10edo: Difference between revisions
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: | : 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> | : 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 || | 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 | 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]]. | |||
[[media type="custom" key="24802496"]] | [[media type="custom" key="24802496"]] | ||
| Line 130: | Line 137: | ||
Ratios*<br /> | Ratios*<br /> | ||
</td> | </td> | ||
<td>Additional Ratios of 3, 5 and 9<br /> | <td>Additional Ratios <br /> | ||
of 3, 5 and 9<br /> | |||
</td> | |||
<td>Interval Names<br /> | |||
</td> | </td> | ||
<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> | </td> | ||
</tr> | </tr> | ||
| Line 143: | Line 154: | ||
</td> | </td> | ||
<td>256/243, 50/49, 25/24<br /> | <td>256/243, 50/49, 25/24<br /> | ||
</td> | |||
<td>unison<br /> | |||
</td> | </td> | ||
<td>unison<br /> | <td>unison<br /> | ||
| Line 157: | Line 170: | ||
<td>10/9, 13/12, 81/80<br /> | <td>10/9, 13/12, 81/80<br /> | ||
</td> | </td> | ||
<td>small neutral second/large minor second<br /> | <td>small neutral second,<br /> | ||
large minor second<br /> | |||
</td> | |||
<td>mid 2nd<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 170: | Line 186: | ||
</td> | </td> | ||
<td>second/third<br /> | <td>second/third<br /> | ||
</td> | |||
<td>M2, m3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 182: | Line 200: | ||
</td> | </td> | ||
<td>large neutral third<br /> | <td>large neutral third<br /> | ||
</td> | |||
<td>mid 3rd<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 194: | Line 214: | ||
</td> | </td> | ||
<td>smaller fourth<br /> | <td>smaller fourth<br /> | ||
</td> | |||
<td>M3, P4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 202: | Line 224: | ||
180°<br /> | 180°<br /> | ||
</td> | </td> | ||
<td>91/64, 128/91, 169/120, 240/169<br /> | <td>91/64, 128/91, <br /> | ||
169/120, 240/169<br /> | |||
</td> | </td> | ||
<td>7/5, 10/7, 13/9, 18/13<br /> | <td>7/5, 10/7, 13/9, 18/13<br /> | ||
</td> | </td> | ||
<td>tritone<br /> | <td>tritone<br /> | ||
</td> | |||
<td>up 4th,<br /> | |||
down 5th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 219: | Line 245: | ||
</td> | </td> | ||
<td>bigger fifth<br /> | <td>bigger fifth<br /> | ||
</td> | |||
<td>P5, m6<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 231: | Line 259: | ||
</td> | </td> | ||
<td>neutral sixth<br /> | <td>neutral sixth<br /> | ||
</td> | |||
<td>mid 6th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 243: | Line 273: | ||
</td> | </td> | ||
<td>sixth/seventh<br /> | <td>sixth/seventh<br /> | ||
</td> | |||
<td>M6, m7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 255: | Line 287: | ||
</td> | </td> | ||
<td>small major 7th<br /> | <td>small major 7th<br /> | ||
</td> | |||
<td>mid 7th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 267: | Line 301: | ||
</td> | </td> | ||
<td>octave<br /> | <td>octave<br /> | ||
</td> | |||
<td>8ve<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 273: | Line 309: | ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.<br /> | *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 /> | 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 /> | <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> | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:9 -->Linear temperaments</h1> | ||
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<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 /> | <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 /> | ||
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<!-- ws:start:WikiTextFileRule: | <!-- 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: | <!-- 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/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/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 /> | ||
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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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- 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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