111edo
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- This revision was by author xenwolf and made on 2011-06-29 09:38:20 UTC.
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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>