EDL - Revision history

FloraC: Merge is done

2023-10-12T12:21:07Z

Merge is done

← Older revision		Revision as of 12:21, 12 October 2023
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	~~{{Todo\|inline=1\|Merge articles\|comment=EDL →~~ [[IFDO~~]].}}~~		#redirect [[IFDO #Equal divisions of length]]

	==Equal divisions of length==

	For an intervallic system with n divisions, [https://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29 EDL] is considered as equal divisions of length by dividing string length to '''n''' equal divisions (so, we have '''n/2''' divisions per octave). If the first division is '''L1''' and the last, '''Ln''', we have:

	~~:: L1 = L2 = L3 = ... = Ln~~

	~~So sum of the divisions is '''L''' or the string length. Note that the number of divisions in octave is half of the string length. By dividing string length of '''L''' to '''n''' division we have:~~

	~~:: n : n-1 : n-2 : n-3 : ... : n-m : ... : n-n~~

	~~where '''n-m''' is '''n/2'''.~~


	~~For example, by dividing string length to 12 equal divisions we have a series as:~~

	~~:: 12:11:10:9:8:7:6:5:4:3:2:1:0 or 12 11 10 9 8 7 6 5 4 3 2 1 0~~

	~~which shows '''12-EDL''':~~

	~~[[file:edl1.jpg]]~~

	'''12:12''' means 12 from 12 divisions, '''12:11''' means 11 from 12 divisions and so on. Ratios as 12:11 shows active string length for each degree, which is vibrating. EDL system shows ascending trend of divisions sizes due to its inner structure and if compared with [[EDO]]:

	~~[[file:Edl2.JPG]]~~

	~~==Relation between Utonality and EDL system==~~

	We can consider EDL system as [https://en.wikipedia.org/wiki/Otonal Utonal system]. '''Utonality''' is a term introduced by [https://en.wikipedia.org/wiki/Harry_Partch Harry Partch] to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.

	In the other hand, a utonality is a collection of pitches which can be expressed in ratios that have the same numerators. For example, 7/4, 7/5, 7/6 form an utonality which 7 as numerator is called "[http://tonalsoft.com/enc/n/nexus.aspx Numerary nexus]".

	If a string is divided into equal parts, it will produce an utonality and so we have EDL system. EDL systems are classified as systems with unequal [http://tonalsoft.com/enc/e/epimorios.aspx epimorios] ([https://en.wikipedia.org/wiki/Superparticular_number Superparticular]) divisions which show descending series with ascending sizes.

	~~==Alternate names==~~

	~~In 1/1, The Journal of the Just Intonation Network, Volume 4, Number 1, Winter 1988, p.6, Michael Sloper refers to this type of scale as an "aliquot scale".~~

	~~==Further Reading==~~

	* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)
	* [[Overtone scales#Introduction - Modes of the Harmonic Series]]
	* [[UD\|UD, or utonal division]]: An n-EDL is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n).
	* Not to be confused with [[ELD\|ELD, equal length division]], another type of [[Arithmetic tunings\|arithmetic tuning]].

	~~[[Category:Utonality]]~~
	~~[[Category:Just intonation]]~~
	~~[[Category:Subharmonic series~~]]

FloraC: +todo

2023-10-08T16:48:43Z

+todo

← Older revision		Revision as of 16:48, 8 October 2023
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			{{Todo\|inline=1\|Merge articles\|comment=EDL → [[IFDO]].}}

	==Equal divisions of length==		==Equal divisions of length==

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	[[Category:Utonality]]		[[Category:Utonality]]
	~~[[Category:Edl]]~~
	[[Category:Just intonation]]		[[Category:Just intonation]]
	[[Category:Subharmonic series]]		[[Category:Subharmonic series]]

	~~{{Todo\| review \| cleanup }}~~

FloraC: -incorrect statements (n-ifdo isn't n-edl)

2023-04-26T08:14:48Z

-incorrect statements (n-ifdo isn't n-edl)

← Older revision		Revision as of 08:14, 26 April 2023
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	In 1/1, The Journal of the Just Intonation Network, Volume 4, Number 1, Winter 1988, p.6, Michael Sloper refers to this type of scale as an "aliquot scale".		In 1/1, The Journal of the Just Intonation Network, Volume 4, Number 1, Winter 1988, p.6, Michael Sloper refers to this type of scale as an "aliquot scale".

	~~An EDL is the same as an [[IFDO]]. For example, 42-EDL is the same thing as 42ifdo.~~

	~~An EDL is the same as a [[UDO]]. For example, 42-EDL is the same thing as 42udo.~~

	==Further Reading==		==Further Reading==
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	[[Category:Just intonation]]		[[Category:Just intonation]]
	[[Category:Subharmonic series]]		[[Category:Subharmonic series]]

			{{Todo\| review \| cleanup }}

BudjarnLambeth: /* Alternate names */

2023-04-26T06:09:36Z

Alternate names

← Older revision		Revision as of 06:09, 26 April 2023
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	An EDL is the same as an [[IFDO]]. For example, 42-EDL is the same thing as 42ifdo.		An EDL is the same as an [[IFDO]]. For example, 42-EDL is the same thing as 42ifdo.

			An EDL is the same as a [[UDO]]. For example, 42-EDL is the same thing as 42udo.

	==Further Reading==		==Further Reading==

BudjarnLambeth: Added sentence about IFDOs.

2023-04-26T06:00:17Z

Added sentence about IFDOs.

← Older revision		Revision as of 06:00, 26 April 2023
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	==Equal divisions of length==		==Equal divisions of length==

	For an intervallic system with n divisions, [~~http~~://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29 EDL] is considered as equal divisions of length by dividing string length to '''n''' equal divisions (so, we have '''n/2''' divisions per octave). If the first division is '''L1''' and the last, '''Ln''', we have:		For an intervallic system with n divisions, [https://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29 EDL] is considered as equal divisions of length by dividing string length to '''n''' equal divisions (so, we have '''n/2''' divisions per octave). If the first division is '''L1''' and the last, '''Ln''', we have:

	:: L1 = L2 = L3 = ... = Ln		:: L1 = L2 = L3 = ... = Ln
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	==Relation between Utonality and EDL system==		==Relation between Utonality and EDL system==

	We can consider EDL system as [~~http~~://en.wikipedia.org/wiki/Otonal Utonal system]. '''Utonality''' is a term introduced by [~~http~~://en.wikipedia.org/wiki/Harry_Partch Harry Partch] to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.		We can consider EDL system as [https://en.wikipedia.org/wiki/Otonal Utonal system]. '''Utonality''' is a term introduced by [https://en.wikipedia.org/wiki/Harry_Partch Harry Partch] to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.

	In the other hand, a utonality is a collection of pitches which can be expressed in ratios that have the same numerators. For example, 7/4, 7/5, 7/6 form an utonality which 7 as numerator is called "[http://tonalsoft.com/enc/n/nexus.aspx Numerary nexus]".		In the other hand, a utonality is a collection of pitches which can be expressed in ratios that have the same numerators. For example, 7/4, 7/5, 7/6 form an utonality which 7 as numerator is called "[http://tonalsoft.com/enc/n/nexus.aspx Numerary nexus]".

	If a string is divided into equal parts, it will produce an utonality and so we have EDL system. EDL systems are classified as systems with unequal [http://tonalsoft.com/enc/e/epimorios.aspx epimorios]([~~http~~://en.wikipedia.org/wiki/Superparticular_number Superparticular]) divisions which show descending series with ascending sizes.		If a string is divided into equal parts, it will produce an utonality and so we have EDL system. EDL systems are classified as systems with unequal [http://tonalsoft.com/enc/e/epimorios.aspx epimorios] ([https://en.wikipedia.org/wiki/Superparticular_number Superparticular]) divisions which show descending series with ascending sizes.

	==~~Aliquot scales~~==		==Alternate names==

	In 1/1, The Journal of the Just Intonation Network, Volume 4, Number 1, Winter 1988, p.6, Michael Sloper refers to this type of scale as an "aliquot scale".		In 1/1, The Journal of the Just Intonation Network, Volume 4, Number 1, Winter 1988, p.6, Michael Sloper refers to this type of scale as an "aliquot scale".

			An EDL is the same as an [[IFDO]]. For example, 42-EDL is the same thing as 42ifdo.

	==Further Reading==		==Further Reading==
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	[[Category:Edl]]		[[Category:Edl]]
	[[Category:Just intonation]]		[[Category:Just intonation]]
			[[Category:Subharmonic series]]

FloraC: FloraC moved page IDO to EDL over redirect: "Ido" hasn't been quite established yet, also not exactly the same thing as an edl

2023-03-18T15:57:21Z

FloraC moved page IDO to EDL over redirect: "Ido" hasn't been quite established yet, also not exactly the same thing as an edl

← Older revision	Revision as of 15:57, 18 March 2023
(No difference)

CompactStar: CompactStar moved page EDL to IDO

2023-03-18T07:16:48Z

CompactStar moved page EDL to IDO

← Older revision	Revision as of 07:16, 18 March 2023
(No difference)

Cmloegcmluin at 18:48, 22 March 2021

2021-03-22T18:48:33Z

← Older revision		Revision as of 18:48, 22 March 2021
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	* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)		* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)
	* [[Overtone scales#Introduction - Modes of the Harmonic Series]]		* [[Overtone scales#Introduction - Modes of the Harmonic Series]]
	* [[UD\|UD, or utonal division]]: An n-EDL is equivalent to an n~~-UDn~~.		* [[UD\|UD, or utonal division]]: An n-EDL is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n).
			* Not to be confused with [[ELD\|ELD, equal length division]], another type of [[Arithmetic tunings\|arithmetic tuning]].

	[[Category:Utonality]]		[[Category:Utonality]]
	[[Category:Edl]]		[[Category:Edl]]
	[[Category:Just intonation]]		[[Category:Just intonation]]

Cmloegcmluin at 00:39, 22 March 2021

2021-03-22T00:39:04Z

← Older revision		Revision as of 00:39, 22 March 2021
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	* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)		* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)
	* [[Overtone scales#Introduction - Modes of the Harmonic Series]]		* [[Overtone scales#Introduction - Modes of the Harmonic Series]]
	* [[UD, or utonal division]]: An n-EDL is equivalent to an n-UDn.		* [[UD\|UD, or utonal division]]: An n-EDL is equivalent to an n-UDn.

	[[Category:Utonality]]		[[Category:Utonality]]
	[[Category:Edl]]		[[Category:Edl]]
	[[Category:Just intonation]]		[[Category:Just intonation]]

Cmloegcmluin at 00:37, 22 March 2021

2021-03-22T00:37:48Z

← Older revision		Revision as of 00:37, 22 March 2021
Line 40:		Line 40:
	* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)		* https://sites.google.com/site/240edo/equaldivisionsoflength(edl)
	* [[Overtone scales#Introduction - Modes of the Harmonic Series]]		* [[Overtone scales#Introduction - Modes of the Harmonic Series]]
			* [[UD, or utonal division]]: An n-EDL is equivalent to an n-UDn.

	[[Category:Utonality]]		[[Category:Utonality]]
	[[Category:Edl]]		[[Category:Edl]]
	[[Category:Just intonation]]		[[Category:Just intonation]]