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:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-17 20:40:14 UTC</tt>.<br>

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-17 20:41:19 UTC</tt>.<br>

: The original revision id was <tt>~~311993566~~</tt>.<br>

: The original revision id was <tt>311993670</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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<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">=<span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span>=

= =

//43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. It has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]]

//43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]]

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|.

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<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>

<h1 id="toc1"> </h1>

<em>43edo</em> divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. It has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank">Joseph Saveur</a> based his system on 43 equal tones to the octave, calling them &quot;merides&quot;. Further information: <a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow">http://tonalsoft.com/enc/m/meride.aspx</a><br />

<em>43edo</em> divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank">Joseph Saveur</a> based his system on 43 equal tones to the octave, calling them &quot;merides&quot;. Further information: <a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow">http://tonalsoft.com/enc/m/meride.aspx</a><br />

<br />

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 />

@@ 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:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-17 20:40:14 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-17 20:41:19 UTC</tt>.<br>
-: The original revision id was <tt>311993566</tt>.<br>
+: The original revision id was <tt>311993670</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 8: / Line 8: @@
 <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">=&lt;span style="color: #027bac; font-size: 103%;"&gt;43 tone equal temperament&lt;/span&gt;=
 = =
-//43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. It has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]]
+//43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]]
 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|.
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 <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;
   &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h1&gt;
-  &lt;em&gt;43edo&lt;/em&gt; divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. It has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank"&gt;Joseph Saveur&lt;/a&gt; based his system on 43 equal tones to the octave, calling them &amp;quot;merides&amp;quot;. Further information: &lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow"&gt;http://tonalsoft.com/enc/m/meride.aspx&lt;/a&gt;&lt;br /&gt;
+  &lt;em&gt;43edo&lt;/em&gt; divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank"&gt;Joseph Saveur&lt;/a&gt; based his system on 43 equal tones to the octave, calling them &amp;quot;merides&amp;quot;. Further information: &lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow"&gt;http://tonalsoft.com/enc/m/meride.aspx&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 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;