19edo

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[[media type="custom" key="9458830"]][[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 ||   ||

==Commas== 
19 EDO tempers out the following commas. (Note: This assumes the val < 19 30 44 53 66 70 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
|| 16875/16384 || | -14 3 4 > || 51.12 || Negri Comma || Double Augmentation Diesis ||   ||
|| 3125/3072 || | -10 -1 5 > || 29.61 || Small Diesis || Magic Comma ||   ||
|| 81/80 || | -4 4 -1 > || 21.51 || Syntonic Comma || Didymos Comma || Meantone Comma ||
|| 78732/78125 || | 2 9 -7 > || 13.40 || Medium Semicomma || Sensipent Comma ||   ||
|| 15625/15552 || | -6 -5 6 > || 8.11 || Kleisma || Semicomma Majeur ||   ||
|| 1792620/1787149 || | 8 14 -13 > || 5.29 || Parakleisma ||   ||   ||
|| 4830148/4822299 || | -14 -19 19 > || 2.82 || Enneadeca || 19-Tone-Comma ||   ||
|| 1029/1000 || | -3 1 -3 3 > || 49.49 || Keega ||   ||   ||
|| 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || Avicenna's Enharmonic Diesis ||   ||
|| 49/48 || | -4 -1 2 > || 35.70 || Slendro Diesis ||   ||   ||
|| 686/675 || | 1 -3 -2 3 > || 27.99 || Senga ||   ||   ||
|| 875/864 || | -5 -3 3 1 > || 21.90 || Keema ||   ||   ||
|| 245/243 || | -5 1 2 > || 14.19 || Sensamagic ||   ||   ||
|| 126/125 || | 1 2 -3 1 > || 13.79 || Septimal Semicomma || Starling Comma ||   ||
|| 225/224 || | -5 2 2 -1 > || 7.71 || Septimal Kleisma || Marvel Comma ||   ||
|| 19683/19600 || | -4 9 -2 -2 > || 7.32 || Cataharry ||   ||   ||
|| 10976/10935 || | 5 -7 -1 3 > || 6.48 || Hemimage ||   ||   ||
|| 3136/3125 || | 6 -5 2 > || 6.08 || Hemimean ||   ||   ||
|| 703125/702464 || | -11 2 7 -3 > || 1.63 || Meter ||   ||   ||
|| 4375/4374 || | -1 -7 4 1 > || 0.40 || Ragisma ||   ||   ||
|| 100/99 || | 2 -2 2 -1 > || 17.40 || Ptolemisma ||   ||   ||
|| 896/891 || | 7 -4 0 1 -1 > || 9.69 || Pentacircle ||   ||   ||
|| 65536/65219 || | 16 -2 -3 > || 8.39 || Orgonisma ||   ||   ||
|| 385/384 || | -7 -1 1 1 1 > || 4.50 || Keenanisma ||   ||   ||
|| 540/539 || | 2 3 1 -2 -1 > || 3.21 || Swetisma ||   ||   ||
|| 91/90 || | -1 -2 -1 1 1 > || 19.13 || Superleap ||   ||   ||
|| 676/675 || | 2 -3 -2 2 > || 2.56 || Parizeksma ||   ||   ||


==Articles== 

* [[http://sonic-arts.org/darreg/case.htm|A Case For Nineteen]] by [[Ivor Darreg]] [[http://www.webcitation.org/5xZzBtDGF|Permalink]]
* [[http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html|19-Tone Theory and Applications]] by Hubert S. Howe Jr. [[http://www.webcitation.org/5xbMKVaqa|Permalink]]
* [[http://sethares.engr.wisc.edu/tet19/guitarchords19.html|Tunings for 19 Tone Equal Tempered Guitar]] by William A. Sethares [[http://www.webcitation.org/5xeCbEPZ0|Permalink]]
* [[http://www.n-ism.org/Projects/microtonalism.php|Microtonalism]] by Bailey, Morrison, Pearson and Parncutt [[http://www.webcitation.org/5xeDFQDvn|Permalink]]
* [[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|Permalink]]
* [[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]].
* [[http://www.ronsword.com/books.html|Enneadecaphonic Scales for Guitar]] by Ron Sword

==References== 

Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament//, CIM04_proceedings.
Levy, Kenneth J., //Costeley's Chromatic Chanson//, Annales Musicologues:
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.
19 note per octave Ibanez conversion by Brad Smith (Indianapolis)
[[image:http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg width="800" height="600"]]

----
=Compositions= 

<span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac">[[http://www.akjmusic.com/audio/juggler.mp3|The Juggler]] </span> by Aaron Krister Johnson
[[http://music.columbia.edu/%7Echris/sand.html|Sand]] by Christopher Bailey
<span class="ymp-btn-page-play ymp-media-1ec26b280d7788ac0e790719d577a218">[[http://works.music.columbia.edu/%7Echris/19mix1.mp3|Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me]] </span> by Christopher Bailey
<span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820">[[http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3|Ditty]] </span> 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
<span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da">[[http://www.h-pi.com/mp3/Rondo19ET.mp3|Rondo in 19ET]] </span> 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
[[http://www.ziaspace.com/ZIA/sections/music.html|19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.]]
[[@http://chrisvaisvil.com/?p=865|Forgetting Even Her Beauty blog]] <span class="ymp-btn-page-play ymp-media-7cdb4644c05849d85c1a04ed2a07a5a7">[[http://micro.soonlabel.com/19-ET/daily20110516-19-forgetting_even_her_beauty.mp3|play Forgetting Even Her Beauty]] </span> by Chris Vaisvil
[[@http://chrisvaisvil.com/?p=855|19 Black Hawks for Osama blog]] <span class="ymp-media-3badeb9b3b5a5768a5e43cea7e10b377 ymp-btn-page-play">[[http://www.youtube.com/watch?v=gGO0R381HQs|play video for 19 Black Hawks for Osama]] </span> by Chris Vaisvil
[[@http://chrisvaisvil.com/?p=823|Summer Song blog]] <span class="ymp-media-44691c8e07e030770b33e146e0d88212 ymp-btn-page-play">[[http://micro.soonlabel.com/19-ET/daily20110501-19-summer_song_mix3.mp3|play Summer Song]] </span> by Trevor (The TwoRegs) and Norm Harris and Chris Vaisvil
[[@http://chrisvaisvil.com/?p=820|19 ImprovFridays blog]] <span class="ymp-btn-page-play ymp-media-c6d81d29a5290997eac85574c62b39e3">[[http://www.youtube.com/watch?v=-KaRXFoYwT4|play video of performance of 19 ImprovFridays]] </span> by Chris Vaisvil
[[@http://chrisvaisvil.com/?p=800|The World has Changed blog]] <span class="ymp-media-d1cc76332b281044aecd4287b683de9d ymp-btn-page-play">[[http://micro.soonlabel.com/19-ET/daily20110429-19edo-the_world_has_changed3.mp3|play The World has Changed]] </span> by Chris Vaisvil

Original HTML content:

<html><head><title>19edo</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9458830?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9458830&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
</script><!-- ws:end:WikiTextMediaRule:0 --><!-- ws:start:WikiTextTocRule:15:&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:15 --><!-- ws:start:WikiTextTocRule:16: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: -->
<!-- ws:end:WikiTextTocRule:23 --><br />
<hr />
<!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:1 -->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:3:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:3 -->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:937: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:937 -->. 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:5:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->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 />
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="Theory-Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h2>
 19 EDO tempers out the following commas. (Note: This assumes the val &lt; 19 30 44 53 66 70 |.)<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>Value (Cents)<br />
</th>
        <th>Name 1<br />
</th>
        <th>Name 2<br />
</th>
        <th>Name 3<br />
</th>
    </tr>
    <tr>
        <td>16875/16384<br />
</td>
        <td>| -14 3 4 &gt;<br />
</td>
        <td>51.12<br />
</td>
        <td>Negri Comma<br />
</td>
        <td>Double Augmentation Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3125/3072<br />
</td>
        <td>| -10 -1 5 &gt;<br />
</td>
        <td>29.61<br />
</td>
        <td>Small Diesis<br />
</td>
        <td>Magic Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>81/80<br />
</td>
        <td>| -4 4 -1 &gt;<br />
</td>
        <td>21.51<br />
</td>
        <td>Syntonic Comma<br />
</td>
        <td>Didymos Comma<br />
</td>
        <td>Meantone Comma<br />
</td>
    </tr>
    <tr>
        <td>78732/78125<br />
</td>
        <td>| 2 9 -7 &gt;<br />
</td>
        <td>13.40<br />
</td>
        <td>Medium Semicomma<br />
</td>
        <td>Sensipent Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15625/15552<br />
</td>
        <td>| -6 -5 6 &gt;<br />
</td>
        <td>8.11<br />
</td>
        <td>Kleisma<br />
</td>
        <td>Semicomma Majeur<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1792620/1787149<br />
</td>
        <td>| 8 14 -13 &gt;<br />
</td>
        <td>5.29<br />
</td>
        <td>Parakleisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4830148/4822299<br />
</td>
        <td>| -14 -19 19 &gt;<br />
</td>
        <td>2.82<br />
</td>
        <td>Enneadeca<br />
</td>
        <td>19-Tone-Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1029/1000<br />
</td>
        <td>| -3 1 -3 3 &gt;<br />
</td>
        <td>49.49<br />
</td>
        <td>Keega<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>525/512<br />
</td>
        <td>| -9 1 2 1 &gt;<br />
</td>
        <td>43.41<br />
</td>
        <td>Avicennma<br />
</td>
        <td>Avicenna's Enharmonic Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49/48<br />
</td>
        <td>| -4 -1 2 &gt;<br />
</td>
        <td>35.70<br />
</td>
        <td>Slendro Diesis<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>686/675<br />
</td>
        <td>| 1 -3 -2 3 &gt;<br />
</td>
        <td>27.99<br />
</td>
        <td>Senga<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>875/864<br />
</td>
        <td>| -5 -3 3 1 &gt;<br />
</td>
        <td>21.90<br />
</td>
        <td>Keema<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>245/243<br />
</td>
        <td>| -5 1 2 &gt;<br />
</td>
        <td>14.19<br />
</td>
        <td>Sensamagic<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>126/125<br />
</td>
        <td>| 1 2 -3 1 &gt;<br />
</td>
        <td>13.79<br />
</td>
        <td>Septimal Semicomma<br />
</td>
        <td>Starling Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>225/224<br />
</td>
        <td>| -5 2 2 -1 &gt;<br />
</td>
        <td>7.71<br />
</td>
        <td>Septimal Kleisma<br />
</td>
        <td>Marvel Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19683/19600<br />
</td>
        <td>| -4 9 -2 -2 &gt;<br />
</td>
        <td>7.32<br />
</td>
        <td>Cataharry<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10976/10935<br />
</td>
        <td>| 5 -7 -1 3 &gt;<br />
</td>
        <td>6.48<br />
</td>
        <td>Hemimage<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3136/3125<br />
</td>
        <td>| 6 -5 2 &gt;<br />
</td>
        <td>6.08<br />
</td>
        <td>Hemimean<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>703125/702464<br />
</td>
        <td>| -11 2 7 -3 &gt;<br />
</td>
        <td>1.63<br />
</td>
        <td>Meter<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4375/4374<br />
</td>
        <td>| -1 -7 4 1 &gt;<br />
</td>
        <td>0.40<br />
</td>
        <td>Ragisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>100/99<br />
</td>
        <td>| 2 -2 2 -1 &gt;<br />
</td>
        <td>17.40<br />
</td>
        <td>Ptolemisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>896/891<br />
</td>
        <td>| 7 -4 0 1 -1 &gt;<br />
</td>
        <td>9.69<br />
</td>
        <td>Pentacircle<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>65536/65219<br />
</td>
        <td>| 16 -2 -3 &gt;<br />
</td>
        <td>8.39<br />
</td>
        <td>Orgonisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>385/384<br />
</td>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
        <td>4.50<br />
</td>
        <td>Keenanisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>540/539<br />
</td>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td>3.21<br />
</td>
        <td>Swetisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>91/90<br />
</td>
        <td>| -1 -2 -1 1 1 &gt;<br />
</td>
        <td>19.13<br />
</td>
        <td>Superleap<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>676/675<br />
</td>
        <td>| 2 -3 -2 2 &gt;<br />
</td>
        <td>2.56<br />
</td>
        <td>Parizeksma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="Theory-Articles"></a><!-- ws:end:WikiTextHeadingRule:9 -->Articles</h2>
 <br />
<ul><li><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">A Case For Nineteen</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow">19-Tone Theory and Applications</a> by Hubert S. Howe Jr. <a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow">Tunings for 19 Tone Equal Tempered Guitar</a> by William A. Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow">Microtonalism</a> by Bailey, Morrison, Pearson and Parncutt <a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow">Permalink</a></li><li><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> <a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow">Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar</a>.</li><li><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow">Enneadecaphonic Scales for Guitar</a> by Ron Sword</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:11 -->References</h2>
 <br />
Bucht, Saku and Huovinen, Erkki, <em>Perceived consonance of harmonic intervals in 19-tone equal temperament</em>, CIM04_proceedings.<br />
Levy, Kenneth J., <em>Costeley's Chromatic Chanson</em>, Annales Musicologues:<br />
Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.<br />
19 note per octave Ibanez conversion by Brad Smith (Indianapolis)<br />
<!-- ws:start:WikiTextRemoteImageRule:598:&lt;img src=&quot;http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 600px; width: 800px;&quot; /&gt; --><img src="http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" alt="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" title="external image Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" style="height: 600px; width: 800px;" /><!-- ws:end:WikiTextRemoteImageRule:598 --><br />
<br />
<hr />
<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:13 -->Compositions</h1>
 <br />
<span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac"><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/juggler.mp3" rel="nofollow">The Juggler</a> </span> 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 />
<span class="ymp-btn-page-play ymp-media-1ec26b280d7788ac0e790719d577a218"><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> </span> by Christopher Bailey<br />
<span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"><a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3" rel="nofollow">Ditty</a> </span> 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 />
<span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da"><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Rondo19ET.mp3" rel="nofollow">Rondo in 19ET</a> </span> 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<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 />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=865" rel="nofollow" target="_blank">Forgetting Even Her Beauty blog</a> <span class="ymp-btn-page-play ymp-media-7cdb4644c05849d85c1a04ed2a07a5a7"><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/daily20110516-19-forgetting_even_her_beauty.mp3" rel="nofollow">play Forgetting Even Her Beauty</a> </span> by Chris Vaisvil<br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=855" rel="nofollow" target="_blank">19 Black Hawks for Osama blog</a> <span class="ymp-media-3badeb9b3b5a5768a5e43cea7e10b377 ymp-btn-page-play"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=gGO0R381HQs" rel="nofollow">play video for 19 Black Hawks for Osama</a> </span> by Chris Vaisvil<br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=823" rel="nofollow" target="_blank">Summer Song blog</a> <span class="ymp-media-44691c8e07e030770b33e146e0d88212 ymp-btn-page-play"><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/daily20110501-19-summer_song_mix3.mp3" rel="nofollow">play Summer Song</a> </span> by Trevor (The TwoRegs) and Norm Harris and Chris Vaisvil<br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=820" rel="nofollow" target="_blank">19 ImprovFridays blog</a> <span class="ymp-btn-page-play ymp-media-c6d81d29a5290997eac85574c62b39e3"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=-KaRXFoYwT4" rel="nofollow">play video of performance of 19 ImprovFridays</a> </span> by Chris Vaisvil<br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=800" rel="nofollow" target="_blank">The World has Changed blog</a> <span class="ymp-media-d1cc76332b281044aecd4287b683de9d ymp-btn-page-play"><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/daily20110429-19edo-the_world_has_changed3.mp3" rel="nofollow">play The World has Changed</a> </span> by Chris Vaisvil</body></html>