246edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~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.

== 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]]. The same 11 and 19 are straight-up inherited by the monstrous [[2460edo]].

~~=Scales=~~

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]].

[[~~cata7~~]]

[[~~cata11~~]]

[[~~cata15~~]]

[[~~cata19~~]]

~~[[image:cata_246edo.jpg]]</pre></div>~~

=== Prime harmonics ===

~~<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 />~~

~~<br />~~

=== Subsets and supersets ===

~~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 />~~

Since 246 factors into {{factorization|246}}, 246edo has subset edos {{EDOs| 2, 3, 6, 41, 82, and 123 }}.

~~<br />~~

~~<h1 id~~=~~"toc0"><a name~~=~~"Scales"></a>~~Scales~~</h1>~~

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

~~<a class~~=~~"wiki_link" href~~=~~"/cata7">cata7</a><br />~~

~~<a class="wiki_link" href="/cata11">cata11</a><br />~~

== Scales ==

~~<a class="wiki_link" href="/cata15">cata15</a><br />~~

[[File:cata_246edo.jpg|thumb|alt=cata_246edo.jpg|Cata in 246edo]]

~~<a class="wiki_link" href="/cata19">cata19</a><br />~~

~~<br />~~

* [[Cata7]]

~~<img src="/file/view/~~cata_246edo.jpg~~/270808508/cata_246edo.jpg" alt="cata_246edo.jpg" title="cata_246edo.jpg" /></body></html></pre></div>~~

* [[Cata11]]

* [[Cata15]]

* [[Cata19]]

[[Category:Kleismic]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+{{ED intro}}
-: 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.
+== Theory ==
+= 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]].
-=Scales=
+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]].
-[[cata7]]
-[[cata11]]
-[[cata15]]
-[[cata19]]
-[[image:cata_246edo.jpg]]</pre></div>
+=== Prime harmonics ===
-<h4>Original HTML content:</h4>
+{{Harmonics in equal|246}}
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;246edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;246edo divides the 2/1 (octave) into 246 equal steps of 4.878 &lt;a class="wiki_link" href="/cents"&gt;cents&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
+=== Subsets and supersets ===
-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.&lt;br /&gt;
+Since 246 factors into {{factorization|246}}, 246edo has subset edos {{EDOs| 2, 3, 6, 41, 82, and 123 }}.
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Scales&lt;/h1&gt;
+A step of 246edo is exactly 10 [[mina]]s.
- &lt;a class="wiki_link" href="/cata7"&gt;cata7&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/cata11"&gt;cata11&lt;/a&gt;&lt;br /&gt;
+== Scales ==
-&lt;a class="wiki_link" href="/cata15"&gt;cata15&lt;/a&gt;&lt;br /&gt;
+[[File:cata_246edo.jpg|thumb|alt=cata_246edo.jpg|Cata in 246edo]]
-&lt;a class="wiki_link" href="/cata19"&gt;cata19&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
+* [[Cata7]]
-&lt;!-- ws:start:WikiTextLocalImageRule:2:&amp;lt;img src=&amp;quot;/file/view/cata_246edo.jpg/270808508/cata_246edo.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/cata_246edo.jpg/270808508/cata_246edo.jpg" alt="cata_246edo.jpg" title="cata_246edo.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+* [[Cata11]]
+* [[Cata15]]
+* [[Cata19]]
+[[Category:Kleismic]]