10edo: Difference between revisions
Wikispaces>seraph57 **Imported revision 435681956 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 480703054 - 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:spt3125|spt3125]] and made on <tt>2014-01-05 12:50:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>480703054</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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*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. | ||
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=Linear temperaments= | =Linear temperaments= | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>10edo</title></head><body>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 droll 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 /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>10edo</title></head><body>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 droll 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 /> | ||
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<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:15:&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:15 --><!-- ws:start:WikiTextTocRule:16: --><a href="#toc0"></a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | ||
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</script><!-- ws:end:WikiTextMediaRule:0 --></h1> | </script><!-- ws:end:WikiTextMediaRule:0 --></h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals</h1> | ||
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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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc2"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Linear temperaments</h1> | |||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:9 -->Commas</h1> | ||
10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)<br /> | 10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)<br /> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:11 -->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">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://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 /> | ||
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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:547:&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:547 --> A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:548:&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:548 -->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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<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="http://soundcloud.com/martinsj013/sirmdbidnud2" rel="nofollow">Sirmdbidnud2 by martinsj013 on SoundCloud</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc5"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:13 --><strong>Instruments</strong></h1> | ||
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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 /> | 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 /> | ||
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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 /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:544:&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:544 --><!-- ws:start:WikiTextLocalImageRule:545:&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:545 --><!-- 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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