246edo - Revision history

FloraC: Recategorize

2025-06-05T04:14:29Z

Recategorize

← Older revision		Revision as of 04:14, 5 June 2025
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	* [[Cata19]]		* [[Cata19]]

	[[Category:~~Cata~~]]		[[Category:Kleismic]]

ArrowHead294 at 14:25, 20 February 2025

2025-02-20T14:25:15Z

← Older revision		Revision as of 14:25, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ expand

2024-04-03T13:13:20Z

Theory: expand

← Older revision		Revision as of 13:13, 3 April 2024
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	== Theory ==		== Theory ==
	246 = 6 × 41, and 246edo shares its [[perfect fifth\|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1\|11]], [[19/1\|19]], and [[29/1\|29]], and quite good approximations (within one cent) of [[5/1\|5]] and [[23/1\|23]]. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament [[~~tempering out~~]] [[~~325/324~~]] ~~and~~ [[~~625/624~~]].		246 = 6 × 41, and 246edo shares its [[perfect fifth\|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1\|11]], [[19/1\|19]], and [[29/1\|29]], and quite good approximations (within one cent) of [[5/1\|5]] and [[23/1\|23]]. The same 11 and 19 are straight-up inherited by the monstrous [[2460edo]].

			As an equal temperament, 246et [[tempering out\|tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) in the 5-limit; [[5120/5103]] and 118098/117649 in the 7-limit; and [[540/539]], [[9801/9800]] in the 11-limit; [[325/324]], [[625/624]] in the 13-limit. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament tempering out 325/324 and 625/624. The 246d val [[support]]s [[tritikleismic]]. The 246ee val supports [[countercata]]. The 246f val supports [[supers]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 246 factors into {{factorization\|246}}, 246edo has subset edos {{EDOs\| 2, 3, 6, 41, 82, and 123 }}.		Since 246 factors into {{factorization\|246}}, 246edo has subset edos {{EDOs\| 2, 3, 6, 41, 82, and 123 }}.

			A step of 246edo is exactly 10 [[mina]]s.

	== Scales ==		== Scales ==

FloraC: Expansion

2024-03-24T11:50:41Z

Expansion

← Older revision		Revision as of 11:50, 24 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~246edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents\|cents]].~~		{{EDO intro}}

	~~The~~ patent val offers excellent approximations (within half a cent) of ~~primes 3,~~ 11, 19, and 29, and quite good approximations (within one cent) of ~~primes~~ 5 and 23.		== Theory ==
			246 = 6 × 41, and 246edo shares its [[perfect fifth\|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1\|11]], [[19/1\|19]], and [[29/1\|29]], and quite good approximations (within one cent) of [[5/1\|5]] and [[23/1\|23]]. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament [[tempering out]] [[325/324]] and [[625/624]].

	== ~~Harmonics~~ ==		=== Prime harmonics ===
	{{Harmonics in equal\|246}}		{{Harmonics in equal\|246}}

	==~~Scales~~==		=== Subsets and supersets ===
	* [[cata7]]		Since 246 factors into {{factorization\|246}}, 246edo has subset edos {{EDOs\| 2, 3, 6, 41, 82, and 123 }}.
	* [[cata11]]
	* [[cata15]]
	* [[cata19]]
	* [[File:cata_246edo.jpg\|~~alt=cata_246edo.jpg~~\|~~cata_246edo~~.~~jpg]]~~

	[[Category:~~Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		== Scales ==
			[[File:cata_246edo.jpg\|thumb\|alt=cata_246edo.jpg\|Cata in 246edo]]

			* [[Cata7]]
			* [[Cata11]]
			* [[Cata15]]
			* [[Cata19]]

			[[Category:Cata]]

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T03:32:49Z

Added "harmonics in equal" table

← Older revision		Revision as of 03:32, 24 June 2023
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	The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.		The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.

	=Scales=		== Harmonics ==
			{{Harmonics in equal\|246}}

			==Scales==
	* [[cata7]]		* [[cata7]]
	* [[cata11]]		* [[cata11]]

Plumtree: Infobox ET added

2022-10-04T21:27:14Z

Infobox ET added

← Older revision		Revision as of 21:27, 4 October 2022
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			{{Infobox ET}}
	246edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents\|cents]].		246edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents\|cents]].

Fredg999 category edits: Sort key

2022-07-03T18:55:58Z

Sort key

← Older revision		Revision as of 18:55, 3 July 2022
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	=Scales=		=Scales=
	[[cata7\|~~cata7~~]]		* [[cata7]]
			* [[cata11]]
			* [[cata15]]
			* [[cata19]]
			* [[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]]

	~~[[cata11\|cata11]]~~		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

	~~[[cata15\|cata15]]~~

	~~[[cata19\|cata19]]~~

	~~[[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]]~~ [[Category:Equal divisions of the octave]]

Fredg999 category edits: Removing from Category:Scales using Cat-a-lot

2022-02-25T14:54:42Z

Removing from Category:Scales using Cat-a-lot

← Older revision		Revision as of 14:54, 25 February 2022
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	[[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]] [[Category:Equal divisions of the octave]]		[[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]] [[Category:Equal divisions of the octave]]
	~~[[Category:scales]]~~

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

2020-12-04T23:13:21Z

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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	[[cata19\|cata19]]		[[cata19\|cata19]]

	[[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]] [[Category:~~edo~~]]		[[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]] [[Category:Equal divisions of the octave]]
	[[Category:scales]]		[[Category:scales]]

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>~~		246edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents\|cents]].
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:spt3125\|spt3125]] and made on <tt>2017-07-30 15:26:18 UTC</tt>.<br>~~
	~~: The original revision id was <tt>616004921</tt>.<br>~~
	~~: The revision comment was: <tt>added image (deorphaning), basic content</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">246edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents]].

	The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.		The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.

	=Scales=		=Scales=
	[[cata7]]		[[cata7\|cata7]]
	~~[[cata11]]~~
	~~[[cata15]]~~
	~~[[cata19~~]]

	[[~~image:cata_246edo.jpg~~]]~~</pre></div>~~		[[cata11\|cata11]]
	~~<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>246edo</title></head><body>246edo divides the 2/1 (octave) into 246 equal steps of 4.878 <a class="wiki_link" href="/cents">cents</a>.<br />		[[cata15\|cata15]]
	~~<br />~~
	~~The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.<br />~~		[[cata19\|cata19]]
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1>~~		[[File:cata_246edo.jpg\|alt=cata_246edo.jpg\|cata_246edo.jpg]] [[Category:edo]]
	~~<a class="wiki_link" href="/cata7">cata7</a><br />~~		[[Category:scales]]
	~~<a class="wiki_link" href="/cata11">cata11</a><br />~~
	~~<a class="wiki_link" href="/~~cata15~~">~~cata15~~</a><br />~~
	~~<a class="wiki_link" href="/~~cata19~~">~~cata19~~</a><br />~~
	~~<br />~~
	~~<!-- ws:start~~:~~WikiTextLocalImageRule:2:&lt;img src=&quot;/file/view/cata_246edo.jpg/270808508/~~cata_246edo.jpg~~&quot;~~ alt=~~&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/~~cata_246edo.jpg~~/270808508/~~cata_246edo.jpg~~" alt="cata_246edo.jpg" title="cata_246edo.jpg" /><!-- ws~~:~~end~~:~~WikiTextLocalImageRule:2 --></body></html></pre></div>~~