16edf - Revision history

ArrowHead294 at 19:09, 25 June 2025

2025-06-25T19:09:26Z

← Older revision		Revision as of 19:09, 25 June 2025
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	; [[nationalsolipsism]]		; [[nationalsolipsism]]
	* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue''] (2011)		* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue''] (2011)

			== See also ==
			* [[27edo]] – relative edo
			* [[43edt]] – relative edt
			* [[70ed6]] – relative ed6
			* [[90ed10]] – relative ed10
			* [[97ed12]] – relative ed12

	{{Todo\|expand}}		{{Todo\|expand}}

	[[Category:27edo]]		[[Category:27edo]]

2025-06-19T15:26:10Z

Theory

← Older revision		Revision as of 15:26, 19 June 2025
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	== Theory ==		== Theory ==
	16edf corresponds to 27.3522…[[edo]]. It is ~~not quite~~ similar to [[~~27edo~~]], but ~~it is~~ similar to ~~every third step of~~ [[~~82edo~~]]; the octave is compressed by 15.45{{c}}, a significant deviation. It contains good approximations of the [[7/1\|7th]] and [[13/1\|13th]] [[harmonic]]s.		16edf corresponds to 27.3522…[[edo]]. It is similar to every third step of [[82edo]] but not quite similar to [[27edo]]; the octave is compressed by 15.45{{c}}, a small but significant deviation. It contains good approximations of the [[7/1\|7th]] and [[13/1\|13th]] [[harmonic]]s.

	It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.		It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.

2025-06-10T13:23:07Z

← Older revision		Revision as of 13:23, 10 June 2025
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	== Theory ==		== Theory ==
	16edf corresponds to 27.3522…[[edo]]. It is not quite similar to [[27edo]], but it is similar to every third step of [[82edo]]. It contains good approximations of the [[7/1\|7th]] and [[13/1\|13th]] [[harmonic]]s.		16edf corresponds to 27.3522…[[edo]]. It is not quite similar to [[27edo]], but it is similar to every third step of [[82edo]]; the octave is compressed by 15.45{{c}}, a significant deviation. It contains good approximations of the [[7/1\|7th]] and [[13/1\|13th]] [[harmonic]]s.

	It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.		It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.
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	{{Todo\|expand}}		{{Todo\|expand}}

			[[Category:27edo]]

2025-03-04T08:33:12Z

+years; cleanup +1

← Older revision		Revision as of 08:33, 4 March 2025
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	\| 22		\| 22
	\| 965.2		\| 965.2
	\|
	\| [[7/4]]		\| [[7/4]]
			\|
	\|		\|
	\|-		\|-
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	== Music ==		== Music ==
	; [[Nae Ayy]]		; [[Nae Ayy]]
	* [https://www.youtube.com/watch?v=8YegsoiO1Co ''Neptune'']		* [https://www.youtube.com/watch?v=8YegsoiO1Co ''Neptune''] (2021)

	; [[nationalsolipsism]]		; [[nationalsolipsism]]
	* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue'']		* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue''] (2011)

	{{Todo\|expand}}		{{Todo\|expand}}

2025-03-04T08:29:16Z

Theory: +subsets and supersets

← Older revision		Revision as of 08:29, 4 March 2025
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	== Theory ==		== Theory ==
	16edf corresponds to 27.3522…[[edo]]. It is not quite similar to [[27edo]], but it is similar to every third step of [[82edo]]. It contains good approximations of the [[7/1\|7th]] and [[13/1\|13th]] [[~~harmonics~~]].		16edf corresponds to 27.3522…[[edo]]. It is not quite similar to [[27edo]], but it is similar to every third step of [[82edo]]. It contains good approximations of the [[7/1\|7th]] and [[13/1\|13th]] [[harmonic]]s.

	It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.		It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.
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	{{Harmonics in equal\|16\|3\|2}}		{{Harmonics in equal\|16\|3\|2}}
	{{Harmonics in equal\|16\|3\|2\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 16edf (continued)}}		{{Harmonics in equal\|16\|3\|2\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 16edf (continued)}}

			=== Subsets and supersets ===
			Since 16 factors into primes as 2<sup>4</sup>, 16edf contains subset edfs {{EDs\|equave=f\| 2, 4, and 8 }}.

	== Intervals ==		== Intervals ==

2025-03-04T08:27:25Z

Cleanup; note its lack of similarity to 27edo

2024-12-21T03:26:55Z

add todo:expand, add harmonics, make table collapsible

← Older revision		Revision as of 03:26, 21 December 2024
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	Lookalikes: [[27edo]], [[43edt]]		Lookalikes: [[27edo]], [[43edt]]

			== Harmonics ==
			{{Harmonics in equal\|16\|3\|2}}
			{{Harmonics in equal\|16\|3\|2\|start=12\|collapsed=1}}

	== Intervals ==		== Intervals ==
			{\| class="wikitable right-2 mw-collapsible"
	{\| class="wikitable right-2"		\|+ Intervals of 16edf
	\|-		\|-
	! degree		! degree
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	== Music ==		== Music ==
	[https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue] by nationalsolipsism		* [https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue] by [[nationalsolipsism]]
	[https://www.youtube.com/watch?v=8YegsoiO1Co Neptune] by Nae Ayy		* [https://www.youtube.com/watch?v=8YegsoiO1Co Neptune] by [[Nae Ayy]]

	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			{{todo\|expand}}

2024-05-07T13:22:11Z

-irrelevant shit

2023-07-08T09:48:08Z

Changed "Compositions" to "Music" and added music

← Older revision		Revision as of 09:48, 8 July 2023
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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.
	~~== Compositions ==~~

	[https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue]		== Music ==
			[https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue] by nationalsolipsism
			[https://www.youtube.com/watch?v=8YegsoiO1Co Neptune] by Nae Ayy

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

2023-06-19T04:24:56Z

← Older revision		Revision as of 04:24, 19 June 2023
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	! cents value		! cents value
	! corresponding <br>JI intervals		! corresponding <br>JI intervals
	! Halftone[6] notation		! Halftone[6] notation (using [[ups and downs notation\|ups and downs]])
	! comments		! comments
	\|-		\|-