11edo: Difference between revisions
Wikispaces>vaisvil **Imported revision 229421938 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 232644840 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-05-28 22:21:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>232644840</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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=Subgroup= | =Subgroup= | ||
11edo provides the same tuning on the 2.9.15.7.11 | 11edo provides the same tuning on the [[k*N subgroups|2*11 subgroup]] 2.9.15.7.11 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords. | ||
=Intervals= | =Intervals= | ||
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<ul><li>The &quot;minor second,&quot; at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The &quot;major second,&quot; at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a &quot;bluesy&quot; seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The &quot;minor third,&quot; at 327.27 cents, is rather sharp and encroaching upon &quot;neutral third.&quot;</li><li>The &quot;major third,&quot; at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.</li><li>The &quot;perfect fourth,&quot; at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.</li></ul><br /> | <ul><li>The &quot;minor second,&quot; at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>The &quot;major second,&quot; at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less harmonious. Its inversion, at 981.82 cents, can function as a &quot;bluesy&quot; seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.</li><li>The &quot;minor third,&quot; at 327.27 cents, is rather sharp and encroaching upon &quot;neutral third.&quot;</li><li>The &quot;major third,&quot; at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.</li><li>The &quot;perfect fourth,&quot; at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Subgroup"></a><!-- ws:end:WikiTextHeadingRule:5 -->Subgroup</h1> | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Subgroup"></a><!-- ws:end:WikiTextHeadingRule:5 -->Subgroup</h1> | ||
11edo provides the same tuning on the 2.9.15.7.11 | 11edo provides the same tuning on the <a class="wiki_link" href="/k%2AN%20subgroups">2*11 subgroup</a> 2.9.15.7.11 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:7 -->Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:7 -->Intervals</h1> | ||