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 Syntonic Comma Meantone|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 [[Meantone#|meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its //twelfths.// For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and 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. It does make for a good tuning for muggles, which in 19et is the same as magic. 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) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. 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]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. ==Intervals== || degrees of 19edo || cents value || generator for || || 0 ||= 0 || || || 1 || 63.1579 || || || 2 || 126.326 || Negri || || 3 || 189.474 || Deutone || || 4 || 252.632 || Godzilla || || 5 || 315.789 || Kleismic || || 6 || 378.947 || Magic || || 7 || 442.105 || Sensi || || 8 || 505.263 || Meantone || || 9 || 568.421 || Triton || || 10 || 631.579 || Triton || || 11 || 694.737 || Meantone || || 12 || 757.895 || Sensi || || 13 || 821.053 || Magic || || 14 || 884.211 || Kleismic || || 15 || 947.368 || Godzilla || || 16 || 1010.53 || Deutone || || 17 || 1073.68 || Negri || || 18 || 1136.84 || || ==Commas== 19 EDO [[tempering out|tempers out]] the following [[comma]]s. (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://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=1008195|Foum]] <span class="ymp-btn-page-play ymp-media-2b0116564acb823413278e931e9bca8e">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3|play]]</span> by [[Jacob Barton]] [[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]] <span class="ymp-btn-page-play ymp-media-e4e0069ea45121cc80c2ce578a945837">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3|play]]</span> by [[William Sethares]] [[http://www.webcitation.org/5zFdC6u4V|Permalink]] [[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] <span class="ymp-btn-page-play ymp-media-526d4e563c03aca7835db55159692c7d">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]]</span> by William Sethares [[http://www.webcitation.org/5zFdSw1g4|Permalink]] <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]] <span class="ymp-btn-page-play ymp-media-c1ba958b4d29ea779eb3e6e1cb5779c7">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3|Citified Notions]]</span> by [[John Starrett]]. <span class="ymp-btn-page-play ymp-media-e5a2a3d148bc1b07acdba10ca90219c7">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/betelgeuse.mp3|The Light Of My Betelgeuse]]</span> 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 [[http://chrisvaisvil.com/?p=883|jjj]] <span class="ymp-btn-page-play ymp-media-35bea9630e48d0842ee9259bac028257">[[http://micro.soonlabel.com/19-ET/daily20110523-19take2.mp3|play]]</span> by Chris Vaisvil
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<html><head><title>19edo</title></head><body><!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/9458830?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;9458830&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
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<hr />
<!-- ws:start:WikiTextHeadingRule:1:<h1> --><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 <a class="wiki_link" href="/1-3%20Syntonic%20Comma%20Meantone">1/3-comma meantone</a>, 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:<h2> --><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 [[Meantone#|meantone]] temperament. It is also a suitable for <a class="wiki_link" href="/Regular%20Temperaments#magic">magic/muggles</a> temperament, because five of its major thirds are equivalent to one of its <em>twelfths.</em> For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and 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. It does make for a good tuning for muggles, which in 19et is the same as magic.<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) <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a>. 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>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. <br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:<h2> --><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 style="text-align: center;">0<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>63.1579<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>126.326<br />
</td>
<td>Negri<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>189.474<br />
</td>
<td>Deutone<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>252.632<br />
</td>
<td>Godzilla<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>315.789<br />
</td>
<td>Kleismic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>378.947<br />
</td>
<td>Magic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>442.105<br />
</td>
<td>Sensi<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>505.263<br />
</td>
<td>Meantone<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>568.421<br />
</td>
<td>Triton<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>631.579<br />
</td>
<td>Triton<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>694.737<br />
</td>
<td>Meantone<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>757.895<br />
</td>
<td>Sensi<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>821.053<br />
</td>
<td>Magic<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>884.211<br />
</td>
<td>Kleismic<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>947.368<br />
</td>
<td>Godzilla<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>1010.53<br />
</td>
<td>Deutone<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>1073.68<br />
</td>
<td>Negri<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>1136.84<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:7:<h2> --><h2 id="toc3"><a name="Theory-Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h2>
19 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> < 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 ><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 ><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 ><br />
</td>
<td style="text-align: right;">21.51<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/Syntonic%20Comma">Syntonic Comma</a><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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:<h2> --><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 <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:11:<h2> --><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:<img src="http://chrisvaisvil.com/wp-content/uploads/2011/04/Media-Card_BlackBerry_pictures_IMG00145-1024x768.jpg" alt="" title="" style="height: 600px; width: 800px;" /> --><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:<h1> --><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 <a class="wiki_link" href="/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a><br />
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=1008195" rel="nofollow">Foum</a> <span class="ymp-btn-page-play ymp-media-2b0116564acb823413278e931e9bca8e"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Jacob%20Barton">Jacob Barton</a><br />
<a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sand.html" rel="nofollow">Sand</a> by <a class="wiki_link" href="/Christopher%20Bailey">Christopher Bailey</a><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> <span class="ymp-btn-page-play ymp-media-e4e0069ea45121cc80c2ce578a945837"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/William%20Sethares">William Sethares</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5zFdC6u4V" rel="nofollow">Permalink</a><br />
<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow">Truth on a bus</a> <span class="ymp-btn-page-play ymp-media-526d4e563c03aca7835db55159692c7d"><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></span> by William Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5zFdSw1g4" rel="nofollow">Permalink</a><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 <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<span class="ymp-btn-page-play ymp-media-c1ba958b4d29ea779eb3e6e1cb5779c7"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3" rel="nofollow">Citified Notions</a></span> by <a class="wiki_link" href="/John%20Starrett">John Starrett</a>.<br />
<span class="ymp-btn-page-play ymp-media-e5a2a3d148bc1b07acdba10ca90219c7"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/betelgeuse.mp3" rel="nofollow">The Light Of My Betelgeuse</a></span> by <a class="wiki_link" href="/Mykhaylo%20Khramov">Mykhaylo Khramov</a><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 <a class="wiki_link" href="/Milan%20Gu%C5%A1tar">Milan Guštar</a><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 <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><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<br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=883" rel="nofollow">jjj</a> <span class="ymp-btn-page-play ymp-media-35bea9630e48d0842ee9259bac028257"><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/daily20110523-19take2.mp3" rel="nofollow">play</a></span> by Chris Vaisvil</body></html>