111edo: Difference between revisions
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Wikispaces>hstraub **Imported revision 239085907 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 239311847 - 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:xenwolf|xenwolf]] and made on <tt>2011-06-29 09:38:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>239311847</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html"> | <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">**111edo** is the [[equal division of the octave]] into 111 parts, each of size 10.81 [[cent]]s. It is [[consistent]] through to the 21 odd limit, and the [[tonality diamond]] is distinct through to the [[15-limit]], marking it as an important higher limit temperament. It is also significant for lower limits, especially in terms of what it tempers out; for example it tempers out 176/175 and gives an excellent [[optimal patent val]] tuning for the corresponding [[11-limit]] rank four temperament. In fact in the [[7-limit]] it tempers out 1728/1715, 3136/3125 and 5120/5103, and in the 11-limit, 1331/1323, 176/175, 1375/1372 and 540/539. It is a particularly good tuning for the 11- or 13- versions of semisept, the 31&111 temperament, and buzzard, the 58&111 temperament. The Trio piece below is in [[Orwellismic family|guanyin temperament]], the [[planar temperament]] [[tempering out]] 176/175 and 540/539, for which 111 also provides the optimal patent val. | ||
=Music= | The prime factorization is | ||
[[math]] | |||
111 = 3 \cdot 37 | |||
[[math]] | |||
== Music == | |||
[[http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297|Trio for SoftSaturn, NebulaSing and TromBonehead]] [[http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3|play]] by [[Gene Ward Smith]]</pre></div> | [[http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297|Trio for SoftSaturn, NebulaSing and TromBonehead]] [[http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3|play]] by [[Gene Ward Smith]]</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>111edo</title></head><body> | <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>111edo</title></head><body><strong>111edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 111 parts, each of size 10.81 <a class="wiki_link" href="/cent">cent</a>s. It is <a class="wiki_link" href="/consistent">consistent</a> through to the 21 odd limit, and the <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> is distinct through to the <a class="wiki_link" href="/15-limit">15-limit</a>, marking it as an important higher limit temperament. It is also significant for lower limits, especially in terms of what it tempers out; for example it tempers out 176/175 and gives an excellent <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> tuning for the corresponding <a class="wiki_link" href="/11-limit">11-limit</a> rank four temperament. In fact in the <a class="wiki_link" href="/7-limit">7-limit</a> it tempers out 1728/1715, 3136/3125 and 5120/5103, and in the 11-limit, 1331/1323, 176/175, 1375/1372 and 540/539. It is a particularly good tuning for the 11- or 13- versions of semisept, the 31&amp;111 temperament, and buzzard, the 58&amp;111 temperament. The Trio piece below is in <a class="wiki_link" href="/Orwellismic%20family">guanyin temperament</a>, the <a class="wiki_link" href="/planar%20temperament">planar temperament</a> <a class="wiki_link" href="/tempering%20out">tempering out</a> 176/175 and 540/539, for which 111 also provides the optimal patent val.<br /> | ||
<br /> | |||
The prime factorization is<br /> | |||
<!-- ws:start:WikiTextMathRule:0: | |||
[[math]]&lt;br/&gt; | |||
111 = 3 \cdot 37&lt;br/&gt;[[math]] | |||
--><script type="math/tex">111 = 3 \cdot 37</script><!-- ws:end:WikiTextMathRule:0 --><br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:1:&lt;h2&gt; --><h2 id="toc0"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:1 --> Music </h2> | |||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297" rel="nofollow">Trio for SoftSaturn, NebulaSing and TromBonehead</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297" rel="nofollow">Trio for SoftSaturn, NebulaSing and TromBonehead</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a></body></html></pre></div> | ||
Revision as of 09:38, 29 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2011-06-29 09:38:20 UTC.
- The original revision id was 239311847.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
**111edo** is the [[equal division of the octave]] into 111 parts, each of size 10.81 [[cent]]s. It is [[consistent]] through to the 21 odd limit, and the [[tonality diamond]] is distinct through to the [[15-limit]], marking it as an important higher limit temperament. It is also significant for lower limits, especially in terms of what it tempers out; for example it tempers out 176/175 and gives an excellent [[optimal patent val]] tuning for the corresponding [[11-limit]] rank four temperament. In fact in the [[7-limit]] it tempers out 1728/1715, 3136/3125 and 5120/5103, and in the 11-limit, 1331/1323, 176/175, 1375/1372 and 540/539. It is a particularly good tuning for the 11- or 13- versions of semisept, the 31&111 temperament, and buzzard, the 58&111 temperament. The Trio piece below is in [[Orwellismic family|guanyin temperament]], the [[planar temperament]] [[tempering out]] 176/175 and 540/539, for which 111 also provides the optimal patent val. The prime factorization is [[math]] 111 = 3 \cdot 37 [[math]] == Music == [[http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297|Trio for SoftSaturn, NebulaSing and TromBonehead]] [[http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3|play]] by [[Gene Ward Smith]]
Original HTML content:
<html><head><title>111edo</title></head><body><strong>111edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 111 parts, each of size 10.81 <a class="wiki_link" href="/cent">cent</a>s. It is <a class="wiki_link" href="/consistent">consistent</a> through to the 21 odd limit, and the <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> is distinct through to the <a class="wiki_link" href="/15-limit">15-limit</a>, marking it as an important higher limit temperament. It is also significant for lower limits, especially in terms of what it tempers out; for example it tempers out 176/175 and gives an excellent <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> tuning for the corresponding <a class="wiki_link" href="/11-limit">11-limit</a> rank four temperament. In fact in the <a class="wiki_link" href="/7-limit">7-limit</a> it tempers out 1728/1715, 3136/3125 and 5120/5103, and in the 11-limit, 1331/1323, 176/175, 1375/1372 and 540/539. It is a particularly good tuning for the 11- or 13- versions of semisept, the 31&111 temperament, and buzzard, the 58&111 temperament. The Trio piece below is in <a class="wiki_link" href="/Orwellismic%20family">guanyin temperament</a>, the <a class="wiki_link" href="/planar%20temperament">planar temperament</a> <a class="wiki_link" href="/tempering%20out">tempering out</a> 176/175 and 540/539, for which 111 also provides the optimal patent val.<br /> <br /> The prime factorization is<br /> <!-- ws:start:WikiTextMathRule:0: [[math]]<br/> 111 = 3 \cdot 37<br/>[[math]] --><script type="math/tex">111 = 3 \cdot 37</script><!-- ws:end:WikiTextMathRule:0 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:1:<h2> --><h2 id="toc0"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:1 --> Music </h2> <br /> <a class="wiki_link_ext" href="http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297" rel="nofollow">Trio for SoftSaturn, NebulaSing and TromBonehead</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a></body></html>