19edo: Difference between revisions

Wikispaces>xenjacob
**Imported revision 4823549 - Original comment: reformatted**
Wikispaces>hstraub
**Imported revision 5478151 - Original comment: link to "magic"**
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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:xenjacob|xenjacob]] and made on <tt>2007-06-07 02:24:25 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-06-25 09:09:46 UTC</tt>.<br>
: The original revision id was <tt>4823549</tt>.<br>
: The original revision id was <tt>5478151</tt>.<br>
: The revision comment was: <tt>reformatted</tt><br>
: The revision comment was: <tt>link to "magic"</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>
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==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 //twelfths//.
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 [[Regular Temperaments#magic|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 [[Regular Temperaments#magic|magic]] temperament is a major third, and again 19-et's is flatter; [[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 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).
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==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|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.]]//


==References==  
==References==  


Levy, Kenneth J., //Costeley's Chromatic Chanson//, Annales Musicologues:
Levy, Kenneth J., Costeley's Chromatic Chanson//, Annales Musicologues:
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.</pre></div>
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-As an approximation of other temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;As an approximation of other temperaments&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-As an approximation of other temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;As an approximation of other temperaments&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
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 &lt;em&gt;twelfths&lt;/em&gt;.&lt;br /&gt;
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 &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; temperament, because five of its major thirds are equivalent to one of its &lt;em&gt;twelfths&lt;/em&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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 &lt;a class="wiki_link" href="/31%20equal%20temperament"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41%20equal%20temperament"&gt;41 equal temperament&lt;/a&gt; more closely matches it.&lt;br /&gt;
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 &lt;a class="wiki_link" href="/31%20equal%20temperament"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41%20equal%20temperament"&gt;41 equal temperament&lt;/a&gt; more closely matches it.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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).&lt;br /&gt;
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).&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;External links&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;External links&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow"&gt;Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament&lt;/a&gt;&lt;em&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow"&gt;Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/CASE.HTM" rel="nofollow"&gt;Darreg, Ivor, //A Case for Nineteen//&lt;/a&gt;&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/CASE.HTM" rel="nofollow"&gt;Darreg, Ivor, //A Case for Nineteen//&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow"&gt;Howe, Hubert S. Jr., //9-Tone Theory and Applications//&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow"&gt;Howe, Hubert S. Jr., //9-Tone Theory and Applications//&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html" rel="nofollow"&gt;Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html" rel="nofollow"&gt;Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//&lt;/a&gt;&lt;br /&gt;
[&lt;!-- ws:start:WikiTextUrlRule:36:http://www.n-ism.org/Projects/microtonalism.php --&gt;&lt;a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow"&gt;http://www.n-ism.org/Projects/microtonalism.php&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:36 --&gt;|Hair, Bailey, Morrison, Pearson and Parncutt, &lt;/em&gt;Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems// (project summary)]]&lt;br /&gt;
[&lt;a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php%7CHair" rel="nofollow"&gt;http://www.n-ism.org/Projects/microtonalism.php|Hair&lt;/a&gt;, Bailey, Morrison, Pearson and Parncutt,&lt;/em&gt; Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems &lt;em&gt;(project summary)]]&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/sections/music.html" rel="nofollow"&gt; 19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/sections/music.html" rel="nofollow"&gt; 19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;References&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;References&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Levy, Kenneth J., &lt;em&gt;Costeley's Chromatic Chanson&lt;/em&gt;, Annales Musicologues:&lt;br /&gt;
Levy, Kenneth J., Costeley's Chromatic Chanson//, Annales Musicologues:&lt;br /&gt;
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.&lt;/body&gt;&lt;/html&gt;</pre></div>
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.&lt;/body&gt;&lt;/html&gt;</pre></div>