19edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 4821473 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 4823549 - Original comment: reformatted** |
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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:xenjacob|xenjacob]] and made on <tt>2007-06-07 02:24:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>4823549</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>reformatted</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"> | <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">In music, **19 equal temperament**, called 19-TET, 19-EDO, or 19-ET, is the scale derived by dividing the octave into 19 equally large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 cents. | ||
In music, | |||
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson | Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson //Seigneur Dieu ta pitié// of 1558. Costeley understood and desired the circulating aspect of this tuning; in 1577 music theorist Francisco de Salinas in effect proposed it. Salinas discussed 1/3-comma meantone, in which the fifth is of size 694.786 cents; the fifth of 19-et is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which fails to close by less than a cent, so that his suggestion is effectively 19-et. In the nineteenth century mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([[http://sonic-arts.org/monzo/woolhouse/essay.htm|summary of Woolhouse's essay]]). | ||
== As an approximation of other temperaments == | ==As an approximation of other temperaments== | ||
The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for meantone temperament. It is also a suitable for magic temperament, because five of its major thirds are equivalent to one of its | The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for meantone temperament. It is also a suitable for magic temperament, because five of its major thirds are equivalent to one of its //twelfths//. | ||
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 [[31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[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 [[31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41 equal temperament]] more closely matches it. | ||
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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 5-limit music in a tolerable manner. 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). | 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 5-limit music in a tolerable manner. 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). | ||
== 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://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://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|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.]] | |||
== References == | ==References== | ||
Levy, Kenneth J., | Levy, Kenneth J., //Costeley's Chromatic Chanson//, Annales Musicologues: | ||
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261. | Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.</pre></div> | ||
</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>< | <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>In music, <strong>19 equal temperament</strong>, called 19-TET, 19-EDO, or 19-ET, is the scale derived by dividing the octave into 19 equally large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 cents.<br /> | ||
<br /> | <br /> | ||
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson | Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson <em>Seigneur Dieu ta pitié</em> of 1558. Costeley understood and desired the circulating aspect of this tuning; in 1577 music theorist Francisco de Salinas in effect proposed it. Salinas discussed 1/3-comma meantone, in which the fifth is of size 694.786 cents; the fifth of 19-et is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which fails to close by less than a cent, so that his suggestion is effectively 19-et. In the nineteenth century mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as <a class="wiki_link" href="/50edo">50 equal temperament</a> (<a class="wiki_link_ext" href="http://sonic-arts.org/monzo/woolhouse/essay.htm" rel="nofollow">summary of Woolhouse's essay</a>).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 --> As an approximation of other temperaments </h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->As an approximation of other temperaments</h2> | ||
<br /> | <br /> | ||
The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for meantone temperament. It is also a suitable for magic temperament, because five of its major thirds are equivalent to one of its | The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for meantone temperament. It is also a suitable for magic temperament, because five of its major thirds are equivalent to one of its <em>twelfths</em>.<br /> | ||
<br /> | <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="/31%20equal%20temperament">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="/41%20equal%20temperament">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="/31%20equal%20temperament">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="/41%20equal%20temperament">41 equal temperament</a> more closely matches it.<br /> | ||
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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 5-limit music in a tolerable manner. 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 /> | 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 5-limit music in a tolerable manner. 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-External links"></a><!-- ws:end:WikiTextHeadingRule:2 --> External links </h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-External links"></a><!-- ws:end:WikiTextHeadingRule:2 -->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><em><br /> | |||
<a class="wiki_link_ext" href="http://sonic-arts.org/darreg/CASE.HTM" rel="nofollow">Darreg, Ivor, //A Case for Nineteen//</a><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 /> | |||
<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 /> | |||
[<!-- ws:start:WikiTextUrlRule:36:http://www.n-ism.org/Projects/microtonalism.php --><a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow">http://www.n-ism.org/Projects/microtonalism.php</a><!-- ws:end:WikiTextUrlRule:36 -->|Hair, Bailey, Morrison, Pearson and Parncutt, </em>Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems// (project summary)]]<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><br /> | |||
<br / | |||
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Levy, Kenneth J., | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-References"></a><!-- ws:end:WikiTextHeadingRule:4 -->References</h2> | ||
<br /> | |||
Levy, Kenneth J., <em>Costeley's Chromatic Chanson</em>, Annales Musicologues:<br /> | |||
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.</body></html></pre></div> | Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.</body></html></pre></div> | ||