41edo: Difference between revisions

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-02-22 15:50:28 UTC</tt>.<br>

: The original revision id was <tt>204104438</tt>.<br>

<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">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]] &lt;ref&gt;[http://x31eq.com/schismic.htm "Schismic Temperaments "], ''Intonation Information''.&lt;/ref&gt; , the [[http://en.wikipedia.org/wiki/Schismatic_temperament|miracle temperament]], &lt;ref&gt;[http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"], ''Intonation Information''.&lt;/ref&gt; the [[http://en.wikipedia.org/wiki/Magic_temperament|magic temperament]] and the valentine (41&amp;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/%7Enjas/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.

<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;41edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;41 equal temperament&lt;/em&gt;, 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 &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow"&gt;Garibaldi temperament&lt;/a&gt; &lt;!-- ws:start:WikiTextRefRule:1:&amp;amp;lt;ref&amp;amp;gt;[http://x31eq.com/schismic.htm &amp;amp;quot;Schismic Temperaments &amp;amp;quot;], ''Intonation Information''.&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:1 --&gt; , the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow"&gt;miracle temperament&lt;/a&gt;, &lt;!-- ws:start:WikiTextRefRule:3:&amp;amp;lt;ref&amp;amp;gt;[http://x31eq.com/decimal_lattice.htm &amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;], ''Intonation Information''.&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:3 --&gt; the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow"&gt;magic temperament&lt;/a&gt; and the valentine (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of 12-ET, and is the seventh &lt;a class="wiki_link_ext" href="http://www.research.att.com/%7Enjas/sequences/A117538" rel="nofollow"&gt;Zeta integral tuning&lt;/a&gt; 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.&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Harmonic Scale&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Nonoctave Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Nonoctave Temperaments&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Links&lt;/h2&gt;

  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow"&gt;Wikipedia article on 41edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis"&gt;Magic22 as srutis&lt;/a&gt; describes a possible use of 41edo for &lt;a class="wiki_link" href="/indian"&gt;indian&lt;/a&gt; music.&lt;/li&gt;&lt;li&gt;see also &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Sword, Ron.&lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"&gt; &amp;quot;Tetracontamonophonic Scales for Guitar&amp;quot;&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextReferencesRule:2045: --&gt;&lt;hr class="references" /&gt;&lt;ol class="references"&gt;

&lt;/ol&gt;&lt;!-- ws:end:WikiTextReferencesRule:2045 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>