User:Cmloegcmluin/EPD - Revision history

BudjarnLambeth at 01:40, 19 May 2025

2025-05-19T01:40:46Z

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

BudjarnLambeth: BudjarnLambeth moved page User:User:Cmloegcmluin/EPD to User:Cmloegcmluin/EPD

2025-05-19T01:21:45Z

BudjarnLambeth moved page User:User:Cmloegcmluin/EPD to User:Cmloegcmluin/EPD

← Older revision	Revision as of 01:21, 19 May 2025
(No difference)

BudjarnLambeth: BudjarnLambeth moved page EPD to User:User:Cmloegcmluin/EPD: Semi merging into Equal step tuning as discussed on EPD talk page

2025-05-19T01:21:27Z

BudjarnLambeth moved page EPD to User:User:Cmloegcmluin/EPD: Semi merging into Equal step tuning as discussed on EPD talk page

← Older revision	Revision as of 01:21, 19 May 2025
(No difference)

BudjarnLambeth: /* Vs. rank-1 temperaments & equal multiplications */ typo

2025-05-18T12:51:56Z

Vs. rank-1 temperaments & equal multiplications: typo

← Older revision		Revision as of 12:51, 18 May 2025
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	=== Vs. rank-1 temperaments & equal multiplications ===		=== Vs. rank-1 temperaments & equal multiplications ===

	An n-~~EPDn~~ is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29\|rank-1 temperament]] of p/n, or an [[Equal-step_tuning#Equal_multiplications\|equal multiplication]] of p/n.		An n-EPDp is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29\|rank-1 temperament]] of p/n, or an [[Equal-step_tuning#Equal_multiplications\|equal multiplication]] of p/n.

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

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

2023-10-19T20:36:33Z

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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	! 4		! 4
	\|-		\|-
	! frequency (f)		! frequency (''f'', ratio)
	\|(1)		\|(1)
	\|1.19		\|1.19
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	\|2		\|2
	\|-		\|-
	! pitch (~~log₂f~~)		! pitch (log₂''f'', octaves)
	\|(2⁰⸍⁴)		\|(2⁰⸍⁴)
	\|2¹⸍⁴		\|2¹⸍⁴
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	\|2⁴⸍⁴		\|2⁴⸍⁴
	\|-		\|-
	! length (1/f)		! length (1/''f'', ratio)
	\|(1)		\|(1)
	\|0.84		\|0.84

Cmloegcmluin: /* Vs. APS */ correction re: periodicity (thanks Flora!)

2023-03-28T21:23:06Z

Vs. APS: correction re: periodicity (thanks Flora!)

← Older revision		Revision as of 21:23, 28 March 2023
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	=== Vs. APS ===		=== Vs. APS ===

	An EPD will be equivalent to some [[APS\|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).		One period of an EPD will be equivalent to some [[APS\|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).

	== Examples ==		== Examples ==

Cmloegcmluin: this important face has apparently not been clarified on this page yet

2023-03-28T21:22:08Z

this important face has apparently not been clarified on this page yet

← Older revision		Revision as of 21:22, 28 March 2023
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	An '''EPD''', or '''equal pitch division''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.		An '''EPD''', or '''equal pitch division''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.

			Because pitch is the overwhelmingly most common musical resource to divide equally, this may be abbreviated to '''ED''', or '''equal division'''.

	== Specification ==		== Specification ==

Cmloegcmluin: Undo revision 102841 by FloraC (talk) The contents were not reproduced at the redirect site. I think this page is better as it was, primarily for parallel structure with the other related arithmetic tunings, to make it easier to understand them

2023-03-20T17:57:50Z

Undo revision 102841 by FloraC (talk) The contents were not reproduced at the redirect site. I think this page is better as it was, primarily for parallel structure with the other related arithmetic tunings, to make it easier to understand them

← Older revision		Revision as of 17:57, 20 March 2023
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	#~~redirect~~ [[Equal-step ~~tuning~~]]		An '''EPD''', or '''equal pitch division''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.

			== Specification ==

			Its full specification is n-EPDp: n equal (pitch) divisions of interval p.

			== Formula ==

			To find the step size for an n-EPDp, take the nth root of p. For example, the step of 12-EDO is <span><math>2^{\frac{1}{12}}</math></span>. So the formula for the kth step of an n-EPDp is:

			<math>
			c(k) = p^{\frac{k}{n}}
			</math>

			This way, when <span><math>k</math></span> is <span><math>0</math></span>, <span><math>c(k)</math></span> is simply <span><math>1</math></span>, because any number to the 0th power is 1. And when <span><math>k</math></span> is <span><math>n</math></span>, <span><math>c(k)</math></span> is simply <span><math>p</math></span>, because any number to the 1st power is itself.

			== Relationship to other tunings ==

			=== Vs. rank-1 temperaments & equal multiplications ===

			An n-EPDn is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29\|rank-1 temperament]] of p/n, or an [[Equal-step_tuning#Equal_multiplications\|equal multiplication]] of p/n.

			=== Vs. APS ===

			An EPD will be equivalent to some [[APS\|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).

			== Examples ==

			The most common example of this type of tuning is 12-EDO, standard tuning, which takes the interval of the octave, and equally divides its pitch into 12 parts. For long, we could call this 12-EPDO, for 12 equal '''pitch''' divisions of the octave (whenever pitch is the chosen kind of quality, we can assume it, and skip pointing it out; that's why 12-EDO is the better name).

			{\| class="wikitable"
			\|+example: 4-EPDO = 4-EDO
			\|-
			! quantity
			! (0)
			! 1
			! 2
			! 3
			! 4
			\|-
			! frequency (f)
			\|(1)
			\|1.19
			\|1.41
			\|1.68
			\|2
			\|-
			! pitch (log₂f)
			\|(2⁰⸍⁴)
			\|2¹⸍⁴
			\|2²⸍⁴
			\|2³⸍⁴
			\|2⁴⸍⁴
			\|-
			! length (1/f)
			\|(1)
			\|0.84
			\|0.71
			\|0.59
			\|0.5
			\|}

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

FloraC: Synonym and contents are mostly ported to the target page

2023-02-14T19:55:20Z

Synonym and contents are mostly ported to the target page

← Older revision		Revision as of 19:55, 14 February 2023
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	~~An '''EPD''', or '''equal pitch division''', is a kind of [[Arithmetic tunings\|arithmetic]] and [[Harmonotonic tunings\|harmonotonic]] tuning.~~		#redirect [[Equal-step tuning]]

	~~== Specification ==~~

	~~Its full specification is n-EPDp: n equal (pitch) divisions of interval p.~~

	~~== Formula ==~~

	~~To find the step size for an n-EPDp, take the nth root of p. For example, the step of 12-EDO is <span><math>2^{\frac{1}{12}}</math></span>. So the formula for the kth step of an n-EPDp is:~~

	~~<math>~~
	~~c(k) = p^{\frac{k}{n}}~~
	~~</math>~~

	This way, when <span><math>k</math></span> is <span><math>0</math></span>, <span><math>c(k)</math></span> is simply <span><math>1</math></span>, because any number to the 0th power is 1. And when <span><math>k</math></span> is <span><math>n</math></span>, <span><math>c(k)</math></span> is simply <span><math>p</math></span>, because any number to the 1st power is itself.

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

	~~=== Vs. rank-1 temperaments & equal multiplications ===~~

	~~An n-EPDn is equivalent to a [[Tour_of_Regular_Temperaments~~#~~Equal_temperaments_.28Rank-1_temperaments.29\|rank-1 temperament]] of p/n, or an~~ [[Equal-~~step_tuning#Equal_multiplications\|equal multiplication]] of p/n.~~

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

	An EPD will be equivalent to some [[APS\|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).

	~~== Examples ==~~

	~~The most common example of this type of~~ tuning is 12-EDO, standard tuning, which takes the interval of the octave, and equally divides its pitch into 12 parts. For long, we could call this 12-EPDO, for 12 equal '''pitch''' divisions of the octave (whenever pitch is the chosen kind of quality, we can assume it, and skip pointing it out; that's why 12-EDO is the better name).

	~~{\| class="wikitable"~~
	~~\|+example: 4-EPDO = 4-EDO~~
	\|-
	~~! quantity~~
	~~! (0)~~
	~~! 1~~
	~~! 2~~
	~~! 3~~
	~~! 4~~
	\|-
	~~! frequency (f)~~
	~~\|(1)~~
	~~\|1.19~~
	~~\|1.41~~
	~~\|1.68~~
	\|2
	\|-
	~~! pitch (log₂f)~~
	~~\|(2⁰⸍⁴)~~
	~~\|2¹⸍⁴~~
	~~\|2²⸍⁴~~
	~~\|2³⸍⁴~~
	~~\|2⁴⸍⁴~~
	\|-
	~~! length (1/f)~~
	~~\|(1)~~
	~~\|0.84~~
	~~\|0.71~~
	~~\|0.59~~
	~~\|0.5~~
	\|}

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

Cmloegcmluin: fix section capitalization

2021-11-11T19:39:03Z

fix section capitalization

← Older revision		Revision as of 19:39, 11 November 2021
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	== Relationship to other tunings ==		== Relationship to other tunings ==

	=== vs. rank-1 temperaments & equal multiplications ===		=== Vs. rank-1 temperaments & equal multiplications ===

	An n-EPDn is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29\|rank-1 temperament]] of p/n, or an [[Equal-step_tuning#Equal_multiplications\|equal multiplication]] of p/n.		An n-EPDn is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29\|rank-1 temperament]] of p/n, or an [[Equal-step_tuning#Equal_multiplications\|equal multiplication]] of p/n.

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

	An EPD will be equivalent to some [[APS\|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).		An EPD will be equivalent to some [[APS\|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).