162edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-19T18:03:08Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:03, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].		Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].

FloraC: Paragraphing; +subsets and supersets

2024-05-07T11:12:23Z

Paragraphing; +subsets and supersets

← Older revision		Revision as of 11:12, 7 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}} ~~Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].~~		{{EDO intro}}

	The non-patent val {{val\| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val\| 162 257 377 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val\| 162 257 377 455 561 }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val\| 162 257 377 455 561 600 }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.		Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].

			The non-patent val {{val\| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val\| 162 257 '''377''' 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val\| 162 257 '''377''' 455 '''561''' }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val\| 162 257 '''377''' 455 '''561''' '''600''' }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|162}}		{{Harmonics in equal\|162}}

			=== Subsets and supersets ===
			Since 162 factors into {{factorization\|162}}, 162edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 27, 54, and 81 }}.

FloraC: Cleanup and -redundant categories

2024-05-07T11:10:30Z

Cleanup and -redundant categories

← Older revision		Revision as of 11:10, 7 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~162edo divides~~ the ~~octave into 162 parts of 7.407 cents each. In~~ the ~~7-limit it~~ tempers out 4000/3969, 10976/10935 and 65625/65536.		{{EDO intro}} Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].

	The ~~[[Patent_val\|~~non-patent val~~]] <~~162 257 377\| and its ~~extensions~~ are of considerable interest, as this tempers out 2048/2025. In the 7-limit, ~~<~~162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[~~Diaschismic_family\|~~diaschismic]]. In the 11-limit ~~<~~162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[~~POTE_tuning\|~~POTE tuning]]. The 13-limit is even closer: ~~the 13-limit~~ val ~~<~~162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363~~, 2048/2025~~ giving 13-limit diaschismic, and the ~~162~~ fifth of 95/162 ~~octave~~ is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.		The non-patent val {{val\| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val\| 162 257 377 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val\| 162 257 377 455 561 }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val\| 162 257 377 455 561 600 }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

			=== Prime harmonics ===
	{{Harmonics in equal\|162}}		{{Harmonics in equal\|162}}
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T07:09:53Z

Added "harmonics in equal" table

← Older revision		Revision as of 07:09, 24 June 2023
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	The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.		The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

			{{Harmonics in equal\|162}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Aura at 19:10, 4 October 2022

2022-10-04T19:10:52Z

← Older revision		Revision as of 19:10, 4 October 2022
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			{{Infobox ET}}
	162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.		162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.

Fredg999 category edits: Categories

2022-07-02T21:14:31Z

Cmloegcmluin: link to new page for Supports

2022-01-25T18:34:45Z

link to new page for Supports

← Older revision		Revision as of 18:34, 25 January 2022
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	162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.		162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.

	The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so ~~supports~~ 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.		The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

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>~~		162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.
	~~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>2011-01-29 17:58:48 UTC</tt>.<br>~~
	~~: The original revision id was <tt>197086548</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">162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.

	The [[~~Patent val~~\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[~~Diaschismic family~~\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.~~</pre></div>~~		The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.
	~~<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>162edo</title></head><body>162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536. <br />
	~~<br />~~
	The <a class="wiki_link" href="/Patent%20val">non-patent val</a> &lt;162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit <a class="wiki_link" href="/Diaschismic%20family">diaschismic</a>. In the 11-limit &lt;162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 197086548 - Original comment:

2011-01-29T17:58:48Z

**Imported revision 197086548 - Original comment: **

Wikispaces>genewardsmith: Imported revision 187246847 - Original comment:

2010-12-10T17:59:32Z

**Imported revision 187246847 - Original comment: **

← Older revision		Revision as of 07:09, 24 June 2023
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	The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.		The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

			{{Harmonics in equal\|162}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

← Older revision		Revision as of 21:14, 2 July 2022
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	The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.		The [[Patent_val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE_tuning\|POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

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

← Older revision		Revision as of 17:58, 29 January 2011
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	<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>~~2010~~-12-10 17:59:32 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-01-29 17:58:48 UTC</tt>.<br>
	: The original revision id was <tt>~~187246847~~</tt>.<br>		: The original revision id was <tt>197086548</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>
Line 8:		Line 8:
	<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">162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.		<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">162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.

	The non-patent val <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</pre></div>		The [[Patent val\|non-patent val]] <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</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>162edo</title></head><body>162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536. <br />		<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>162edo</title></head><body>162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536. <br />
	<br />		<br />
	The non-patent val &lt;162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit <a class="wiki_link" href="/Diaschismic%20family">diaschismic</a>. In the 11-limit &lt;162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</body></html></pre></div>		The <a class="wiki_link" href="/Patent%20val">non-patent val</a> &lt;162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit <a class="wiki_link" href="/Diaschismic%20family">diaschismic</a>. In the 11-limit &lt;162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</body></html></pre></div>

← Older revision		Revision as of 17:59, 10 December 2010
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>2010-12-10 17:49:11 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-12-10 17:59:32 UTC</tt>.<br>
	: The original revision id was <tt>~~187245061~~</tt>.<br>		: The original revision id was <tt>187246847</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>
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	<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">162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.		<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">162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.

	The non-patent val <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit diaschismic. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</pre></div>		The non-patent val <162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic family\|diaschismic]]. In the 11-limit <162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</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>162edo</title></head><body>162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536. <br />		<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>162edo</title></head><body>162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536. <br />
	<br />		<br />
	The non-patent val &lt;162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit diaschismic. In the 11-limit &lt;162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</body></html></pre></div>		The non-patent val &lt;162 257 377\| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455\| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit <a class="wiki_link" href="/Diaschismic%20family">diaschismic</a>. In the 11-limit &lt;162 257 377 455 561\| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600\| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</body></html></pre></div>