7edt - Revision history

FloraC: +subsets and supersets; cleanup; -redundant categories

2025-02-23T13:40:01Z

+subsets and supersets; cleanup; -redundant categories

← Older revision		Revision as of 13:40, 23 February 2025
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|7\|3\|1\|}}		{{Harmonics in equal\|7\|3\|1\|columns=15}}

	=== ~~Prime harmonics~~ ===		=== Subsets and supersets ===
	~~{{Harmonics in~~ equal\|~~7\|3\|1\|intervals=~~prime}}		7edt is the 4th [[prime equal division\|prime edt]], after [[5edt]] and before [[11edt]].

	== ~~Scale degrees of 7edt~~ ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable center-1 right-2 right-3"
	\|-		\|-
	! ~~Degrees~~		! #
	! Cents		! Cents
	! [[Hekt]]s		! [[Hekt]]s
	! Approximate ~~ratio~~		! Approximate ratios
	! [[Electra]] notation<br />({{nowrap\|J {{=}} 1/1}})		! [[Electra]] notation<br>({{nowrap\|J {{=}} 1/1}})
	\|-		\|-
	~~! colspan="3"~~ \| 0		\| 0
			\| 0
			\| 0
	\| [[1/1]]		\| [[1/1]]
	\| J		\| J
	\|-		\|-
	\| 1		\| 1
	\| ~~271.708~~		\| 272
	\| ~~185.714~~		\| 186
	\| [[7/6]]		\| [[7/6]]
	\| K		\| K
	\|-		\|-
	\| 2		\| 2
	\| 543~~.416~~		\| 543
	\| 371~~.429~~		\| 371
	\| [[15/11]], [[11/8]]		\| [[11/8]], [[15/11]]
	\| L		\| L
	\|-		\|-
	\| 3		\| 3
	\| 815~~.124~~		\| 815
	\| 557~~.143~~		\| 557
	\| [[8/5]]		\| [[8/5]]
	\| M		\| M
	\|-		\|-
	\| 4		\| 4
	\| ~~1086.831~~		\| 1087
	\| ~~742.857~~		\| 743
	\| [[15/8]]		\| [[15/8]]
	\| N		\| N
	\|-		\|-
	\| 5		\| 5
	\| ~~1358.539~~		\| 1359
	\| ~~928.571~~		\| 929
	\| [[11/5]] ~~([[11/10]] plus an octave)~~		\| [[11/5]]
	\| O		\| O
	\|-		\|-
	\| 6		\| 6
	\| 1630~~.247~~		\| 1630
	\| 1114~~.286~~		\| 1114
	\| [[18/7]] ~~([[9/7]] plus an octave)~~		\| [[18/7]]
	\| P		\| P
	\|-		\|-
	\| 7		\| 7
	\| ~~1901.955~~		\| 1902
	\| 1300		\| 1300
	\| [[3/1]]		\| [[3/1]]
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	\|}		\|}

	~~[[category:Macrotonal]]~~
	[[Category:Orwell]]		[[Category:Orwell]]
	[[Category:Subminor third]]		[[Category:Subminor third]]
	~~[[Category:Edt]]~~

ArrowHead294: /* Scale degrees of 7edt */

2025-02-20T16:19:23Z

Scale degrees of 7edt

← Older revision		Revision as of 16:19, 20 February 2025
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	! Cents		! Cents
	! [[Hekt]]s		! [[Hekt]]s
	! Approximate ~~Ratio~~		! Approximate ratio
	! [[Electra]] notation ({{nowrap\|J {{=}} 1/1}})		! [[Electra]] notation<br />({{nowrap\|J {{=}} 1/1}})
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0

ArrowHead294 at 16:19, 20 February 2025

2025-02-20T16:19:12Z

← Older revision		Revision as of 16:19, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==
	Since one step of 7edt approximates a [[7/6]] subminor third (4.84 ~~cents~~ sharp) quite nicely, three steps are almost exactly [[8/5]] (tempering out [[1728/1715]], the orwellisma), and four steps are very nearly [[15/8]] (tempering out [[2430/2401]], the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony, along with some elements of the [[11-limit]], such as the [[11/8]] major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.		Since one step of 7edt approximates a [[7/6]] subminor third (4.84{{c}} sharp) quite nicely, three steps are almost exactly [[8/5]] (tempering out [[1728/1715]], the orwellisma), and four steps are very nearly [[15/8]] (tempering out [[2430/2401]], the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony, along with some elements of the [[11-limit]], such as the [[11/8]] major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.

	Due to the proximity of the step size with 7/6, 7edt supports [[orwell]] temperament. One step of 7edt is almost identical to 12\53, the [[53edo]] orwell generator, at about 271.698 cents. 7edt is also a good tuning for [[Electra]] temperament, with two steps of 7edt being a close approximation to [[15/11]].		Due to the proximity of the step size with 7/6, 7edt supports [[orwell]] temperament. One step of 7edt is almost identical to 12\53, the [[53edo]] orwell generator, at about 271.698 cents. 7edt is also a good tuning for [[Electra]] temperament, with two steps of 7edt being a close approximation to [[15/11]].
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	== Scale degrees of 7edt ==		== Scale degrees of 7edt ==

	{\| class="wikitable"		{\| class="wikitable"
			\|-
	! Degrees		! Degrees
	! Cents		! Cents
	! [[Hekt]]s		! [[Hekt]]s
	! Approximate Ratio		! Approximate Ratio
	! [[Electra]] notation (J = 1/1)		! [[Electra]] notation ({{nowrap\|J {{=}} 1/1}})
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0
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	\| 1		\| 1
	\| 271.708		\| 271.708
	\|185.714		\| 185.714
	\| [[7/6]]		\| [[7/6]]
	\| K		\| K
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	\| 2		\| 2
	\| 543.416		\| 543.416
	\|371.429		\| 371.429
	\| [[15/11]], [[11/8]]		\| [[15/11]], [[11/8]]
	\| L		\| L
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	\| 3		\| 3
	\| 815.124		\| 815.124
	\|557.143		\| 557.143
	\| [[8/5]]		\| [[8/5]]
	\| M		\| M
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	\| 4		\| 4
	\| 1086.831		\| 1086.831
	\|742.857		\| 742.857
	\| [[15/8]]		\| [[15/8]]
	\| N		\| N
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	\| 5		\| 5
	\| 1358.539		\| 1358.539
	\|928.571		\| 928.571
	\| [[11/5]] ([[11/10]] plus an octave)		\| [[11/5]] ([[11/10]] plus an octave)
	\| O		\| O
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	\| 6		\| 6
	\| 1630.247		\| 1630.247
	\|1114.286		\| 1114.286
	\| [[18/7]] ([[9/7]] plus an octave)		\| [[18/7]] ([[9/7]] plus an octave)
	\| P		\| P
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	\| 7		\| 7
	\| 1901.955		\| 1901.955
	\|1300		\| 1300
	\| [[3/1]]		\| [[3/1]]
	\| J		\| J
	\|}		\|}

			[[category:Macrotonal]]
	[[category:~~macrotonal~~]]		[[Category:Orwell]]
	[[Category:~~orwell~~]]		[[Category:Subminor third]]
	[[Category:~~subminor~~ third]]
	[[Category:Edt]]		[[Category:Edt]]

Akselai: clean up

2024-04-29T11:02:01Z

clean up

← Older revision		Revision as of 11:02, 29 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''7edt''' (short for '''7''' '''e'''qual '''d'''ivision of '''t'''ritave) divides the interval [[3/1]] it into 7 equal parts of 271.708 [[cent]]s each, corresponding to 4.4165 edo.~~		{{EDO intro}}

	~~__FORCETOC__~~		== Theory ==
	== ~~Properties~~ ==		Since one step of 7edt approximates a [[7/6]] subminor third (4.84 cents sharp) quite nicely, three steps are almost exactly [[8/5]] (tempering out [[1728/1715]], the orwellisma), and four steps are very nearly [[15/8]] (tempering out [[2430/2401]], the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony, along with some elements of the [[11-limit]], such as the [[11/8]] major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.
	~~The~~ step ~~size is~~ very ~~close to~~ the ~~271~~.~~509 cents~~ of 7-limit [[~~Orwell\|orwell temperament~~]] ~~and also close~~ to the ~~271.426 cents~~ of [[~~11-limit~~]] ~~orwell~~. It is almost identical to 12\53, the [[53edo]] orwell generator ~~which is~~ 271.698 cents. 7edt is a good tuning for [[Electra]] temperament, with ~~its second degree~~ being a close approximation to [[15/11]].
			Due to the proximity of the step size with 7/6, 7edt supports [[orwell]] temperament. One step of 7edt is almost identical to 12\53, the [[53edo]] orwell generator, at about 271.698 cents. 7edt is also a good tuning for [[Electra]] temperament, with two steps of 7edt being a close approximation to [[15/11]].

			=== Harmonics ===
			{{Harmonics in equal\|7\|3\|1\|}}

			=== Prime harmonics ===
			{{Harmonics in equal\|7\|3\|1\|intervals=prime}}

	== Scale degrees of 7edt ==		== Scale degrees of 7edt ==
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	! Degrees		! Degrees
	! Cents		! Cents
	!~~hekts~~		! [[Hekt]]s
	! Approximate Ratio		! Approximate Ratio
	! [[Electra]] notation (J = 1/1)		! [[Electra]] notation (J = 1/1)
Line 62:		Line 69:
	\|}		\|}

	Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].

	~~== Prime harmonics ==~~
	~~{{Harmonics in equal\|7\|3\|1\|intervals=prime}}~~

	~~== 7n-edt Family ==~~
	* [[14edt]]
	* [[21edt]]
	* [[28edt]]
	* [[56edt]]

	[[category:macrotonal]]		[[category:macrotonal]]
	~~[[Category:53edo]]~~
	[[Category:orwell]]		[[Category:orwell]]
	[[Category:subminor third]]		[[Category:subminor third]]
	[[Category:Edt]]		[[Category:Edt]]

Akselai: /* Prime harmonics */

2024-01-17T09:40:42Z

Prime harmonics

← Older revision		Revision as of 09:40, 17 January 2024
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	== Prime harmonics ==		== Prime harmonics ==
	{{Harmonics in equal\|7\|3\|1}}		{{Harmonics in equal\|7\|3\|1\|intervals=prime}}

	== 7n-edt Family ==		== 7n-edt Family ==

Akselai: /* Prime harmonics */ h

2024-01-17T09:26:16Z

Prime harmonics: h

← Older revision		Revision as of 09:26, 17 January 2024
Line 64:		Line 64:
	Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].		Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].

	=== Prime harmonics ===		== Prime harmonics ==
	{{Harmonics in equal\|7\|3\|1}}		{{Harmonics in equal\|7\|3\|1}}

Akselai: add harmonics in equal

2024-01-17T09:25:24Z

add harmonics in equal

← Older revision		Revision as of 09:25, 17 January 2024
Line 63:		Line 63:

	Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].		Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].

			=== Prime harmonics ===
			{{Harmonics in equal\|7\|3\|1}}

	== 7n-edt Family ==		== 7n-edt Family ==

CompactStar at 02:18, 5 March 2023

2023-03-05T02:18:58Z

← Older revision		Revision as of 02:18, 5 March 2023
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	!hekts		!hekts
	! Approximate Ratio		! Approximate Ratio
	! [[Electra]] notation		! [[Electra]] notation (J = 1/1)
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0

CompactStar at 02:18, 5 March 2023

2023-03-05T02:18:29Z

← Older revision		Revision as of 02:18, 5 March 2023
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	! colspan="3" \| 0		! colspan="3" \| 0
	\| [[1/1]]		\| [[1/1]]
			\| J
	\|-		\|-
	\| 1		\| 1

CompactStar at 02:18, 5 March 2023

2023-03-05T02:18:22Z

← Older revision		Revision as of 02:18, 5 March 2023
Line 13:		Line 13:
	!hekts		!hekts
	! Approximate Ratio		! Approximate Ratio
			! [[Electra]] notation
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0
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	\|185.714		\|185.714
	\| [[7/6]]		\| [[7/6]]
			\| K
	\|-		\|-
	\| 2		\| 2
Line 26:		Line 28:
	\|371.429		\|371.429
	\| [[15/11]], [[11/8]]		\| [[15/11]], [[11/8]]
			\| L
	\|-		\|-
	\| 3		\| 3
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	\|557.143		\|557.143
	\| [[8/5]]		\| [[8/5]]
			\| M
	\|-		\|-
	\| 4		\| 4
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	\|742.857		\|742.857
	\| [[15/8]]		\| [[15/8]]
			\| N
	\|-		\|-
	\| 5		\| 5
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	\|928.571		\|928.571
	\| [[11/5]] ([[11/10]] plus an octave)		\| [[11/5]] ([[11/10]] plus an octave)
			\| O
	\|-		\|-
	\| 6		\| 6
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	\|1114.286		\|1114.286
	\| [[18/7]] ([[9/7]] plus an octave)		\| [[18/7]] ([[9/7]] plus an octave)
			\| P
	\|-		\|-
	\| 7		\| 7
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	\|1300		\|1300
	\| [[3/1]]		\| [[3/1]]
			\| J
	\|}		\|}