8edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author jdfreivald and made on 2011-05-31 17:30:28 UTC.
- The original revision id was 233286326.
- The revision comment was: Added comma table.
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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. 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]] 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 -1 > || 17.40 |||| Ptolemisma || || || 121/120 || | -3 -1 -1 2 > || 14.37 |||| Biyatisma || || || 176/175 || | 4 -2 -1 1 > || 9.86 |||| Valinorsma || || || 65536/65219 || | 16 -2 -3 > || 8.39 |||| Orgonisma || || || 385/384 || | -7 -1 1 1 1 > || 4.50 |||| Keenanisma || || || 4000/3993 || | 5 -1 3 -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 />
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> 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>648/625<br />
</td>
<td>| 3 4 -4 ><br />
</td>
<td>62.57<br />
</td>
<td>Major Diesis<br />
</td>
<td>Diminished Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>250/243<br />
</td>
<td>| 1 -5 3 ><br />
</td>
<td>49.17<br />
</td>
<td>Maximal Diesis<br />
</td>
<td>Porcupine Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>78732/78125<br />
</td>
<td>| 2 9 -7 ><br />
</td>
<td>13.40<br />
</td>
<td>Medium Semicomma<br />
</td>
<td>Sensipent Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>64/63<br />
</td>
<td>| 6 -2 0 -1 ><br />
</td>
<td>27.26<br />
</td>
<td>Septimal Comma<br />
</td>
<td>Archytas' Comma<br />
</td>
<td>Leipziger Komma<br />
</td>
</tr>
<tr>
<td>875/864<br />
</td>
<td>| -5 -3 3 1 ><br />
</td>
<td>21.90<br />
</td>
<td colspan="2">Keema<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>321489/320000<br />
</td>
<td>| -9 8 -4 2 ><br />
</td>
<td>8.04<br />
</td>
<td colspan="2">Varunisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6144/6125<br />
</td>
<td>| 11 1 -3 -2 ><br />
</td>
<td>5.36<br />
</td>
<td colspan="2">Porwell<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>100/99<br />
</td>
<td>| 2 -2 2 -1 ><br />
</td>
<td>17.40<br />
</td>
<td colspan="2">Ptolemisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>121/120<br />
</td>
<td>| -3 -1 -1 2 ><br />
</td>
<td>14.37<br />
</td>
<td colspan="2">Biyatisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>176/175<br />
</td>
<td>| 4 -2 -1 1 ><br />
</td>
<td>9.86<br />
</td>
<td colspan="2">Valinorsma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>65536/65219<br />
</td>
<td>| 16 -2 -3 ><br />
</td>
<td>8.39<br />
</td>
<td colspan="2">Orgonisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>385/384<br />
</td>
<td>| -7 -1 1 1 1 ><br />
</td>
<td>4.50<br />
</td>
<td colspan="2">Keenanisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4000/3993<br />
</td>
<td>| 5 -1 3 -3 ><br />
</td>
<td>3.03<br />
</td>
<td colspan="2">Wizardharry<br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>