36edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 155970161 - Original comment: ** |
Wikispaces>JinowKeatiuku **Imported revision 163354251 - 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:JinowKeatiuku|JinowKeatiuku]] and made on <tt>2010-09-17 00:39:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>163354251</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> | ||
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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). | 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). | ||
Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale. | |||
==3-limit (Pythagorean) approximations (same as 12edo):== | ==3-limit (Pythagorean) approximations (same as 12edo):== | ||
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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 /> | 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 /> | ||
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Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="As a harmonic temperament-3-limit (Pythagorean) approximations (same as 12edo):"></a><!-- ws:end:WikiTextHeadingRule:2 -->3-limit (Pythagorean) approximations (same as 12edo):</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="As a harmonic temperament-3-limit (Pythagorean) approximations (same as 12edo):"></a><!-- ws:end:WikiTextHeadingRule:2 -->3-limit (Pythagorean) approximations (same as 12edo):</h2> | ||