36edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>2010-08-~~07 12~~:57:51 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-10 15:48:29 UTC</tt>.<br>

: The original revision id was <tt>~~155546299~~</tt>.<br>

: The original revision id was <tt>155970161</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>

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=As a harmonic temperament=

For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since ~~it's~~ nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 & 7. As a 3 & 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [[http://en.wikipedia.org/wiki/Septimal_diesis|Slendro diesis]] of around 36 cents, and as 64:63, the so-called [[http://en.wikipedia.org/wiki/Septimal_comma|septimal comma]] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [[http://en.wikipedia.org/wiki/Septimal_third-tone|Septimal third-tone]] (which = 49:48 x 64:63).

For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since its nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 & 7. As a 3 & 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [[http://en.wikipedia.org/wiki/Septimal_diesis|Slendro diesis]] of around 36 cents, and as 64:63, the so-called [[http://en.wikipedia.org/wiki/Septimal_comma|septimal comma]] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [[http://en.wikipedia.org/wiki/Septimal_third-tone|Septimal third-tone]] (which = 49:48 x 64:63).

==3-limit (Pythagorean) approximations (same as 12edo):==

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<h1 id="toc0"><a name="As a harmonic temperament"></a>As a harmonic temperament</h1>

<br />

For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since ~~it's~~ nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 &amp; 7. As a 3 &amp; 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_diesis" rel="nofollow">Slendro diesis</a> of around 36 cents, and as 64:63, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">septimal comma</a> of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_third-tone" rel="nofollow">Septimal third-tone</a> (which = 49:48 x 64:63).<br />

For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since its nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 &amp; 7. As a 3 &amp; 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_diesis" rel="nofollow">Slendro diesis</a> of around 36 cents, and as 64:63, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">septimal comma</a> of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_third-tone" rel="nofollow">Septimal third-tone</a> (which = 49:48 x 64:63).<br />

<br />

<h2 id="toc1"><a name="As a harmonic temperament-3-limit (Pythagorean) approximations (same as 12edo):"></a>3-limit (Pythagorean) approximations (same as 12edo):</h2>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-08-07 12:57:51 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-10 15:48:29 UTC</tt>.<br>
-: The original revision id was <tt>155546299</tt>.<br>
+: The original revision id was <tt>155970161</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>
@@ Line 14: / Line 14: @@
 =As a harmonic temperament=
-For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since it's nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 &amp; 7. As a 3 &amp; 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [[http://en.wikipedia.org/wiki/Septimal_diesis|Slendro diesis]] of around 36 cents, and as 64:63, the so-called [[http://en.wikipedia.org/wiki/Septimal_comma|septimal comma]] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [[http://en.wikipedia.org/wiki/Septimal_third-tone|Septimal third-tone]] (which = 49:48 x 64:63).
+For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since its nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 &amp; 7. As a 3 &amp; 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [[http://en.wikipedia.org/wiki/Septimal_diesis|Slendro diesis]] of around 36 cents, and as 64:63, the so-called [[http://en.wikipedia.org/wiki/Septimal_comma|septimal comma]] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [[http://en.wikipedia.org/wiki/Septimal_third-tone|Septimal third-tone]] (which = 49:48 x 64:63).
 ==3-limit (Pythagorean) approximations (same as 12edo):==
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 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="As a harmonic temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;As a harmonic temperament&lt;/h1&gt;
   &lt;br /&gt;
-For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since it's nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 &amp;amp; 7. As a 3 &amp;amp; 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_diesis" rel="nofollow"&gt;Slendro diesis&lt;/a&gt; of around 36 cents, and as 64:63, the so-called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;septimal comma&lt;/a&gt; of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_third-tone" rel="nofollow"&gt;Septimal third-tone&lt;/a&gt; (which = 49:48 x 64:63).&lt;br /&gt;
+For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since its nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 &amp;amp; 7. As a 3 &amp;amp; 7 tuning, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_diesis" rel="nofollow"&gt;Slendro diesis&lt;/a&gt; of around 36 cents, and as 64:63, the so-called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;septimal comma&lt;/a&gt; of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_third-tone" rel="nofollow"&gt;Septimal third-tone&lt;/a&gt; (which = 49:48 x 64:63).&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="As a harmonic temperament-3-limit (Pythagorean) approximations (same as 12edo):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;3-limit (Pythagorean) approximations (same as 12edo):&lt;/h2&gt;