11edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 597692160 - Original comment: removed tel links** |
Wikispaces>TallKite **Imported revision 599950052 - 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:TallKite|TallKite]] and made on <tt>2016-11-21 05:08:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599950052</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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|| degrees of 11edo || cents value (coarse/fine) | || degrees of 11edo || cents value (coarse/fine) | ||
DMS value || solfege || ratios* || Sagittal notation || [[Tútim Dennsuul Wafiil|TDW]] Machine notation || | DMS value || solfege || ratios* || Sagittal | ||
|| 0 || 0.00 || **do** || 1/1 || A || Q\P# || | notation || up/down | ||
notation || [[Tútim Dennsuul Wafiil|TDW]] Machine | |||
notation || | |||
|| 0 || 0.00 || **do** || 1/1 || A || A || Q\P# || | |||
|| 1 || 109.09, 130.91 | || 1 || 109.09, 130.91 | ||
32°43'38" || **ra** || 15/14, 16/15, 17/16, 18/17 || AII\ or B!!/ || Q#\Rb || | 32°43'38" || **ra** || 15/14, 16/15, | ||
17/16, 18/17 || AII\ or B!!/ || B || Q#\Rb || | |||
|| 2 || 218.18, 261.82 | || 2 || 218.18, 261.82 | ||
65°27'16" || **re** || 8/7, 9/8, 17/15 || B || R || | 65°27'16" || **re** || 8/7, 9/8, 17/15 || B || B^, C# || R || | ||
|| 3 || 327.27, 392.73 | || 3 || 327.27, 392.73 | ||
98°10'55" || **me** || 6/5, 11/9, 17/14 || C/I or BII\ or D\!!/ || R#\Sb || | 98°10'55" || **me** || 6/5, 11/9, 17/14 || C/I or BII\ or D\!!/ || Bb, Cv || R#\Sb || | ||
|| 4 || 436.36, 523.64 | || 4 || 436.36, 523.64 | ||
120°54'33" || **mo** || 9/7, 14/11, 22/17 || D\! or C/II\ || S || | 120°54'33" || **mo** || 9/7, 14/11, 22/17 || D\! or C/II\ || C || S || | ||
|| 5 || 545.455, 654.545 | || 5 || 545.455, 654.545 | ||
163°38'11" || **fu** || 11/8, 15/11 || D/I or E\!!/ || S#\Tb || | 163°38'11" || **fu** || 11/8, 15/11 || D/I or E\!!/ || D || S#\Tb || | ||
|| 6 || 654.545, 785.455 | || 6 || 654.545, 785.455 | ||
196°21'49" || **su** || 16/11, 22/15 || E\! or D/II\ || T || | 196°21'49" || **su** || 16/11, 22/15 || E\! or D/II\ || E || T || | ||
|| 7 || 763.64, 916.36 | || 7 || 763.64, 916.36 | ||
229°5'27" || **lo** || 11/7, 14/9, 17/11 || F || T#\Ub || | 229°5'27" || **lo** || 11/7, 14/9, 17/11 || F || E^, F# || T#\Ub || | ||
|| 8 || 872.73, 1047.27 | || 8 || 872.73, 1047.27 | ||
261°49'5" || **la** || 5/3, 18/11, 28/17 || FII\ or G!!/ || U || | 261°49'5" || **la** || 5/3, 18/11, 28/17 || FII\ or G!!/ || Eb, Fv || U || | ||
|| 9 || 981.82, 1178.18 | || 9 || 981.82, 1178.18 | ||
294°31'44" || **ta** || 7/4, 16/9, 30/17 || G || U#\Pb || | 294°31'44" || **ta** || 7/4, 16/9, 30/17 || G || F || U#\Pb || | ||
|| 10 || 1090.91, 1309.09 | || 10 || 1090.91, 1309.09 | ||
327°16'22" || **ti** || 15/8, 17/9, 28/15, 32/17 || GII\ or A!!/ || P\Qb || | 327°16'22" || **ti** || 15/8, 17/9, | ||
28/15, 32/17 || GII\ or A!!/ || G || P\Qb || | |||
*in 2.7.9.11.15.17 subgroup | *in 2.7.9.11.15.17 subgroup | ||
For alternative notations, see [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs|Ups and Downs Notation -"Superflat" EDOs]] and [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]]. | |||
=MOS Scales= | =MOS Scales= | ||
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. | 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. | ||
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11edo also may be considered a 2.7.9.11.15.17 subgroup temperament. See diagram:<br /> | 11edo also may be considered a 2.7.9.11.15.17 subgroup temperament. See diagram:<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:565:&lt;img src=&quot;/file/view/11edo_approx_2-7-9-11-15-17_2ndsave.png/284598982/11edo_approx_2-7-9-11-15-17_2ndsave.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/11edo_approx_2-7-9-11-15-17_2ndsave.png/284598982/11edo_approx_2-7-9-11-15-17_2ndsave.png" alt="11edo_approx_2-7-9-11-15-17_2ndsave.png" title="11edo_approx_2-7-9-11-15-17_2ndsave.png" /><!-- ws:end:WikiTextLocalImageRule:565 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="Intervals-11 edo solfege"></a><!-- ws:end:WikiTextHeadingRule:11 -->11 edo solfege</h2> | <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="Intervals-11 edo solfege"></a><!-- ws:end:WikiTextHeadingRule:11 -->11 edo solfege</h2> | ||
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<td>ratios*<br /> | <td>ratios*<br /> | ||
</td> | </td> | ||
<td>Sagittal notation<br /> | <td>Sagittal <br /> | ||
notation<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a> Machine notation<br /> | <td>up/down<br /> | ||
notation<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a> Machine<br /> | |||
notation<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 346: | Line 359: | ||
</td> | </td> | ||
<td>1/1<br /> | <td>1/1<br /> | ||
</td> | |||
<td>A<br /> | |||
</td> | </td> | ||
<td>A<br /> | <td>A<br /> | ||
| Line 360: | Line 375: | ||
<td><strong>ra</strong><br /> | <td><strong>ra</strong><br /> | ||
</td> | </td> | ||
<td>15/14, 16/15, 17/16, 18/17<br /> | <td>15/14, 16/15, <br /> | ||
17/16, 18/17<br /> | |||
</td> | </td> | ||
<td>AII\ or B!!/<br /> | <td>AII\ or B!!/<br /> | ||
</td> | |||
<td>B<br /> | |||
</td> | </td> | ||
<td>Q#\Rb<br /> | <td>Q#\Rb<br /> | ||
| Line 378: | Line 396: | ||
</td> | </td> | ||
<td>B<br /> | <td>B<br /> | ||
</td> | |||
<td>B^, C#<br /> | |||
</td> | </td> | ||
<td>R<br /> | <td>R<br /> | ||
| Line 393: | Line 413: | ||
</td> | </td> | ||
<td>C/I or BII\ or D\!!/<br /> | <td>C/I or BII\ or D\!!/<br /> | ||
</td> | |||
<td>Bb, Cv<br /> | |||
</td> | </td> | ||
<td>R#\Sb<br /> | <td>R#\Sb<br /> | ||
| Line 408: | Line 430: | ||
</td> | </td> | ||
<td>D\! or C/II\<br /> | <td>D\! or C/II\<br /> | ||
</td> | |||
<td>C<br /> | |||
</td> | </td> | ||
<td>S<br /> | <td>S<br /> | ||
| Line 423: | Line 447: | ||
</td> | </td> | ||
<td>D/I or E\!!/<br /> | <td>D/I or E\!!/<br /> | ||
</td> | |||
<td>D<br /> | |||
</td> | </td> | ||
<td>S#\Tb<br /> | <td>S#\Tb<br /> | ||
| Line 438: | Line 464: | ||
</td> | </td> | ||
<td>E\! or D/II\<br /> | <td>E\! or D/II\<br /> | ||
</td> | |||
<td>E<br /> | |||
</td> | </td> | ||
<td>T<br /> | <td>T<br /> | ||
| Line 453: | Line 481: | ||
</td> | </td> | ||
<td>F<br /> | <td>F<br /> | ||
</td> | |||
<td>E^, F#<br /> | |||
</td> | </td> | ||
<td>T#\Ub<br /> | <td>T#\Ub<br /> | ||
| Line 468: | Line 498: | ||
</td> | </td> | ||
<td>FII\ or G!!/<br /> | <td>FII\ or G!!/<br /> | ||
</td> | |||
<td>Eb, Fv<br /> | |||
</td> | </td> | ||
<td>U<br /> | <td>U<br /> | ||
| Line 483: | Line 515: | ||
</td> | </td> | ||
<td>G<br /> | <td>G<br /> | ||
</td> | |||
<td>F<br /> | |||
</td> | </td> | ||
<td>U#\Pb<br /> | <td>U#\Pb<br /> | ||
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<td><strong>ti</strong><br /> | <td><strong>ti</strong><br /> | ||
</td> | </td> | ||
<td>15/8, 17/9, 28/15, 32/17<br /> | <td>15/8, 17/9, <br /> | ||
28/15, 32/17<br /> | |||
</td> | </td> | ||
<td>GII\ or A!!/<br /> | <td>GII\ or A!!/<br /> | ||
</td> | |||
<td>G<br /> | |||
</td> | </td> | ||
<td>P\Qb<br /> | <td>P\Qb<br /> | ||
| Line 505: | Line 542: | ||
*in 2.7.9.11.15.17 subgroup<br /> | *in 2.7.9.11.15.17 subgroup<br /> | ||
<br /> | |||
For alternative notations, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs">Ups and Downs Notation -&quot;Superflat&quot; EDOs</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs">Ups and Downs Notation -&quot;Supersharp&quot; EDOs</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a>.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:13 -->MOS Scales</h1> | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:13 -->MOS Scales</h1> | ||
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 /> | 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 /> | ||
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<ul><li><span class="ymp-btn-page-play ymp-media-2b0ac7aee582cc2952d261655b7ab213"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AhPjsCoMy-Q" rel="nofollow">11-equal Improvisation</a></em></span></span></span>, <a class="wiki_link" href="/Mike%20Battaglia%20FAQ">Mike Battaglia</a> - youtube</li></ul><!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc12"><a name="Compositions-Instruments"></a><!-- ws:end:WikiTextHeadingRule:25 -->Instruments</h2> | <ul><li><span class="ymp-btn-page-play ymp-media-2b0ac7aee582cc2952d261655b7ab213"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AhPjsCoMy-Q" rel="nofollow">11-equal Improvisation</a></em></span></span></span>, <a class="wiki_link" href="/Mike%20Battaglia%20FAQ">Mike Battaglia</a> - youtube</li></ul><!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc12"><a name="Compositions-Instruments"></a><!-- ws:end:WikiTextHeadingRule:25 -->Instruments</h2> | ||
<br /> | <br /> | ||
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