8edo: Difference between revisions

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<span style="display: block; text-align: right;">[[８平均律|日本語]]
</span>
[[toc|flat]]
=Theory= 
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[Just intonation subgroups|just intonation subgroup]] 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.

Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.

=Intervals= 

[[media type="custom" key="24802404"]]

[[file:8ed2-001.svg]]


=Scala scale file= 
For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO [[file:08-EDO.scl]]

0. 1/1 C Unison
1. 150.000 cents C# (50 cents sharper than C# of 12tet) Neutral 2nd
2. 300.000 cents D# Minor 3rd (identical to 12-tet)
3. 450.000 cents E Sub-4th, Supermajor 3rd (50 cents sharper than E of 12tet)
4. 600.000 cents F# Tritone (identical to 12-tet)
5. 750.000 cents G Super 5th, Subminor 6th (50 cents sharper than G of 12tet)
6. 900.000 cents A Major 6th (identical to 12-tet)
7. 1050.000 cents A# Neutral 7th (50 cents sharper than A# of 12tet)
8. 2/1 C Octave

=Compositions= 
//[[http://www.h-pi.com/mp3/Fantasia8ET.mp3|Fantasia in 8ET]]// by Aaron Andrew Hunt
//[[http://www.h-pi.com/mp3/Fugue8ET.mp3|Fugue in 8ET]]// by Aaron Andrew Hunt
[[http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html|Špendlíky]] //[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Gustar/spendliky.mp3|play]]// by Milan Guštar
//[[@http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3|Acoustic Improvisation in 8-edo]]// by Ron Sword (dead link)
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/07%20-%207.%208%20octave.mp3|Comets Over Flatland 7]]// by [[Randy Winchester]]
//[[@http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3|Malebolge]]// Igliashon Jones
//[[@http://www.youtube.com/watch?v=0mpDeL7iybI|News To Me]]// Jake Sherman
//[[@http://www.youtube.com/watch?v=HvDEoZ4LIdc|Tomorrow Night (pop music from 2045)]]// Jake Sherman
//[[http://www.seraph.it/dep/det/FunkEight1.mp3|FunkEight 1]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html|blog entry]])
[[file:8edo-pre-improv.ogg]]Preliminary noodling in 8 EDO with ZynAddSubFX synth.(by Cenobyte)
[[file:darkreflections(sketch).ogg]]8EDO Ukulele (cenobyte)
[[file:skiphop(sketch).ogg]]8EDO Ukulele (cenobyte)
[[file:octo-icy-pensive(sketch).ogg]] [[file:octo-icy-pensive-echo(sketch).ogg]]2 versions of the same song, one with echo, one without. (cenobyte)

=See also= 
*[[Octatonic scale]] - a scale based on alternating whole and half steps

=Commas= 
8 EDO tempers out the following commas. (Note: This assumes val < 8 13 19 22 28 30 |).

||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 648/625 || | 3 4 -4 > ||> 62.57 ||= Major Diesis ||= Diminished Comma ||   ||
||= 250/243 || | 1 -5 3 > ||> 49.17 ||= Maximal Diesis ||= Porcupine Comma ||   ||
||= 78732/78125 || | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||   ||
||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma ||
||= 875/864 || | -5 -3 3 1 > ||> 21.90 ||= Keema ||   ||   ||
||= 321489/320000 || | -9 8 -4 2 > ||> 8.04 ||= Varunisma ||   ||   ||
||= 6144/6125 || | 11 1 -3 -2 > ||> 5.36 ||= Porwell ||   ||   ||
||= 100/99 || | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||   ||   ||
||= 121/120 || | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||   ||   ||
||= 176/175 || | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||   ||   ||
||= 65536/65219 || | 16 0 0 -2 -3 > ||> 8.39 ||= Orgonisma ||   ||   ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||   ||   ||
||= 4000/3993 || | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||   ||   ||

Original HTML content:

<html><head><title>8edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/%EF%BC%98%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
</span><br />
<!-- ws:start:WikiTextTocRule:13:&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:13 --><!-- ws:start:WikiTextTocRule:14: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Scala scale file">Scala scale file</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#See also">See also</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: -->
<!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:1 -->Theory</h1>
 8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a &quot;barbaric&quot; harmonic system; even so, it does a good job representing the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.<br />
<br />
Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:3 -->Intervals</h1>
 <br />
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<br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Scala scale file"></a><!-- ws:end:WikiTextHeadingRule:5 -->Scala scale file</h1>
 For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO <!-- ws:start:WikiTextFileRule:220:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/08-EDO.scl?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@08-EDO.scl&quot; title=&quot;File: 08-EDO.scl&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/08-EDO.scl/244588383/08-EDO.scl" onclick="ws.common.trackFileLink('/file/view/08-EDO.scl/244588383/08-EDO.scl');"><img src="http://www.wikispaces.com/i/mime/32/text/plain.png" height="32" width="32" alt="08-EDO.scl" /></a><div><a href="/file/view/08-EDO.scl/244588383/08-EDO.scl" onclick="ws.common.trackFileLink('/file/view/08-EDO.scl/244588383/08-EDO.scl');" class="filename" title="08-EDO.scl">08-EDO.scl</a><br /><ul><li><a href="/file/detail/08-EDO.scl">Details</a></li><li><a href="/file/view/08-EDO.scl/244588383/08-EDO.scl">Download</a></li><li style="color: #666">1 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:220 --><br />
<br />
0. 1/1 C Unison<br />
1. 150.000 cents C# (50 cents sharper than C# of 12tet) Neutral 2nd<br />
2. 300.000 cents D# Minor 3rd (identical to 12-tet)<br />
3. 450.000 cents E Sub-4th, Supermajor 3rd (50 cents sharper than E of 12tet)<br />
4. 600.000 cents F# Tritone (identical to 12-tet)<br />
5. 750.000 cents G Super 5th, Subminor 6th (50 cents sharper than G of 12tet)<br />
6. 900.000 cents A Major 6th (identical to 12-tet)<br />
7. 1050.000 cents A# Neutral 7th (50 cents sharper than A# of 12tet)<br />
8. 2/1 C Octave<br />
<br />
<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:7 -->Compositions</h1>
 <em><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fantasia8ET.mp3" rel="nofollow">Fantasia in 8ET</a></em> by Aaron Andrew Hunt<br />
<em><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fugue8ET.mp3" rel="nofollow">Fugue in 8ET</a></em> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html" rel="nofollow">Špendlíky</a> <em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Gustar/spendliky.mp3" rel="nofollow">play</a></em> by Milan Guštar<br />
<em><a class="wiki_link_ext" href="http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3" rel="nofollow" target="_blank">Acoustic Improvisation in 8-edo</a></em> by Ron Sword (dead link)<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/07%20-%207.%208%20octave.mp3" rel="nofollow">Comets Over Flatland 7</a></em> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<em><a class="wiki_link_ext" href="http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3" rel="nofollow" target="_blank">Malebolge</a></em> Igliashon Jones<br />
<em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=0mpDeL7iybI" rel="nofollow" target="_blank">News To Me</a></em> Jake Sherman<br />
<em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=HvDEoZ4LIdc" rel="nofollow" target="_blank">Tomorrow Night (pop music from 2045)</a></em> Jake Sherman<br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/FunkEight1.mp3" rel="nofollow">FunkEight 1</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html" rel="nofollow">blog entry</a>)<br />
<!-- ws:start:WikiTextFileRule:221:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/8edo-pre-improv.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@8edo-pre-improv.ogg&quot; title=&quot;File: 8edo-pre-improv.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg" onclick="ws.common.trackFileLink('/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="8edo-pre-improv.ogg" /></a><div><a href="/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg" onclick="ws.common.trackFileLink('/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg');" class="filename" title="8edo-pre-improv.ogg">8edo-pre-improv.ogg</a><br /><ul><li><a href="/file/detail/8edo-pre-improv.ogg">Details</a></li><li><a href="/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg">Download</a></li><li style="color: #666">1 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:221 -->Preliminary noodling in 8 EDO with ZynAddSubFX synth.(by Cenobyte)<br />
<!-- ws:start:WikiTextFileRule:222:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/darkreflections%28sketch%29.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@darkreflections(sketch).ogg&quot; title=&quot;File: darkreflections(sketch).ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="darkreflections(sketch).ogg" /></a><div><a href="/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg');" class="filename" title="darkreflections(sketch).ogg">darkreflections(sketch).ogg</a><br /><ul><li><a href="/file/detail/darkreflections%28sketch%29.ogg">Details</a></li><li><a href="/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg">Download</a></li><li style="color: #666">3 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:222 -->8EDO Ukulele (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:223:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/skiphop%28sketch%29.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@skiphop(sketch).ogg&quot; title=&quot;File: skiphop(sketch).ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="skiphop(sketch).ogg" /></a><div><a href="/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg');" class="filename" title="skiphop(sketch).ogg">skiphop(sketch).ogg</a><br /><ul><li><a href="/file/detail/skiphop%28sketch%29.ogg">Details</a></li><li><a href="/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg">Download</a></li><li style="color: #666">3 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:223 -->8EDO Ukulele (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:224:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/octo-icy-pensive%28sketch%29.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@octo-icy-pensive(sketch).ogg&quot; title=&quot;File: octo-icy-pensive(sketch).ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="octo-icy-pensive(sketch).ogg" /></a><div><a href="/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg');" class="filename" title="octo-icy-pensive(sketch).ogg">octo-icy-pensive(sketch).ogg</a><br /><ul><li><a href="/file/detail/octo-icy-pensive%28sketch%29.ogg">Details</a></li><li><a href="/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:224 --> <!-- ws:start:WikiTextFileRule:225:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/octo-icy-pensive-echo%28sketch%29.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@octo-icy-pensive-echo(sketch).ogg&quot; title=&quot;File: octo-icy-pensive-echo(sketch).ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="octo-icy-pensive-echo(sketch).ogg" /></a><div><a href="/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg');" class="filename" title="octo-icy-pensive-echo(sketch).ogg">octo-icy-pensive-echo(sketch).ogg</a><br /><ul><li><a href="/file/detail/octo-icy-pensive-echo%28sketch%29.ogg">Details</a></li><li><a href="/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:225 -->2 versions of the same song, one with echo, one without. (cenobyte)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:9 -->See also</h1>
 *<a class="wiki_link" href="/Octatonic%20scale">Octatonic scale</a> - a scale based on alternating whole and half steps<br />
<br />
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc5"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1>
 8 EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |).<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>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;">648/625<br />
</td>
        <td>| 3 4 -4 &gt;<br />
</td>
        <td style="text-align: right;">62.57<br />
</td>
        <td style="text-align: center;">Major Diesis<br />
</td>
        <td style="text-align: center;">Diminished Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">250/243<br />
</td>
        <td>| 1 -5 3 &gt;<br />
</td>
        <td style="text-align: right;">49.17<br />
</td>
        <td style="text-align: center;">Maximal Diesis<br />
</td>
        <td style="text-align: center;">Porcupine Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">78732/78125<br />
</td>
        <td>| 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><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;">875/864<br />
</td>
        <td>| -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><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">321489/320000<br />
</td>
        <td>| -9 8 -4 2 &gt;<br />
</td>
        <td style="text-align: right;">8.04<br />
</td>
        <td style="text-align: center;">Varunisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6144/6125<br />
</td>
        <td>| 11 1 -3 -2 &gt;<br />
</td>
        <td style="text-align: right;">5.36<br />
</td>
        <td style="text-align: center;">Porwell<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td>| 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><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">121/120<br />
</td>
        <td>| -3 -1 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">14.37<br />
</td>
        <td style="text-align: center;">Biyatisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">176/175<br />
</td>
        <td>| 4 0 -2 -1 1 &gt;<br />
</td>
        <td style="text-align: right;">9.86<br />
</td>
        <td style="text-align: center;">Valinorsma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">65536/65219<br />
</td>
        <td>| 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><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><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3993<br />
</td>
        <td>| 5 -1 3 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">3.03<br />
</td>
        <td style="text-align: center;">Wizardharry<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

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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:hstraub|hstraub]] and made on <tt>2015-07-28 04:27:51 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-07-30 06:45:53 UTC</tt>.<br>
-: The original revision id was <tt>555834475</tt>.<br>
+: The original revision id was <tt>555946763</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">&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/8edo|Deutsch]] - [[８平均律|日本語]]
+<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">&lt;span style="display: block; text-align: right;"&gt;[[８平均律|日本語]]
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 ||= 4000/3993 || | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||   ||   ||</pre></div>
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+<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;8edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="/%EF%BC%98%E5%B9%B3%E5%9D%87%E5%BE%8B"&gt;日本語&lt;/a&gt;&lt;br /&gt;
 &lt;/span&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextTocRule:13:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Scala scale file"&gt;Scala scale file&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#See also"&gt;See also&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;

8edo: Difference between revisions

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