10ed5 - Revision history

Squib at 02:04, 10 April 2026

2026-04-10T02:04:49Z

← Older revision		Revision as of 02:04, 10 April 2026
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	As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.		As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.

	~~Adding octaves relates this tuning~~ to [[13edo]], ~~which divides~~ the step in ~~three~~.		Octaves can be added by dividing the step in three to get [[13edo]] with octaves 7 cents sharp. If octaves are instead made just, prime 7 becomes very flat, as well as prime 5 to a lesser extent. Alternatively, the step can be divided in ten to get [[43edo]].

	== Music ==		== Music ==

Squib: interval table, reorganization

2026-04-10T01:59:19Z

interval table, reorganization

← Older revision		Revision as of 01:59, 10 April 2026
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}

	In general, 10ed5 is simply a smashing tuning. The relatively large steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.		In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.

	It is especially important as a structural framework for the [[5.7.11.13 subgroup]].		It is especially important as a structural framework for the [[5.7.11.13 subgroup]].
Line 76:		Line 76:
	As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.		As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.

	Adding octaves relates this tuning to 13edo, which divides the step in three~~, although the octaves are 7 cents sharp. If octaves are instead made just, everything else (especially prime 7) becomes flatter. Alternatively, the step can be divided in 10 to get 43edo~~.		Adding octaves relates this tuning to [[13edo]], which divides the step in three.

	== Music ==		== Music ==

Squib: interval table, reorganization

2026-04-10T01:59:00Z

interval table, reorganization

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-Half of [[20ed5|20ed5]]. But it has important characteristics of its own:
+In general, 10ed5 is simply a smashing tuning. The relatively large steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.
-In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.
+It is especially important as a structural framework for the [[5.7.11.13 subgroup]].
 == Harmonics ==
@@ Line 24: / Line 20: @@
 == Intervals ==
-: 1/1
+== Subsets and supersets ==
+Half of [[20ed5]].
-: 2507.682 cents 21/5
+As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.
-: 5/1
+Adding octaves relates this tuning to 13edo, which divides the step in three, although the octaves are 7 cents sharp. If octaves are instead made just, everything else (especially prime 7) becomes flatter. Alternatively, the step can be divided in 10 to get 43edo.
 == Music ==

Squib: partial cleanup, +note about structure

2026-03-12T02:50:24Z

partial cleanup, +note about structure

← Older revision		Revision as of 02:50, 12 March 2026
Line 5:		Line 5:
	In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.		In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.

	As 5ed5 is the simplest [[~~Hyperpyth\|~~hyperpyth]] tuning, analogous to [[~~5edo\|~~5edo]] and [[~~4edt\|~~4edt]] in their own spheres, this, its double, can be compared, structurally, to, [[10edo\|10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.		As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo\|10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals. It is especially important as a structural framework for the [[5.7.11.13 subgroup]].

	Adding octaves~~, strangely enough,~~ relates this tuning to [[43edo]].		Adding octaves relates this tuning to [[43edo]], which divides the step in ten.

	== Harmonics ==		== Harmonics ==

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

2025-08-01T19:20:34Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:20, 1 August 2025
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	[http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky		[http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky
	[[Category:5th_harmonic]]		[[Category:5th_harmonic]]
	~~[[Category:edonoi]]~~

Fredg999 category edits: Removing from Category:Ed5 using Cat-a-lot

2025-08-01T18:39:02Z

Removing from Category:Ed5 using Cat-a-lot

← Older revision		Revision as of 18:39, 1 August 2025
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	[http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky		[http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky
	[[Category:5th_harmonic]]		[[Category:5th_harmonic]]
	~~[[Category:ed5]]~~
	[[Category:edonoi]]		[[Category:edonoi]]

BudjarnLambeth: /* Harmonics */

2024-10-06T01:11:41Z

Harmonics

← Older revision		Revision as of 01:11, 6 October 2024
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	== Harmonics ==		== Harmonics ==
			{{Harmonics in equal
	{{~~harmonics~~ in equal\|10\|5\|1}}		\| steps = 10
			\| num = 5
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 10
			\| num = 5
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

	== Intervals ==		== Intervals ==

BudjarnLambeth at 09:44, 15 January 2024

2024-01-15T09:44:38Z

← Older revision		Revision as of 09:44, 15 January 2024
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	{{Infobox ET}}		{{Infobox ET}}

	Half of [[20ed5\|20ed5]] ~~(obviously)~~. But it has important characteristics of its own:		Half of [[20ed5\|20ed5]]. But it has important characteristics of its own:

	In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.		In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.

BudjarnLambeth: Changed headings to conform with the style of other wiki pages. Added table of harmonics.

2024-01-15T09:44:18Z

Changed headings to conform with the style of other wiki pages. Added table of harmonics.

← Older revision		Revision as of 09:44, 15 January 2024
Line 8:		Line 8:

	Adding octaves, strangely enough, relates this tuning to [[43edo]].		Adding octaves, strangely enough, relates this tuning to [[43edo]].

			== Harmonics ==

			{{harmonics in equal\|10\|5\|1}}

			== Intervals ==

	0: 1/1		0: 1/1
Line 31:		Line 37:
	10: 5/1		10: 5/1

	Music:		== Music ==

	[http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky		[http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky

Plumtree: Infobox ET added

2022-10-05T20:37:24Z

Infobox ET added

← Older revision		Revision as of 20:37, 5 October 2022
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	~~=10 equal divisions of the 5th harmonic=~~		{{Infobox ET}}

	Half of [[20ed5\|20ed5]] (obviously). But it has important characteristics of its own:		Half of [[20ed5\|20ed5]] (obviously). But it has important characteristics of its own: