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:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 13:02:19 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 13:02:56 UTC</tt>.<br>

: The original revision id was <tt>~~250340494~~</tt>.<br>

: The original revision id was <tt>250340648</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 tempering out 78/77, the other 144/143. The first has generator mapping <0 1 4 10 18 27|, and the second <0 1 4 10 18 -16|.

The 43 patent val <43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|~~jermome~~ temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits.

The 43 patent val <43 68 100 121 149 169| 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.

==Intervals==

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In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping &lt;0 1 4 10 18 27|, and the second &lt;0 1 4 10 18 -16|.<br />

<br />

The 43 patent val &lt;43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to <a class="wiki_link" href="/Meantone%20family#Jerome">~~jermome~~ 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.<br />

The 43 patent val &lt;43 68 100 121 149 169| 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.<br />

<br />

<h2 id="toc2"><a name="x43 tone equal temperament-Intervals"></a>Intervals</h2>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 13:02:19 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 13:02:56 UTC</tt>.<br>
-: The original revision id was <tt>250340494</tt>.<br>
+: The original revision id was <tt>250340648</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 tempering out 78/77, the other 144/143. The first has generator mapping &lt;0 1 4 10 18 27|, and the second &lt;0 1 4 10 18 -16|.
-The 43 patent val &lt;43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jermome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits.
+The 43 patent val &lt;43 68 100 121 149 169| 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.
 ==Intervals==
@@ Line 67: / Line 67: @@
 In the 13-limit, we get two versions of meantone equivalent in 43et, one tempering out 78/77, the other 144/143. The first has generator mapping &amp;lt;0 1 4 10 18 27|, and the second &amp;lt;0 1 4 10 18 -16|.&lt;br /&gt;
 &lt;br /&gt;
-The 43 patent val &amp;lt;43 68 100 121 149 169| 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;jermome 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.&lt;br /&gt;
+The 43 patent val &amp;lt;43 68 100 121 149 169| 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.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x43 tone equal temperament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;