10edo: Difference between revisions

Revision as of 04:59, 19 August 2011

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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 EDO lists|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]]
----

=Intervals= 
|| Degree || Cent
Values || Approximate
Ratios* ||
|| 0 || 0 || 1/1 ||
|| 1 || 120 || 15/14, 16/15, 13/14 ||
|| 2 || 240 || 15/13, 8/7 ||
|| 3 || 360 || 16/13 ||
|| 4 || 480 || 64/49, 169/128 ||
|| 5 || 600 || 91/64, 169/120 ||
|| 6 || 720 || 49/32, 256/169 ||
|| 7 || 840 || 13/8 ||
|| 8 || 960 || 7/4, 26/15 ||
|| 9 || 1080 || 15/8, 28/15, 13/7 ||
|| 10 || 1200 || 2/1 ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
=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">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3|play]]</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">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3|play]]</span> by Bill Sethares (synth ens.)
[[http://www.akjmusic.com/works.html|10_fantasy]] <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/AKJ/10_fantasy.mp3|play]]</span> by [[Aaron Krister Johnson]] (synth monody)
<span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2010ET.mp3|Prelude in 10ET]]</span> by [[Aaron Andrew Hunt]]
[[http://www.ziaspace.com/ZIA/mp3s/Future.html|Future]] <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357">[[http://ziaspace.com/ZIA/mp3s/Future.mp3|play]]</span> and [[http://www.ziaspace.com/ZIA/mp3s/Sol.html|Sol]] <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4">[[http://ziaspace.com/ZIA/mp3s/Sol.mp3|play]]</span> by ZIA (synths and voice in 10)
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428">[[http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3|Prelude]]</span> by [[Rick McGowan]] (Rhino synthesizer)
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca">[[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> by [[Iglashion Jones]] (synth)
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493">[[http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3|For two violas and gongs]]</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)
=**Instruments**= 

[[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[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 EDO lists">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 />
<!-- ws:start:WikiTextTocRule:9:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: -->
<!-- ws:end:WikiTextTocRule:14 --><hr />
<br />
<!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:1 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <td>Degree<br />
</td>
        <td>Cent<br />
Values<br />
</td>
        <td>Approximate<br />
Ratios*<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>1/1<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>120<br />
</td>
        <td>15/14, 16/15, 13/14<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>240<br />
</td>
        <td>15/13, 8/7<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>360<br />
</td>
        <td>16/13<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>480<br />
</td>
        <td>64/49, 169/128<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>600<br />
</td>
        <td>91/64, 169/120<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>720<br />
</td>
        <td>49/32, 256/169<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>840<br />
</td>
        <td>13/8<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>960<br />
</td>
        <td>7/4, 26/15<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1080<br />
</td>
        <td>15/8, 28/15, 13/7<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>1200<br />
</td>
        <td>2/1<br />
</td>
    </tr>
</table>

*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.<br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:3 -->Commas</h1>
 10 EDO tempers out the following commas. (Note: This assumes the val &lt; 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 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9931568/9752117<br />
</td>
        <td>| -25 7 6 &gt;<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 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td>| -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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50/49<br />
</td>
        <td>| 1 0 2 -2 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td>| 6 -2 0 -1 &gt;<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 &gt;<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 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16807<br />
</td>
        <td>| 0 3 4 -5 &gt;<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 &gt;<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 &gt;<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 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3025/3024<br />
</td>
        <td>| -4 -3 2 -1 2 &gt;<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 &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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td>| 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><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:5 -->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"><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> 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"><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> 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"><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> 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"><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> 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"><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Future.mp3" rel="nofollow">play</a></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"><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Sol.mp3" rel="nofollow">play</a></span> by ZIA (synths and voice in 10)<br />
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><a class="wiki_link_ext" href="http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3" rel="nofollow">Prelude</a></span> by <a class="wiki_link" href="/Rick%20McGowan">Rick McGowan</a> (Rhino synthesizer)<br />
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><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> by <a class="wiki_link" href="/Iglashion%20Jones">Iglashion Jones</a> (synth)<br />
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><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> 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:439:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@10preview.ogg&quot; title=&quot;File: 10preview.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><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:439 --> A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)<br />
<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:7 --><strong>Instruments</strong></h1>
 <br />
<!-- ws:start:WikiTextLocalImageRule:438:&lt;img src=&quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&quot; alt=&quot;A Decaphonic (10-EDO) Classical Guitar&quot; title=&quot;A Decaphonic (10-EDO) Classical Guitar&quot; /&gt; --><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:438 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10021077&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Cenobyte|Cenobyte]] and made on <tt>2011-08-19 00:35:54 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-19 04:59:55 UTC</tt>.<br>
-: The original revision id was <tt>246873735</tt>.<br>
+: The original revision id was <tt>246904167</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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 EDO lists|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.
-=== ===
-===Intervals===
+[[toc|flat]]
+----
+=Intervals=
 || Degree || Cent
 Values || Approximate
@@ Line 24: / Line 27: @@
 || 10 || 1200 || 2/1 ||
 *based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
-==Commas==
+=Commas=
 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)
@@ Line 50: / Line 53: @@
 ||= 91/90 || | -1 -2 -1 1 0 1 &gt; ||&gt; 19.13 ||= Superleap ||=   ||   ||
 ||= 676/675 || | 2 -3 -2 0 0 2 &gt; ||&gt; 2.56 ||= Parizeksma ||=   ||   ||
-===Music===
+=Music=
 [[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Ten Fingers]] &lt;span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3|play]]&lt;/span&gt; by [[Bill Sethares]] (synth guitar)
 [[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Circle of Thirds]] &lt;span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3|play]]&lt;/span&gt; by Bill Sethares (synth ens.)
@@ Line 60: / Line 63: @@
 &lt;span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"&gt;[[http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3|For two violas and gongs]]&lt;/span&gt; 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)
-===**Instruments**===
+=**Instruments**=
 [[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[media type="custom" key="10021077"]]</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;10edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;10edo, or 10-tone equal temperament, is a tuning system which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 10 equal parts of exactly 120 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. It can be thought of as two circles of &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; separated by 120 cents (or 5 circles of &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;). 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 &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; and its inversion &lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;; 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 &lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry scale&lt;/a&gt; of the form 1 2 1 2 1 2 1 (&lt;a class="wiki_link" href="/3L%204s"&gt;3L 4s - mosh&lt;/a&gt;). While not an integral or gap edo, it is a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta peak edo&lt;/a&gt;. 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.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt; &lt;/h3&gt;
+&lt;br /&gt;
- &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Intervals&lt;/h3&gt;
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+&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;hr /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Intervals&lt;/h1&gt;
@@ Line 171: / Line 177: @@
 *based on treating 10-EDO as a 2.7.13.15 subgroup temperament.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Commas&lt;/h2&gt;
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 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 10 16 23 28 35 37 |.)&lt;br /&gt;
 &lt;br /&gt;
@@ Line 501: / Line 507: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Commas-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Music&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Music&lt;/h1&gt;
   &lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow"&gt;Ten Fingers&lt;/a&gt; &lt;span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Bill%20Sethares"&gt;Bill Sethares&lt;/a&gt; (synth guitar)&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow"&gt;Circle of Thirds&lt;/a&gt; &lt;span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Bill Sethares (synth ens.)&lt;br /&gt;
@@ Line 510: / Line 516: @@
 &lt;span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"&gt;&lt;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"&gt;Ideas on the Waterfall of Expression&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Iglashion%20Jones"&gt;Iglashion Jones&lt;/a&gt; (synth)&lt;br /&gt;
 &lt;span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3" rel="nofollow"&gt;For two violas and gongs&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank"&gt;Chris Vaisvil (website)&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1039" rel="nofollow" target="_blank"&gt;more composition information&lt;/a&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextFileRule:434:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@10preview.ogg&amp;quot; title=&amp;quot;File: 10preview.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;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"&gt;10preview.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/10preview.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;3 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:434 --&gt; A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)&lt;br /&gt;
+&lt;!-- ws:start:WikiTextFileRule:439:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@10preview.ogg&amp;quot; title=&amp;quot;File: 10preview.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;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"&gt;10preview.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/10preview.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/10preview.ogg/246873297/10preview.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;3 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:439 --&gt; A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Commas-Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;&lt;strong&gt;Instruments&lt;/strong&gt;&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;&lt;strong&gt;Instruments&lt;/strong&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:433:&amp;lt;img src=&amp;quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&amp;quot; alt=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; title=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;A Decaphonic (10-EDO) Classical Guitar&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:433 --&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10021077&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:438:&amp;lt;img src=&amp;quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&amp;quot; alt=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; title=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;A Decaphonic (10-EDO) Classical Guitar&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:438 --&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10021077&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
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