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Wikispaces>JosephRuhf
**Imported revision 597475228 - Original comment: **
Wikispaces>TallKite
**Imported revision 599950462 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-30 07:03:59 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 05:14:28 UTC</tt>.<br>
: The original revision id was <tt>597475228</tt>.<br>
: The original revision id was <tt>599950462</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>
Line 17: Line 17:
|| Degree || Cents (coarse and fine)
|| Degree || Cents (coarse and fine)
DMS || Approximate
DMS || Approximate
Ratios* || Additional Ratios of 3, 5 and 9 || Name ||
Ratios* || Additional Ratios  
|| 0 || 0, 0° || 1/1 || 256/243, 50/49, 25/24 || unison ||
of 3, 5 and 9 || Interval Names || [[Ups and Downs Notation|up/down]]
[[Ups and Downs Notation|notation]] ||
|| 0 || 0, 0° || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||
|| 1 || 120, 144
|| 1 || 120, 144
36° || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second ||
36° || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second,
|| 2 || 240, 288, 72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third ||
large minor second || mid 2nd ||
|| 3 || 360, 432, 108° || 16/13 || 5/4 || large neutral third ||
|| 2 || 240, 288, 72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || M2, m3 ||
|| 4 || 480, 576, 144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||
|| 3 || 360, 432, 108° || 16/13 || 5/4 || large neutral third || mid 3rd ||
|| 4 || 480, 576, 144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || M3, P4 ||
|| 5 || 600, 720
|| 5 || 600, 720
180° || 91/64, 128/91, 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone ||
180° || 91/64, 128/91,  
|| 6 || 720, 864, 216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||
169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th,
|| 7 || 840, 1008, 252° || 13/8 || 8/5 || neutral sixth ||
down 5th ||
|| 8 || 960, 1152, 288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||
|| 6 || 720, 864, 216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || P5, m6 ||
|| 9 || 1080, 1296, 324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th ||
|| 7 || 840, 1008, 252° || 13/8 || 8/5 || neutral sixth || mid 6th ||
|| 10 || 1200, 1440, 360° || 2/1 || 243/128, 49/25, 48/25 || octave ||
|| 8 || 960, 1152, 288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || M6, m7 ||
|| 9 || 1080, 1296, 324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||
|| 10 || 1200, 1440, 360° || 2/1 || 243/128, 49/25, 48/25 || octave || 8ve ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.
For alternative notations, see [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs|Ups and Downs Notation -"Pentatonic" EDOs]] and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]].


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Ratios*&lt;br /&gt;
Ratios*&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Additional Ratios of 3, 5 and 9&lt;br /&gt;
         &lt;td&gt;Additional Ratios &lt;br /&gt;
of 3, 5 and 9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Interval Names&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Name&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;up/down&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;256/243, 50/49, 25/24&lt;br /&gt;
         &lt;td&gt;256/243, 50/49, 25/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;unison&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;unison&lt;br /&gt;
         &lt;td&gt;unison&lt;br /&gt;
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         &lt;td&gt;10/9, 13/12, 81/80&lt;br /&gt;
         &lt;td&gt;10/9, 13/12, 81/80&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small neutral second/large minor second&lt;br /&gt;
         &lt;td&gt;small neutral second,&lt;br /&gt;
large minor second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 2nd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;second/third&lt;br /&gt;
         &lt;td&gt;second/third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;M2, m3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;large neutral third&lt;br /&gt;
         &lt;td&gt;large neutral third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 3rd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;smaller fourth&lt;br /&gt;
         &lt;td&gt;smaller fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;M3, P4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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180°&lt;br /&gt;
180°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;91/64, 128/91, 169/120, 240/169&lt;br /&gt;
         &lt;td&gt;91/64, 128/91, &lt;br /&gt;
169/120, 240/169&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7/5, 10/7, 13/9, 18/13&lt;br /&gt;
         &lt;td&gt;7/5, 10/7, 13/9, 18/13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;tritone&lt;br /&gt;
         &lt;td&gt;tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;up 4th,&lt;br /&gt;
down 5th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;bigger fifth&lt;br /&gt;
         &lt;td&gt;bigger fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P5, m6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;neutral sixth&lt;br /&gt;
         &lt;td&gt;neutral sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 6th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;sixth/seventh&lt;br /&gt;
         &lt;td&gt;sixth/seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;M6, m7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small major 7th&lt;br /&gt;
         &lt;td&gt;small major 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 7th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;octave&lt;br /&gt;
         &lt;td&gt;octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8ve&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.&lt;br /&gt;
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.&lt;br /&gt;
adding the ratios of 3, 5 and 9 introduces greater &lt;a class="wiki_link" href="/error"&gt;error&lt;/a&gt; while giving several more harmonic identities to the 10-EDO intervals.&lt;br /&gt;
adding the ratios of 3, 5 and 9 introduces greater &lt;a class="wiki_link" href="/error"&gt;error&lt;/a&gt; while giving several more harmonic identities to the 10-EDO intervals.&lt;br /&gt;
&lt;br /&gt;
For alternative notations, see &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs"&gt;Ups and Downs Notation -&amp;quot;Pentatonic&amp;quot; EDOs&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators"&gt;Ups and Downs Notation - Natural Generators&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Smooth10.mp3" rel="nofollow"&gt;Smooth 10&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/65405f5999f3960d5704b83c7318c673-170.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Smooth10.mp3" rel="nofollow"&gt;Smooth 10&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/65405f5999f3960d5704b83c7318c673-170.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
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&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:565:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@10preview.ogg&amp;quot; title=&amp;quot;File: 10preview.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');" class="filename" title="10preview.ogg"&gt;10preview.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/10preview.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;3 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:565 --&gt; A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:589:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@10preview.ogg&amp;quot; title=&amp;quot;File: 10preview.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');" class="filename" title="10preview.ogg"&gt;10preview.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/10preview.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;3 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:589 --&gt; A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:566:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/decexperiment.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@decexperiment.ogg&amp;quot; title=&amp;quot;File: decexperiment.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="decexperiment.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');" class="filename" title="decexperiment.ogg"&gt;decexperiment.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/decexperiment.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;2 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:566 --&gt;3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:590:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/decexperiment.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@decexperiment.ogg&amp;quot; title=&amp;quot;File: decexperiment.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="decexperiment.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');" class="filename" title="decexperiment.ogg"&gt;decexperiment.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/decexperiment.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;2 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:590 --&gt;3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)&lt;br /&gt;
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3" rel="nofollow"&gt;10 Earwigs Invasive&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1397" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3" rel="nofollow"&gt;10 Earwigs Invasive&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1397" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 9&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;br /&gt;
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 9&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;br /&gt;
Line 710: Line 748:
Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt; which approximates the 11th harmonic with relative accuracy, among other features.&lt;br /&gt;
Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt; which approximates the 11th harmonic with relative accuracy, among other features.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:562:&amp;lt;img src=&amp;quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&amp;quot; alt=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; title=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;A Decaphonic (10-EDO) Classical Guitar&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:562 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:563:&amp;lt;img src=&amp;quot;/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 406px; width: 526px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:563 --&gt;&lt;!-- ws:start:WikiTextMediaRule:2:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10021077&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:586:&amp;lt;img src=&amp;quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&amp;quot; alt=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; title=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;A Decaphonic (10-EDO) Classical Guitar&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:586 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:587:&amp;lt;img src=&amp;quot;/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 406px; width: 526px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:587 --&gt;&lt;!-- ws:start:WikiTextMediaRule:2:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10021077&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:2 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:2 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 05:14, 21 November 2016

IMPORTED REVISION FROM WIKISPACES

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This revision was by author TallKite and made on 2016-11-21 05:14:28 UTC.
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<span style="display: block; text-align: right;">[[10平均律|日本語]]
</span>
10edo, or 10-tone equal temperament, is a tuning system which divides the [[octave]] into 10 equal parts of exactly 120 [[cent]]s. It can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13_8|13/8]] and its inversion [[16_13|16/13]]; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOSScales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]]. One way to interpret it in terms of a temperament of Just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.

[[toc|flat]]
----

=[[media type="custom" key="10886138"]]= 
=Intervals= 
|| Degree || Cents (coarse and fine)
DMS || Approximate
Ratios* || Additional Ratios 
of 3, 5 and 9 || Interval Names || [[Ups and Downs Notation|up/down]]
[[Ups and Downs Notation|notation]] ||
|| 0 || 0, 0° || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||
|| 1 || 120, 144
36° || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second,
large minor second || mid 2nd ||
|| 2 || 240, 288, 72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || M2, m3 ||
|| 3 || 360, 432, 108° || 16/13 || 5/4 || large neutral third || mid 3rd ||
|| 4 || 480, 576, 144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || M3, P4 ||
|| 5 || 600, 720
180° || 91/64, 128/91, 
169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th,
down 5th ||
|| 6 || 720, 864, 216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || P5, m6 ||
|| 7 || 840, 1008, 252° || 13/8 || 8/5 || neutral sixth || mid 6th ||
|| 8 || 960, 1152, 288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || M6, m7 ||
|| 9 || 1080, 1296, 324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||
|| 10 || 1200, 1440, 360° || 2/1 || 243/128, 49/25, 48/25 || octave || 8ve ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.

For alternative notations, see [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs|Ups and Downs Notation -"Pentatonic" EDOs]] and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]].

[[media type="custom" key="24802496"]]

[[file:10ed2-001.svg]]

=Images= 

[[image:10edo wheel.png width="280" height="285"]]

=Linear temperaments= 
||~ Periods
per octave ||~ Generator ||~ Temperament(s) ||
|| 1 || 1\10 || Messed-up [[Negri|negri]] (or [[Miracle|miracle]]) ||
|| 1 || 3\10 || [[Dicot]]/[[Beatles|beatles]]/neutral thirds scale ||
|| 2 || 1\10 || Messed-up [[pajara]] ||
|| 2 || 2\10 || [[Decimal]] / messed-up [[Lemba|lemba]] ||
|| 5 || 1\10 || [[Blackwood]]/[[blacksmith]] ||
=Commas= 
10 EDO tempers out the following commas. (Note: This assumes the val < 10 16 23 28 35 37 |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 || | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||   ||
||= 25/24 || | -3 -1 2 > ||> 70.67 ||= 5-limit large semitone ||= 5-limit chromatic semitone ||   ||
||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||   ||
||= 9931568/9752117 || | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||=   ||   ||
||= 2048/2025 || | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||=   ||   ||
||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicennma's Enharmonic Diesis ||   ||
||= 49/48 || | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||=   ||   ||
||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||   ||
||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||=   ||   ||
||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma ||
||= 9859966/9733137 || | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||=   ||   ||
||= 1029/1024 || | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||=   ||   ||
||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma ||   ||
||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||=   ||   ||
||= 6772805/6751042 || | 11 -10 -10 10 > ||> 5.57 ||= Linus ||=   ||   ||
||= 2401/2400 || | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||=   ||   ||
||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||=   ||   ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||   ||
||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||=   ||   ||
||= 540/539 || | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||=   ||   ||
||= 3025/3024 || | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||=   ||   ||
||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||=   ||   ||
||= 676/675 || | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||=   ||   ||
=Music= 
[[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Ten Fingers]] <span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3|play]]//</span></span> by [[Bill Sethares]] (synth guitar)
[[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Circle of Thirds]] <span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3|play]]//</span></span> by Bill Sethares (synth ens.)
[[http://www.akjmusic.com/works.html|10_fantasy]] <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/AKJ/10_fantasy.mp3|play]]//</span></span> by [[Aaron Krister Johnson]] (synth monody)
<span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2010ET.mp3|Prelude in 10ET]]//</span></span> by [[Aaron Andrew Hunt]]
[[http://www.ziaspace.com/ZIA/mp3s/Future.html|Future]] <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://ziaspace.com/ZIA/mp3s/Future.mp3|play]]//</span></span> and [[http://www.ziaspace.com/ZIA/mp3s/Sol.html|Sol]] <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://ziaspace.com/ZIA/mp3s/Sol.mp3|play]]//</span></span> by ZIA (synths and voice in 10)
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3|Prelude]]//</span></span> by [[Rick McGowan]] (Rhino synthesizer)
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3|Ideas on the Waterfall of Expression]]//</span></span> by Igliashon Jones (synth)
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3|For two violas and gongs]]//</span></span> by [[@http://www.chrisvaisvil.com|Chris Vaisvil (website)]] [[@http://chrisvaisvil.com/?p=1039|more composition information]]
//[[http://www.seraph.it/dep/det/Blues10.mp3|Blues 10]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/dd7ee3a756851e812778e2fb222b5c47-168.html|blog entry]])
//[[http://www.seraph.it/dep/det/Waltz10.mp3|Waltz 10]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/875fbcf1467c4ed837ac1ba4b666d417-169.html|blog entry]])
//[[http://www.seraph.it/dep/det/Smooth10.mp3|Smooth 10]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/65405f5999f3960d5704b83c7318c673-170.html|blog entry]])

[[file:10preview.ogg]] A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)
[[file:decexperiment.ogg]]3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3|10 Earwigs Invasive]]//</span> by [[@http://chrisvaisvil.com/?p=1397|Chris Vaisvil]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3|Comets Over Flatland 9]]//</span> by [[Randy Winchester]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3|The Dramatic Squirrel Overture]]//</span> by [[Chris Vaisvil]] [[@http://chrisvaisvil.com/?p=1368|Details]]
[[@http://andrewheathwaite.bandcamp.com/track/shimmerwing|Shimmerwing]] by [[Andrew Heathwaite]] and [[Chris Vaisvil]]
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20The%20Csx%20Freight%20at%201-20%20am.mp3|The Csx Freight at 1:20 am]]// by [[Zach Curley]]
[[http://soundcloud.com/martinsj013/sirmdbidnud2|Sirmdbidnud2 by martinsj013 on SoundCloud]]
[[@https://soundcloud.com/clem-fortuna/10tone|10tone demo]] by [[@http://clemfortuna.com|Clem Fortuna]]

=**Instruments**= 

10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.

Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from [[20edo]] which approximates the 11th harmonic with relative accuracy, among other features.

[[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[image:decaphonic-uke.JPG width="526" height="406"]][[media type="custom" key="10021077"]]

Original HTML content:

<html><head><title>10edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/10%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
</span><br />
10edo, or 10-tone equal temperament, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 10 equal parts of exactly 120 <a class="wiki_link" href="/cent">cent</a>s. It can be thought of as two circles of <a class="wiki_link" href="/5edo">5edo</a> separated by 120 cents (or 5 circles of <a class="wiki_link" href="/2edo">2edo</a>). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of <a class="wiki_link" href="/13_8">13/8</a> and its inversion <a class="wiki_link" href="/16_13">16/13</a>; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic <a class="wiki_link" href="/MOSScales">moment of symmetry scale</a> of the form 1 2 1 2 1 2 1 (<a class="wiki_link" href="/3L%204s">3L 4s - mosh</a>). While not an integral or gap edo, it is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak edo</a>. One way to interpret it in terms of a temperament of Just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.<br />
<br />
<!-- ws:start:WikiTextTocRule:17:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><a href="#toc0"></a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Images">Images</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: -->
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<br />
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<table class="wiki_table">
    <tr>
        <td>Degree<br />
</td>
        <td>Cents (coarse and fine)<br />
DMS<br />
</td>
        <td>Approximate<br />
Ratios*<br />
</td>
        <td>Additional Ratios <br />
of 3, 5 and 9<br />
</td>
        <td>Interval Names<br />
</td>
        <td><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down</a><br />
<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0, 0°<br />
</td>
        <td>1/1<br />
</td>
        <td>256/243, 50/49, 25/24<br />
</td>
        <td>unison<br />
</td>
        <td>unison<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>120, 144<br />
36°<br />
</td>
        <td>16/15, 15/14, 13/14<br />
</td>
        <td>10/9, 13/12, 81/80<br />
</td>
        <td>small neutral second,<br />
large minor second<br />
</td>
        <td>mid 2nd<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>240, 288, 72°<br />
</td>
        <td>8/7, 15/13, 144/125<br />
</td>
        <td>9/8, 7/6<br />
</td>
        <td>second/third<br />
</td>
        <td>M2, m3<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>360, 432, 108°<br />
</td>
        <td>16/13<br />
</td>
        <td>5/4<br />
</td>
        <td>large neutral third<br />
</td>
        <td>mid 3rd<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>480, 576, 144°<br />
</td>
        <td>64/49, 169/128<br />
</td>
        <td>4/3, 9/7, 13/10<br />
</td>
        <td>smaller fourth<br />
</td>
        <td>M3, P4<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>600, 720<br />
180°<br />
</td>
        <td>91/64, 128/91, <br />
169/120, 240/169<br />
</td>
        <td>7/5, 10/7, 13/9, 18/13<br />
</td>
        <td>tritone<br />
</td>
        <td>up 4th,<br />
down 5th<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>720, 864, 216°<br />
</td>
        <td>49/32, 256/169<br />
</td>
        <td>3/2, 14/9, 20/13<br />
</td>
        <td>bigger fifth<br />
</td>
        <td>P5, m6<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>840, 1008, 252°<br />
</td>
        <td>13/8<br />
</td>
        <td>8/5<br />
</td>
        <td>neutral sixth<br />
</td>
        <td>mid 6th<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>960, 1152, 288°<br />
</td>
        <td>7/4, 26/15, 125/72<br />
</td>
        <td>16/9, 12/7<br />
</td>
        <td>sixth/seventh<br />
</td>
        <td>M6, m7<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1080, 1296, 324°<br />
</td>
        <td>15/8, 28/15, 13/7<br />
</td>
        <td>9/5, 24/13, 160/81<br />
</td>
        <td>small major 7th<br />
</td>
        <td>mid 7th<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>1200, 1440, 360°<br />
</td>
        <td>2/1<br />
</td>
        <td>243/128, 49/25, 48/25<br />
</td>
        <td>octave<br />
</td>
        <td>8ve<br />
</td>
    </tr>
</table>

*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.<br />
adding the ratios of 3, 5 and 9 introduces greater <a class="wiki_link" href="/error">error</a> while giving several more harmonic identities to the 10-EDO intervals.<br />
<br />
For alternative notations, see <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs">Ups and Downs Notation -&quot;Pentatonic&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 />
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc2"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:7 -->Images</h1>
 <br />
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:9 -->Linear temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Temperament(s)<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\10<br />
</td>
        <td>Messed-up <a class="wiki_link" href="/Negri">negri</a> (or <a class="wiki_link" href="/Miracle">miracle</a>)<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>3\10<br />
</td>
        <td><a class="wiki_link" href="/Dicot">Dicot</a>/<a class="wiki_link" href="/Beatles">beatles</a>/neutral thirds scale<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>1\10<br />
</td>
        <td>Messed-up <a class="wiki_link" href="/pajara">pajara</a><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>2\10<br />
</td>
        <td><a class="wiki_link" href="/Decimal">Decimal</a> / messed-up <a class="wiki_link" href="/Lemba">lemba</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>1\10<br />
</td>
        <td><a class="wiki_link" href="/Blackwood">Blackwood</a>/<a class="wiki_link" href="/blacksmith">blacksmith</a><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1>
 10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>Value (Cents)<br />
</th>
        <th>Name 1<br />
</th>
        <th>Name 2<br />
</th>
        <th>Name 3<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">256/243<br />
</td>
        <td>| 8 -5 &gt;<br />
</td>
        <td style="text-align: right;">90.22<br />
</td>
        <td style="text-align: center;">Limma<br />
</td>
        <td style="text-align: center;">Pythagorean Minor 2nd<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25/24<br />
</td>
        <td>| -3 -1 2 &gt;<br />
</td>
        <td style="text-align: right;">70.67<br />
</td>
        <td style="text-align: center;">5-limit large semitone<br />
</td>
        <td style="text-align: center;">5-limit chromatic semitone<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16384<br />
</td>
        <td>| -14 3 4 &gt;<br />
</td>
        <td style="text-align: right;">51.12<br />
</td>
        <td style="text-align: center;">Negri Comma<br />
</td>
        <td style="text-align: center;">Double Augmentation Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9931568/9752117<br />
</td>
        <td>| -25 7 6 &gt;<br />
</td>
        <td style="text-align: right;">31.57<br />
</td>
        <td style="text-align: center;">Ampersand's Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2048/2025<br />
</td>
        <td>| 11 -4 -2 &gt;<br />
</td>
        <td style="text-align: right;">19.55<br />
</td>
        <td style="text-align: center;">Diaschisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">525/512<br />
</td>
        <td>| -9 1 2 1 &gt;<br />
</td>
        <td style="text-align: right;">43.41<br />
</td>
        <td style="text-align: center;">Avicennma<br />
</td>
        <td style="text-align: center;">Avicennma's Enharmonic Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td>| -4 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">35.70<br />
</td>
        <td style="text-align: center;">Slendro Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50/49<br />
</td>
        <td>| 1 0 2 -2 &gt;<br />
</td>
        <td style="text-align: right;">34.98<br />
</td>
        <td style="text-align: center;">Tritonic Diesis<br />
</td>
        <td style="text-align: center;">Jubilisma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">686/675<br />
</td>
        <td>| 1 -3 -2 3 &gt;<br />
</td>
        <td style="text-align: right;">27.99<br />
</td>
        <td style="text-align: center;">Senga<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td>| 6 -2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">27.26<br />
</td>
        <td style="text-align: center;">Septimal Comma<br />
</td>
        <td style="text-align: center;">Archytas' Comma<br />
</td>
        <td>Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9859966/9733137<br />
</td>
        <td>| -10 7 8 -7 &gt;<br />
</td>
        <td style="text-align: right;">22.41<br />
</td>
        <td style="text-align: center;">Blackjackisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1024<br />
</td>
        <td>| -10 1 0 3 &gt;<br />
</td>
        <td style="text-align: right;">8.43<br />
</td>
        <td style="text-align: center;">Gamelisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">225/224<br />
</td>
        <td>| -5 2 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">7.71<br />
</td>
        <td style="text-align: center;">Septimal Kleisma<br />
</td>
        <td style="text-align: center;">Marvel Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16807<br />
</td>
        <td>| 0 3 4 -5 &gt;<br />
</td>
        <td style="text-align: right;">6.99<br />
</td>
        <td style="text-align: center;">Mirkwai<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6772805/6751042<br />
</td>
        <td>| 11 -10 -10 10 &gt;<br />
</td>
        <td style="text-align: right;">5.57<br />
</td>
        <td style="text-align: center;">Linus<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2401/2400<br />
</td>
        <td>| -5 -1 -2 4 &gt;<br />
</td>
        <td style="text-align: right;">0.72<br />
</td>
        <td style="text-align: center;">Breedsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">243/242<br />
</td>
        <td>| -1 5 0 0 -2 &gt;<br />
</td>
        <td style="text-align: right;">7.14<br />
</td>
        <td style="text-align: center;">Rastma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.93<br />
</td>
        <td style="text-align: center;">Werckisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">540/539<br />
</td>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.21<br />
</td>
        <td style="text-align: center;">Swetisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3025/3024<br />
</td>
        <td>| -4 -3 2 -1 2 &gt;<br />
</td>
        <td style="text-align: right;">0.57<br />
</td>
        <td style="text-align: center;">Lehmerisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td>| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td style="text-align: right;">19.13<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td>| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td style="text-align: right;">2.56<br />
</td>
        <td style="text-align: center;">Parizeksma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:13 -->Music</h1>
 <a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Ten Fingers</a> <span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3" rel="nofollow">play</a></em></span></span> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (synth guitar)<br />
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Circle of Thirds</a> <span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3" rel="nofollow">play</a></em></span></span> by Bill Sethares (synth ens.)<br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">10_fantasy</a> <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/AKJ/10_fantasy.mp3" rel="nofollow">play</a></em></span></span> by <a class="wiki_link" href="/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a> (synth monody)<br />
<span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2010ET.mp3" rel="nofollow">Prelude in 10ET</a></em></span></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Future.html" rel="nofollow">Future</a> <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Future.mp3" rel="nofollow">play</a></em></span></span> and <a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Sol.html" rel="nofollow">Sol</a> <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Sol.mp3" rel="nofollow">play</a></em></span></span> by ZIA (synths and voice in 10)<br />
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3" rel="nofollow">Prelude</a></em></span></span> by <a class="wiki_link" href="/Rick%20McGowan">Rick McGowan</a> (Rhino synthesizer)<br />
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3" rel="nofollow">Ideas on the Waterfall of Expression</a></em></span></span> by Igliashon Jones (synth)<br />
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3" rel="nofollow">For two violas and gongs</a></em></span></span> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil (website)</a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1039" rel="nofollow" target="_blank">more composition information</a><br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Blues10.mp3" rel="nofollow">Blues 10</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/dd7ee3a756851e812778e2fb222b5c47-168.html" rel="nofollow">blog entry</a>)<br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Waltz10.mp3" rel="nofollow">Waltz 10</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/875fbcf1467c4ed837ac1ba4b666d417-169.html" rel="nofollow">blog entry</a>)<br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Smooth10.mp3" rel="nofollow">Smooth 10</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/65405f5999f3960d5704b83c7318c673-170.html" rel="nofollow">blog entry</a>)<br />
<br />
<!-- ws:start:WikiTextFileRule:589:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@10preview.ogg&quot; title=&quot;File: 10preview.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /></a><div><a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');" class="filename" title="10preview.ogg">10preview.ogg</a><br /><ul><li><a href="/file/detail/10preview.ogg">Details</a></li><li><a href="/file/view/10preview.ogg/246873297/10preview.ogg">Download</a></li><li style="color: #666">3 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:589 --> A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:590:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/decexperiment.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@decexperiment.ogg&quot; title=&quot;File: decexperiment.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="decexperiment.ogg" /></a><div><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');" class="filename" title="decexperiment.ogg">decexperiment.ogg</a><br /><ul><li><a href="/file/detail/decexperiment.ogg">Details</a></li><li><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:590 -->3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3" rel="nofollow">10 Earwigs Invasive</a></em></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1397" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3" rel="nofollow">Comets Over Flatland 9</a></em></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3" rel="nofollow">The Dramatic Squirrel Overture</a></em></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1368" rel="nofollow" target="_blank">Details</a><br />
<a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/shimmerwing" rel="nofollow" target="_blank">Shimmerwing</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> and <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20The%20Csx%20Freight%20at%201-20%20am.mp3" rel="nofollow">The Csx Freight at 1:20 am</a></em> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />
<a class="wiki_link_ext" href="http://soundcloud.com/martinsj013/sirmdbidnud2" rel="nofollow">Sirmdbidnud2 by martinsj013 on SoundCloud</a><br />
<a class="wiki_link_ext" href="https://soundcloud.com/clem-fortuna/10tone" rel="nofollow" target="_blank">10tone demo</a> by <a class="wiki_link_ext" href="http://clemfortuna.com" rel="nofollow" target="_blank">Clem Fortuna</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc6"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:15 --><strong>Instruments</strong></h1>
 <br />
10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an &quot;E&quot; chord would be 0-2-2-1-0-0 (low to high), an &quot;A&quot; chord would be 0-0-2-2-1-0, and a &quot;D&quot; chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.<br />
<br />
Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from <a class="wiki_link" href="/20edo">20edo</a> which approximates the 11th harmonic with relative accuracy, among other features.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:586:&lt;img src=&quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&quot; alt=&quot;A Decaphonic (10-EDO) Classical Guitar&quot; title=&quot;A Decaphonic (10-EDO) Classical Guitar&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /></td></tr><tr><td class="imageCaption">A Decaphonic (10-EDO) Classical Guitar</td></tr></table><!-- ws:end:WikiTextLocalImageRule:586 --><!-- ws:start:WikiTextLocalImageRule:587:&lt;img src=&quot;/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 406px; width: 526px;&quot; /&gt; --><img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /><!-- ws:end:WikiTextLocalImageRule:587 --><!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10021077&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
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