User:BudjarnLambeth/272ed23 - Revision history

FloraC: Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}"

2025-08-01T14:43:06Z

Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}"

2025-05-18T12:08:45Z

← Older revision		Revision as of 12:08, 18 May 2025
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			{{Editable user page}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}.		{{ED intro}}

	272ed23 is primarily intended to be used as [[60edo]] but with slightly [[Octave shrinking\|compressed]] octaves.		272ed23 is primarily intended to be used as [[60edo]] but with slightly [[Octave shrinking\|compressed]] octaves.

2025-05-18T12:08:26Z

← Older revision	Revision as of 12:08, 18 May 2025
(No difference)

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Theory

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	== Theory ==		== Theory ==
	Compared to pure-[[octave]]s 60edo, ~~272ed3~~ features a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].		Compared to pure-[[octave]]s 60edo, 272ed23 features a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].

	It also causes the [[val]]s to flip for [[5/1]], [[7/1]], [[13/1]] and [[17/1]].		It also causes the [[val]]s to flip for [[5/1]], [[7/1]], [[13/1]] and [[17/1]].

2024-12-25T08:33:16Z

Intervals

2024-12-25T08:30:15Z

60edo for comparison

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	==== 60edo for comparison ====		==== 60edo for comparison ====
	In the [[47-limit]], 60edo has less than 40% relative error on primes 2, 3, 5, 13, 17, 19, 31, 47.		In the 47-limit, 60edo has less than 40% relative error on primes 2, 3, 5, 13, 17, 19, 31, 47.

	This makes it a solid tuning for the no-7, no-11 [[19-limit]] (or [[dual-n\|dual]]-7, dual-11).		This makes it a solid tuning for the no-7, no-11 [[19-limit]] (or [[dual-n\|dual]]-7, dual-11).

2024-12-25T08:29:42Z

Prime harmonics

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	=== Prime harmonics ===		=== Prime harmonics ===
	In the [[47-limit]], 272ed3 has less than 40% relative error on primes 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 41, 43 and 47.		In the [[47-limit]], 272ed3 has less than 40% [[relative error]] on primes 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 41, 43 and 47.

	This makes it a solid tuning for the entire no-13, no-19 47-limit.		This makes it a solid tuning for the entire no-13, no-19 47-limit.

2024-12-25T08:24:53Z

Nearby equal-step tunings

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	; 272ed23		; 272ed23
			{{Harmonics in equal\|272\|23\|1\|intervals=prime\|columns=11\|collapsed=1}}

	== Instruments ==		== Instruments ==

2024-12-25T08:24:20Z

Nearby equal-step tunings

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	== Nearby equal-step tunings ==		== Nearby equal-step tunings ==
	There are a few other useful [[equal-step tuning]]s which occur close to ~~60edo~~ in step size:		There are a few other useful [[equal-step tuning]]s which occur close to 272ed23 in step size:

2024-12-25T08:23:54Z

Scales

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	== Scales ==		== Scales ==

			; 60edo scales

			These are useable in 272ed23, simply apply an octave compression of 0.99784 in [[Scale Workshop]].
	* [[5- to 10-tone scales in 60edo]]		* [[5- to 10-tone scales in 60edo]]