11edo: Difference between revisions
Wikispaces>guest **Imported revision 196242112 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 201014924 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-02-11 15:48:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>201014924</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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* The "perfect fourth," 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. | * The "perfect fourth," 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. | ||
11edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat | 11edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat with harmonic timbres. | ||
|| Harmonic || 8 || || 9 || || 11 || || 14 || || 16 || | || Harmonic || 8 || || 9 || || 11 || || 14 || || 16 || | ||
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===MOS Scales=== | ===MOS Scales=== | ||
Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11, 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included. | Although 11edo has one fewer interval in the octave than 12edo, in terms of [[MOSScales|moment-of-symmetry scales]], it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11 (two degrees of 11edo), 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included. | ||
2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1. | 2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1. | ||
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See [[11edo Modes]] | See [[11edo Modes]] | ||
===11edo Solfege=== | |||
An 11edo solfege system can easily be applied from the [[22edo solfege]] system. | |||
A chromatic scale would thus be sung: **do ra re me mo fu su lo la te ti do**. | |||
===Compositions=== | ===Compositions=== | ||
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Compared to 12edo, the intervals of 11edo are stretched:<br /> | Compared to 12edo, the intervals of 11edo are stretched:<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 /> | <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 /> | ||
11edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat | 11edo can produce an approximation of an 11-limit JI chord, lacking a third and fifth harmonic: 8:9:11:14:16. The error is rather large, and this chord is sure to beat with harmonic timbres.<br /> | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x11 tone equal temperament--MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->MOS Scales</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x11 tone equal temperament--MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->MOS Scales</h3> | ||
<br /> | <br /> | ||
Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11, 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.<br /> | Although 11edo has one fewer interval in the octave than 12edo, in terms of <a class="wiki_link" href="/MOSScales">moment-of-symmetry scales</a>, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11 (two degrees of 11edo), 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.<br /> | ||
<br /> | <br /> | ||
2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.<br /> | 2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.<br /> | ||
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See <a class="wiki_link" href="/11edo%20Modes">11edo Modes</a><br /> | See <a class="wiki_link" href="/11edo%20Modes">11edo Modes</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x11 tone equal temperament--Compositions"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x11 tone equal temperament--11edo Solfege"></a><!-- ws:end:WikiTextHeadingRule:6 -->11edo Solfege</h3> | ||
<br /> | |||
An 11edo solfege system can easily be applied from the <a class="wiki_link" href="/22edo%20solfege">22edo solfege</a> system.<br /> | |||
A chromatic scale would thus be sung: <strong>do ra re me mo fu su lo la te ti do</strong>.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x11 tone equal temperament--Compositions"></a><!-- ws:end:WikiTextHeadingRule:8 -->Compositions</h3> | |||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow">Turquoise Dabo Girl</a> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (spectrally bent synth ens.)<br /> | <a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow">Turquoise Dabo Girl</a> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (spectrally bent synth ens.)<br /> | ||