8edf - Revision history

BudjarnLambeth: /* Music */

2024-11-10T06:41:31Z

Music

← Older revision		Revision as of 06:41, 10 November 2024
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	== Music ==		== Music ==
	* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (~~2024~~) - uses the [[Kartvelian scales#8edf Kartvelian tetradecatonic scale\|8edf Kartvelian tetradecatonic scale]], alternating blocks of [[8edf]] and [[6ed4/3]]		* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (Dec 2023) - uses the [[Kartvelian scales#8edf Kartvelian tetradecatonic scale\|8edf Kartvelian tetradecatonic scale]], alternating blocks of [[8edf]] and [[6ed4/3]]

	== Images ==		== Images ==

BudjarnLambeth: Add music

2024-11-10T06:31:46Z

Add music

← Older revision		Revision as of 06:31, 10 November 2024
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	\| \| (augmented-like)		\| \| (augmented-like)
	\|}		\|}

			== Music ==
			* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (2024) - uses the [[Kartvelian scales#8edf Kartvelian tetradecatonic scale\|8edf Kartvelian tetradecatonic scale]], alternating blocks of [[8edf]] and [[6ed4/3]]

	== Images ==		== Images ==
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	[[Category:Nonoctave]]		[[Category:Nonoctave]]

	{{Todo\| review }}		{{Todo\| review }}

FloraC: -irrelevant shit

2024-05-07T13:19:24Z

-irrelevant shit

Show changes

CompactStar: it's equalized of any tetratonic MOS

2023-05-11T08:31:53Z

it's equalized of any tetratonic MOS

← Older revision		Revision as of 08:31, 11 May 2023
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	== Intervals ==		== Intervals ==
	8edf can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth\|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4\|major diatonic ninth]]). This interprets 8edf as [[16ed9/4]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using ~~equalized~~ [[~~1L 3s (fifth-equivalent)\|neptunian~~]] ~~(1L 3s<3/2>)~~ notation ~~as a superset of [[4edf]]~~.		8edf can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth\|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4\|major diatonic ninth]]). This interprets 8edf as [[16ed9/4]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using tetratonic [[4edf]]-based notation.

	The naturals result from a [[semiwolf]] generator (~[[7/6]]). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).		The naturals result from a [[semiwolf]] generator (~[[7/6]]). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).
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	!Uranian		!Uranian
	!Annapolis		!Annapolis
	!~~Equalized [[1L 3s (fifth-equivalent)\|Neptunian]] using 6\8edf~~		!Tetratonic notation
	\|-		\|-
	\|'''0'''		\|'''0'''

FloraC: Cleanup

2023-05-07T06:52:47Z

Cleanup

← Older revision		Revision as of 06:52, 7 May 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''8~~[[EDF]]~~ (~~8ED3~~/2)''' is the ~~equal division of~~ the fifth into 8 steps of 87.7444 [[cent]]s each, making it very nearly [[88cET]]. It is related to the [[~~Tetracot family~~\|octacot temperament]]. ~~8EDF~~ corresponds to 13.~~6761 edo~~ (similar to every third step of [[41edo]]).		'''8 equal divisions of the fifth''' ('''8edf''', '''8ed3/2''') is the [[tuning system]] that divides the fifth into 8 steps of 87.7444 [[cent]]s each, making it very nearly [[88cET]]. It is related to the [[Octacot\|octacot temperament]]. 8edf corresponds to about 13.6761edo (similar to every third step of [[41edo]]).

	==Intervals==		== Intervals ==
			8edf can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth\|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4\|major diatonic ninth]]). This interprets 8edf as [[16ed9/4]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using equalized [[1L 3s (fifth-equivalent)\|neptunian]] (1L 3s<3/2>) notation as a superset of [[4edf]].
	~~8EDF~~ can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth\|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4\|major diatonic ninth]]). This interprets 8edf as 16[[~~edIX~~]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using equalized [[1L 3s (fifth-equivalent)\|neptunian]] (1L 3s<3/2>) notation as a superset of [[4edf]].

	The naturals result from a [[semiwolf]] generator (~[[7/6]]). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).		The naturals result from a [[semiwolf]] generator (~[[7/6]]). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).
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	[[File:8EDF_cheat_sheet_circle.png\|400px\|thumb\|left\|8EDF cheat sheet (sesquitave notation) - [[Media:8EDF cheat sheet.pdf\|table only]]]]		[[File:8EDF_cheat_sheet_circle.png\|400px\|thumb\|left\|8EDF cheat sheet (sesquitave notation) - [[Media:8EDF cheat sheet.pdf\|table only]]]]

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

			{{Todo\| review }}

CompactStar at 03:41, 5 April 2023

2023-04-05T03:41:25Z

← Older revision		Revision as of 03:41, 5 April 2023
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	[https://sevish.com/scaleworkshop/?name=8EDF%20Uranian&data=87.74437510817343%0A175.48875021634686%0A263.2331253245203%0A350.9775004326937%0A438.72187554086713%0A526.4662506490406%0A614.210625757214%0A701.9550008653874&freq=220&midi=57&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white&waveform=square&ampenv=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)]		[https://sevish.com/scaleworkshop/?name=8EDF%20Uranian&data=87.74437510817343%0A175.48875021634686%0A263.2331253245203%0A350.9775004326937%0A438.72187554086713%0A526.4662506490406%0A614.210625757214%0A701.9550008653874&freq=220&midi=57&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white&waveform=square&ampenv=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)]
	==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 */

2023-03-22T18:14:01Z

Scale tree

← Older revision		Revision as of 18:14, 22 March 2023
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	\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|87.692\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|87.692\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|87.736 \|\|The ~~generator~~ closest to a just [[3/2]] for EDOs less than 200		\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|87.736 \|\|The fifth closest to a just [[3/2]] for EDOs less than 200
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|87.766\|\|[[Garibaldi]] / [[Cassandra]]		\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|87.766\|\|[[Garibaldi]] / [[Cassandra]]

Moremajorthanmajor at 22:00, 16 March 2023

2023-03-16T22:00:21Z

← Older revision		Revision as of 22:00, 16 March 2023
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	\| \|\| \|\| \|\| \|\| \|\|33\56\|\| \|\|88.392\|\|		\| \|\| \|\| \|\| \|\| \|\|33\56\|\| \|\|88.392\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|56\95\|\|88.421\|\|The generator closest to a just [[5/3]] for EDOs less than ~~1400~~		\| \|\| \|\| \|\| \|\| \|\| \|\|56\95\|\|88.421\|\|The generator closest to a just [[5/3]] for EDOs less than 1600
	\|-		\|-
	\| \|\| \|\| \|\| \|\|23\39\|\| \|\| \|\|88.4615\|\|		\| \|\| \|\| \|\| \|\|23\39\|\| \|\| \|\|88.4615\|\|

Moremajorthanmajor at 03:59, 15 March 2023

2023-03-15T03:59:00Z

Show changes

Moremajorthanmajor at 03:02, 15 March 2023

2023-03-15T03:02:51Z

← Older revision		Revision as of 03:02, 15 March 2023
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	\|C#		\|C#
	\|Η#		\|Η#
	\|F		\|E
	\|-		\|-
	\|13		\|13
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	\|D		\|D
	\|Θ		\|Θ
	\|^F, vE		\|^E, vF
	\|-		\|-
	\|14		\|14
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	\|D#		\|D#
	\|Θ#		\|Θ#
	\|		\|F
	\|-		\|-
	\|15		\|15
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	\|E		\|E
	\|Ι		\|Ι
	\|		\|^F, vC
	\|-		\|-
	\|'''16'''		\|'''16'''
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	\|'''A'''		\|'''A'''
	\|'''Α'''		\|'''Α'''
	\|		\|C
	\|}		\|}
	[https://sevish.com/scaleworkshop/?name=8EDF%20Uranian&data=87.74437510817343%0A175.48875021634686%0A263.2331253245203%0A350.9775004326937%0A438.72187554086713%0A526.4662506490406%0A614.210625757214%0A701.9550008653874&freq=220&midi=57&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white&waveform=square&ampenv=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)]		[https://sevish.com/scaleworkshop/?name=8EDF%20Uranian&data=87.74437510817343%0A175.48875021634686%0A263.2331253245203%0A350.9775004326937%0A438.72187554086713%0A526.4662506490406%0A614.210625757214%0A701.9550008653874&freq=220&midi=57&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white&waveform=square&ampenv=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)]