415edo - Revision history

ArrowHead294 at 14:55, 20 February 2025

2025-02-20T14:55:04Z

← Older revision		Revision as of 14:55, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|415~~}}		{{ED intro}}

	If [[5/1\|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]].		If [[5/1\|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]].

FloraC: Expand on theory; adopt template: Factorization

2023-11-06T14:32:58Z

Expand on theory; adopt template: Factorization

← Older revision		Revision as of 14:32, 6 November 2023
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	{{EDO intro\|415}}		{{EDO intro\|415}}

	If [[5/1\|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament tempers out the [[parakleisma]], {{monzo\| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s ~~the~~ [[parakleismic]] temperament and provides the [[optimal patent val]].		If [[5/1\|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	~~415edo has subset edos~~ {{~~EDOs~~\| ~~5 and 83~~ }}.		Since 415 factors into {{factorization\|415}}, 415edo contains [[5edo]] and [[83edo]] as subsets.

	[[Category:Parakleismic]]		[[Category:Parakleismic]]

BudjarnLambeth at 06:33, 9 July 2023

2023-07-09T06:33:07Z

← Older revision		Revision as of 06:33, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|415}}		{{EDO intro\|415}}

BudjarnLambeth at 05:55, 9 July 2023

2023-07-09T05:55:52Z

← Older revision		Revision as of 05:55, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|415}}		{{EDO intro\|415}}

FloraC: Cleanup; +prime error table; +subsets and supersets

2023-06-16T04:11:52Z

Cleanup; +prime error table; +subsets and supersets

← Older revision		Revision as of 04:11, 16 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~415 ~~equal division''' divides the octave into 415 equal parts of 2.892 cents each~~. In the 5-limit it tempers out the parakleisma, \|8 14 -13~~>~~; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[~~Optimal_patent_val\|~~optimal patent val]].		{{EDO intro\|415}}

			If [[5/1\|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament tempers out the [[parakleisma]], {{monzo\| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s the [[parakleismic]] temperament and provides the [[optimal patent val]].

			=== Odd harmonics ===
			{{Harmonics in equal\|415}}

			=== Subsets and supersets ===
			415edo has subset edos {{EDOs\| 5 and 83 }}.

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Parakleismic]]		[[Category:Parakleismic]]

Plumtree: Infobox ET added

2022-10-04T21:54:59Z

Infobox ET added

← Older revision		Revision as of 21:54, 4 October 2022
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			{{Infobox ET}}
	The '''415 equal division''' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].		The '''415 equal division''' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Parakleismic]]		[[Category:Parakleismic]]

Fredg999 category edits: Sort key

2022-07-04T00:57:09Z

Sort key

← Older revision		Revision as of 00:57, 4 July 2022
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	The ''415 equal division'' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].		The '''415 equal division''' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].
	[[Category:Equal divisions of the octave]]
	[[Category:~~parakleismic~~]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
			[[Category:Parakleismic]]

Cmloegcmluin: link to new page for Supports

2022-01-25T17:53:04Z

link to new page for Supports

← Older revision		Revision as of 17:53, 25 January 2022
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	The ''415 equal division'' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it ~~supports~~ parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].		The ''415 equal division'' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:parakleismic]]		[[Category:parakleismic]]

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:53Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
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	The ''415 equal division'' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].		The ''415 equal division'' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].
	[[Category:~~edo~~]]		[[Category:Equal divisions of the octave]]
	[[Category:parakleismic]]		[[Category:parakleismic]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		The ''415 equal division'' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic temperament and provides the [[Optimal_patent_val\|optimal patent val]].
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~		[[Category:edo]]
	~~: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-07-13 15:17:14 UTC</tt>.<br>~~		[[Category:parakleismic]]
	~~: The original revision id was <tt>241210949</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	The ~~revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //415 equal division// divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic temperament and provides the [[optimal patent val]]. ~~</pre></div>~~
	~~<h4>Original HTML content~~:~~</h4>~~
	~~<div style="width:100%; max-height:400pt; overflow:auto; background-color~~:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>415edo</title></head><body>The <em>415 equal division</em> divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, \|8 14 -13&gt;; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic ~~temperament and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>.</body></html></pre></div>~~