23edo: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 233694570 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 237767001 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-20 14:12:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>237767001</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. | However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. | ||
=Music= | |||
[[http://home.vicnet.net.au/%7Eepoetry/family.mp3|The Family Supper]] by Warren Burt | |||
__Allegro Moderato__ by Easley Blackwood | |||
[[http://www.youtube.com/watch?v=Hqst8MaRiYM|Icositriphonic Heptatonic MOS]] by Igliashon Jones | |||
[[http://soundclick.com/share?songid=5683734|A Walk Through the Valley of Ashes]] by Iglashion Jones | |||
[[http://www.nonoctave.com/tunes/CosmicChamber.mp3|Cosmic Chamber]] by X. J. Scott | |||
[[http://www.nonoctave.com/tunes/Daisies.mp3|Daisies on the Beach]] by X. J. Scott | |||
<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;">[[http://www.akjmusic.com/audio/boogie_pie.mp3|Boogie Pie]]</span>by Aaron Krister Johnson | |||
[[http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3|23 Chilled]] by Chris Vaisvil | |||
==Intervals== | ==Intervals== | ||
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**2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** | **2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** | ||
2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 | ||
=Books= | =Books= | ||
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However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &quot;anti-pentatonic&quot;) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br /> | However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &quot;anti-pentatonic&quot;) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://home.vicnet.net.au/%7Eepoetry/family.mp3" rel="nofollow">The Family Supper</a> by Warren Burt<br /> | |||
<u>Allegro Moderato</u> by Easley Blackwood<br /> | |||
<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Hqst8MaRiYM" rel="nofollow">Icositriphonic Heptatonic MOS</a> by Igliashon Jones<br /> | |||
<a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683734" rel="nofollow">A Walk Through the Valley of Ashes</a> by Iglashion Jones<br /> | |||
<a class="wiki_link_ext" href="http://www.nonoctave.com/tunes/CosmicChamber.mp3" rel="nofollow">Cosmic Chamber</a> by X. J. Scott<br /> | |||
<a class="wiki_link_ext" href="http://www.nonoctave.com/tunes/Daisies.mp3" rel="nofollow">Daisies on the Beach</a> by X. J. Scott<br /> | |||
<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/boogie_pie.mp3" rel="nofollow">Boogie Pie</a></span>by Aaron Krister Johnson<br /> | |||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3" rel="nofollow">23 Chilled</a> by Chris Vaisvil<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Music-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2> | |||
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<!-- ws:start:WikiTextLocalImageRule:292:&lt;img src=&quot;/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/492x490/Ciclo_Icositrifon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 23 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 23 steps Equal per Octave&quot; style=&quot;height: 490px; width: 492px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/492x490/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 490px; width: 492px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 23 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:292 --><br /> | <!-- ws:start:WikiTextLocalImageRule:292:&lt;img src=&quot;/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/492x490/Ciclo_Icositrifon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 23 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 23 steps Equal per Octave&quot; style=&quot;height: 490px; width: 492px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/492x490/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 490px; width: 492px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 23 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:292 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Music-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h2> | ||
23 EDO tempers out the following commas. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).<br /> | 23 EDO tempers out the following commas. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Music-Commas-INSTRUMENTS"></a><!-- ws:end:WikiTextHeadingRule:10 -->INSTRUMENTS</h3> | ||
<!-- ws:start:WikiTextLocalImageRule:293:&lt;img src=&quot;/file/view/Icositriphonic_Bass.JPG/206711470/594x216/Icositriphonic_Bass.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 216px; width: 594px;&quot; /&gt; --><img src="/file/view/Icositriphonic_Bass.JPG/206711470/594x216/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 216px; width: 594px;" /><!-- ws:end:WikiTextLocalImageRule:293 --><br /> | <!-- ws:start:WikiTextLocalImageRule:293:&lt;img src=&quot;/file/view/Icositriphonic_Bass.JPG/206711470/594x216/Icositriphonic_Bass.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 216px; width: 594px;&quot; /&gt; --><img src="/file/view/Icositriphonic_Bass.JPG/206711470/594x216/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 216px; width: 594px;" /><!-- ws:end:WikiTextLocalImageRule:293 --><br /> | ||
<em>An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.</em><br /> | <em>An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.</em><br /> | ||
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<em>An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.</em><br /> | <em>An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.</em><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Music-23 tone Equal Modes:"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong>23 tone <a class="wiki_link" href="/Equal%20Modes">Equal Modes</a>:</strong></h2> | ||
10 10 3<br /> | 10 10 3<br /> | ||
9 9 5<br /> | 9 9 5<br /> | ||
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<strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong><br /> | <strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong><br /> | ||
2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1<br /> | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:14 -->Books</h1> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:14 -->Books</h1> | ||