10edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599962014 - Original comment: ** |
Wikispaces>TallKite **Imported revision 599962808 - 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:TallKite|TallKite]] and made on <tt>2016-11-21 07: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 07:25:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599962808</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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DMS || Approximate | DMS || Approximate | ||
Ratios* || Additional Ratios | Ratios* || Additional Ratios | ||
of 3, 5 and 9 || Interval Names ||||= [[Ups and Downs Notation|ups and downs]] | of 3, 5 and 9 || Interval Names ||||||= [[Ups and Downs Notation|ups and downs]] | ||
[[Ups and Downs Notation|notation]] || | [[Ups and Downs Notation|notation]] || | ||
|| 0 || 0, 0° || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= D || | || 0 || 0, 0° || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D || | ||
|| 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, | ||
large minor second || mid 2nd ||= D^, Ev || | large minor second || mid 2nd ||= ~2 ||= D^, Ev || | ||
|| 2 || 240, 288, 72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || M2, m3 ||= E, F || | || 2 || 240, 288, 72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd, | ||
|| 3 || 360, 432, 108° || 16/13 || 5/4 || large neutral third || mid 3rd ||= F^, Gv || | min 3rd ||= M2,m3 ||= E, F || | ||
|| 4 || 480, 576, 144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || M3, P4 ||= F#, G || | || 3 || 360, 432, 108° || 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv || | ||
|| 4 || 480, 576, 144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd, | |||
perf 4th ||= M3,P4 ||= F#, G || | |||
|| 5 || 600, 720 | || 5 || 600, 720 | ||
180° || 91/64, 128/91, | 180° || 91/64, 128/91, | ||
169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th, | 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th, | ||
down 5th ||= G^, Av || | down 5th ||= ^4,v5 ||= G^, Av || | ||
|| 6 || 720, 864, 216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || P5, m6 ||= A, Bb || | || 6 || 720, 864, 216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th, | ||
|| 7 || 840, 1008, 252° || 13/8 || 8/5 || neutral sixth || mid 6th ||= A^, Bv || | min 6th ||= P5,m6 ||= A, Bb || | ||
|| 8 || 960, 1152, 288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || M6, m7 ||= B, C || | || 7 || 840, 1008, 252° || 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv || | ||
|| 9 || 1080, 1296, 324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= C^, Dv || | || 8 || 960, 1152, 288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th, | ||
|| 10 || 1200, 1440, 360° || 2/1 || 243/128, 49/25, 48/25 || octave || | min 7th ||= M6,m7 ||= B, C || | ||
|| 9 || 1080, 1296, 324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv || | |||
|| 10 || 1200, 1440, 360° || 2/1 || 243/128, 49/25, 48/25 || octave || octave ||= P8 ||= D || | |||
*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. | ||
| Line 142: | Line 146: | ||
<td>Interval Names<br /> | <td>Interval Names<br /> | ||
</td> | </td> | ||
<td colspan=" | <td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs</a><br /> | ||
<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br /> | <a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br /> | ||
</td> | </td> | ||
| Line 158: | Line 162: | ||
</td> | </td> | ||
<td>unison<br /> | <td>unison<br /> | ||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
| Line 176: | Line 182: | ||
</td> | </td> | ||
<td>mid 2nd<br /> | <td>mid 2nd<br /> | ||
</td> | |||
<td style="text-align: center;">~2<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">D^, Ev<br /> | <td style="text-align: center;">D^, Ev<br /> | ||
| Line 191: | Line 199: | ||
<td>second/third<br /> | <td>second/third<br /> | ||
</td> | </td> | ||
<td>M2, m3<br /> | <td>maj 2nd,<br /> | ||
min 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">M2,m3<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">E, F<br /> | <td style="text-align: center;">E, F<br /> | ||
| Line 208: | Line 219: | ||
</td> | </td> | ||
<td>mid 3rd<br /> | <td>mid 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">~3<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">F^, Gv<br /> | <td style="text-align: center;">F^, Gv<br /> | ||
| Line 223: | Line 236: | ||
<td>smaller fourth<br /> | <td>smaller fourth<br /> | ||
</td> | </td> | ||
<td>M3, P4<br /> | <td>maj 3rd,<br /> | ||
perf 4th<br /> | |||
</td> | |||
<td style="text-align: center;">M3,P4<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">F#, G<br /> | <td style="text-align: center;">F#, G<br /> | ||
| Line 243: | Line 259: | ||
<td>up 4th,<br /> | <td>up 4th,<br /> | ||
down 5th<br /> | down 5th<br /> | ||
</td> | |||
<td style="text-align: center;">^4,v5<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">G^, Av<br /> | <td style="text-align: center;">G^, Av<br /> | ||
| Line 258: | Line 276: | ||
<td>bigger fifth<br /> | <td>bigger fifth<br /> | ||
</td> | </td> | ||
<td>P5, m6<br /> | <td>perf 5th,<br /> | ||
min 6th<br /> | |||
</td> | |||
<td style="text-align: center;">P5,m6<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">A, Bb<br /> | <td style="text-align: center;">A, Bb<br /> | ||
| Line 275: | Line 296: | ||
</td> | </td> | ||
<td>mid 6th<br /> | <td>mid 6th<br /> | ||
</td> | |||
<td style="text-align: center;">~6<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">A^, Bv<br /> | <td style="text-align: center;">A^, Bv<br /> | ||
| Line 290: | Line 313: | ||
<td>sixth/seventh<br /> | <td>sixth/seventh<br /> | ||
</td> | </td> | ||
<td>M6, m7<br /> | <td>maj 6th,<br /> | ||
min 7th<br /> | |||
</td> | |||
<td style="text-align: center;">M6,m7<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">B, C<br /> | <td style="text-align: center;">B, C<br /> | ||
| Line 307: | Line 333: | ||
</td> | </td> | ||
<td>mid 7th<br /> | <td>mid 7th<br /> | ||
</td> | |||
<td style="text-align: center;">~7<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C^, Dv<br /> | <td style="text-align: center;">C^, Dv<br /> | ||
| Line 322: | Line 350: | ||
<td>octave<br /> | <td>octave<br /> | ||
</td> | </td> | ||
<td> | <td>octave<br /> | ||
</td> | |||
<td style="text-align: center;">P8<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<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:633:&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:633 --> A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:634:&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:634 -->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:630:&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:630 --><!-- ws:start:WikiTextLocalImageRule:631:&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:631 --><!-- 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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