19edo: Difference between revisions

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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 0 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 ||< | 0 -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 0 -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 0 -1 > ||> 17.40 ||= Ptolemisma ||=   ||=   ||
||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.69 ||= Pentacircle ||=   ||=   ||
||= 65536/65219 ||< | 16 0 0 -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 0 1 > ||> 19.13 ||= Superleap ||=   ||=   ||
||= 676/675 ||< | 2 -3 -2 0 0 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://www.microstick.net/nineteenarticle.htm|Nineteen for the Nineties]] by Ivor Darreg
* [[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://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] by William Sethares
[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]] 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://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3|Citified Notions]] by John Starrett.
[[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:943: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:943 -->. 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 style="text-align: center;">16875/16384<br />
</td>
        <td style="text-align: left;">| -14 3 4 &gt;<br />
</td>
        <td style="text-align: right;">51.12<br />
</td>
        <td style="text-align: center;">Negri Comma<br />
</td>
        <td style="text-align: center;">Double Augmentation Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3125/3072<br />
</td>
        <td style="text-align: left;">| -10 -1 5 &gt;<br />
</td>
        <td style="text-align: right;">29.61<br />
</td>
        <td style="text-align: center;">Small Diesis<br />
</td>
        <td style="text-align: center;">Magic Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: left;">| -4 4 -1 &gt;<br />
</td>
        <td style="text-align: right;">21.51<br />
</td>
        <td style="text-align: center;">Syntonic Comma<br />
</td>
        <td style="text-align: center;">Didymos Comma<br />
</td>
        <td style="text-align: center;">Meantone Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">78732/78125<br />
</td>
        <td style="text-align: left;">| 2 9 -7 &gt;<br />
</td>
        <td style="text-align: right;">13.40<br />
</td>
        <td style="text-align: center;">Medium Semicomma<br />
</td>
        <td style="text-align: center;">Sensipent Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15625/15552<br />
</td>
        <td style="text-align: left;">| -6 -5 6 &gt;<br />
</td>
        <td style="text-align: right;">8.11<br />
</td>
        <td style="text-align: center;">Kleisma<br />
</td>
        <td style="text-align: center;">Semicomma Majeur<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1792620/1787149<br />
</td>
        <td style="text-align: left;">| 8 14 -13 &gt;<br />
</td>
        <td style="text-align: right;">5.29<br />
</td>
        <td style="text-align: center;">Parakleisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4830148/4822299<br />
</td>
        <td style="text-align: left;">| -14 -19 19 &gt;<br />
</td>
        <td style="text-align: right;">2.82<br />
</td>
        <td style="text-align: center;">Enneadeca<br />
</td>
        <td style="text-align: center;">19-Tone-Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1000<br />
</td>
        <td style="text-align: left;">| -3 1 -3 3 &gt;<br />
</td>
        <td style="text-align: right;">49.49<br />
</td>
        <td style="text-align: center;">Keega<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">525/512<br />
</td>
        <td style="text-align: left;">| -9 1 2 1 &gt;<br />
</td>
        <td style="text-align: right;">43.41<br />
</td>
        <td style="text-align: center;">Avicennma<br />
</td>
        <td style="text-align: center;">Avicenna's Enharmonic Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td style="text-align: left;">| -4 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">35.70<br />
</td>
        <td style="text-align: center;">Slendro Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">686/675<br />
</td>
        <td style="text-align: left;">| 1 -3 -2 3 &gt;<br />
</td>
        <td style="text-align: right;">27.99<br />
</td>
        <td style="text-align: center;">Senga<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">875/864<br />
</td>
        <td style="text-align: left;">| -5 -3 3 1 &gt;<br />
</td>
        <td style="text-align: right;">21.90<br />
</td>
        <td style="text-align: center;">Keema<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">245/243<br />
</td>
        <td style="text-align: left;">| 0 -5 1 2 &gt;<br />
</td>
        <td style="text-align: right;">14.19<br />
</td>
        <td style="text-align: center;">Sensamagic<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">126/125<br />
</td>
        <td style="text-align: left;">| 1 2 -3 1 &gt;<br />
</td>
        <td style="text-align: right;">13.79<br />
</td>
        <td style="text-align: center;">Septimal Semicomma<br />
</td>
        <td style="text-align: center;">Starling Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">225/224<br />
</td>
        <td style="text-align: left;">| -5 2 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">7.71<br />
</td>
        <td style="text-align: center;">Septimal Kleisma<br />
</td>
        <td style="text-align: center;">Marvel Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19683/19600<br />
</td>
        <td style="text-align: left;">| -4 9 -2 -2 &gt;<br />
</td>
        <td style="text-align: right;">7.32<br />
</td>
        <td style="text-align: center;">Cataharry<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10976/10935<br />
</td>
        <td style="text-align: left;">| 5 -7 -1 3 &gt;<br />
</td>
        <td style="text-align: right;">6.48<br />
</td>
        <td style="text-align: center;">Hemimage<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3136/3125<br />
</td>
        <td style="text-align: left;">| 6 0 -5 2 &gt;<br />
</td>
        <td style="text-align: right;">6.08<br />
</td>
        <td style="text-align: center;">Hemimean<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">703125/702464<br />
</td>
        <td style="text-align: left;">| -11 2 7 -3 &gt;<br />
</td>
        <td style="text-align: right;">1.63<br />
</td>
        <td style="text-align: center;">Meter<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4375/4374<br />
</td>
        <td style="text-align: left;">| -1 -7 4 1 &gt;<br />
</td>
        <td style="text-align: right;">0.40<br />
</td>
        <td style="text-align: center;">Ragisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td style="text-align: left;">| 2 -2 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">17.40<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">896/891<br />
</td>
        <td style="text-align: left;">| 7 -4 0 1 -1 &gt;<br />
</td>
        <td style="text-align: right;">9.69<br />
</td>
        <td style="text-align: center;">Pentacircle<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">65536/65219<br />
</td>
        <td style="text-align: left;">| 16 0 0 -2 -3 &gt;<br />
</td>
        <td style="text-align: right;">8.39<br />
</td>
        <td style="text-align: center;">Orgonisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">540/539<br />
</td>
        <td style="text-align: left;">| 2 3 1 -2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.21<br />
</td>
        <td style="text-align: center;">Swetisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td style="text-align: left;">| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td style="text-align: right;">19.13<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td style="text-align: left;">| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td style="text-align: right;">2.56<br />
</td>
        <td style="text-align: center;">Parizeksma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><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://www.microstick.net/nineteenarticle.htm" rel="nofollow">Nineteen for the Nineties</a> by Ivor Darreg</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:600:&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:600 --><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://sethares.engr.wisc.edu/mp3s/sympathetic.html" rel="nofollow">Sympathetic Metaphor</a> by William Sethares<br />
<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow">Truth on a bus</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3" rel="nofollow">play</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://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3" rel="nofollow">Citified Notions</a> by John Starrett.<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>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 20:07:23 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 20:11:16 UTC</tt>.<br>
-: The original revision id was <tt>234716956</tt>.<br>
+: The original revision id was <tt>234717640</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 104: / Line 104: @@
 &lt;span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"&gt;[[http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3|Ditty]] &lt;/span&gt; by Christopher Bailey
 [[http://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] by William Sethares
-[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://tinyurl.com/3fo8vl8|play]] by William Sethares
+[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]] by William Sethares
 &lt;span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da"&gt;[[http://www.h-pi.com/mp3/Rondo19ET.mp3|Rondo in 19ET]] &lt;/span&gt; by Aaron Andrew Hunt
 [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3|Citified Notions]] by John Starrett.
@@ Line 724: / Line 724: @@
 &lt;span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"&gt;&lt;a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3" rel="nofollow"&gt;Ditty&lt;/a&gt; &lt;/span&gt; by Christopher Bailey&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/sympathetic.html" rel="nofollow"&gt;Sympathetic Metaphor&lt;/a&gt; by William Sethares&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow"&gt;Truth on a bus&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://tinyurl.com/3fo8vl8" rel="nofollow"&gt;play&lt;/a&gt; by William Sethares&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow"&gt;Truth on a bus&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3" rel="nofollow"&gt;play&lt;/a&gt; by William Sethares&lt;br /&gt;
 &lt;span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da"&gt;&lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Rondo19ET.mp3" rel="nofollow"&gt;Rondo in 19ET&lt;/a&gt; &lt;/span&gt; by Aaron Andrew Hunt&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3" rel="nofollow"&gt;Citified Notions&lt;/a&gt; by John Starrett.&lt;br /&gt;

19edo: Difference between revisions

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