43edo: 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:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>2013-05-~~15 22~~:05:30 UTC</tt>.<br>

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2013-05-29 21:43:10 UTC</tt>.<br>

: The original revision id was <tt>~~431953504~~</tt>.<br>

: The original revision id was <tt>435171490</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>

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In the 13-limit, we get two versions of meantone equivalent in 43et, one, [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone|meridetone]], tempering out 78/77, the other, [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone|grosstone]], 144/143. Meridetone has generator mapping <0 1 4 10 18 27|, and grosstone <0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.

The 43 patent val <43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel temperaments#Amavil|amavil temperament]], which is not a meantone temperament.

The 43 patent val <43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel temperaments#Amavil|amavil temperament]], which is not a meantone temperament. [[Thuja]] temperament is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with MOS of 15 and 28.

43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].

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|| 2 || 55.814 || ||

|| 3 || 83.721 || ||

|| 4 || 111.628 || 16/15, 15/14 ||

|| 4 || 111.628 || 17/16, 16/15, 15/14 ||

|| 5 || 139.535 || 12/11, 13/12, 14/13 ||

|| 6 || 167.442 || 11/10 ||

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|| 8 || 223.256 || 8/7 ||

|| 9 || 251.163 || 15/13 ||

|| 10 || 279.07 || 7/6 ||

|| 10 || 279.07 || 7/6, 13/11 ||

|| 11 || 306.977 || 6/5 ||

|| 12 || 334.884 || ||

|| 12 || 334.884 || 17/14, 39/32 ||

|| 13 || 362.791 || 11/9, 16/13 ||

|| 14 || 390.698 || 5/4 ||

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[[file:xenharmonic/43 edo counterpoint.mid|43 edo counterpoint.mid]] ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]]//// Peter Kosmorsky (late 2011)</pre></div>

[[file:xenharmonic/43 edo counterpoint.mid|43 edo counterpoint.mid]] //[[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]]// Peter Kosmorsky (late 2011) (in meantone)</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>43edo</title></head><body><h1 id="toc0"><a name="x43 tone equal temperament"></a><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1>

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In the 13-limit, we get two versions of meantone equivalent in 43et, one, <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone">meridetone</a>, tempering out 78/77, the other, <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone">grosstone</a>, 144/143. Meridetone has generator mapping &lt;0 1 4 10 18 27|, and grosstone &lt;0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.<br />

<br />

The 43 patent val &lt;43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to <a class="wiki_link" href="/Meantone%20family#Jerome">jerome temperament</a>, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit <a class="wiki_link" href="/Marvel%20temperaments#Amavil">amavil temperament</a>, which is not a meantone temperament.<br />

The 43 patent val &lt;43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to <a class="wiki_link" href="/Meantone%20family#Jerome">jerome temperament</a>, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit <a class="wiki_link" href="/Marvel%20temperaments#Amavil">amavil temperament</a>, which is not a meantone temperament. <a class="wiki_link" href="/Thuja">Thuja</a> temperament is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with MOS of 15 and 28.<br />

<br />

43edo is the 14th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/41edo">41edo</a> and coming before <a class="wiki_link" href="/47edo">47edo</a>.<br />

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<a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid');">43 edo counterpoint.mid</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow">mp3</a> Peter Kosmorsky (late 2011)</body></html></pre></div>

<a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid');">43 edo counterpoint.mid</a> <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow">mp3</a></em> Peter Kosmorsky (late 2011) (in meantone)</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-05-15 22:05:30 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2013-05-29 21:43:10 UTC</tt>.<br>
-: The original revision id was <tt>431953504</tt>.<br>
+: The original revision id was <tt>435171490</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>
@@ Line 12: / Line 12: @@
 In the 13-limit, we get two versions of meantone equivalent in 43et, one, [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone|meridetone]], tempering out 78/77, the other, [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone|grosstone]], 144/143. Meridetone has generator mapping &lt;0 1 4 10 18 27|, and grosstone &lt;0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.
-The 43 patent val &lt;43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel temperaments#Amavil|amavil temperament]], which is not a meantone temperament.
+The 43 patent val &lt;43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel temperaments#Amavil|amavil temperament]], which is not a meantone temperament. [[Thuja]] temperament is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with MOS of 15 and 28.
 edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].
@@ Line 23: / Line 23: @@
 || 2 || 55.814 ||   ||
 || 3 || 83.721 ||   ||
-|| 4 || 111.628 || 16/15, 15/14 ||
+|| 4 || 111.628 || 17/16, 16/15, 15/14 ||
 || 5 || 139.535 || 12/11, 13/12, 14/13 ||
 || 6 || 167.442 || 11/10 ||
@@ Line 29: / Line 29: @@
 || 8 || 223.256 || 8/7 ||
 || 9 || 251.163 || 15/13 ||
-|| 10 || 279.07 || 7/6 ||
+|| 10 || 279.07 || 7/6, 13/11 ||
 || 11 || 306.977 || 6/5 ||
-|| 12 || 334.884 ||   ||
+|| 12 || 334.884 || 17/14, 39/32 ||
 || 13 || 362.791 || 11/9, 16/13 ||
 || 14 || 390.698 || 5/4 ||
@@ Line 64: / Line 64: @@
-[[file:xenharmonic/43 edo counterpoint.mid|43 edo counterpoint.mid]] ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]]//// Peter Kosmorsky (late 2011)</pre></div>
+[[file:xenharmonic/43 edo counterpoint.mid|43 edo counterpoint.mid]] //[[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]]// Peter Kosmorsky (late 2011) (in meantone)</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;43edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x43 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #027bac; font-size: 103%;"&gt;43 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
@@ Line 72: / Line 72: @@
 In the 13-limit, we get two versions of meantone equivalent in 43et, one, &lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone"&gt;meridetone&lt;/a&gt;, tempering out 78/77, the other, &lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone"&gt;grosstone&lt;/a&gt;, 144/143. Meridetone has generator mapping &amp;lt;0 1 4 10 18 27|, and grosstone &amp;lt;0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.&lt;br /&gt;
 &lt;br /&gt;
-The 43 patent val &amp;lt;43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to &lt;a class="wiki_link" href="/Meantone%20family#Jerome"&gt;jerome temperament&lt;/a&gt;, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit &lt;a class="wiki_link" href="/Marvel%20temperaments#Amavil"&gt;amavil temperament&lt;/a&gt;, which is not a meantone temperament.&lt;br /&gt;
+The 43 patent val &amp;lt;43 68 100 121 149 159| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to &lt;a class="wiki_link" href="/Meantone%20family#Jerome"&gt;jerome temperament&lt;/a&gt;, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit &lt;a class="wiki_link" href="/Marvel%20temperaments#Amavil"&gt;amavil temperament&lt;/a&gt;, which is not a meantone temperament. &lt;a class="wiki_link" href="/Thuja"&gt;Thuja&lt;/a&gt; temperament is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with MOS of 15 and 28.&lt;br /&gt;
 &lt;br /&gt;
 edo is the 14th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/47edo"&gt;47edo&lt;/a&gt;.&lt;br /&gt;
@@ Line 126: / Line 126: @@
          &lt;td&gt;111.628&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/15, 15/14&lt;br /&gt;
+         &lt;td&gt;17/16, 16/15, 15/14&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 174: / Line 174: @@
          &lt;td&gt;279.07&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/6&lt;br /&gt;
+         &lt;td&gt;7/6, 13/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 190: / Line 190: @@
          &lt;td&gt;334.884&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;17/14, 39/32&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 437: / Line 437: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid');"&gt;43 edo counterpoint.mid&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow"&gt;mp3&lt;/a&gt; Peter Kosmorsky (late 2011)&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid');"&gt;43 edo counterpoint.mid&lt;/a&gt; &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow"&gt;mp3&lt;/a&gt;&lt;/em&gt; Peter Kosmorsky (late 2011) (in meantone)&lt;/body&gt;&lt;/html&gt;</pre></div>