6edf - Revision history

Videogamer1002: /* Intervals */

2026-04-30T16:56:58Z

Intervals

← Older revision		Revision as of 16:56, 30 April 2026
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	\| 15		\| 15
	\| 1755		\| 1755
	\|		\|11/4
	\| D		\| D
	\|-		\|-

BudjarnLambeth: {{todo|expand}}

2024-12-19T08:55:55Z

← Older revision		Revision as of 08:55, 19 December 2024
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	[[Category:Listen]]		[[Category:Listen]]

			{{todo\|expand}}

FloraC: /* Intervals */ rework, including removing irrelevant stuff

2024-05-10T06:34:04Z

Intervals: rework, including removing irrelevant stuff

← Older revision		Revision as of 06:34, 10 May 2024
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	== Intervals ==		== Intervals ==

	{\| class="wikitable"		{\| class="wikitable center-1 right-2 center-4"
	\|-		\|-
	! ~~degrees~~		! #
	! ~~cents ~ cents octave-reduced~~		! Cents
	! ~~approximate ratios~~		! Approximate Ratios
	! [[1L 3s (fifth-equivalent)\|Neptunian]] ~~notation~~		! [[1L 3s (fifth-equivalent)\|Neptunian]]<br>Notation
	\|-		\|-
	\| 0		\| 0
	\| 0 ~~(perfect unison, 1:1)~~		\| 0
	\| [[1/1]]		\| [[1/1]]
	\| C		\| C
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	\|-		\|-
	\| 6		\| 6
	\| 702 ~~(just perfect fifth, 3:2)~~		\| 702
	\| [[3/2]]		\| [[3/2]]
	\| C		\| C
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	\|-		\|-
	\| 11		\| 11
	\| 1287 ~~~ 87~~		\| 1287
	\|		\|
	\| F		\| F
	\|-		\|-
	\| 12		\| 12
	\| 1404 ~~~ 204 (just major whole tone~~/~~ninth, 9:~~4)		\| 1404
	\|		\| 9/4
	\| C		\| C
	\|-		\|-
	\| 13		\| 13
	\| 1521 ~~~ 321~~		\| 1521
	\|		\|
	\| C#		\| C#
	\|-		\|-
	\| 14		\| 14
	\| 1638 ~~~ 438~~		\| 1638
	\|		\|
	\| Db		\| Db
	\|-		\|-
	\| 15		\| 15
	\| 1755 ~~~ 555~~		\| 1755
	\|		\|
	\| D		\| D
	\|-		\|-
	\| 16		\| 16
	\| 1872 ~~~ 672~~		\| 1872
	\|		\|
	\| E		\| E
	\|-		\|-
	\| 17		\| 17
	\| 1988 ~~~ 788~~		\| 1988
	\|		\|
	\| F		\| F
	\|-		\|-
	\| 18		\| 18
	\| 2106 ~~~ 906 (Pythagorean major sixth,~~ 27:8)		\| 2106
	\|		\| 27/8
	\| C		\| C
	\|-		\|-
	\| 19		\| 19
	\| 2223 ~~~ 1023~~		\| 2223
	\|		\|
	\| C#		\| C#
	\|-		\|-
	\| 20		\| 20
	\| 2340 ~~~ 1140~~		\| 2340
	\|		\|
	\| Db		\| Db
	\|-		\|-
	\| 21		\| 21
	\| 2457 ~~~ 57~~		\| 2457
	\|		\|
	\| D		\| D
	\|-		\|-
	\| 22		\| 22
	\| 2574 ~~~ 174~~		\| 2574
	\|		\|
	\| E		\| E
	\|-		\|-
	\| 23		\| 23
	\| 2691 ~~~ 291~~		\| 2691
	\|		\|
	\| F		\| F
	\|-		\|-
	\| 24		\| 24
	\| 2808 ~~~ 408 (Pythagorean major third,~~ 81:16)		\| 2808
	\|		\| 81/16
	\| C		\| C
	\|}		\|}

FloraC: Adopt template: ED intro; +harmonics table; misc. cleanup

2024-05-10T06:30:32Z

Adopt template: ED intro; +harmonics table; misc. cleanup

← Older revision		Revision as of 06:30, 10 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''6EDF''' is the [[EDF\|equal division of the just perfect fifth]] into six parts of 116.9925 [[cent\|cents]] each, corresponding~~ to 10.2571 [[edo]]. It is related to the [[~~Gamelismic clan\|~~miracle ~~temperament~~]], which tempers out 225/224 and 1029/1024 in the 7-limit.		{{ED intro}} It corresponds to 10.2571 [[edo]].

			== Theory ==
			6edf is related to the [[miracle]] temperament, which [[tempering out\|tempers out]] [[225/224]] and [[1029/1024]] in the 7-limit.

			=== Harmonics ===
			{{Harmonics in equal\|6\|3\|2}}

	== Intervals ==		== Intervals ==
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	\|}		\|}

	== ~~Compositions~~ ==		== Music ==
	* [http://www.seraph.it/dep/det/metashakti.mp3 Metashakti] by [[~~Carlo Serafini~~]]		; [[Carlo Serafini]]
	* [https://youtu.be/OSQljL4ANf8~~?si=clHoEfUJTXaAzwI9~~ The Blame Game] ~~by [[XэнкøрX]]~~		* [http://www.seraph.it/dep/det/metashakti.mp3 ''Metashakti'']

			; [[XэнкøрX]]
			* [https://youtu.be/OSQljL4ANf8 "The Blame Game"] from ''State of the World (XLP)'' (2023)

	~~[[Category:Edf]]~~
	~~[[Category:Nonoctave]]~~
	[[Category:Listen]]		[[Category:Listen]]

FloraC: -irrelevant shit

2024-05-07T13:18:28Z

-irrelevant shit

Show changes

Triethylamine: /* Compositions */ added a composition

2023-12-28T04:26:39Z

Compositions: added a composition

← Older revision		Revision as of 04:26, 28 December 2023
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	== Compositions ==		== Compositions ==
	* [http://www.seraph.it/dep/det/metashakti.mp3 Metashakti] by [[Carlo Serafini]]		* [http://www.seraph.it/dep/det/metashakti.mp3 Metashakti] by [[Carlo Serafini]]
			* [https://youtu.be/OSQljL4ANf8?si=clHoEfUJTXaAzwI9 The Blame Game] by [[XэнкøрX]]

	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Listen]]		[[Category:Listen]]

CompactStar at 03:41, 5 April 2023

2023-04-05T03:41:03Z

← Older revision		Revision as of 03:41, 5 April 2023
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	\|}		\|}
	==Scale tree==		==Scale tree==
	If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant\|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.		EDF scales can be approximated in [[EDO]]s by subdividing diatonic fifths. If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant\|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.

	If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.		If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.

Moremajorthanmajor: /* Scale tree */

2023-03-22T18:15:34Z

Scale tree

← Older revision		Revision as of 18:15, 22 March 2023
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	\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|116.923\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|116.923\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|116.981\|\|The ~~generator~~ closest to a just [[3/2]] for EDOs less than 200		\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|116.981\|\|The fifth closest to a just [[3/2]] for EDOs less than 200
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|117.021\|\|[[Garibaldi]] / [[Cassandra]]		\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|117.021\|\|[[Garibaldi]] / [[Cassandra]]

Moremajorthanmajor at 01:58, 15 March 2023

2023-03-15T01:58:40Z

← Older revision		Revision as of 01:58, 15 March 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''6EDF''' is the [[EDF\|equal division of the just perfect fifth]] into six parts of ~~[[Tel:~~116.9925~~\|116.9925]]~~ [[cent\|cents]] each, corresponding to 10.2571 [[edo]]. It is related to the [[Gamelismic clan\|miracle temperament]], which tempers out 225/224 and 1029/1024 in the 7-limit.		'''6EDF''' is the [[EDF\|equal division of the just perfect fifth]] into six parts of 116.9925 [[cent\|cents]] each, corresponding to 10.2571 [[edo]]. It is related to the [[Gamelismic clan\|miracle temperament]], which tempers out 225/224 and 1029/1024 in the 7-limit.

	== Intervals ==		== Intervals ==

Moremajorthanmajor: /* Scale tree */

2023-03-12T15:40:09Z

Scale tree

← Older revision		Revision as of 15:40, 12 March 2023
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	\| \|\| \|\|10\17\|\| \|\| \|\| \|\| \|\|117.647\|\|		\| \|\| \|\|10\17\|\| \|\| \|\| \|\| \|\|117.647\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|43\73\|\|~~141~~.~~370~~\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|43\73\|\|117.808\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|33\56\|\| \|\|117.857\|\|		\| \|\| \|\| \|\| \|\| \|\|33\56\|\| \|\|117.857\|\|
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	\| \|\| \|\| \|\| \|\| \|\|36\61\|\| \|\|118.033\|\|		\| \|\| \|\| \|\| \|\| \|\|36\61\|\| \|\|118.033\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|49\83\|\|~~141~~.~~687~~\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|49\83\|\|118.072\|\|
	\|-		\|-
	\| \|\| \|\| \|\|13\22\|\| \|\| \|\| \|\|~~141~~.{{Overline\|81}}\|\|[[Archy]] is in this region		\| \|\| \|\| \|\|13\22\|\| \|\| \|\| \|\|118.{{Overline\|18}}\|\|[[Archy]] is in this region
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|42\71\|\|~~141~~.~~972~~\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|42\71\|\|118.310\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|29\49\|\| \|\|~~142~~.~~041~~\|\|		\| \|\| \|\| \|\| \|\| \|\|29\49\|\| \|\|118.367\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|45\76\|\|~~142~~.~~105~~\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|45\76\|\|118.421\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\|16\27\|\| \|\| \|\|~~142~~.{{Overline\|2}}\|\|		\| \|\| \|\| \|\| \|\|16\27\|\| \|\| \|\|118.{{Overline\|518}}\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|35\59\|\|~~142~~.~~373~~\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|35\59\|\|118.644\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|19\32\|\| \|\|~~142~~.~~500~~\|\|		\| \|\| \|\| \|\| \|\| \|\|19\32\|\| \|\|118.750\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|22\37\|\|~~142~~.{{Overline\|~~702~~}}\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|22\37\|\|118.{{Overline\|918}}\|\|The generator closest to a just [[15/14]] for EDOs less than 1200
	\|-		\|-
	\|3\5\|\| \|\| \|\| \|\| \|\| \|\| \|\|~~144~~.000\|\|		\|3\5\|\| \|\| \|\| \|\| \|\| \|\| \|\|120.000\|\|
	\|}Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.		\|}Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.