User:Cmloegcmluin/AS - Revision history

BudjarnLambeth at 01:40, 19 May 2025

2025-05-19T01:40:24Z

← Older revision		Revision as of 01:40, 19 May 2025
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			{{Editable user page}}
	An '''AS''', or '''ambitonal sequence''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.		An '''AS''', or '''ambitonal sequence''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.

BudjarnLambeth: BudjarnLambeth moved page AS to User:Cmloegcmluin/AS: Merge w equal step tuning but in the manner described by Cmlo on talk page

2025-05-19T01:39:25Z

BudjarnLambeth moved page AS to User:Cmloegcmluin/AS: Merge w equal step tuning but in the manner described by Cmlo on talk page

← Older revision	Revision as of 01:39, 19 May 2025
(No difference)

BudjarnLambeth: /* List of ASs */pseudo - subheadings

2025-05-03T23:33:39Z

List of ASs: pseudo - subheadings

← Older revision		Revision as of 23:33, 3 May 2025
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	{{See also\| APS #List of APSs }}		{{See also\| APS #List of APSs }}

	* [[~~1ed13/10\|AS13/10~~]]		; [[Superparticular]]
	* [[1ed8/7\|AS8/7]]		* [[1ed8/7\|AS8/7]]
	* [[1ed9/8\|AS9/8]]		* [[1ed9/8\|AS9/8]]
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	* [[1ed33/32\|AS33/32]]		* [[1ed33/32\|AS33/32]]
	* [[1ed81/80\|AS81/80]]		* [[1ed81/80\|AS81/80]]

			; Others
			* [[1ed13/10\|AS13/10]]

	[[Category:Equal-step tuning‏‎]]		[[Category:Equal-step tuning‏‎]]
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:Xenharmonic series]]		[[Category:Xenharmonic series]]

BudjarnLambeth: /* List of ASs */ AS13/10

2025-05-03T23:32:36Z

List of ASs: AS13/10

← Older revision		Revision as of 23:32, 3 May 2025
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	{{See also\| APS #List of APSs }}		{{See also\| APS #List of APSs }}

			* [[1ed13/10\|AS13/10]]
	* [[1ed8/7\|AS8/7]]		* [[1ed8/7\|AS8/7]]
	* [[1ed9/8\|AS9/8]]		* [[1ed9/8\|AS9/8]]

FloraC: /* List of ASs */ update

2024-12-05T08:12:12Z

List of ASs: update

← Older revision		Revision as of 08:12, 5 December 2024
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	== List of ASs ==		== List of ASs ==
			{{See also\| APS #List of APSs }}

	* [[AS8/7]]		* [[1ed8/7\|AS8/7]]
	* [[AS15/14]]		* [[1ed9/8\|AS9/8]]
	* [[AS16/15]]		* [[1ed10/9\|AS10/9]]
	* [[AS18/17]]		* [[1ed15/14\|AS15/14]]
	* [[AS21/20]]		* [[1ed16/15\|AS16/15]]
	* [[AS25/24]]		* [[1ed18/17\|AS18/17]]
	* [[~~AS33~~/32]]		* [[1ed21/20\|AS21/20]]
	* [[~~AS81~~/80]]		* [[1ed25/24\|AS25/24]]
			* [[1ed26/25\|AS26/25]]
	~~See also:~~ [[~~APS#List of APSs~~]]		* [[1ed33/32\|AS33/32]]
			* [[1ed81/80\|AS81/80]]

	[[Category:Equal-step tuning‏‎]]		[[Category:Equal-step tuning‏‎]]
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:Xenharmonic series]]		[[Category:Xenharmonic series]]

Cmloegcmluin: add links to AS pages in new "List of ASs" section, linking them by their AS name, and including link to APS list, per https://en.xen.wiki/w/Talk:CET

2023-11-07T20:07:43Z

add links to AS pages in new "List of ASs" section, linking them by their AS name, and including link to APS list, per https://en.xen.wiki/w/Talk:CET

← Older revision		Revision as of 20:07, 7 November 2023
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	\|65536/390625		\|65536/390625
	\|}		\|}

			== List of ASs ==

			* [[AS8/7]]
			* [[AS15/14]]
			* [[AS16/15]]
			* [[AS18/17]]
			* [[AS21/20]]
			* [[AS25/24]]
			* [[AS33/32]]
			* [[AS81/80]]

			See also: [[APS#List of APSs]]

	[[Category:Equal-step tuning‏‎]]		[[Category:Equal-step tuning‏‎]]
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:Xenharmonic series]]		[[Category:Xenharmonic series]]

Cmloegcmluin: /* Examples */ update row headers per agreement at https://en.xen.wiki/w/Talk:APS

2023-10-19T20:36:47Z

Examples: update row headers per agreement at https://en.xen.wiki/w/Talk:APS

← Older revision		Revision as of 20:36, 19 October 2023
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	! 8		! 8
	\|-		\|-
	! frequency (f)		! frequency (''f'', ratio)
	\|(5⁰/4⁰)		\|(5⁰/4⁰)
	\|5¹/4¹		\|5¹/4¹
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	\|5⁸/4⁸		\|5⁸/4⁸
	\|-		\|-
	! pitch (~~log₂f~~)		! pitch (log₂''f'', octaves)
	\|(0)		\|(0)
	\|0.32		\|0.32
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	\|2.58		\|2.58
	\|-		\|-
	! length (1/f)		! length (1/''f'', ratio)
	\|(1/1)		\|(1/1)
	\|4/5		\|4/5

FloraC: (Temporarily) clarify that this can be specified two ways. In the end it may entail distinct symbols for pitch relation and frequency ratio

2023-10-18T15:55:03Z

(Temporarily) clarify that this can be specified two ways. In the end it may entail distinct symbols for pitch relation and frequency ratio

← Older revision		Revision as of 15:55, 18 October 2023
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	== Specification ==		== Specification ==

	Its full specification is (n-)~~ASp~~: (n pitches of an) [[ambitonal]] sequence adding by rational interval p. The n is optional. If not provided, the sequence is open-ended.		Its full specification is (''n''-)AS-''p'': (''n'' pitches of an) [[ambitonal]] sequence adding by rational interval ''p''.

			'''Note''':
			* The ''n'' is optional. If not provided, the sequence is open-ended.
			* The ''p'' can be dimensionless, in which case it refers to an interval by its [[frequency ratio]]. It can also take a unit proportional to [[octave]]s, in which case it refers to an interval by its pitch relation.

	== Relationship to other tunings ==		== Relationship to other tunings ==
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	=== Vs. 1D JI Lattice & equal multiplications ===		=== Vs. 1D JI Lattice & equal multiplications ===

	It is equivalent to a 1-dimensional [[~~Harmonic_Lattice_Diagram~~\|JI lattice]] of p. These are sequences which are rational but ambiguous between otonality and utonality, such as a chain of the same JI pitch. It is also equivalent to an [[~~Equal-step_tuning#Equal_multiplications\|~~equal multiplication]] of a rational interval p.		AS-''p'' is equivalent to a 1-dimensional [[Harmonic lattice diagram\|JI lattice]] of ''p''. These are sequences which are rational but ambiguous between otonality and utonality, such as a chain of the same JI pitch. It is also equivalent to an [[equal multiplication]] of a rational interval ''p''.

	=== Vs. APS ===		=== Vs. APS ===

	The only difference between an (n-)~~ASp~~ and an [[APS\|(n-)~~APSp~~ (arithmetic pitch sequence)]] is that the p for an AS must be rational.		The only difference between an (''n''-)AS-''p'' and an [[APS\|(''n''-)APS-''p'' (arithmetic pitch sequence)]] is that the ''p'' for an AS must be rational.

	== Examples ==		== Examples ==
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	[[Category:Equal-step tuning‏‎]]		[[Category:Equal-step tuning‏‎]]
	[[Category:Equal divisions of the ~~octave‏‎~~ ]]		[[Category:Equal divisions of the octave]]
	[[Category:Xenharmonic series]]		[[Category:Xenharmonic series]]

BudjarnLambeth: Added to category "xenharmonic series"

2023-04-26T05:15:20Z

Added to category "xenharmonic series"

← Older revision		Revision as of 05:15, 26 April 2023
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	[[Category:Equal-step tuning‏‎]]		[[Category:Equal-step tuning‏‎]]
	[[Category:Equal divisions of the octave‏‎ ]]		[[Category:Equal divisions of the octave‏‎ ]]
			[[Category:Xenharmonic series]]

Cmloegcmluin: add link

2023-03-30T15:30:21Z

add link

← Older revision		Revision as of 15:30, 30 March 2023
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	== Specification ==		== Specification ==

	Its full specification is (n-)ASp: (n pitches of an) ambitonal sequence adding by rational interval p. The n is optional. If not provided, the sequence is open-ended.		Its full specification is (n-)ASp: (n pitches of an) [[ambitonal]] sequence adding by rational interval p. The n is optional. If not provided, the sequence is open-ended.

	== Relationship to other tunings ==		== Relationship to other tunings ==

← Older revision		Revision as of 23:32, 3 May 2025
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	{{See also\| APS #List of APSs }}		{{See also\| APS #List of APSs }}

			* [[1ed13/10\|AS13/10]]
	* [[1ed8/7\|AS8/7]]		* [[1ed8/7\|AS8/7]]
	* [[1ed9/8\|AS9/8]]		* [[1ed9/8\|AS9/8]]