8edo
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[[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, and 169/168 are tempered out. =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 1. 150.000 cents C# (50 cents sharper than C# of 12tet) 2. 300.000 cents D# 3. 450.000 cents E (50 cents sharper than E of 12tet) 4. 600.000 cents F# 5. 750.000 cents G (50 cents sharper than G of 12tet) 6. 900.000 cents A 7. 1050.000 cents A# (50 cents sharper than A# of 12tet) 8. 2/1 C =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://www.jamendo.com/en/track/42776|8 / octave by Randy Winchester]] [[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 || || || =8 - Equal Divisions of the Octave= Possible Graphic (currently unlabeled; feel free to if you want) [[image:8-EDO.png width="183" height="144"]]
Original HTML content:
<html><head><title>8edo</title></head><body><!-- ws:start:WikiTextTocRule:12:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Scala scale file">Scala scale file</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#See also">See also</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#x8 - Equal Divisions of the Octave">8 - Equal Divisions of the Octave</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: -->
<!-- ws:end:WikiTextTocRule:19 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1>
<br />
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 <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, and 169/168 are tempered out.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Scala scale file"></a><!-- ws:end:WikiTextHeadingRule:2 -->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:219:<img src="http://www.wikispaces.com/site/embedthumbnail/file/08-EDO.scl?h=52&w=320" class="WikiFile" id="wikitext@@file@@08-EDO.scl" title="File: 08-EDO.scl" width="320" height="52" /> --><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:219 --><br />
<br />
0. 1/1 C<br />
1. 150.000 cents C# (50 cents sharper than C# of 12tet)<br />
2. 300.000 cents D#<br />
3. 450.000 cents E (50 cents sharper than E of 12tet)<br />
4. 600.000 cents F#<br />
5. 750.000 cents G (50 cents sharper than G of 12tet)<br />
6. 900.000 cents A<br />
7. 1050.000 cents A# (50 cents sharper than A# of 12tet)<br />
8. 2/1 C<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h1>
<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fantasia8ET.mp3" rel="nofollow">Fantasia in 8ET</a> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fugue8ET.mp3" rel="nofollow">Fugue in 8ET</a> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html" rel="nofollow">Špendlíky</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Gustar/spendliky.mp3" rel="nofollow">play</a> by Milan Guštar<br />
<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> by Ron Sword (dead link)<br />
<a class="wiki_link_ext" href="http://www.jamendo.com/en/track/42776" rel="nofollow">8 / octave by Randy Winchester</a><br />
<br />
<!-- ws:start:WikiTextFileRule:220:<img src="http://www.wikispaces.com/site/embedthumbnail/file/8edo-pre-improv.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@8edo-pre-improv.ogg" title="File: 8edo-pre-improv.ogg" width="320" height="52" /> --><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:220 -->Preliminary noodling in 8 EDO with ZynAddSubFX synth.(by Cenobyte)<br />
<!-- ws:start:WikiTextFileRule:221:<img src="http://www.wikispaces.com/site/embedthumbnail/file/darkreflections%28sketch%29.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@darkreflections(sketch).ogg" title="File: darkreflections(sketch).ogg" width="320" height="52" /> --><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:221 -->8EDO Ukulele (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:222:<img src="http://www.wikispaces.com/site/embedthumbnail/file/skiphop%28sketch%29.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@skiphop(sketch).ogg" title="File: skiphop(sketch).ogg" width="320" height="52" /> --><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:222 -->8EDO Ukulele (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:223:<img src="http://www.wikispaces.com/site/embedthumbnail/file/octo-icy-pensive%28sketch%29.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@octo-icy-pensive(sketch).ogg" title="File: octo-icy-pensive(sketch).ogg" width="320" height="52" /> --><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:223 --> <!-- ws:start:WikiTextFileRule:224:<img src="http://www.wikispaces.com/site/embedthumbnail/file/octo-icy-pensive-echo%28sketch%29.ogg?h=52&w=320" class="WikiFile" id="wikitext@@file@@octo-icy-pensive-echo(sketch).ogg" title="File: octo-icy-pensive-echo(sketch).ogg" width="320" height="52" /> --><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:224 -->2 versions of the same song, one with echo, one without. (cenobyte)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:6 -->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:8:<h1> --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h1>
8 EDO tempers out the following commas. (Note: This assumes val < 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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="x8 - Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:10 -->8 - Equal Divisions of the Octave</h1>
Possible Graphic (currently unlabeled; feel free to if you want)<br />
<!-- ws:start:WikiTextLocalImageRule:218:<img src="/file/view/8-EDO.png/244674727/183x144/8-EDO.png" alt="" title="" style="height: 144px; width: 183px;" /> --><img src="/file/view/8-EDO.png/244674727/183x144/8-EDO.png" alt="8-EDO.png" title="8-EDO.png" style="height: 144px; width: 183px;" /><!-- ws:end:WikiTextLocalImageRule:218 --></body></html>