2edf - Revision history

Overthink: /* Theory */ + harmonics

2026-03-20T19:43:41Z

Theory: + harmonics

← Older revision		Revision as of 19:43, 20 March 2026
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	== Theory ==		== Theory ==
	~~'''~~2edf~~'''~~, if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into two equal parts, each of size 350.9775 [[cent]]s, which is to say sqrt (3/2) as a frequency ratio. It corresponds to 3.4190 [[edo]]. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.		2edf, if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into two equal parts, each of size 350.9775 [[cent]]s, which is to say sqrt (3/2) as a frequency ratio. It corresponds to 3.4190 [[edo]]. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

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

	== Factoids about 2edf ==		== Factoids about 2edf ==

Overthink: use ED intro

2026-03-20T19:37:27Z

use ED intro

← Older revision		Revision as of 19:37, 20 March 2026
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	{{Infobox ET}}		{{Infobox ET}}
			{{ED intro}}

			== Theory ==
	'''2edf''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into two equal parts, each of size 350.9775 [[cent]]s, which is to say sqrt (3/2) as a frequency ratio. It corresponds to 3.4190 [[edo]]. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.		'''2edf''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into two equal parts, each of size 350.9775 [[cent]]s, which is to say sqrt (3/2) as a frequency ratio. It corresponds to 3.4190 [[edo]]. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

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

2025-08-01T19:21:51Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:21, 1 August 2025
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	Tunings below 7\12 on this chart are called "positive tunings" and they include Pythagorean tuning itself (well approximated by 31\53) as well as superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 13\22 through 16\27, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.		Tunings below 7\12 on this chart are called "positive tunings" and they include Pythagorean tuning itself (well approximated by 31\53) as well as superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 13\22 through 16\27, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.

	~~[[Category:Edonoi]]~~

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

2025-08-01T19:00:10Z

Removing from Category:Edf using Cat-a-lot

← Older revision		Revision as of 19:00, 1 August 2025
Line 170:		Line 170:
	Tunings below 7\12 on this chart are called "positive tunings" and they include Pythagorean tuning itself (well approximated by 31\53) as well as superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 13\22 through 16\27, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.		Tunings below 7\12 on this chart are called "positive tunings" and they include Pythagorean tuning itself (well approximated by 31\53) as well as superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 13\22 through 16\27, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.

	~~[[Category:Edf]]~~
	[[Category:Edonoi]]		[[Category:Edonoi]]

MisterShafXen at 14:47, 23 June 2025

2025-06-23T14:47:21Z

← Older revision		Revision as of 14:47, 23 June 2025
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	! #		! #
	! Cents		! Cents
			!JI ratios
	\|-		\|-
	\| 1		\| 1
	\| 350.98		\| 350.98
			\|11/9
	\|-		\|-
	\| 2		\| 2
	\| 701.96		\| 701.96
			\|exact 3/2
	\|}		\|}

Fredg999: /* Scale tree */ Todo: correct maths, review

2024-09-03T23:31:35Z

Scale tree: Todo: correct maths, review

← Older revision		Revision as of 23:31, 3 September 2024
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	==Scale tree==		==Scale tree==
			{{todo\|correct maths\|review\|inline=1\|text=The text and the table incoherently mix up EDO and EDF calculations. This section should also be moved to a more appropriate page.}}
	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.		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.

CompactStar: not "irrelevant"

2024-09-03T22:20:00Z

not "irrelevant"

Show changes

FloraC: -irrelevant shit

2024-05-07T13:16:49Z

-irrelevant shit

Show changes

CompactStar at 08:31, 19 June 2023

2023-06-19T08:31:38Z

← Older revision		Revision as of 08:31, 19 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''2edf''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into two equal parts, each of size ~~[[Tel:~~350.9775~~\|350.9775]]~~ [[cent]]s, which is to say sqrt (3/2) as a frequency ratio. It corresponds to 3.4190 [[edo]]. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.		'''2edf''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into two equal parts, each of size 350.9775 [[cent]]s, which is to say sqrt (3/2) as a frequency ratio. It corresponds to 3.4190 [[edo]]. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

	== Factoids about 2edf ==		== Factoids about 2edf ==

CompactStar at 03:40, 5 April 2023

2023-04-05T03:40:28Z

← Older revision		Revision as of 03:40, 5 April 2023
Line 20:		Line 20:

	==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.