [[sensi]] temperament or factoring into chord inversions. 5/3 is also the most consonant interval in the range between 3/2 and 2/1, which makes the equivalence easier to hear than for more complex ratios. Many, though not all, ~~of these~~ scales have a 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~~.		Division of 5/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/3 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way to treat~~ 5/3 as an equivalence is the use of the 6:7:8:(10) 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 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s\|armotonic]].		5/3 is the most consonant interval in between 1/1 and 2/1, so this suggests it could be useful either as an equivalence, or as just an important structural feature.

			[[Joseph Ruhf]] suggested the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone as a way to evoke 5/3-equivalence. Though it could also be used just as a useful sonority, even without equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s\|armotonic]].

	If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.		If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.

Lériendil at 13:51, 9 January 2025

2025-01-09T13:51:27Z

← Older revision		Revision as of 13:51, 9 January 2025
Line 2:		Line 2:

	== Properties ==		== Properties ==
	Division of 5/3 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 5/3, 11/7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based [[sensi]] temperament or factoring into chord inversions. 5/3 is also the most consonant interval in the range between 3/2 and 2/1, which makes the equivalence easier to hear than for more complex ratios. Many, though not all, of these scales have a 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.		Division of 5/3 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 5/3, [[11/7]] or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based [[sensi]] temperament or factoring into chord inversions. 5/3 is also the most consonant interval in the range between 3/2 and 2/1, which makes the equivalence easier to hear than for more complex ratios. Many, though not all, of these scales have a 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.

	Incidentally, one way to treat 5/3 as an equivalence is the use of the 6:7:8:(10) 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 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) if it ~~has not been named yet~~.		Incidentally, one way to treat 5/3 as an equivalence is the use of the 6:7:8:(10) 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 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s\|armotonic]].

	If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.		If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.

Contribution at 01:18, 28 August 2024

2024-08-28T01:18:46Z

← Older revision		Revision as of 01:18, 28 August 2024
Line 9:		Line 9:

	ED5/3 tuning systems that accurately represent the intervals 5/4 and 4/3 include: [[7ed5/3]] (7.30 cent error), [[9ed5/3]] (6.73 cent error), and [[16ed5/3]] (0.59 cent error).		ED5/3 tuning systems that accurately represent the intervals 5/4 and 4/3 include: [[7ed5/3]] (7.30 cent error), [[9ed5/3]] (6.73 cent error), and [[16ed5/3]] (0.59 cent error).

			[[7ed5/3]], [[9ed5/3]], and [[16ed5/3]] are to the [[Ed5/3\|division of 5/3]] what [[5edo]], [[7edo]], and [[12edo]] are to the [[EDO\|division of 2/1]].

	== Individual pages for ed5/3's ==		== Individual pages for ed5/3's ==

Contribution at 23:44, 27 August 2024

2024-08-27T23:44:37Z

← Older revision		Revision as of 23:44, 27 August 2024
Line 7:		Line 7:

	If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.		If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.

			ED5/3 tuning systems that accurately represent the intervals 5/4 and 4/3 include: [[7ed5/3]] (7.30 cent error), [[9ed5/3]] (6.73 cent error), and [[16ed5/3]] (0.59 cent error).

	== Individual pages for ed5/3's ==		== Individual pages for ed5/3's ==