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 [[cent]]s.

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|7/6]]), and a septimal whole tone ([[8_7|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]]
//[[Ivor Darreg]]. A Case For Nineteen. URL:http://sonic-arts.org/darreg/case.htm. Accessed: 2011-03-30. (Archived by WebCite® at http://www.webcitation.org/5xZzBtDGF)//
//[[http://www.webcitation.org/5xbMKVaqa|Howe, Hubert S. Jr., //19-Tone Theory and Applications//]]//
//[[http://sethares.engr.wisc.edu/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 <a class="wiki_link" href="/octave">octave</a> 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 <a class="wiki_link" href="/cent">cent</a>s.<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:315: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:315 -->. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>).<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" href="/Ivor%20Darreg">Ivor Darreg</a>. A Case For Nineteen. URL:<!-- ws:start:WikiTextUrlRule:316:http://sonic-arts.org/darreg/case.htm --><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">http://sonic-arts.org/darreg/case.htm</a><!-- ws:end:WikiTextUrlRule:316 -->. Accessed: 2011-03-30. (Archived by WebCite® at <!-- ws:start:WikiTextUrlRule:317:http://www.webcitation.org/5xZzBtDGF --><a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">http://www.webcitation.org/5xZzBtDGF</a><!-- ws:end:WikiTextUrlRule:317 -->)</em><br />
<em><a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Howe, Hubert S. Jr., //19-Tone Theory and Applications//</a></em><br />
<em><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/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>