17ed4 - Revision history

Fredg999 category edits: Removing from Category:Ed4 using Cat-a-lot

2025-07-31T21:18:55Z

Removing from Category:Ed4 using Cat-a-lot

← Older revision		Revision as of 21:18, 31 July 2025
Line 139:		Line 139:
	[[Category:Macrotonal]]		[[Category:Macrotonal]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Ed4]]~~
	{{todo\|expand}}		{{todo\|expand}}

BudjarnLambeth: {{todo|expand}}

2024-12-22T04:14:57Z

← Older revision		Revision as of 04:14, 22 December 2024
Line 140:		Line 140:
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Ed4]]		[[Category:Ed4]]
			{{todo\|expand}}

BudjarnLambeth: Harmonics

2024-10-05T02:38:56Z

Harmonics

← Older revision		Revision as of 02:38, 5 October 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding~~ to 8.5edo or every second step of [[17edo]].		{{ED intro}} It corresponds to 8.5edo or every second step of [[17edo]].

	==Theory==		==Theory==
	17ed4 is the smallest ED4 to contain a diatonic fifth, in this case [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)\|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.		17ed4 is the smallest ED4 to contain a diatonic fifth, in this case [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)\|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.

	==Intervals==		==Intervals==
	{\|class="wikitable"		{\|class="wikitable"
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	\|J		\|J
	\|}		\|}

			== Harmonics ==
			{{Harmonics in equal
			\| steps = 17
			\| num = 4
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 17
			\| num = 4
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

	[[Category:Macrotonal]]		[[Category:Macrotonal]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Ed4]]		[[Category:Ed4]]

CompactStar at 02:11, 8 June 2023

2023-06-08T02:11:12Z

← Older revision		Revision as of 02:11, 8 June 2023
Line 2:		Line 2:
	'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].		'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].
	==Theory==		==Theory==
	17ed4 is the smallest ED4 to contain a diatonic fifth, in this ~~cas~~ [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)\|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.		17ed4 is the smallest ED4 to contain a diatonic fifth, in this case [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)\|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.
	==Intervals==		==Intervals==
	{\|class="wikitable"		{\|class="wikitable"

CompactStar at 01:01, 9 May 2023

2023-05-09T01:01:32Z

← Older revision		Revision as of 01:01, 9 May 2023
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	!Approximate ratios		!Approximate ratios
	![[17edo]] notation		![[17edo]] notation
	![[7L 3s (4/1-equivalent)\|~~7L 3s<4/1>~~]] notation (J = 1/1)		![[7L 3s (4/1-equivalent)\|Diaquadic]] notation (J = 1/1)
	\|-		\|-
	\|0		\|0

CompactStar at 01:01, 9 May 2023

2023-05-09T01:01:23Z

← Older revision		Revision as of 01:01, 9 May 2023
Line 2:		Line 2:
	'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].		'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].
	==Theory==		==Theory==
	17ed4 is the smallest ED4 to contain a diatonic fifth, in this cas [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s) and decatonic (7L 3s) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.		17ed4 is the smallest ED4 to contain a diatonic fifth, in this cas [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)\|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.
	==Intervals==		==Intervals==
	{\|class="wikitable"		{\|class="wikitable"
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	\|[[13/12]], [[12/11]], [[14/13]], [[25/23]]		\|[[13/12]], [[12/11]], [[14/13]], [[25/23]]
	\|C#		\|C#
	\|J#, ~~Kbb~~		\|J#, Kb
	\|-		\|-
	\|2		\|2
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	\|[[13/11]], [[7/6]]		\|[[13/11]], [[7/6]]
	\|Eb		\|Eb
	\|~~Jx, Kb~~		\|K
	\|-		\|-
	\|3		\|3
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	\|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]		\|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]
	\|E		\|E
	\|K		\|K#, Lb
	\|-		\|-
	\|4		\|4
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	\|[[11/8]], [[18/13]], [[32/23]]		\|[[11/8]], [[18/13]], [[32/23]]
	\|^F		\|^F
	\|~~K#, Lb~~		\|L
	\|-		\|-
	\|5		\|5
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	\|[[3/2]], [[32/21]]		\|[[3/2]], [[32/21]]
	\|G		\|G
	\|L		\|M
	\|-		\|-
	\|6		\|6
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	\|[[13/8]], [[18/11]], [[23/14]]		\|[[13/8]], [[18/11]], [[23/14]]
	\|G#, vA		\|G#, vA
	\|M		\|M#, Nb
	\|-		\|-
	\|7		\|7
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	\|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]		\|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
	\|Bb		\|Bb
	\|~~M#, Nb~~		\|N
	\|-		\|-
	\|8		\|8
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	\|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]]		\|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]]
	\|B		\|B
	\|N		\|N#, Ob
	\|-		\|-
	\|9		\|9
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	\|[[15/7]]		\|[[15/7]]
	\|^C		\|^C
	\|~~N#, Ob~~		\|O
	\|-		\|-
	\|10		\|10
	\|1411.80		\|1411.80
	\|[[16/7]]		\|[[9/4]], [[16/7]]
	\|D		\|D
	\|O		\|O#, Pb
	\|-		\|-
	\|11		\|11
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	\|[[8/3]]		\|[[8/3]]
	\|F		\|F
	\|~~P#, Qb~~		\|Q
	\|-		\|-
	\|13		\|13
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	\|[[3/1]]		\|[[3/1]]
	\|F#		\|F#
	\|Q		\|Q#, Rb
	\|-		\|-
	\|14		\|14
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	\|[[16/5]]		\|[[16/5]]
	\|^G, Ab		\|^G, Ab
	\|~~Q#, Rb~~		\|R
	\|-		\|-
	\|15		\|15
Line 106:		Line 106:
	\|[[10/3]]		\|[[10/3]]
	\|A		\|A
	\|R		\|R#, Sb
	\|-		\|-
	\|16		\|16
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	\|[[11/3]]		\|[[11/3]]
	\|vB		\|vB
	\|~~R#, Jb~~		\|S
	\|-		\|-
	\|17		\|17

Plumtree: Infobox ET

2023-05-02T11:02:19Z

Infobox ET

← Older revision		Revision as of 11:02, 2 May 2023
Line 1:		Line 1:
	{{Infobox ET~~\|1ed27059/24940~~}}		{{Infobox ET}}
	~~<!--Using continued fraction convergent of 4^(1/17) until Infobox ET starts working with ED4s-->~~
	'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].		'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].
	==Theory==		==Theory==

CompactStar at 04:09, 2 May 2023

2023-05-02T04:09:04Z

← Older revision		Revision as of 04:09, 2 May 2023
Line 3:		Line 3:
	'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].		'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].
	==Theory==		==Theory==
	17ed4 ~~contains~~ [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s) and decatonic (7L 3s) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.		17ed4 is the smallest ED4 to contain a diatonic fifth, in this cas [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s) and decatonic (7L 3s) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.
	==Intervals==		==Intervals==
	{\|class="wikitable"		{\|class="wikitable"

CompactStar at 04:06, 2 May 2023

2023-05-02T04:06:24Z

← Older revision		Revision as of 04:06, 2 May 2023
Line 1:		Line 1:
	{{Infobox ET\|~~1ed1840616~~/~~1678131~~}}		{{Infobox ET\|1ed27059/24940}}
	<!--Using continued fraction convergent of 4^(1/17) until Infobox ET starts working with ED4s-->		<!--Using continued fraction convergent of 4^(1/17) until Infobox ET starts working with ED4s-->
	'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].		'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].

CompactStar at 04:05, 2 May 2023

2023-05-02T04:05:58Z

← Older revision		Revision as of 04:05, 2 May 2023
Line 1:		Line 1:
	{{Infobox ET\|~~17ed1840616~~/1678131}}		{{Infobox ET\|1ed1840616/1678131}}
	<!--Using continued fraction convergent of 4^(1/17) until Infobox ET starts working with ED4s-->		<!--Using continued fraction convergent of 4^(1/17) until Infobox ET starts working with ED4s-->
	'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].		'''17ed4''' is the [[Ed4\|equal division of the double octave]] into 17 parts of 141.18 [[cent\|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].