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:

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

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-05-30 03:52:29 UTC</tt>.

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

: The original revision id was <tt>435215878</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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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. [[Thuja]] temperament is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with MOS of 15 and 28.

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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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.

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.

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 <a class="wiki_link" href="/MOS">MOS</a> of 15 and 28.

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>.

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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:Kosmorsky|Kosmorsky]] and made on <tt>2013-05-29 21:43:10 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-05-30 03:52:29 UTC</tt>.<br>
-: The original revision id was <tt>435171490</tt>.<br>
+: The original revision id was <tt>435215878</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. [[Thuja]] temperament is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with MOS of 15 and 28.
+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]].
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 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;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;
+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 &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt; 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;