Edϕ - Revision history

Lucius Chiaraviglio: Add Music section, starting with Bryan Deister's ''12edΦ improv'' (2026)

2026-03-09T05:59:00Z

Add Music section, starting with Bryan Deister's ''12edΦ improv'' (2026)

← Older revision		Revision as of 05:59, 9 March 2026
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	cet33.scl 25 25th root of phi, Walter O´Connell (1993)		cet33.scl 25 25th root of phi, Walter O´Connell (1993)
	cet46.scl 18 18th root of phi, Walter O´Connell (1993)		cet46.scl 18 18th root of phi, Walter O´Connell (1993)

			== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/JrGYILddm64 ''12edΦ improv''] (2026)

	== See also ==		== See also ==

Hotcrystal0 at 20:57, 7 February 2026

2026-02-07T20:57:42Z

← Older revision		Revision as of 20:57, 7 February 2026
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	Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢.		Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢.

	If the <math>m^{th}</math> step of <math>n</math><span>~~ed2~~ is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.		If the <math>m^{th}</math> step of <math>n</math><span>edo is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.

	For example, the 7th step of [[10edo]] is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.		For example, the 7th step of [[10edo]] is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.
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	\|+		\|+
	\| rowspan="2" \|'''scale step'''		\| rowspan="2" \|'''scale step'''
	\| colspan="4" \|'''~~10edo~~'''		\| colspan="4" \|'''10ed2'''
	\| colspan="4" \|'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''		\| colspan="4" \|'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''
	\|-		\|-
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	\|+		\|+
	\| rowspan="2" \|'''scale step'''		\| rowspan="2" \|'''scale step'''
	\| colspan="4" \|'''~~13edo~~'''		\| colspan="4" \|'''13ed2'''
	\| colspan="4" \|'''9edφ or 13ed(<math>2^{\frac{13log_2{φ}}{9}} ≈ 2.003876886</math>)'''		\| colspan="4" \|'''9edφ or 13ed(<math>2^{\frac{13log_2{φ}}{9}} ≈ 2.003876886</math>)'''
	\|-		\|-

Hotcrystal0: slight polishing

2026-02-07T20:56:50Z

slight polishing

← Older revision		Revision as of 20:56, 7 February 2026
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	If the <math>m^{th}</math> step of <math>n</math><span>ed2 is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.		If the <math>m^{th}</math> step of <math>n</math><span>ed2 is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.

	For example, the 7th step of ~~10ed2~~ is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.		For example, the 7th step of [[10edo]] is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.
	As another example, the 9th step of ~~13ed2~~ is ≈830.7692308¢, and the 13th step of [[9edϕ\|9ed<math>φ</math>]] is ≈1203.35265¢.		As another example, the 9th step of [[13edo]] is ≈830.7692308¢, and the 13th step of [[9edϕ\|9ed<math>φ</math>]] is ≈1203.35265¢.

	Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers.		Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers.
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	\|+		\|+
	\| rowspan="2" \|'''scale step'''		\| rowspan="2" \|'''scale step'''
	\| colspan="4" \|'''~~10ed2~~'''		\| colspan="4" \|'''10edo'''
	\| colspan="4" \|'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''		\| colspan="4" \|'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''
	\|-		\|-
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	\|+		\|+
	\| rowspan="2" \|'''scale step'''		\| rowspan="2" \|'''scale step'''
	\| colspan="4" \|'''~~13ed2~~'''		\| colspan="4" \|'''13edo'''
	\| colspan="4" \|'''9edφ or 13ed(<math>2^{\frac{13log_2{φ}}{9}} ≈ 2.003876886</math>)'''		\| colspan="4" \|'''9edφ or 13ed(<math>2^{\frac{13log_2{φ}}{9}} ≈ 2.003876886</math>)'''
	\|-		\|-

Fredg999 category edits: Removing from Category:Equal-step tuning using Cat-a-lot

2025-08-01T15:32:05Z

Removing from Category:Equal-step tuning using Cat-a-lot

← Older revision		Revision as of 15:32, 1 August 2025
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	* [[User:Eliora/Phi to the phi]]		* [[User:Eliora/Phi to the phi]]

	~~[[Category:Equal-step tuning]]~~
	[[Category:Golden ratio]]		[[Category:Golden ratio]]


	{{todo\|inline=1\|improve synopsis\|improve readability}}		{{todo\|inline=1\|improve synopsis\|improve readability}}

BudjarnLambeth: Todo

2025-05-22T03:12:36Z

Todo

← Older revision		Revision as of 03:12, 22 May 2025
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	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Golden ratio]]		[[Category:Golden ratio]]


			{{todo\|inline=1\|improve synopsis\|improve readability}}

BudjarnLambeth: see also

2025-05-19T03:43:51Z

CompactStar: CompactStar moved page Eedϕ to Edϕ: Misspelling

2024-04-04T07:38:29Z

CompactStar moved page Eedϕ to Edϕ: Misspelling

← Older revision	Revision as of 07:38, 4 April 2024
(No difference)

CompactStar: CompactStar moved page Edφ to Eedϕ: I have now found there are apparently 2 variants of lowercase phi, changed title to use the same variant as is on the page "9edϕ" for consistency

2024-04-04T07:38:20Z

CompactStar moved page Edφ to Eedϕ: I have now found there are apparently 2 variants of lowercase phi, changed title to use the same variant as is on the page "9edϕ" for consistency

← Older revision	Revision as of 07:38, 4 April 2024
(No difference)

R-4981 at 10:43, 26 January 2024

2024-01-26T10:43:15Z

← Older revision		Revision as of 10:43, 26 January 2024
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	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
			[[Category:Golden ratio]]

Cmloegcmluin: add link to new dedicated 9edϕ page

2023-03-06T20:26:14Z

add link to new dedicated 9edϕ page

← Older revision		Revision as of 20:26, 6 March 2023
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	For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.		For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.
	As another example, the 9th step of 13ed2 is ≈830.7692308¢, and the 13th step of 9ed<math>φ</math> is ≈1203.35265¢.		As another example, the 9th step of 13ed2 is ≈830.7692308¢, and the 13th step of [[9edϕ\|9ed<math>φ</math>]] is ≈1203.35265¢.

	Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers.		Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers.

← Older revision		Revision as of 03:43, 19 May 2025
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	cet46.scl 18 18th root of phi, Walter O´Connell (1993)		cet46.scl 18 18th root of phi, Walter O´Connell (1993)

			== See also ==
			* [[EDe]]
			* [[Acoustic pi]]
			* [[User:Eliora/Phi to the phi]]

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Golden ratio]]		[[Category:Golden ratio]]