AFS - Revision history

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

2023-10-19T20:36:17Z

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)
	\|(1 + 0/⁴√2)		\|(1 + 0/⁴√2)
	\|1 + 1/⁴√2		\|1 + 1/⁴√2
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	\|1 + 8/⁴√2		\|1 + 8/⁴√2
	\|-		\|-
	! pitch (~~log₂f~~)		! pitch (log₂''f'', octaves)
	\| (0) \|\| 0.88		\| (0) \|\| 0.88
	\|1.42		\|1.42
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	\|2.95		\|2.95
	\|-		\|-
	! length (1/f)		! length (1/''f'', ratio)
	\| (1) \|\| 0.54		\| (1) \|\| 0.54
	\|0.37		\|0.37

BudjarnLambeth: Added to category "xenharmonic series"

2023-04-26T05:16:20Z

Added to category "xenharmonic series"

← Older revision		Revision as of 05:16, 26 April 2023
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	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]
			[[Category:Xenharmonic series]]

BudjarnLambeth: Undo revision 109515 by BudjarnLambeth (talk)

2023-04-26T05:15:46Z

Undo revision 109515 by BudjarnLambeth (talk)

← Older revision		Revision as of 05:15, 26 April 2023
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	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]
	~~[[Category:Xenharmonic series]]~~

BudjarnLambeth: Added to category "xenharmonic series"

2023-04-26T05:15:33Z

Added to category "xenharmonic series"

← Older revision		Revision as of 05:15, 26 April 2023
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	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]
			[[Category:Xenharmonic series]]

Fredg999: Fix typo

2023-04-10T05:58:45Z

Fix typo

← Older revision		Revision as of 05:58, 10 April 2023
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	== Specification ==		== Specification ==

	Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (~~irrtional~~) interval p. The n is optional. If not provided, the sequence is open-ended.		Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (irrational) interval p. The n is optional. If not provided, the sequence is open-ended.

	== Formula ==		== Formula ==

Cmloegcmluin: /* Relationship to other tunings */ address Flora's recent concerns about rationality vs. irrationality in this system

2023-03-28T21:40:55Z

Relationship to other tunings: address Flora's recent concerns about rationality vs. irrationality in this system

← Older revision		Revision as of 21:40, 28 March 2023
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	=== Vs. OS ===		=== Vs. OS ===

	The only difference between an [[OS\|OS (overtone sequence)]] and AFS is that for OS the p is rational.		The only difference between an [[OS\|OS (overtone sequence)]] and AFS is that for OS the p must be rational.

	=== As shifted overtone series ===		=== As shifted overtone series ===

Cmloegcmluin: /* Vs. EFD */

2023-03-28T18:29:21Z

Vs. EFD

← Older revision		Revision as of 18:29, 28 March 2023
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	=== Vs. EFD ===		=== Vs. EFD ===

	By specifying n, your sequence will be equivalent to some [[EFD\|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n).		By specifying n, your sequence will be equivalent to one period of some [[EFD\|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n).

	=== Vs. ALS ===		=== Vs. ALS ===

Cmloegcmluin: /* Relationship to other tunings */ fix section capitalization

2021-11-11T19:34:11Z

Relationship to other tunings: fix section capitalization

← Older revision		Revision as of 19:34, 11 November 2021
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	== Relationship to other tunings ==		== Relationship to other tunings ==

	=== vs. OS ===		=== Vs. OS ===

	The only difference between an [[OS\|OS (overtone sequence)]] and AFS is that for OS the p is rational.		The only difference between an [[OS\|OS (overtone sequence)]] and AFS is that for OS the p is rational.
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	An AFS could also be described as a shifted [[overtone series]] (± frequency). Both AFS and OS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency. By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see [[OS#Derivation\|derivation of OS]].		An AFS could also be described as a shifted [[overtone series]] (± frequency). Both AFS and OS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency. By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see [[OS#Derivation\|derivation of OS]].

	=== vs. EFD ===		=== Vs. EFD ===

	By specifying n, your sequence will be equivalent to some [[EFD\|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n).		By specifying n, your sequence will be equivalent to some [[EFD\|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n).

	=== vs. ALS ===		=== Vs. ALS ===

	The analogous utonal equivalent of an AFS is an [[ALS\|ALS (arithmetic length sequence)]].		The analogous utonal equivalent of an AFS is an [[ALS\|ALS (arithmetic length sequence)]].

Fredg999: Categories

2021-08-30T04:03:39Z

Cmloegcmluin: break up wall of information into helpful sections that are consistent across all arithmetic tuning pages

2021-03-24T20:38:08Z

break up wall of information into helpful sections that are consistent across all arithmetic tuning pages

← Older revision		Revision as of 20:38, 24 March 2021
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	An '''AFS''', or '''arithmetic frequency sequence''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.		An '''AFS''', or '''arithmetic frequency sequence''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.

	Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (irrtional) interval p. The only difference between an [[OS\|OS (overtone sequence)]] and AFS is that for OS the p is rational.		== Specification ==

	The n is optional. If not provided, the sequence is open-ended~~. By specifying n, your sequence will be equivalent to some [[EFD\|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n)~~.		Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (irrtional) interval p. The n is optional. If not provided, the sequence is open-ended.

	~~The analogous utonal equivalent of an AFS is an [[ALS\|ALS (arithmetic length sequence)]].~~		== Formula ==

	~~An AFS could also be described as a shifted [[overtone series]] (± frequency).~~

	OS and AFS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency. By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see the later section on the [[OS#Derivation\|derivation of OS]].

	The formula for step <span><math>k</math></span> of an AFSp is:		The formula for step <span><math>k</math></span> of an AFSp is:
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	</math>		</math>

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

			=== vs. OS ===

			The only difference between an [[OS\|OS (overtone sequence)]] and AFS is that for OS the p is rational.

			=== As shifted overtone series ===

			An AFS could also be described as a shifted [[overtone series]] (± frequency). Both AFS and OS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency. By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see [[OS#Derivation\|derivation of OS]].

			=== vs. EFD ===

			By specifying n, your sequence will be equivalent to some [[EFD\|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n).

			=== vs. ALS ===

			The analogous utonal equivalent of an AFS is an [[ALS\|ALS (arithmetic length sequence)]].

			== Examples ==

	If we wanted to move by steps of φ, like this: <span><math>1, 1+φ, 1+2φ, 1+3φ...</math></span> etc. we could have the AFSφ.		If we wanted to move by steps of φ, like this: <span><math>1, 1+φ, 1+2φ, 1+3φ...</math></span> etc. we could have the AFSφ.

← Older revision		Revision as of 04:03, 30 August 2021
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	\|}		\|}

	~~[[Category:Overtone]]~~
	~~[[Category:Overtone‏‎ series]]~~
	[[Category:Otonality]]		[[Category:Otonality]]
	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]