Xenharmonic Wiki

19edo

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[[toc]]
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=Theory= 

In music, **19 equal temperament**, called 19-TET, 19-[[xenharmonic/EDO|EDO]], or 19-ET, is the scale derived by dividing the [[xenharmonic/octave|octave]] into 19 [[xenharmonic/equal|equal]]ly large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[xenharmonic/cent|cents]]. It is the 8th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/17edo|17edo]] and coming before [[xenharmonic/23edo|23edo]].

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 [[xenharmonic/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 [[xenharmonic/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 [[xenharmonic/Meantone family|meantone]] temperament. It is also a suitable for [[xenharmonic/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 [[xenharmonic/31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[xenharmonic/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 [[xenharmonic/Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]]. It is less successful with [[xenharmonic/7-limit|7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[xenharmonic/7_6|7/6]]), and a septimal whole tone ([[xenharmonic/8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. 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. The [[xenharmonic/Graham complexity|Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and 13 for sensi.

Being a zeta integral tuning, the 13-limit is represented relatively well, and practically [[19edo|19-edo]] can be used //adaptively// on instruments which are allowing you to bend notes up: by different amounts, the 3rd, 5th, 7th and 13th harmonics are all tuned flat. The same cannot be said of 12edo, in which the 5th, 7th and 11th are - not only farther than they are in 19, but fairly sharp already.

==Intervals and linear temperaments== 
[[xenharmonic/List of 19et rank two temperaments by badness|List of 19et rank two temperaments by badness]]
[[List of 19et rank two temperaments by complexity]]
[[List of edo-distinct 19et rank two temperaments]]

Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate.
||~ Degrees of 19edo ||~ Solfege ||~ **Dodecatonic notation A** ||~ **<span style="text-align: center;">Dodecatonic notation B</span>** ||~ **<span style="text-align: center;">Dodecatonic notation C</span>** ||~ **<span style="font-size: 13.3333339691162px; text-align: center;">Dodecatonic notation D</span>** ||~ Cents value ||~ Ratios* ||~ Generator for ||
|| 0 || do || C || C || C || C ||= 0 || 1/1 ||   ||
|| 1 || di || Ç || C#/Δb || <span style="font-size: 13.3333339691162px;">Ç</span> || <span style="font-size: 13.3333339691162px;">C#/Δb</span> || 63.1579 || 25/24, 26/25, 27/26, 28/27 || Unicorn/rhinocerus ||
|| 2 || ra || Ç#/Db || Δ || <span style="font-size: 13.3333339691162px;">Ç#/Db</span> || <span style="font-size: 13.3333339691162px;">Δ</span> || 126.326 || 13/12, 14/13, 15/14, 16/15 || [[xenharmonic/Negri|Negri]] ||
|| 3 || re || D || D || D || D || 189.474 || 9/8, 10/9 || Deutone (2-meantone) / spell ||
|| 4 || ri/ma || Þ || D#/εb || <span style="font-size: 13.3333339691162px;">Þ</span> || <span style="font-size: 13.3333339691162px;">D#/εb</span> || 252.632 || 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] ||
|| 5 || me || Þ#/Eb || ε || <span style="font-size: 13.3333339691162px;">Þ#/Eb</span> || <span style="font-size: 13.3333339691162px;">ε</span> || 315.789 || 6/5 || [[xenharmonic/Kleismic|Kleismic]] ([[xenharmonic/hanson|hanson]], [[xenharmonic/keemun|keemun]], [[xenharmonic/catakleismic|catakleismic]]) ||
|| 6 || mi || E || E || E || E || 378.947 || 5/4, 16/13 || [[xenharmonic/Magic|Magic]]/charisma/glamour ||
|| 7 || mo || E#/Fb || E#/Fb || <span style="font-size: 13.3333339691162px;">E#/Fb</span> || E#/Fb || 442.105 || 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] ||
|| 8 || fa || F || F || F || F || 505.263 || 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] ||
|| 9 || fi || ϕ || ϕ || <span style="font-size: 13.3333339691162px;">ϕ</span> || F#/Γb || 568.421 || 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa ||
|| 10 || se || ϕ#/Gb || <span style="font-size: 12.8000001907349px;">ϕ#/Gb</span> || <span style="font-size: 13.3333339691162px;">ϕ#/Gb</span> || Γ || 631.579 || 10/7, 13/9 || Liese/triton/lisa ||
|| 11 || sol || G || G || G || G || 694.737 || 3/2 || Meantone ||
|| 12 || lo || Z || G#/αb || Z || <span style="font-size: 13.3333339691162px;">G#/αb</span> || 757.895 || 14/9, 20/13 || Sensi ||
|| 13 || le || Z#/Ab || α || <span style="font-size: 13.3333339691162px;">Z#/Ab</span> || <span style="font-size: 13.3333339691162px;">α</span> || 821.053 || 8/5, 13/8 || Magic ||
|| 14 || la || A || A || A || A || 884.211 || 5/3 || Kleismic (hanson, keemun, catakleismic) ||
|| 15 || li/ta || Æ || A#/βb, A#/Bb || <span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span> || <span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span> || 947.368 || 7/4, 12/7, 26/15 || Godzilla ||
|| 16 || te || Æ#/Bb || β, B || <span style="font-size: 13.3333339691162px;">β, B</span> || <span style="font-size: 13.3333339691162px;">β, B</span> || 1010.53 || 9/5, 16/9 || Deutone / spell ||
|| 17 || ti || B || B, H || <span style="font-size: 13.3333339691162px;">B, H</span> || <span style="font-size: 13.3333339691162px;">B, H</span> || 1073.68 || 13/7, 15/8, 24/13, 28/15 || Negri ||
|| 18 || da || B#/Cb || B#, H#/Cb || <span style="font-size: 13.3333339691162px;">B#, H#/Cb</span> || <span style="font-size: 13.3333339691162px;">B#, H#/Cb</span> || 1136.84 || 48/25, 25/13, 52/27, 27/14 || Unicorn/rhinocerus ||
*based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.

===Intervals by patent val error=== 
|| Interval || Error ||
|| 6/5 || 0.148 ||
|| 14/13 || -1.982 ||
|| 15/13 || 4.891 ||
|| 18/13 || 5.039 ||
|| 15/14 || 6.873 ||
|| 9/7 || 7.021 ||
|| 10/9 || 7.070 ||
|| 4/3 || 7.218 ||
|| 5/4 || -7.366 ||
|| 13/10 || -12.109 ||
|| 13/12 || -12.257 ||
|| 7/5 || -14.091 ||
|| 7/6 || -14.239 ||
|| 9/8 || -14.436 ||
|| 16/15 || 14.585 ||
|| 11/8 || 17.103 ||
|| 16/13 || 19.475 ||
|| 8/7 || 21.457 ||
|| 12/11 || -24.321 ||
|| 11/10 || 24.469 ||
|| 11/9 || 31.539 ||
|| 15/11 || -31.688 ||
|| 13/11 || -36.578 ||
|| 14/11 || -38.561 ||

[[media type="custom" key="24906428"]]
[[file:19ed2-001.svg]]

==Commas== 
19 EDO [[xenharmonic/tempering out|tempers out]] the following [[xenharmonic/comma|comma]]s. (Note: This assumes the [[xenharmonic/val|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 ||=   ||
||= [[xenharmonic/81_80|81/80]] ||< | -4 4 -1 > ||> 21.51 ||= [[xenharmonic/Syntonic Comma|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 ||=   ||
||= [[xenharmonic/49_48|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 ||=   ||=   ||
||= [[xenharmonic/245_243|245/243]] ||< | 0 -5 1 2 > ||> 14.19 ||= Sensamagic ||=   ||=   ||
||= [[xenharmonic/126_125|126/125]] ||< | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||=   ||
||= [[xenharmonic/225_224|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 ||=   ||=   ||
||= [[xenharmonic/100_99|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|385/384]] ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||=   ||
||= 540/539 ||< | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||=   ||=   ||
||= [[xenharmonic/91_90|91/90]] ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||=   ||=   ||
||= 676/675 ||< | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||=   ||=   ||


==See also== 
* [[19edo Modes]]
* [[Strictly proper 19edo scales|Strictly prope]][[Strictly proper 19edo scales|r 19edo scales]]
* [[How to tune a 19edo guitar by ear]]

==Articles== 
* [[http://sonic-arts.org/darreg/case.htm|A Case For Nineteen]] by [[xenharmonic/Ivor Darreg|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 [[xenharmonic/Ron Sword|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.
= = 
==Photos== 
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="560" height="420"]]

----
=Compositions[[media type="custom" key="23473446"]]= 
**[[http://micro.soonlabel.com/19-ET/|XA 19-ET Index]]**

<span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[https://soundcloud.com/aaron-krister-johnson/the-juggler|The Juggler]]</span></span></span></span> </span>by [[xenharmonic/Aaron Krister Johnson|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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3|play]]</span></span></span></span></span> by [[xenharmonic/Jacob Barton|Jacob Barton]]
[[http://music.columbia.edu/%7Echris/sand.html|Sand]] by [[xenharmonic/Christopher Bailey|Christopher Bailey]]
<span class="ymp-btn-page-play ymp-media-1ec26b280d7788ac0e790719d577a218"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://works.music.columbia.edu/%7Echris/19mix1.mp3|Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me]]</span></span></span></span> </span>by Christopher Bailey
<span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3|Ditty]]</span></span></span></span> </span>by Christopher Bailey
//[[http://micro.soonlabel.com/gene_ward_smith/misc/Guillaume%20Costeley%20-%20Seigneur%20Dieu%20ta%20piti%e9.mp3|Seigneur Dieu ta pitié]]// by Guillaume Costeley
//[[http://micro.soonlabel.com/0-hosted-albums/ivor/02%20Prelude%202%20for%2019%20tone%20guitar.mp3|Prelude 2 for 19 tone guitar]]// by [[Ivor Darreg]]
[[http://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] <span class="ymp-btn-page-play ymp-media-e4e0069ea45121cc80c2ce578a945837"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3|play]]</span></span></span></span></span> by [[xenharmonic/William Sethares|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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]]</span></span></span></span></span> by William Sethares [[http://www.webcitation.org/5zFdSw1g4|Permalink]]
<span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.h-pi.com/mp3/Rondo19ET.mp3|Rondo in 19ET]]</span></span></span></span> </span>by [[xenharmonic/Aaron Andrew Hunt|Aaron Andrew Hunt]]
<span class="ymp-btn-page-play ymp-media-c1ba958b4d29ea779eb3e6e1cb5779c7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3|Citified Notions]]//</span></span></span></span></span> and
//[[http://archive.org/download/LimpOffToSchool/LimpOffToSchool19tet.mp3|Limp Off to School]]// by [[xenharmonic/John Starrett|John Starrett]].
<span class="ymp-btn-page-play ymp-media-e5a2a3d148bc1b07acdba10ca90219c7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/betelgeuse.mp3|The Light Of My Betelgeuse]]//</span></span></span></span></span> by [[xenharmonic/Mykhaylo Khramov|Mykhaylo Khramov]]
//[[http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/01.Undines.mp3|Undines]]//, //[[http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/02.Sylphs.mp3|Sylphs]]//, //[[http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/03.Gnomes.mp3|Gnomes]]//, and //[[http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/04.Salamanders.mp3|Salamanders]]// by Jon Lyle Smith
[[http://archive.org/details/AnotherAireForLute|Another Aire For Lute]] by Jon Lyle Smith
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.mp3|Zvíře]] by [[http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html|Milan Guštar]]
[[http://www.ziaspace.com/ZIA/sections/music.html|19tet downloadable mp3s by ZIA, Elaine Walker and D.D.T.]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/14%20-%2014.%2019%20octave.mp3|Comets Over Flatland 14]]//</span></span></span></span> by [[xenharmonic/Randy Winchester|Randy Winchester]]
[[@http://chrisvaisvil.com/?p=865|Forgetting Even Her Beauty blog]] <span class="ymp-btn-page-play ymp-media-7cdb4644c05849d85c1a04ed2a07a5a7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/19-ET/daily20110516-19-forgetting_even_her_beauty.mp3|play Forgetting Even Her Beauty]]//</span></span></span></span> </span>by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]]
[[@http://chrisvaisvil.com/?p=855|19 Black Hawks for Osama blog]] <span class="ymp-media-3badeb9b3b5a5768a5e43cea7e10b377 ymp-btn-page-play"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=gGO0R381HQs|play video for 19 Black Hawks for Osama]]// </span></span></span></span> </span>by Chris Vaisvil
[[@http://chrisvaisvil.com/?p=823|Summer Song blog]] <span class="ymp-media-44691c8e07e030770b33e146e0d88212 ymp-btn-page-play"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/19-ET/daily20110501-19-summer_song_mix3.mp3|play Summer Song]]//</span></span></span></span> </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"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=-KaRXFoYwT4|play video of performance of 19 ImprovFridays]]// </span></span></span></span> </span>by Chris Vaisvil
[[@http://chrisvaisvil.com/?p=800|The World has Changed blog]] <span class="ymp-media-d1cc76332b281044aecd4287b683de9d ymp-btn-page-play"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/19-ET/daily20110429-19edo-the_world_has_changed3.mp3|play The World has Changed]]//</span></span></span></span> </span>by Chris Vaisvil
[[http://chrisvaisvil.com/?p=883|jjj]] <span class="ymp-btn-page-play ymp-media-35bea9630e48d0842ee9259bac028257"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/19-ET/daily20110523-19take2.mp3|play]]//</span></span></span></span></span> by Chris Vaisvil
[[http://soundcloud.com/omega9/chip-chamber|Now listen! Pitch!]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Now%20listen%21%20Pitch%21.mp3|play]] by Omega9
[[https://www.youtube.com/watch?v=mlvme3ukPLE|Cordas (19-edo version)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas.mp3|play]] by Omega9
//[[http://www.youtube.com/watch?v=DSOGF4gDYu8|A Piece in 19edo]]// by Omega9
[[http://soundcloud.com/omega9/a-piece-in-19edo-version-3|A Piece in 19edo (ver.3)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20A%20Piece%20in%2019edo.mp3|play]] by Omega9
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/WTC2-24/19-edo-A-Prelude.mp3|Bach’s Prelude number 24 from Well Tempered Clavier, Book II]]//</span></span></span>
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/WTC2-24/19-edo-B-Fugue.mp3|Bach’s Fugue number 24 from Well Tempered Clavier, Book II]]//</span></span></span>
rendered by Claudi Meneghin
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/_Movi_Nove__by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3|Movi-Nove]]// by [[https://soundcloud.com/lois-lancaster/movi-nove|Roncevaux (Löis Lancaster)]]

Original HTML content:

<html><head><title>19edo</title></head><body><!-- ws:start:WikiTextTocRule:24:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#Theory">Theory</a></div>
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Theory-As an approximation of other temperaments">As an approximation of other temperaments</a></div>
<!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 2em;"><a href="#Theory-Intervals and linear temperaments">Intervals and linear temperaments</a></div>
<!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 3em;"><a href="#Theory-Intervals and linear temperaments-Intervals by patent val error">Intervals by patent val error</a></div>
<!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 2em;"><a href="#Theory-Commas">Commas</a></div>
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#Theory-See also">See also</a></div>
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Theory-Articles">Articles</a></div>
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#Theory-References">References</a></div>
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#toc8"> </a></div>
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Theory-Photos">Photos</a></div>
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Compositions">Compositions</a></div>
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --></div>
<!-- ws:end:WikiTextTocRule:36 --><hr />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h1>
 <br />
In music, <strong>19 equal temperament</strong>, called 19-TET, 19-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/EDO">EDO</a>, or 19-ET, is the scale derived by dividing the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 19 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/cent">cents</a>. It is the 8th <a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/23edo">23edo</a>.<br />
<br />
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson <a class="wiki_link" href="/Seigneur%20Dieu%20ta%20piti%C3%A9">Seigneur Dieu ta pitié</a> 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="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/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:4:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->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="http://xenharmonic.wikispaces.com/Meantone%20family">meantone</a> temperament. It is also a suitable for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. 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. The <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and 13 for sensi.<br />
<br />
Being a zeta integral tuning, the 13-limit is represented relatively well, and practically <a class="wiki_link" href="/19edo">19-edo</a> can be used <em>adaptively</em> on instruments which are allowing you to bend notes up: by different amounts, the 3rd, 5th, 7th and 13th harmonics are all tuned flat. The same cannot be said of 12edo, in which the 5th, 7th and 11th are - not only farther than they are in 19, but fairly sharp already.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals and linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals and linear temperaments</h2>
 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2019et%20rank%20two%20temperaments%20by%20badness">List of 19et rank two temperaments by badness</a><br />
<a class="wiki_link" href="/List%20of%2019et%20rank%20two%20temperaments%20by%20complexity">List of 19et rank two temperaments by complexity</a><br />
<a class="wiki_link" href="/List%20of%20edo-distinct%2019et%20rank%20two%20temperaments">List of edo-distinct 19et rank two temperaments</a><br />
<br />
Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate.<br />


<table class="wiki_table">
    <tr>
        <th>Degrees of 19edo<br />
</th>
        <th>Solfege<br />
</th>
        <th><strong>Dodecatonic notation A</strong><br />
</th>
        <th><strong><span style="text-align: center;">Dodecatonic notation B</span></strong><br />
</th>
        <th><strong><span style="text-align: center;">Dodecatonic notation C</span></strong><br />
</th>
        <th><strong><span style="font-size: 13.3333339691162px; text-align: center;">Dodecatonic notation D</span></strong><br />
</th>
        <th>Cents value<br />
</th>
        <th>Ratios*<br />
</th>
        <th>Generator for<br />
</th>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>do<br />
</td>
        <td>C<br />
</td>
        <td>C<br />
</td>
        <td>C<br />
</td>
        <td>C<br />
</td>
        <td style="text-align: center;">0<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>di<br />
</td>
        <td>Ç<br />
</td>
        <td>C#/Δb<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">Ç</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">C#/Δb</span><br />
</td>
        <td>63.1579<br />
</td>
        <td>25/24, 26/25, 27/26, 28/27<br />
</td>
        <td>Unicorn/rhinocerus<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>ra<br />
</td>
        <td>Ç#/Db<br />
</td>
        <td>Δ<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">Ç#/Db</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">Δ</span><br />
</td>
        <td>126.326<br />
</td>
        <td>13/12, 14/13, 15/14, 16/15<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Negri">Negri</a><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>re<br />
</td>
        <td>D<br />
</td>
        <td>D<br />
</td>
        <td>D<br />
</td>
        <td>D<br />
</td>
        <td>189.474<br />
</td>
        <td>9/8, 10/9<br />
</td>
        <td>Deutone (2-meantone) / spell<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>ri/ma<br />
</td>
        <td>Þ<br />
</td>
        <td>D#/εb<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">Þ</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">D#/εb</span><br />
</td>
        <td>252.632<br />
</td>
        <td>7/6, 8/7, 15/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Godzilla">Godzilla</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>me<br />
</td>
        <td>Þ#/Eb<br />
</td>
        <td>ε<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">Þ#/Eb</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">ε</span><br />
</td>
        <td>315.789<br />
</td>
        <td>6/5<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kleismic">Kleismic</a> (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/hanson">hanson</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/keemun">keemun</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/catakleismic">catakleismic</a>)<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>mi<br />
</td>
        <td>E<br />
</td>
        <td>E<br />
</td>
        <td>E<br />
</td>
        <td>E<br />
</td>
        <td>378.947<br />
</td>
        <td>5/4, 16/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Magic">Magic</a>/charisma/glamour<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>mo<br />
</td>
        <td>E#/Fb<br />
</td>
        <td>E#/Fb<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">E#/Fb</span><br />
</td>
        <td>E#/Fb<br />
</td>
        <td>442.105<br />
</td>
        <td>9/7, 13/10<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensi">Sensi</a><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>fa<br />
</td>
        <td>F<br />
</td>
        <td>F<br />
</td>
        <td>F<br />
</td>
        <td>F<br />
</td>
        <td>505.263<br />
</td>
        <td>4/3<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone">Meantone</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/flattone">flattone</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/meanennedecal">meanenneadecal</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/meanpop">meanpop</a><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>fi<br />
</td>
        <td>ϕ<br />
</td>
        <td>ϕ<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">ϕ</span><br />
</td>
        <td>F#/Γb<br />
</td>
        <td>568.421<br />
</td>
        <td>7/5, 18/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Liese">Liese</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Triton">triton</a>/lisa<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>se<br />
</td>
        <td>ϕ#/Gb<br />
</td>
        <td><span style="font-size: 12.8000001907349px;">ϕ#/Gb</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">ϕ#/Gb</span><br />
</td>
        <td>Γ<br />
</td>
        <td>631.579<br />
</td>
        <td>10/7, 13/9<br />
</td>
        <td>Liese/triton/lisa<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>sol<br />
</td>
        <td>G<br />
</td>
        <td>G<br />
</td>
        <td>G<br />
</td>
        <td>G<br />
</td>
        <td>694.737<br />
</td>
        <td>3/2<br />
</td>
        <td>Meantone<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>lo<br />
</td>
        <td>Z<br />
</td>
        <td>G#/αb<br />
</td>
        <td>Z<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">G#/αb</span><br />
</td>
        <td>757.895<br />
</td>
        <td>14/9, 20/13<br />
</td>
        <td>Sensi<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>le<br />
</td>
        <td>Z#/Ab<br />
</td>
        <td>α<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">Z#/Ab</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">α</span><br />
</td>
        <td>821.053<br />
</td>
        <td>8/5, 13/8<br />
</td>
        <td>Magic<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>la<br />
</td>
        <td>A<br />
</td>
        <td>A<br />
</td>
        <td>A<br />
</td>
        <td>A<br />
</td>
        <td>884.211<br />
</td>
        <td>5/3<br />
</td>
        <td>Kleismic (hanson, keemun, catakleismic)<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>li/ta<br />
</td>
        <td>Æ<br />
</td>
        <td>A#/βb, A#/Bb<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span><br />
</td>
        <td>947.368<br />
</td>
        <td>7/4, 12/7, 26/15<br />
</td>
        <td>Godzilla<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>te<br />
</td>
        <td>Æ#/Bb<br />
</td>
        <td>β, B<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">β, B</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">β, B</span><br />
</td>
        <td>1010.53<br />
</td>
        <td>9/5, 16/9<br />
</td>
        <td>Deutone / spell<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>ti<br />
</td>
        <td>B<br />
</td>
        <td>B, H<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">B, H</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">B, H</span><br />
</td>
        <td>1073.68<br />
</td>
        <td>13/7, 15/8, 24/13, 28/15<br />
</td>
        <td>Negri<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>da<br />
</td>
        <td>B#/Cb<br />
</td>
        <td>B#, H#/Cb<br />
</td>
        <td><span style="font-size: 13.3333339691162px;">B#, H#/Cb</span><br />
</td>
        <td><span style="font-size: 13.3333339691162px;">B#, H#/Cb</span><br />
</td>
        <td>1136.84<br />
</td>
        <td>48/25, 25/13, 52/27, 27/14<br />
</td>
        <td>Unicorn/rhinocerus<br />
</td>
    </tr>
</table>

*based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc3"><a name="Theory-Intervals and linear temperaments-Intervals by patent val error"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals by patent val error</h3>
 

<table class="wiki_table">
    <tr>
        <td>Interval<br />
</td>
        <td>Error<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>0.148<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>-1.982<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>4.891<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>5.039<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>6.873<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>7.021<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>7.070<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>7.218<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>-7.366<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>-12.109<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>-12.257<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>-14.091<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>-14.239<br />
</td>
    </tr>
    <tr>
        <td>9/8<br />
</td>
        <td>-14.436<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>14.585<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>17.103<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>19.475<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>21.457<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>-24.321<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>24.469<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>31.539<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>-31.688<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>-36.578<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>-38.561<br />
</td>
    </tr>
</table>

<br />
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<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="Theory-Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h2>
 19 EDO <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/val">val</a> &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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/81_80">81/80</a><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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 &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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/49_48">49/48</a><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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/245_243">245/243</a><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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/126_125">126/125</a><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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/225_224">225/224</a><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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/100_99">100/99</a><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;"><a class="wiki_link" href="/385_384">385/384</a><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;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/91_90">91/90</a><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:12:&lt;h2&gt; --><h2 id="toc5"><a name="Theory-See also"></a><!-- ws:end:WikiTextHeadingRule:12 -->See also</h2>
 <ul><li><a class="wiki_link" href="/19edo%20Modes">19edo Modes</a></li><li><a class="wiki_link" href="/Strictly%20proper%2019edo%20scales">Strictly prope</a><a class="wiki_link" href="/Strictly%20proper%2019edo%20scales">r 19edo scales</a></li><li><a class="wiki_link" href="/How%20to%20tune%20a%2019edo%20guitar%20by%20ear">How to tune a 19edo guitar by ear</a></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Theory-Articles"></a><!-- ws:end:WikiTextHeadingRule:14 -->Articles</h2>
 <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="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/Ron%20Sword">Ron Sword</a></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:16 -->References</h2>
 <ul><li>Bucht, Saku and Huovinen, Erkki, <em>Perceived consonance of harmonic intervals in 19-tone equal temperament</em>, CIM04_proceedings.</li><li>Levy, Kenneth J., <em>Costeley's Chromatic Chanson</em>, Annales Musicologues: Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.</li></ul><!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc8"><!-- ws:end:WikiTextHeadingRule:18 --> </h1>
 <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc9"><a name="Theory-Photos"></a><!-- ws:end:WikiTextHeadingRule:20 -->Photos</h2>
 19 note per octave Ibanez conversion by Brad Smith (Indianapolis)<br />
<!-- ws:start:WikiTextRemoteImageRule:1019:&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: 420px; width: 560px;&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: 420px; width: 560px;" /><!-- ws:end:WikiTextRemoteImageRule:1019 --><br />
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc10"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:22 -->Compositions<!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/23473446?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;23473446&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player-beta.js">
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 <strong><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/" rel="nofollow">XA 19-ET Index</a></strong><br />
<br />
<span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="https://soundcloud.com/aaron-krister-johnson/the-juggler" rel="nofollow">The Juggler</a></span></span></span></span> </span>by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a><br />
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&amp;songID=1008195" rel="nofollow">Foum</a> <span class="ymp-btn-page-play ymp-media-2b0116564acb823413278e931e9bca8e"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3" rel="nofollow">play</a></span></span></span></span></span> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/Christopher%20Bailey">Christopher Bailey</a><br />
<span class="ymp-btn-page-play ymp-media-1ec26b280d7788ac0e790719d577a218"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span></span> </span>by Christopher Bailey<br />
<span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3" rel="nofollow">Ditty</a></span></span></span></span> </span>by Christopher Bailey<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/misc/Guillaume%20Costeley%20-%20Seigneur%20Dieu%20ta%20piti%e9.mp3" rel="nofollow">Seigneur Dieu ta pitié</a></em> by Guillaume Costeley<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/0-hosted-albums/ivor/02%20Prelude%202%20for%2019%20tone%20guitar.mp3" rel="nofollow">Prelude 2 for 19 tone guitar</a></em> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a><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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3" rel="nofollow">play</a></span></span></span></span></span> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span></span></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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Rondo19ET.mp3" rel="nofollow">Rondo in 19ET</a></span></span></span></span> </span>by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<span class="ymp-btn-page-play ymp-media-c1ba958b4d29ea779eb3e6e1cb5779c7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3" rel="nofollow">Citified Notions</a></em></span></span></span></span></span> and<br />
<em><a class="wiki_link_ext" href="http://archive.org/download/LimpOffToSchool/LimpOffToSchool19tet.mp3" rel="nofollow">Limp Off to School</a></em> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/John%20Starrett">John Starrett</a>.<br />
<span class="ymp-btn-page-play ymp-media-e5a2a3d148bc1b07acdba10ca90219c7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><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></em></span></span></span></span></span> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mykhaylo%20Khramov">Mykhaylo Khramov</a><br />
<em><a class="wiki_link_ext" href="http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/01.Undines.mp3" rel="nofollow">Undines</a></em>, <em><a class="wiki_link_ext" href="http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/02.Sylphs.mp3" rel="nofollow">Sylphs</a></em>, <em><a class="wiki_link_ext" href="http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/03.Gnomes.mp3" rel="nofollow">Gnomes</a></em>, and <em><a class="wiki_link_ext" href="http://archive.org/download/ElementalsFor2PianosIn19EqualTemperament/04.Salamanders.mp3" rel="nofollow">Salamanders</a></em> by Jon Lyle Smith<br />
<a class="wiki_link_ext" href="http://archive.org/details/AnotherAireForLute" rel="nofollow">Another Aire For Lute</a> by Jon Lyle Smith<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.mp3" rel="nofollow">Zvíře</a> by <a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/flao_yg/zvire.html" rel="nofollow">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 />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/14%20-%2014.%2019%20octave.mp3" rel="nofollow">Comets Over Flatland 14</a></em></span></span></span></span> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Randy%20Winchester">Randy Winchester</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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><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></em></span></span></span></span> </span>by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=gGO0R381HQs" rel="nofollow">play video for 19 Black Hawks for Osama</a></em> </span></span></span></span> </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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/daily20110501-19-summer_song_mix3.mp3" rel="nofollow">play Summer Song</a></em></span></span></span></span> </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"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=-KaRXFoYwT4" rel="nofollow">play video of performance of 19 ImprovFridays</a></em> </span></span></span></span> </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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><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></em></span></span></span></span> </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"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/19-ET/daily20110523-19take2.mp3" rel="nofollow">play</a></em></span></span></span></span></span> by Chris Vaisvil<br />
<a class="wiki_link_ext" href="http://soundcloud.com/omega9/chip-chamber" rel="nofollow">Now listen! Pitch!</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Now%20listen%21%20Pitch%21.mp3" rel="nofollow">play</a> by Omega9<br />
<a class="wiki_link_ext" href="https://www.youtube.com/watch?v=mlvme3ukPLE" rel="nofollow">Cordas (19-edo version)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas.mp3" rel="nofollow">play</a> by Omega9<br />
<em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=DSOGF4gDYu8" rel="nofollow">A Piece in 19edo</a></em> by Omega9<br />
<a class="wiki_link_ext" href="http://soundcloud.com/omega9/a-piece-in-19edo-version-3" rel="nofollow">A Piece in 19edo (ver.3)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20A%20Piece%20in%2019edo.mp3" rel="nofollow">play</a> by Omega9<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/WTC2-24/19-edo-A-Prelude.mp3" rel="nofollow">Bach’s Prelude number 24 from Well Tempered Clavier, Book II</a></em></span></span></span><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><span style="right: auto;"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/WTC2-24/19-edo-B-Fugue.mp3" rel="nofollow">Bach’s Fugue number 24 from Well Tempered Clavier, Book II</a></em></span></span></span><br />
rendered by Claudi Meneghin<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/_Movi_Nove__by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3" rel="nofollow">Movi-Nove</a></em> by <a class="wiki_link_ext" href="https://soundcloud.com/lois-lancaster/movi-nove" rel="nofollow">Roncevaux (Löis Lancaster)</a></body></html>
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