41edo
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- This revision was by author genewardsmith and made on 2010-05-26 18:13:48 UTC.
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Original Wikitext content:
The //41 equal temperament//, often abbreviated 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.27 cents, an interval close in size to 64/63, the [[http://en.wikipedia.org/wiki/Septimal_comma|septimal comma]]. 41-ET can be seen as a tuning of the [[http://en.wikipedia.org/wiki/Schismatic_temperament|Garibaldi temperament]] <ref>[http://x31eq.com/schismic.htm "Schismic Temperaments "], ''Intonation Information''.</ref>, the [[http://en.wikipedia.org/wiki/Schismatic_temperament|miracle temperament]], <ref>[http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"], ''Intonation Information''.</ref> the [[http://en.wikipedia.org/wiki/Magic_temperament|magic temperament]] and the valentine (41&26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of 12-ET, and is the seventh [[http://www.research.att.com/~njas/sequences/A117538|Zeta integral tuning]] after 31. The latter has to do with the fact that it can deal with the 11-limit fairly well, and the 13-limit perhaps close enough for government work, though its 13/10 is 14 cents sharp. ==Links== [[http://en.wikipedia.org/wiki/41_equal_temperament|Wikipedia article on 41edo]] [[Magic22 as srutis#magic22assrutis]] describes a possible use of 41edo for [[indian]] music.
Original HTML content:
<html><head><title>41edo</title></head><body>The <em>41 equal temperament</em>, often abbreviated 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.27 cents, an interval close in size to 64/63, the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">septimal comma</a>. 41-ET can be seen as a tuning of the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Garibaldi temperament</a> <!-- ws:start:WikiTextRefRule:1:&lt;ref&gt;[http://x31eq.com/schismic.htm &quot;Schismic Temperaments &quot;], ''Intonation Information''.&lt;/ref&gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:1 -->, the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">miracle temperament</a>, <!-- ws:start:WikiTextRefRule:3:&lt;ref&gt;[http://x31eq.com/decimal_lattice.htm &quot;Lattices with Decimal Notation&quot;], ''Intonation Information''.&lt;/ref&gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:3 --> the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">magic temperament</a> and the valentine (41&26) temperament. It is the second smallest equal temperament (after <a class="wiki_link" href="/29edo">29edo</a>) whose perfect fifth is closer to just intonation than that of 12-ET, and is the seventh <a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">Zeta integral tuning</a> after 31. The latter has to do with the fact that it can deal with the 11-limit fairly well, and the 13-limit perhaps close enough for government work, though its 13/10 is 14 cents sharp.<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc0"><a name="x-Links"></a><!-- ws:end:WikiTextHeadingRule:4 -->Links</h2> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a><br /> <br /> <a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.<!-- ws:start:WikiTextReferencesRule:22: --><hr class="references" /><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> [<a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">http://x31eq.com/schismic.htm</a> "Schismic Temperaments "], ''Intonation Information''.</li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> [<a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">http://x31eq.com/decimal_lattice.htm</a> "Lattices with Decimal Notation"], ''Intonation Information''.</li> </ol><!-- ws:end:WikiTextReferencesRule:22 --></body></html>