19edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 144742761 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 204107710 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-02-22 16:00:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>204107710</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
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For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. | For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. | ||
However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, http://www.research.att.com/~njas/sequences/A117538. It is less successful with 7-limit (but still better than 12-et), as it eliminates the distinction between a septimal minor third (7/6), and a septimal whole tone (8/7). | ||
==Intervals== | |||
|| degrees of 19edo || cents value || generator for || | |||
|| 0 || 0.00 || || | |||
|| 1 || 63.16 || || | |||
|| 2 || 126.32 || || | |||
|| 3 || 189.47 || || | |||
|| 4 || 252.63 || || | |||
|| 5 || 315.79 || Kleismic || | |||
|| 6 || 378.95 || || | |||
|| 7 || 442.11 || || | |||
|| 8 || 505.26 || Meantone || | |||
|| 9 || 568.42 || || | |||
|| 10 || 631.58 || || | |||
|| 11 || 694.74 || Meantone || | |||
|| 12 || 757.89 || || | |||
|| 13 || 821.05 || || | |||
|| 14 || 884.21 || || | |||
|| 15 || 947.37 || || | |||
|| 16 || 1010.53 || || | |||
|| 17 || 1073.68 || || | |||
|| 18 || 1136.84 || || | |||
==External links== | ==External links== | ||
[[http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf|Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament]] | [[http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf|Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament]] | ||
//[[http://sonic-arts.org/darreg/CASE.HTM|Darreg, Ivor, //A Case for Nineteen//]] | //[[http://sonic-arts.org/darreg/CASE.HTM|Darreg, Ivor, //A Case for Nineteen//]]// | ||
[[http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html|Howe, Hubert S. Jr., //9-Tone Theory and Applications//]] | //[[http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html|Howe, Hubert S. Jr., //9-Tone Theory and Applications//]]// | ||
[[http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html|Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//]] | //[[http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html|Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//]]// | ||
[[[http://www.n-ism.org/Projects/microtonalism.php%7CHair|http://www.n-ism.org/Projects/microtonalism.php|Hair]], Bailey, Morrison, Pearson and Parncutt,// Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems //(project summary)]] | //[[[http://www.n-ism.org/Projects/microtonalism.php%7CHair|http://www.n-ism.org/Projects/microtonalism.php|Hair]], Bailey, Morrison, Pearson and Parncutt,// Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems //(project summary)]]// | ||
[[http://www.ziaspace.com/ZIA/sections/music.html|19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.]]// | //[[http://www.ziaspace.com/ZIA/sections/music.html|19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.]]// | ||
[[http://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]] | [[http://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]] | ||
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[[http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html|Zvíře]] by Milan Guštar</pre></div> | [[http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html|Zvíře]] by Milan Guštar</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<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>19edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>19edo</title></head><body><!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:19 --><br /> | ||
<br /> | |||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1> | ||
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For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.<br /> | For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.<br /> | ||
<br /> | <br /> | ||
However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule:308:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:308 -->. It is less successful with 7-limit (but still better than 12-et), as it eliminates the distinction between a septimal minor third (7/6), and a septimal whole tone (8/7).<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>degrees of 19edo<br /> | |||
</td> | |||
<td>cents value<br /> | |||
</td> | |||
<td>generator for<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>0<br /> | |||
</td> | |||
<td>0.00<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>63.16<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>126.32<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>189.47<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>252.63<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>315.79<br /> | |||
</td> | |||
<td>Kleismic<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>378.95<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>442.11<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>505.26<br /> | |||
</td> | |||
<td>Meantone<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>568.42<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>631.58<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>694.74<br /> | |||
</td> | |||
<td>Meantone<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>757.89<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>821.05<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>884.21<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>947.37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>1010.53<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>1073.68<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>1136.84<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Theory-External links"></a><!-- ws:end:WikiTextHeadingRule:6 -->External links</h2> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow">Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament</a><br /> | <a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow">Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament</a><br /> | ||
<em><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/CASE.HTM" rel="nofollow">Darreg, Ivor, //A Case for Nineteen//</a><br /> | <em><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/CASE.HTM" rel="nofollow">Darreg, Ivor, //A Case for Nineteen//</a></em><br /> | ||
<a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow">Howe, Hubert S. Jr., //9-Tone Theory and Applications//</a><br /> | <em><a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow">Howe, Hubert S. Jr., //9-Tone Theory and Applications//</a></em><br /> | ||
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html" rel="nofollow">Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//</a><br /> | <em><a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html" rel="nofollow">Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//</a></em><br /> | ||
[<a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php%7CHair" rel="nofollow">http://www.n-ism.org/Projects/microtonalism.php|Hair</a>, Bailey, Morrison, Pearson and Parncutt,</em> Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems <em>(project summary)]]<br /> | <em>[<a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php%7CHair" rel="nofollow">http://www.n-ism.org/Projects/microtonalism.php|Hair</a>, Bailey, Morrison, Pearson and Parncutt,</em> Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems <em>(project summary)]]</em><br /> | ||
<a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/sections/music.html" rel="nofollow">19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.</a></em><br /> | <em><a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/sections/music.html" rel="nofollow">19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.</a></em><br /> | ||
<a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory</a><br /> | <a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:8 -->References</h2> | ||
<br /> | <br /> | ||
Levy, Kenneth J., Costeley's Chromatic Chanson//, Annales Musicologues:<br /> | Levy, Kenneth J., Costeley's Chromatic Chanson//, Annales Musicologues:<br /> | ||
| Line 87: | Line 280: | ||
<br /> | <br /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Compositions</h1> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.akjmusic.com/audio/juggler.mp3" rel="nofollow">The Juggler</a> by Aaron Krister Johnson<br /> | <a class="wiki_link_ext" href="http://www.akjmusic.com/audio/juggler.mp3" rel="nofollow">The Juggler</a> by Aaron Krister Johnson<br /> | ||