19edo

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[[toc|flat]]
----
=Theory= 

In music, **19 equal temperament**, called 19-TET, 19-[[EDO]], or 19-ET, is the scale derived by dividing the octave into 19 [[equal]]ly large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 cents.

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== 

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 [[Regular Temperaments#meantone|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 [[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]] 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== 

[[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%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://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]]
[[http://mtg.redkeylabs.com/index.php?topic=6.0]] - Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar.
www.ronsword.com/books.html - Enneadecaphonic Scales for Guitar (Scale chart book)
==References== 

Levy, Kenneth J., Costeley's Chromatic Chanson//, Annales Musicologues:
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.

----
=Compositions= 

[[http://www.akjmusic.com/audio/juggler.mp3|The Juggler]] by Aaron Krister Johnson
[[http://music.columbia.edu/%7Echris/sand.html|Sand]] by Christopher Bailey
[[http://works.music.columbia.edu/%7Echris/19mix1.mp3|Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me]] by Christopher Bailey
[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/sympathetic.html|Sympathetic metaphor]] by William Sethares
[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/truthonabus.html|Truth on a bus]] by William Sethares
[[http://www.h-pi.com/mp3/Rondo19ET.mp3|Rondo in 19ET]] by Aaron Andrew Hunt
[[http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=104038|The Light Of My Betelgeuse]] by Mykhaylo Khramov
A number of compositions that were perfomed at the [[http://midwestmicrofest.org/concerts.html|midwestmicrofest concert in 2007]]
Fanfare in 19-note Equal Tuning by Easley Blackwood
[[http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html|Zvíře]] by Milan Guštar

Original HTML content:

<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:19 --><hr />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1>
 <br />
In music, <strong>19 equal temperament</strong>, called 19-TET, 19-<a class="wiki_link" href="/EDO">EDO</a>, or 19-ET, is the scale derived by dividing the octave into 19 <a class="wiki_link" href="/equal">equal</a>ly large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 cents.<br />
<br />
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 />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->As an approximation of other temperaments</h2>
 <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 <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. It is also a suitable for <a class="wiki_link" href="/Regular%20Temperaments#magic">magic</a> temperament, because five of its major thirds are equivalent to one of its <em>twelfths</em>.<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="/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 />
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:310: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:310 -->. 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 />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Theory-External links"></a><!-- ws:end:WikiTextHeadingRule:6 -->External links</h2>
 <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></em><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 />
<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 />
<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 />
<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://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow">http://mtg.redkeylabs.com/index.php?topic=6.0</a> - Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar.<br />
www.ronsword.com/books.html - Enneadecaphonic Scales for Guitar (Scale chart book)<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:8 -->References</h2>
 <br />
Levy, Kenneth J., Costeley's Chromatic Chanson//, Annales Musicologues:<br />
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.<br />
<br />
<hr />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Compositions</h1>
 <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://music.columbia.edu/%7Echris/sand.html" rel="nofollow">Sand</a> by Christopher Bailey<br />
<a class="wiki_link_ext" href="http://works.music.columbia.edu/%7Echris/19mix1.mp3" rel="nofollow">Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me</a> by Christopher Bailey<br />
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/sympathetic.html" rel="nofollow">Sympathetic metaphor</a> by William Sethares<br />
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/truthonabus.html" rel="nofollow">Truth on a bus</a> by William Sethares<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Rondo19ET.mp3" rel="nofollow">Rondo in 19ET</a> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=104038" rel="nofollow">The Light Of My Betelgeuse</a> by Mykhaylo Khramov<br />
A number of compositions that were perfomed at the <a class="wiki_link_ext" href="http://midwestmicrofest.org/concerts.html" rel="nofollow">midwestmicrofest concert in 2007</a><br />
Fanfare in 19-note Equal Tuning by Easley Blackwood<br />
<a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html" rel="nofollow">Zvíře</a> by Milan Guštar</body></html>