43edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 312142276 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 431846228 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-05-15 14:49:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>431846228</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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//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]] | //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, [[Meantone family#Septimal | 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 | 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. | ||
43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]]. | 43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]]. | ||
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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> | ||
<h4>Original HTML content:</h4> | <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><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x43 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1> | <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><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x43 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1> | ||
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<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 /> | <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 /> | <br /> | ||
In the 13-limit, we get two versions of meantone equivalent in 43et, one, <a class="wiki_link" href="/Meantone%20family#Septimal | 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 /> | <br /> | ||
The 43 patent val &lt;43 68 100 121 149 | 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 /> | ||
<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 /> | 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">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)</body></html></pre></div> | ||