10edo
IMPORTED REVISION FROM WIKISPACES
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Original Wikitext content:
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 and its inversion a large neutral seventh; 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. === === ===Intervals=== || degrees of 10edo || cents value || || 0 || 0 || || 1 || 120 || || 2 || 240 || || 3 || 360 || || 4 || 480 || || 5 || 600 || || 6 || 720 || || 7 || 840 || || 8 || 960 || || 9 || 1080 || ==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]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3|play]] by Bill Sethares (synth guitar) [[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Circle of Thirds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3|play]] by Bill Sethares (synth ens.) [[http://www.akjmusic.com/works.html|10_fantasy]] by Aaron K. Johnson (synth monody) [[http://www.ziaspace.com/ZIA/mp3s/Future.html|Future]] and [[http://www.ziaspace.com/ZIA/mp3s/Sol.html|Sol]] by ZIA (synths and voice in 10) [[http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3|Prelude]] by Rick McGowan (Rhino synthesizer) [[http://soundclick.com/share?songid=5683815|Ideas on the Waterfall of Expression]] by Iglashion Jones (synth) ||~ ||~ ||~ ||~ ||~ ||~ || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || || ||= || ||> ||= ||= || ||
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 and its inversion a large neutral seventh; 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.<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h3>
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x--Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h3>
<table class="wiki_table">
<tr>
<td>degrees of 10edo<br />
</td>
<td>cents value<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>120<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>240<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>360<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>480<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>600<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>720<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>840<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>960<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>1080<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2>
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:6:<h3> --><h3 id="toc3"><a name="x-Commas-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h3>
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Ten Fingers</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3" rel="nofollow">play</a> by Bill Sethares (synth guitar)<br />
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Circle of Thirds</a> <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> by Bill Sethares (synth ens.)<br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">10_fantasy</a> by Aaron K. Johnson (synth monody)<br />
<a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Future.html" rel="nofollow">Future</a> and <a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Sol.html" rel="nofollow">Sol</a> by ZIA (synths and voice in 10)<br />
<a class="wiki_link_ext" href="http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3" rel="nofollow">Prelude</a> by Rick McGowan (Rhino synthesizer)<br />
<a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683815" rel="nofollow">Ideas on the Waterfall of Expression</a> by Iglashion Jones (synth)<br />
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