8edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Cenobyte and made on 2011-08-06 04:56:44 UTC.
- The original revision id was 244588275.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=8 - Equal Divisions of the Octave= ==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. For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO 0. 1/1 C 1. 150.000 cents C# 2. 300.000 cents D# 3. 450.000 cents E 4. 600.000 cents F# 5. 750.000 cents G 6. 900.000 cents A 7. 1050.000 cents A# 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 ==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><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x8 - Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->8 - Equal Divisions of the Octave</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x8 - Equal Divisions of the Octave-Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h2>
<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 />
For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO<br />
<br />
0. 1/1 C<br />
1. 150.000 cents C#<br />
2. 300.000 cents D#<br />
3. 450.000 cents E<br />
4. 600.000 cents F#<br />
5. 750.000 cents G<br />
6. 900.000 cents A<br />
7. 1050.000 cents A#<br />
8. 2/1 C<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x8 - Equal Divisions of the Octave-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h2>
<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<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x8 - Equal Divisions of the Octave-See also"></a><!-- ws:end:WikiTextHeadingRule:6 -->See also</h2>
*<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:<h2> --><h2 id="toc4"><a name="x8 - Equal Divisions of the Octave-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h2>
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>
</body></html>