7edf - Revision history

ArrowHead294: /* See also */

2025-06-10T13:26:36Z

ArrowHead294 at 13:23, 10 June 2025

2025-06-10T13:23:53Z

← Older revision		Revision as of 13:23, 10 June 2025
Line 103:		Line 103:
	* [[40ed10]] – relative ed10		* [[40ed10]] – relative ed10
	* [[43ed12]] – relative ed12		* [[43ed12]] – relative ed12
			* [[76ed80]] – close to the zeta-optimized tuning for 12edo

	{{Todo\|expand}}		{{Todo\|expand}}

	[[Category:12edo]]		[[Category:12edo]]

ArrowHead294 at 13:09, 10 June 2025

2025-06-10T13:09:13Z

← Older revision		Revision as of 13:09, 10 June 2025
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	== Theory ==		== Theory ==
	7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just~~. The~~ octave ~~is about~~ 3.3514 ~~cents stretched and the step size is about 100.2793 cents~~. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.		7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514{{c}}. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13. It forms as a decent approximation to stretched-octave tuning on pianos, since pianos' strings have overtones that tend slightly sharp and are thus often tuned with stretched octaves.

	=== Harmonics ===		=== Harmonics ===
Line 16:		Line 16:
	! #		! #
	! Cents		! Cents
	!Approximate ratios		! Approximate ratios
	! 12edo notation		! 12edo notation
	\|-		\|-
	\| 0		\| 0
	\| 0		\| 0
	\|exact 1/1		\| exact 1/1
	\| C		\| C
	\|-		\|-
	\| 1		\| 1
	\| 100.3		\| 100.3
	\|18/17, 17/16		\| 18/17, 17/16
	\| C#, Db		\| C#, Db
	\|-		\|-
	\| 2		\| 2
	\| 200.6		\| 200.6
	\|9/8		\| 9/8
	\| D		\| D
	\|-		\|-
	\| 3		\| 3
	\| 300.8		\| 300.8
	\|19/16, 44/37		\| 19/16, 44/37
	\| D#, Eb		\| D#, Eb
	\|-		\|-
	\| 4		\| 4
	\| 401.1		\| 401.1
	\|63/50		\| 63/50
	\| E		\| E
	\|-		\|-
	\| 5		\| 5
	\| 501.4		\| 501.4
	\|4/3		\|4/3
	\| F		\| F
	\|-		\|-
	\| 6		\| 6
	\| 601.7		\| 601.7
	\|64/45		\| 64/45
	\| F#, Gb		\| F#, Gb
	\|-		\|-
	\| 7		\| 7
	\| 702.0		\| 702.0
	\|exact 3/2		\| exact 3/2
	\| G		\| G
	\|-		\|-
	\| 8		\| 8
	\| 802.2		\| 802.2
	\|100/63		\| 100/63
	\| G#, Ab		\| G#, Ab
	\|-		\|-
	\| 9		\| 9
	\| 902.5		\| 902.5
	\|27/16		\| 27/16
	\| A		\| A
	\|-		\|-
	\| 10		\| 10
	\| 1002.8		\| 1002.8
	\|16/9		\| 16/9
	\| A#, Bb		\| A#, Bb
	\|-		\|-
	\| 11		\| 11
	\| 1103.1		\| 1103.1
	\|17/9		\| 17/9
	\| B		\| B
	\|-		\|-
	\| 12		\| 12
	\| 1203.4		\| 1203.4
	\|2/1		\| 2/1
	\| C		\| C
	\|-		\|-
	\| 13		\| 13
	\| 1303.6		\| 1303.6
	\|17/8		\| 17/8
	\| C#, Db		\| C#, Db
	\|-		\|-
	\| 14		\| 14
	\| 1403.9		\| 1403.9
	\|exact 9/4		\| exact 9/4
	\| D		\| D
	\|}		\|}
Line 105:		Line 105:

	{{Todo\|expand}}		{{Todo\|expand}}

			[[Category:12edo]]

MisterShafXen at 12:46, 26 April 2025

2025-04-26T12:46:17Z

← Older revision		Revision as of 12:46, 26 April 2025
Line 16:		Line 16:
	! #		! #
	! Cents		! Cents
			!Approximate ratios
	! 12edo notation		! 12edo notation
	\|-		\|-
	\| 0		\| 0
	\| 0		\| 0
			\|exact 1/1
	\| C		\| C
	\|-		\|-
	\| 1		\| 1
	\| 100.3		\| 100.3
			\|18/17, 17/16
	\| C#, Db		\| C#, Db
	\|-		\|-
	\| 2		\| 2
	\| 200.6		\| 200.6
			\|9/8
	\| D		\| D
	\|-		\|-
	\| 3		\| 3
	\| 300.8		\| 300.8
			\|19/16, 44/37
	\| D#, Eb		\| D#, Eb
	\|-		\|-
	\| 4		\| 4
	\| 401.1		\| 401.1
			\|63/50
	\| E		\| E
	\|-		\|-
	\| 5		\| 5
	\| 501.4		\| 501.4
			\|4/3
	\| F		\| F
	\|-		\|-
	\| 6		\| 6
	\| 601.7		\| 601.7
			\|64/45
	\| F#, Gb		\| F#, Gb
	\|-		\|-
	\| 7		\| 7
	\| 702.0		\| 702.0
			\|exact 3/2
	\| G		\| G
	\|-		\|-
	\| 8		\| 8
	\| 802.2		\| 802.2
			\|100/63
	\| G#, Ab		\| G#, Ab
	\|-		\|-
	\| 9		\| 9
	\| 902.5		\| 902.5
			\|27/16
	\| A		\| A
	\|-		\|-
	\| 10		\| 10
	\| 1002.8		\| 1002.8
			\|16/9
	\| A#, Bb		\| A#, Bb
	\|-		\|-
	\| 11		\| 11
	\| 1103.1		\| 1103.1
			\|17/9
	\| B		\| B
	\|-		\|-
	\| 12		\| 12
	\| 1203.4		\| 1203.4
			\|2/1
	\| C		\| C
	\|-		\|-
	\| 13		\| 13
	\| 1303.6		\| 1303.6
			\|17/8
	\| C#, Db		\| C#, Db
	\|-		\|-
	\| 14		\| 14
	\| 1403.9		\| 1403.9
			\|exact 9/4
	\| D		\| D
	\|}		\|}

FloraC: +links to related tunings

2025-02-23T13:48:49Z

+links to related tunings

← Older revision		Revision as of 13:48, 23 February 2025
Line 4:		Line 4:
	== Theory ==		== Theory ==
	7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.		7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

	~~Lookalikes: [[12edo]], [[19ed3]], [[31ed6]], [[43ed12]].~~

	=== Harmonics ===		=== Harmonics ===
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	\| D		\| D
	\|}		\|}

			== See also ==
			* [[12edo]] – relative edo
			* [[19edt]] – relative edt
			* [[28ed5]] – relative ed5
			* [[31ed6]] – relative ed6
			* [[34ed7]] – relative ed7
			* [[40ed10]] – relative ed10
			* [[43ed12]] – relative ed12

	{{Todo\|expand}}		{{Todo\|expand}}

FloraC: +subsets and supersets; cleanup

2025-02-23T13:45:49Z

+subsets and supersets; cleanup

← Older revision		Revision as of 13:45, 23 February 2025
Line 9:		Line 9:
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|7\|3\|2\|prec=2\|columns=15}}		{{Harmonics in equal\|7\|3\|2\|prec=2\|columns=15}}

			=== Subsets and supersets ===
			7edf is the 4th [[prime equal division\|prime edf]], after [[5edf]] and before [[11edf]].

	== Intervals ==		== Intervals ==
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	! #		! #
	! Cents		! Cents
	! 12edo ~~Notation~~		! 12edo notation
	\|-		\|-
	\| 0		\| 0
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	\|}		\|}

	{{~~todo~~\|expand}}		{{Todo\|expand}}

ArrowHead294: /* Intervals */

2025-01-21T13:22:11Z

Intervals

← Older revision		Revision as of 13:22, 21 January 2025
Line 16:		Line 16:
	! Cents		! Cents
	! 12edo Notation		! 12edo Notation
			\|-
			\| 0
			\| 0
			\| C
	\|-		\|-
	\| 1		\| 1

BudjarnLambeth: {{todo|expand}}

2024-12-19T08:56:13Z

← Older revision		Revision as of 08:56, 19 December 2024
Line 73:		Line 73:
	\| D		\| D
	\|}		\|}

			{{todo\|expand}}

FloraC: Adopt template: ED intro; misc. cleanup

2024-05-10T06:43:45Z

Adopt template: ED intro; misc. cleanup

← Older revision		Revision as of 06:43, 10 May 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 7 equal parts''' (7EDF) is related to [[12edo\|12 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.		{{ED intro}}

	~~Lookalikes:~~ [[12edo]], ~~[[19ed3]]~~, ~~[[31ed6]], [[43ed12]]~~		== Theory ==
			7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

	==Harmonics==		Lookalikes: [[12edo]], [[19ed3]], [[31ed6]], [[43ed12]].

			=== Harmonics ===
	{{Harmonics in equal\|7\|3\|2\|prec=2\|columns=15}}		{{Harmonics in equal\|7\|3\|2\|prec=2\|columns=15}}

	==Intervals==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable center-1 right-2 center-3"
	\|-		\|-
	! #		! #
	! Cents		! Cents
	! 12edo ~~notation~~		! 12edo Notation
	\|-		\|-
	\| 1		\| 1
	\| 100.~~2793~~		\| 100.3
	\| C#, Db		\| C#, Db
	\|-		\|-
	\| 2		\| 2
	\| 200.~~5586~~		\| 200.6
	\| D		\| D
	\|-		\|-
	\| 3		\| 3
	\| 300.~~8379~~		\| 300.8
	\| D#, Eb		\| D#, Eb
	\|-		\|-
	\| 4		\| 4
	\| 401.~~1171~~		\| 401.1
	\| E		\| E
	\|-		\|-
	\| 5		\| 5
	\| 501.~~3964~~		\| 501.4
	\| F		\| F
	\|-		\|-
	\| 6		\| 6
	\| 601.~~6757~~		\| 601.7
	\| F#, Gb		\| F#, Gb
	\|-		\|-
	\| 7		\| 7
	\| ~~701~~.~~955~~		\| 702.0
	\| G		\| G
	\|-		\|-
	\| 8		\| 8
	\| 802.~~2343~~		\| 802.2
	\| G#, Ab		\| G#, Ab
	\|-		\|-
	\| 9		\| 9
	\| 902.~~5136~~		\| 902.5
	\| A		\| A
	\|-		\|-
	\| 10		\| 10
	\| 1002.~~7929~~		\| 1002.8
	\| A#, Bb		\| A#, Bb
	\|-		\|-
	\| 11		\| 11
	\| 1103.~~0721~~		\| 1103.1
	\| B		\| B
	\|-		\|-
	\| 12		\| 12
	\| 1203.~~3514~~		\| 1203.4
	\| C		\| C
	\|-		\|-
	\| 13		\| 13
	\| 1303.~~6307~~		\| 1303.6
	\| C#, Db		\| C#, Db
	\|-		\|-
	\| 14		\| 14
	\| 1403.91		\| 1403.9
	\| D		\| D
	\|}		\|}

ArrowHead294 at 17:11, 9 May 2024

2024-05-09T17:11:56Z

← Older revision		Revision as of 17:11, 9 May 2024
Line 2:		Line 2:
	'''[[EDF\|Division of the just perfect fifth]] into 7 equal parts''' (7EDF) is related to [[12edo\|12 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.		'''[[EDF\|Division of the just perfect fifth]] into 7 equal parts''' (7EDF) is related to [[12edo\|12 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

	Lookalikes: [[12edo]], [[~~19ED3\|~~19ed3]], [[31ed6]]		Lookalikes: [[12edo]], [[19ed3]], [[31ed6]], [[43ed12]]

	==Harmonics==		==Harmonics==

← Older revision		Revision as of 13:26, 10 June 2025
Line 104:		Line 104:
	* [[43ed12]] – relative ed12		* [[43ed12]] – relative ed12
	* [[76ed80]] – close to the zeta-optimized tuning for 12edo		* [[76ed80]] – close to the zeta-optimized tuning for 12edo
			* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]

	{{Todo\|expand}}		{{Todo\|expand}}

	[[Category:12edo]]		[[Category:12edo]]