446edo - Revision history

ArrowHead294 at 14:57, 20 February 2025

2025-02-20T14:57:01Z

← Older revision		Revision as of 14:57, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|446~~}}		{{ED intro}}

	446edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1\|5]] is quite large. The equal temperament [[tempering out\|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the [[hemimean]] temperament tempering out 3136/3125, and [[sengagen]], the 99 & 347 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 198 & 248 temperament.		446edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1\|5]] is quite large. The equal temperament [[tempering out\|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the [[hemimean]] temperament tempering out 3136/3125, and [[sengagen]], the {{nowrap\|99 & 347}} temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 198 & 248 temperament.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Rework

2023-11-03T07:47:04Z

Rework

← Older revision		Revision as of 07:47, 3 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''446 equal division''' divides the octave into~~ 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.		{{EDO intro\|446}}

	~~Prime~~ factorization: [[2edo\|2]] × [[223edo~~\|223~~]].		446edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1\|5]] is quite large. The equal temperament [[tempering out\|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the [[hemimean]] temperament tempering out 3136/3125, and [[sengagen]], the 99 & 347 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 198 & 248 temperament.

			=== Odd harmonics ===
			{{Harmonics in equal\|446}}

			=== Subsets and supersets ===
			Since 446 factors into {{factorization\|446}}, 446edo contains [[2edo]] and [[223edo]] as subsets.

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

BudjarnLambeth at 06:34, 9 July 2023

2023-07-09T06:34:51Z

← Older revision		Revision as of 06:34, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.		The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.

BudjarnLambeth at 05:49, 9 July 2023

2023-07-09T05:49:22Z

← Older revision		Revision as of 05:49, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.		The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.

Plumtree: Infobox ET added

2022-10-04T21:56:00Z

Infobox ET added

← Older revision		Revision as of 21:56, 4 October 2022
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			{{Infobox ET}}
	The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.		The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.

Fredg999 category edits: Sort key

2022-07-04T00:58:20Z

Sort key

← Older revision		Revision as of 00:58, 4 July 2022
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	Prime factorization: [[2edo\|2]] × [[223edo\|223]].		Prime factorization: [[2edo\|2]] × [[223edo\|223]].

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

FloraC: Cleanup

2021-01-26T05:00:40Z

Cleanup

← Older revision		Revision as of 05:00, 26 January 2021
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	The ''446 equal division'' divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[~~Optimal_patent_val\|~~optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[~~Hemimean_clan~~#Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament.		The '''446 equal division''' divides the octave into 446 equal parts of 2.691 cents each. It tempers out [[3136/3125]] and [[420175/419904]] in the 7-limit, and provides the [[optimal patent val]] for the [[Hemimean family #Hemimean\|hemimean]] temperament tempering out 3136/3125, and [[Hemimean clan #Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 50&198 temperament.

	~~'''PRIME FACTORIZATION~~:~~'''~~		Prime factorization: [[2edo\|2]] × [[223edo\|223]].

	[[~~2edo\|2~~]] * [[~~223edo\|223~~]] [[Category:~~hemimean~~]]		[[Category:Equal divisions of the octave]]
			[[Category:Hemimean]]
			[[Category:Sengagen]]

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 ''446 equal division'' divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[Optimal_patent_val\|optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[Hemimean_clan#Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament.
	~~This is an imported revision from Wikispaces.~~ The ~~revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:Osmiorisbendi\|Osmiorisbendi]] and made on <tt>2012-05-20 15:37:36 UTC</tt>.<br>~~
	~~: The original revision id was <tt>337607418</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 //446 equal division// divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[~~Hemimean clan~~#Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament.

	PRIME FACTORIZATION:		'''PRIME FACTORIZATION:'''
	[[2edo\|2]] * [[223edo\|223]]~~</pre></div>~~
	~~<h4>Original HTML content:</h4>~~		[[2edo\|2]] * [[223edo\|223]] [[Category:hemimean]]
	~~<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>446edo</title></head><body>The <em>446 equal division</em> divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the hemimean temperament tempering out 3136/3125 and <a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a>, the 49&amp;50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&amp;198 temperament.<br />
	~~<br />~~
	~~<strong>PRIME FACTORIZATION:</strong><br />~~
	~~<a class="wiki_link" href="/2edo">2</a> * <a class="wiki_link" href="/223edo">223</a></body></html></pre></div>~~

Wikispaces>Osmiorisbendi: Imported revision 337607418 - Original comment:

2012-05-20T15:37:36Z

**Imported revision 337607418 - Original comment: **

← Older revision		Revision as of 15:37, 20 May 2012
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~genewardsmith~~\|~~genewardsmith~~]] and made on <tt>2012-02-~~07 10~~:23:27 UTC</tt>.<br>		: This revision was by author [[User:Osmiorisbendi\|Osmiorisbendi]] and made on <tt>2012-05-20 15:37:36 UTC</tt>.<br>
	: The original revision id was <tt>~~299288018~~</tt>.<br>		: The original revision id was <tt>337607418</tt>.<br>
	: The revision comment was: <tt></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>		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>		<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 //446 equal division// divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[Hemimean clan#Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament. </pre></div>		<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 //446 equal division// divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[Hemimean clan#Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament.

			PRIME FACTORIZATION:
			[[2edo\|2]] * [[223edo\|223]]</pre></div>
	<h4>Original HTML content:</h4>		<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>446edo</title></head><body>The <em>446 equal division</em> divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the hemimean temperament tempering out 3136/3125 and <a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a>, the 49&amp;50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&amp;198 temperament.</body></html></pre></div>		<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>446edo</title></head><body>The <em>446 equal division</em> divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the hemimean temperament tempering out 3136/3125 and <a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a>, the 49&amp;50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&amp;198 temperament.<br />
			<br />
			<strong>PRIME FACTORIZATION:</strong><br />
			<a class="wiki_link" href="/2edo">2</a> * <a class="wiki_link" href="/223edo">223</a></body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 299288018 - Original comment:

2012-02-07T10:23:27Z

**Imported revision 299288018 - Original comment: **

← Older revision		Revision as of 10:23, 7 February 2012
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>~~2011~~-07~~-13 16~~:05:20 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2012-02-07 10:23:27 UTC</tt>.<br>
	: The original revision id was <tt>~~241218627~~</tt>.<br>		: The original revision id was <tt>299288018</tt>.<br>
	: The revision comment was: <tt></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>		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>		<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 //446 equal division// divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the hemimean temperament tempering out 3136/3125 and the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament. </pre></div>		<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 //446 equal division// divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[Hemimean clan#Sengagen\|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament. </pre></div>
	<h4>Original HTML content:</h4>		<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>446edo</title></head><body>The <em>446 equal division</em> divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the hemimean temperament tempering out 3136/3125 and the 49&amp;50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&amp;198 temperament.</body></html></pre></div>		<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>446edo</title></head><body>The <em>446 equal division</em> divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the hemimean temperament tempering out 3136/3125 and <a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a>, the 49&amp;50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&amp;198 temperament.</body></html></pre></div>