10edo
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10edo, or 10-tone equal temperament, is a tuning system which divides the [[octave]] into 10 equal parts of exactly 120 [[cent]]s. It can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13_8|13/8]] and its inversion [[16_13|16/13]]; and the droll 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOSScales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]]. One way to interpret it in terms of a temperament of Just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup. [[toc|flat]] ---- =[[media type="custom" key="10886138"]]= =Intervals= || Degree || Cent Values || Approximate Ratios* || Name || || 0 || 0 || 1/1 || unison || || 1 || 120 || 15/14, 16/15, 13/14 || small neutral second/large minor second || || 2 || 240 || 15/13, 8/7 || second/third || || 3 || 360 || 16/13 || large neutral third || || 4 || 480 || 64/49, 169/128 || smaller fourth || || 5 || 600 || 91/64, 169/120 || tritone || || 6 || 720 || 49/32, 256/169 || bigger fifth || || 7 || 840 || 13/8 || neutral sixth || || 8 || 960 || 7/4, 26/15, 125/72 || sixth/seventh || || 9 || 1080 || 15/8, 28/15, 13/7 || small major 7th || || 10 || 1200 || 2/1 || octave || *based on treating 10-EDO as a 2.7.13.15 subgroup temperament. =Linear temperaments= ||~ Periods per octave ||~ Generator ||~ Temperament(s) || || 1 || 1\10 || Messed-up [[Negri|negri]] (or [[Miracle|miracle]]) || || 1 || 3\10 || [[Dicot]]/[[Beatles|beatles]]/neutral thirds scale || || 2 || 1\10 || Messed-up [[pajara]] || || 2 || 2\10 || [[Decimal]] / messed-up [[Lemba|lemba]] || || 5 || 1\10 || [[Blackwood]]/[[blacksmith]] || =Commas= 10 EDO tempers out the following commas. (Note: This assumes the val < 10 16 23 28 35 37 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 256/243 || | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd || || ||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || || ||= 9931568/9752117 || | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||= || || ||= 2048/2025 || | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= || || ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || || ||= 49/48 || | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= || || ||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma || || ||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= || || ||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma || ||= 9859966/9733137 || | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||= || || ||= 1029/1024 || | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= || || ||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma || || ||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= || || ||= 6772805/6751042 || | 11 -10 -10 10 > ||> 5.57 ||= Linus ||= || || ||= 2401/2400 || | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= || || ||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||= || || ||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= || || ||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= || || ||= 540/539 || | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||= || || ||= 3025/3024 || | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||= || || ||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= || || ||= 676/675 || | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= || || =Music= [[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Ten Fingers]] <span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"><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/Ten_Fingers.mp3|play]]</span></span> by [[Bill Sethares]] (synth guitar) [[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Circle of Thirds]] <span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"><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/Circle_of_Thirds.mp3|play]]</span></span> by Bill Sethares (synth ens.) [[http://www.akjmusic.com/works.html|10_fantasy]] <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d"><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/AKJ/10_fantasy.mp3|play]]</span></span> by [[Aaron Krister Johnson]] (synth monody) <span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93"><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/Hunt/Prelude%20in%2010ET.mp3|Prelude in 10ET]]</span></span> by [[Aaron Andrew Hunt]] [[http://www.ziaspace.com/ZIA/mp3s/Future.html|Future]] <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://ziaspace.com/ZIA/mp3s/Future.mp3|play]]</span></span> and [[http://www.ziaspace.com/ZIA/mp3s/Sol.html|Sol]] <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://ziaspace.com/ZIA/mp3s/Sol.mp3|play]]</span></span> by ZIA (synths and voice in 10) <span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3|Prelude]]</span></span> by [[Rick McGowan]] (Rhino synthesizer) <span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><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/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3|Ideas on the Waterfall of Expression]]</span></span> by [[Iglashion Jones]] (synth) <span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3|For two violas and gongs]]</span></span> by [[@http://www.chrisvaisvil.com|Chris Vaisvil (website)]] [[@http://chrisvaisvil.com/?p=1039|more composition information]] [[file:10preview.ogg]] A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte) [[file:decexperiment.ogg]]3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte) <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3|10 Earwigs Invasive]]</span> by [[@http://chrisvaisvil.com/?p=1397|Chris Vaisvil]] <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/09%20-%209.%2010%20octave.mp3|Comets Over Flatland 9]]</span> by [[Randy Winchester]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3|The Dramatic Squirrel Overture]]</span> by [[Chris Vaisvil]] [[@http://chrisvaisvil.com/?p=1368|Details]] [[@http://andrewheathwaite.bandcamp.com/track/shimmerwing|Shimmerwing]] by [[Andrew Heathwaite]] and [[Chris Vaisvil]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20The%20Csx%20Freight%20at%201-20%20am.mp3|The Csx Freight at 1:20 am]] by [[Zach Curley]] =**Instruments**= 10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple. Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from [[20edo]] which approximates the 11th harmonic with relative accuracy, among other features. [[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[image:decaphonic-uke.JPG width="526" height="406"]][[media type="custom" key="10021077"]]
Original HTML content:
<html><head><title>10edo</title></head><body>10edo, or 10-tone equal temperament, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 10 equal parts of exactly 120 <a class="wiki_link" href="/cent">cent</a>s. It can be thought of as two circles of <a class="wiki_link" href="/5edo">5edo</a> separated by 120 cents (or 5 circles of <a class="wiki_link" href="/2edo">2edo</a>). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of <a class="wiki_link" href="/13_8">13/8</a> and its inversion <a class="wiki_link" href="/16_13">16/13</a>; and the droll 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic <a class="wiki_link" href="/MOSScales">moment of symmetry scale</a> of the form 1 2 1 2 1 2 1 (<a class="wiki_link" href="/3L%204s">3L 4s - mosh</a>). While not an integral or gap edo, it is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak edo</a>. One way to interpret it in terms of a temperament of Just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.<br />
<br />
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<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1>
<table class="wiki_table">
<tr>
<td>Degree<br />
</td>
<td>Cent<br />
Values<br />
</td>
<td>Approximate<br />
Ratios*<br />
</td>
<td>Name<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td>1/1<br />
</td>
<td>unison<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>120<br />
</td>
<td>15/14, 16/15, 13/14<br />
</td>
<td>small neutral second/large minor second<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>240<br />
</td>
<td>15/13, 8/7<br />
</td>
<td>second/third<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>360<br />
</td>
<td>16/13<br />
</td>
<td>large neutral third<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>480<br />
</td>
<td>64/49, 169/128<br />
</td>
<td>smaller fourth<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>600<br />
</td>
<td>91/64, 169/120<br />
</td>
<td>tritone<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>720<br />
</td>
<td>49/32, 256/169<br />
</td>
<td>bigger fifth<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>840<br />
</td>
<td>13/8<br />
</td>
<td>neutral sixth<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>960<br />
</td>
<td>7/4, 26/15, 125/72<br />
</td>
<td>sixth/seventh<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>1080<br />
</td>
<td>15/8, 28/15, 13/7<br />
</td>
<td>small major 7th<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>1200<br />
</td>
<td>2/1<br />
</td>
<td>octave<br />
</td>
</tr>
</table>
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc2"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Linear temperaments</h1>
<table class="wiki_table">
<tr>
<th>Periods<br />
per octave<br />
</th>
<th>Generator<br />
</th>
<th>Temperament(s)<br />
</th>
</tr>
<tr>
<td>1<br />
</td>
<td>1\10<br />
</td>
<td>Messed-up <a class="wiki_link" href="/Negri">negri</a> (or <a class="wiki_link" href="/Miracle">miracle</a>)<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>3\10<br />
</td>
<td><a class="wiki_link" href="/Dicot">Dicot</a>/<a class="wiki_link" href="/Beatles">beatles</a>/neutral thirds scale<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>1\10<br />
</td>
<td>Messed-up <a class="wiki_link" href="/pajara">pajara</a><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>2\10<br />
</td>
<td><a class="wiki_link" href="/Decimal">Decimal</a> / messed-up <a class="wiki_link" href="/Lemba">lemba</a><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>1\10<br />
</td>
<td><a class="wiki_link" href="/Blackwood">Blackwood</a>/<a class="wiki_link" href="/blacksmith">blacksmith</a><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h1>
10 EDO tempers out the following commas. (Note: This assumes the val < 10 16 23 28 35 37 |.)<br />
<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;">256/243<br />
</td>
<td>| 8 -5 ><br />
</td>
<td style="text-align: right;">90.22<br />
</td>
<td style="text-align: center;">Limma<br />
</td>
<td style="text-align: center;">Pythagorean Minor 2nd<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">16875/16384<br />
</td>
<td>| -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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">9931568/9752117<br />
</td>
<td>| -25 7 6 ><br />
</td>
<td style="text-align: right;">31.57<br />
</td>
<td style="text-align: center;">Ampersand's Comma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">2048/2025<br />
</td>
<td>| 11 -4 -2 ><br />
</td>
<td style="text-align: right;">19.55<br />
</td>
<td style="text-align: center;">Diaschisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">525/512<br />
</td>
<td>| -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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">49/48<br />
</td>
<td>| -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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">50/49<br />
</td>
<td>| 1 0 2 -2 ><br />
</td>
<td style="text-align: right;">34.98<br />
</td>
<td style="text-align: center;">Tritonic Diesis<br />
</td>
<td style="text-align: center;">Jubilisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">686/675<br />
</td>
<td>| 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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">64/63<br />
</td>
<td>| 6 -2 0 -1 ><br />
</td>
<td style="text-align: right;">27.26<br />
</td>
<td style="text-align: center;">Septimal Comma<br />
</td>
<td style="text-align: center;">Archytas' Comma<br />
</td>
<td>Leipziger Komma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">9859966/9733137<br />
</td>
<td>| -10 7 8 -7 ><br />
</td>
<td style="text-align: right;">22.41<br />
</td>
<td style="text-align: center;">Blackjackisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">1029/1024<br />
</td>
<td>| -10 1 0 3 ><br />
</td>
<td style="text-align: right;">8.43<br />
</td>
<td style="text-align: center;">Gamelisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">225/224<br />
</td>
<td>| -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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">16875/16807<br />
</td>
<td>| 0 3 4 -5 ><br />
</td>
<td style="text-align: right;">6.99<br />
</td>
<td style="text-align: center;">Mirkwai<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">6772805/6751042<br />
</td>
<td>| 11 -10 -10 10 ><br />
</td>
<td style="text-align: right;">5.57<br />
</td>
<td style="text-align: center;">Linus<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">2401/2400<br />
</td>
<td>| -5 -1 -2 4 ><br />
</td>
<td style="text-align: right;">0.72<br />
</td>
<td style="text-align: center;">Breedsma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">243/242<br />
</td>
<td>| -1 5 0 0 -2 ><br />
</td>
<td style="text-align: right;">7.14<br />
</td>
<td style="text-align: center;">Rastma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">385/384<br />
</td>
<td>| -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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">441/440<br />
</td>
<td>| -3 2 -1 2 -1 ><br />
</td>
<td style="text-align: right;">3.93<br />
</td>
<td style="text-align: center;">Werckisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">540/539<br />
</td>
<td>| 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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3025/3024<br />
</td>
<td>| -4 -3 2 -1 2 ><br />
</td>
<td style="text-align: right;">0.57<br />
</td>
<td style="text-align: center;">Lehmerisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">91/90<br />
</td>
<td>| -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><br />
</td>
</tr>
<tr>
<td style="text-align: center;">676/675<br />
</td>
<td>| 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><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music</h1>
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Ten Fingers</a> <span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"><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/Ten_Fingers.mp3" rel="nofollow">play</a></span></span> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (synth guitar)<br />
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Circle of Thirds</a> <span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"><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/Circle_of_Thirds.mp3" rel="nofollow">play</a></span></span> by Bill Sethares (synth ens.)<br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">10_fantasy</a> <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d"><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/AKJ/10_fantasy.mp3" rel="nofollow">play</a></span></span> by <a class="wiki_link" href="/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a> (synth monody)<br />
<span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93"><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/Hunt/Prelude%20in%2010ET.mp3" rel="nofollow">Prelude in 10ET</a></span></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Future.html" rel="nofollow">Future</a> <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Future.mp3" rel="nofollow">play</a></span></span> and <a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Sol.html" rel="nofollow">Sol</a> <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Sol.mp3" rel="nofollow">play</a></span></span> by ZIA (synths and voice in 10)<br />
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3" rel="nofollow">Prelude</a></span></span> by <a class="wiki_link" href="/Rick%20McGowan">Rick McGowan</a> (Rhino synthesizer)<br />
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><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/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3" rel="nofollow">Ideas on the Waterfall of Expression</a></span></span> by <a class="wiki_link" href="/Iglashion%20Jones">Iglashion Jones</a> (synth)<br />
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3" rel="nofollow">For two violas and gongs</a></span></span> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil (website)</a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1039" rel="nofollow" target="_blank">more composition information</a><br />
<!-- ws:start:WikiTextFileRule:521:<img src="http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@10preview.ogg" title="File: 10preview.ogg" width="320" height="52" /> --><div class="objectEmbed"><a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /></a><div><a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');" class="filename" title="10preview.ogg">10preview.ogg</a><br /><ul><li><a href="/file/detail/10preview.ogg">Details</a></li><li><a href="/file/view/10preview.ogg/246873297/10preview.ogg">Download</a></li><li style="color: #666">3 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:521 --> A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:522:<img src="http://www.wikispaces.com/site/embedthumbnail/file/decexperiment.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@decexperiment.ogg" title="File: decexperiment.ogg" width="320" height="52" /> --><div class="objectEmbed"><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="decexperiment.ogg" /></a><div><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');" class="filename" title="decexperiment.ogg">decexperiment.ogg</a><br /><ul><li><a href="/file/detail/decexperiment.ogg">Details</a></li><li><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:522 -->3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3" rel="nofollow">10 Earwigs Invasive</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1397" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3" rel="nofollow">Comets Over Flatland 9</a></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3" rel="nofollow">The Dramatic Squirrel Overture</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1368" rel="nofollow" target="_blank">Details</a><br />
<a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/shimmerwing" rel="nofollow" target="_blank">Shimmerwing</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> and <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20The%20Csx%20Freight%20at%201-20%20am.mp3" rel="nofollow">The Csx Freight at 1:20 am</a> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />
<!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc5"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong>Instruments</strong></h1>
<br />
10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.<br />
<br />
Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from <a class="wiki_link" href="/20edo">20edo</a> which approximates the 11th harmonic with relative accuracy, among other features.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:519:<img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="A Decaphonic (10-EDO) Classical Guitar" title="A Decaphonic (10-EDO) Classical Guitar" /> --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /></td></tr><tr><td class="imageCaption">A Decaphonic (10-EDO) Classical Guitar</td></tr></table><!-- ws:end:WikiTextLocalImageRule:519 --><!-- ws:start:WikiTextLocalImageRule:520:<img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="" title="" style="height: 406px; width: 526px;" /> --><img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /><!-- ws:end:WikiTextLocalImageRule:520 --><!-- ws:start:WikiTextMediaRule:1:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;10021077&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
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