23edo: Difference between revisions
Wikispaces>guest **Imported revision 242552379 - Original comment: ** |
Wikispaces>igliashon **Imported revision 242752883 - 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:igliashon|igliashon]] and made on <tt>2011-07-25 12:48:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>242752883</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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**//23-tET//**, or **//23-EDO//**, is a tempered musical system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony //[Icositrifonía]//. It has good approximations for [[5_3|5/3]], [[11_7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]]·[[46edo]], the larger 17-limit [[k*N subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. | **//23-tET//**, or **//23-EDO//**, is a tempered musical system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony //[Icositrifonía]//. It has good approximations for [[5_3|5/3]], [[11_7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]]·[[46edo]], the larger 17-limit [[k*N subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. | ||
=<span style="font-size: 1.4em;">Intervals</span>= | |||
|| <span style="color: #660000;">[[Degree]]</span> || [[Cent]]s value || Approximate | |||
Ratios* || | |||
|| 0 || 0 || 1/1 || | |||
|| 1 || 52.1739 || 33/32, 34/33 || | |||
|| 2 || 104.3478 || 17/16, 15/16, 18/17 || | |||
|| 3 || 156.5217 || 11/10, 12/11 || | |||
|| 4 || 208.6957 || 9/8 || | |||
|| 5 || 260.8696 || 7/6, 15/13 || | |||
|| 6 || 313.0435 || 6/5 || | |||
|| 7 || 365.2174 || 21/17, 26/21 || | |||
|| 8 || 417.3913 || 14/11, 33/26 || | |||
|| 9 || 469.5652 || 21/16, 17/13 || | |||
|| 10 || 521.7391 || 65/48, 256/189 || | |||
|| 11 || 573.913 || 7/5 || | |||
|| 12 || 626.087 || 10/7 || | |||
|| 13 || 678.2609 || 96/65, 189/128 || | |||
|| 14 || 730.4348 || 32/21, 26/17 || | |||
|| 15 || 782.6087 || 11/7, 52/33 || | |||
|| 16 || 834.7826 || 13/8, 21/13 || | |||
|| 17 || 886.9565 || 5/3 || | |||
|| 18 || 939.1304 || 12/7, 26/15 || | |||
|| 19 || 991.3043 || 16/9 || | |||
|| 20 || 1043.4783 || 11/6, 20/11 || | |||
|| 21 || 1095.6522 || 15/8, 17/9, 32/17 || | |||
|| 22 || 1147.8261 || 33/17, 64/33 || | |||
|| 23 || 1200 || 2/1 || | |||
*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | |||
23-EDO was proposed by ethnomusicologist [[http://en.wikipedia.org/wiki/Erich_von_Hornbostel|Erich von Hornbostel]] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe. | 23-EDO was proposed by ethnomusicologist [[http://en.wikipedia.org/wiki/Erich_von_Hornbostel|Erich von Hornbostel]] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe. | ||
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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 'broad 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 [[13edo|13-EDO]] and [[18edo|18-EDO]] and produces [[MOSScales|MOS scales]] of 5 and 8 notes: 5 5 4 5 4 (the [[3L 2s|"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 Sub-"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 'broad 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 [[13edo|13-EDO]] and [[18edo|18-EDO]] and produces [[MOSScales|MOS scales]] of 5 and 8 notes: 5 5 4 5 4 (the [[3L 2s|"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 Sub-"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. | ||
==Kosmorsky's Sephiroth modes== | |||
I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale ([[3L 7s|3L 7s fair mosh]]); | I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale ([[3L 7s|3L 7s fair mosh]]); | ||
This is derived from extending the ~1/3 comma tempered 13th Harmonic, two of which add up to the Harmonic21 | This is derived from extending the ~1/3 comma tempered 13th Harmonic, two of which add up to the Harmonic21 | ||
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<span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"><span class="ymp-btn-page-play ymp-media-c4aa76ed239a412533a11b438698b09b">[[http://www.akjmusic.com/audio/boogie_pie.mp3|Boogie Pie]]</span></span>by [[Aaron Krister Johnson]] | <span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"><span class="ymp-btn-page-play ymp-media-c4aa76ed239a412533a11b438698b09b">[[http://www.akjmusic.com/audio/boogie_pie.mp3|Boogie Pie]]</span></span>by [[Aaron Krister Johnson]] | ||
<span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b">[[http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3|23 Chilled]]</span> by [[Chris Vaisvil]] | <span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b">[[http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3|23 Chilled]]</span> by [[Chris Vaisvil]] | ||
[[http://www.seraph.it/dep/det/DesertWinds.mp3|Desert Winds]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html|blog entry]]) | <span class="ymp-btn-page-play ymp-media-8ca0c9a378cc362bbcbc24ba13d6974b">[[http://www.seraph.it/dep/det/DesertWinds.mp3|Desert Winds]]</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html|blog entry]]) | ||
//Allegro Moderato// by Easley Blackwood | //Allegro Moderato// by Easley Blackwood | ||
= | = = | ||
[[image:Ciclo_Icositrifonía.png width="492" height="490" caption="Intervallic Cycle of 23 steps Equal per Octave"]] | [[image:Ciclo_Icositrifonía.png width="492" height="490" caption="Intervallic Cycle of 23 steps Equal per Octave"]] | ||
== == | == == | ||
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<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>23edo</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021317?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10021317&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | <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"><html><head><title>23edo</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021317?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10021317&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | ||
</script><!-- ws:end:WikiTextMediaRule:0 --><!-- ws:start:WikiTextTocRule: | </script><!-- ws:end:WikiTextMediaRule:0 --><!-- ws:start:WikiTextTocRule:22:&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:22 --><!-- ws:start:WikiTextTocRule:23: --><a href="#x23 tone equal temperament">23 tone equal temperament</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#toc4"> </a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#x23 tone Equal Modes:">23 tone Equal Modes:</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:33 --><br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
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<strong><em>23-tET</em></strong>, or <strong><em>23-EDO</em></strong>, is a tempered musical system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony <em>[Icositrifonía]</em>. It has good approximations for <a class="wiki_link" href="/5_3">5/3</a>, <a class="wiki_link" href="/11_7">11/7</a>, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. If to this subgroup is added the commas of <a class="wiki_link" href="/17-limit">17-limit</a>·<a class="wiki_link" href="/46edo">46edo</a>, the larger 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*23 subgroup</a> 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes.<br /> | <strong><em>23-tET</em></strong>, or <strong><em>23-EDO</em></strong>, is a tempered musical system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony <em>[Icositrifonía]</em>. It has good approximations for <a class="wiki_link" href="/5_3">5/3</a>, <a class="wiki_link" href="/11_7">11/7</a>, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. If to this subgroup is added the commas of <a class="wiki_link" href="/17-limit">17-limit</a>·<a class="wiki_link" href="/46edo">46edo</a>, the larger 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*23 subgroup</a> 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="font-size: 1.4em;">Intervals</span></h1> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name=" | |||
<span style=" | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><a class="wiki_link" href="/Degree">Degree</a> | <td><span style="color: #660000;"><a class="wiki_link" href="/Degree">Degree</a></span><br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Cent">Cent</a>s value<br /> | <td><a class="wiki_link" href="/Cent">Cent</a>s value<br /> | ||
</td> | |||
<td>Approximate <br /> | |||
Ratios*<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 231: | Line 200: | ||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
</td> | |||
<td>1/1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 237: | Line 208: | ||
</td> | </td> | ||
<td>52.1739<br /> | <td>52.1739<br /> | ||
</td> | |||
<td>33/32, 34/33<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 243: | Line 216: | ||
</td> | </td> | ||
<td>104.3478<br /> | <td>104.3478<br /> | ||
</td> | |||
<td>17/16, 15/16, 18/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 249: | Line 224: | ||
</td> | </td> | ||
<td>156.5217<br /> | <td>156.5217<br /> | ||
</td> | |||
<td>11/10, 12/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 255: | Line 232: | ||
</td> | </td> | ||
<td>208.6957<br /> | <td>208.6957<br /> | ||
</td> | |||
<td>9/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 261: | Line 240: | ||
</td> | </td> | ||
<td>260.8696<br /> | <td>260.8696<br /> | ||
</td> | |||
<td>7/6, 15/13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 267: | Line 248: | ||
</td> | </td> | ||
<td>313.0435<br /> | <td>313.0435<br /> | ||
</td> | |||
<td>6/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 273: | Line 256: | ||
</td> | </td> | ||
<td>365.2174<br /> | <td>365.2174<br /> | ||
</td> | |||
<td>21/17, 26/21<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 279: | Line 264: | ||
</td> | </td> | ||
<td>417.3913<br /> | <td>417.3913<br /> | ||
</td> | |||
<td>14/11, 33/26<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 285: | Line 272: | ||
</td> | </td> | ||
<td>469.5652<br /> | <td>469.5652<br /> | ||
</td> | |||
<td>21/16, 17/13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>521.7391<br /> | <td>521.7391<br /> | ||
</td> | |||
<td>65/48, 256/189<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>573.913<br /> | <td>573.913<br /> | ||
</td> | |||
<td>7/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 303: | Line 296: | ||
</td> | </td> | ||
<td>626.087<br /> | <td>626.087<br /> | ||
</td> | |||
<td>10/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 309: | Line 304: | ||
</td> | </td> | ||
<td>678.2609<br /> | <td>678.2609<br /> | ||
</td> | |||
<td>96/65, 189/128<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 315: | Line 312: | ||
</td> | </td> | ||
<td>730.4348<br /> | <td>730.4348<br /> | ||
</td> | |||
<td>32/21, 26/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>782.6087<br /> | <td>782.6087<br /> | ||
</td> | |||
<td>11/7, 52/33<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>834.7826<br /> | <td>834.7826<br /> | ||
</td> | |||
<td>13/8, 21/13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 333: | Line 336: | ||
</td> | </td> | ||
<td>886.9565<br /> | <td>886.9565<br /> | ||
</td> | |||
<td>5/3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 339: | Line 344: | ||
</td> | </td> | ||
<td>939.1304<br /> | <td>939.1304<br /> | ||
</td> | |||
<td>12/7, 26/15<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 345: | Line 352: | ||
</td> | </td> | ||
<td>991.3043<br /> | <td>991.3043<br /> | ||
</td> | |||
<td>16/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 351: | Line 360: | ||
</td> | </td> | ||
<td>1043.4783<br /> | <td>1043.4783<br /> | ||
</td> | |||
<td>11/6, 20/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>1095.6522<br /> | <td>1095.6522<br /> | ||
</td> | |||
<td>15/8, 17/9, 32/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>1147.8261<br /> | <td>1147.8261<br /> | ||
</td> | |||
<td>33/17, 64/33<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>1200<br /> | |||
</td> | |||
<td>2/1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
<!-- ws:start:WikiTextLocalImageRule: | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | *based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <br /> | ||
23-EDO was proposed by ethnomusicologist <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Erich_von_Hornbostel" rel="nofollow">Erich von Hornbostel</a> as the result of continuing a circle of &quot;blown&quot; fifths of ~678-cent fifths that (he argued) resulted from &quot;overblowing&quot; a bamboo pipe.<br /> | |||
<br /> | |||
23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, and 7th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore unusual harmonic territory. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, and 7/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.<br /> | |||
<br /> | |||
Like<a class="wiki_link" href="/9edo"> 9-EDO</a>, <a class="wiki_link" href="/16edo">16-EDO</a>, and <a class="wiki_link" href="/25edo">25-EDO</a>, one way to treat 23-EDO is as a Pelogic temperament, tempering out the &quot;comma&quot; of 135/128 and equating three 'acute <a class="wiki_link" href="/4_3">4/3</a>'s with 5/1 (related to the Armodue system). This means mapping '<a class="wiki_link" href="/3_2">3/2</a>' to 13 degrees of 23, and results in a 7 notes <a class="wiki_link" href="/2L%205s">Anti-diatonic scale</a> of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes <a class="wiki_link" href="/7L%202s">Superdiatonic scale</a> (3 3 3 1 3 3 3 3 1).<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 <a class="wiki_link" href="/7-limit">7-limit</a> temperament where two 'broad 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 <a class="wiki_link" href="/13edo">13-EDO</a> and <a class="wiki_link" href="/18edo">18-EDO</a> and produces <a class="wiki_link" href="/MOSScales">MOS scales</a> of 5 and 8 notes: 5 5 4 5 4 (the <a class="wiki_link" href="/3L%202s">&quot;anti-pentatonic&quot;</a>) 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 Sub-&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 /> | |||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals-Kosmorsky's Sephiroth modes"></a><!-- ws:end:WikiTextHeadingRule:6 -->Kosmorsky's Sephiroth modes</h2> | |||
I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale (<a class="wiki_link" href="/3L%207s">3L 7s fair mosh</a>);<br /> | |||
This is derived from extending the ~1/3 comma tempered 13th Harmonic, two of which add up to the Harmonic21<br /> | |||
and three add up to the Harmonic17 almost perfectly (I discovered the temperament before I even realised 23 tone fits)<br /> | |||
The chord 8:13:21:34 is a fragment of the fibonacci sequence, and 16:21:26 is harmonically symmetrical<br /> | |||
(The chord 26:29:32 is also symmetric, but only <a class="wiki_link" href="/20edo">20edo</a> and <a class="wiki_link" href="/43edo">43edo</a> approximate the Harmonic29, as well)<br /> | |||
13:17:21 is symmetrical, and 17:21:26:32 has an interesting linear widening pattern, but more importantly,<br /> | |||
the Harmonic13 and Harmonic17 are both dual primes like 3&amp;5 and 7&amp;11<br /> | |||
<br /> | |||
Thus I have named these 10 modes according to the Sephiroth as follows:<br /> | |||
2 2 2 3 2 2 3 2 2 3 - Mode Keter<br /> | |||
2 2 3 2 2 3 2 2 3 2 - Chesed<br /> | |||
2 3 2 2 3 2 2 3 2 2 - Netzach<br /> | |||
3 2 2 3 2 2 3 2 2 2 - Malkuth<br /> | |||
2 2 3 2 2 3 2 2 2 3 - Binah<br /> | |||
2 3 2 2 3 2 2 2 3 2 - Tiferet<br /> | |||
3 2 2 3 2 2 2 3 2 2 - Yesod<br /> | |||
2 2 3 2 2 2 3 2 2 3 - Chokmah<br /> | |||
2 3 2 2 2 3 2 2 3 2 - Gevurah<br /> | |||
3 2 2 2 3 2 2 3 2 2 - Hod<br /> | |||
<br /> | |||
-- Kosmorsky<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:8 -->Music</h1> | |||
<span class="ymp-btn-page-play ymp-media-e8b030b27e37ed744bb651845d914579"><a class="wiki_link_ext" href="http://home.vicnet.net.au/%7Eepoetry/family.mp3" rel="nofollow">The Family Supper</a></span> by <a class="wiki_link" href="/Warren%20Burt">Warren Burt</a><br /> | |||
<span class="ymp-btn-page-play ymp-media-ad0e9a76a742e629379c7c9667584433"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Hqst8MaRiYM" rel="nofollow">Icositriphonic Heptatonic MOS</a></span> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | |||
<span class="ymp-btn-page-play ymp-media-11d44e0c35e6cbb396811396e4304800"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20His%20Wandering%20Kinship%20with%20Ashes.mp3" rel="nofollow">His Wandering Kinship with Ashes</a></span> by Iglashion Jones<br /> | |||
<span class="ymp-btn-page-play ymp-media-09a22042e6869c062a19ee073e5d2372"><a class="wiki_link_ext" href="http://www.nonoctave.com/tunes/CosmicChamber.mp3" rel="nofollow">Cosmic Chamber</a></span> by <a class="wiki_link" href="/X.%20J.%20Scott">X. J. Scott</a><br /> | |||
<span class="ymp-btn-page-play ymp-media-1a0d476bcc56e8699d94050c4bd46398"><a class="wiki_link_ext" href="http://www.nonoctave.com/tunes/Daisies.mp3" rel="nofollow">Daisies on the Beach</a></span> by X. J. Scott<br /> | |||
<span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"><span class="ymp-btn-page-play ymp-media-c4aa76ed239a412533a11b438698b09b"><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/boogie_pie.mp3" rel="nofollow">Boogie Pie</a></span></span>by <a class="wiki_link" href="/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a><br /> | |||
<span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3" rel="nofollow">23 Chilled</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | |||
<span class="ymp-btn-page-play ymp-media-8ca0c9a378cc362bbcbc24ba13d6974b"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DesertWinds.mp3" rel="nofollow">Desert Winds</a></span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html" rel="nofollow">blog entry</a>)<br /> | |||
<em>Allegro Moderato</em> by Easley Blackwood<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><!-- ws:end:WikiTextHeadingRule:10 --> </h1> | |||
<!-- ws:start:WikiTextLocalImageRule:649:&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:649 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->Commas</h1> | |||
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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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc7"><a name="x23 tone Equal Modes:"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>23 tone <a class="wiki_link" href="/Equal%20Modes">Equal Modes</a>:</strong></h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc8"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:18 -->Books</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:650:&lt;img src=&quot;/file/view/Libro_Icositrif%C3%B3nico.PNG/163031733/242x294/Libro_Icositrif%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 294px; width: 242px;&quot; /&gt; --><img src="/file/view/Libro_Icositrif%C3%B3nico.PNG/163031733/242x294/Libro_Icositrif%C3%B3nico.PNG" alt="Libro_Icositrifónico.PNG" title="Libro_Icositrifónico.PNG" style="height: 294px; width: 242px;" /><!-- ws:end:WikiTextLocalImageRule:650 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:20 -->Instruments</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:651:&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:651 --><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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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:652:&lt;img src=&quot;/file/view/Icositriphonic_Guitar.PNG/206712964/601x305/Icositriphonic_Guitar.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 305px; width: 601px;&quot; /&gt; --><img src="/file/view/Icositriphonic_Guitar.PNG/206712964/601x305/Icositriphonic_Guitar.PNG" alt="Icositriphonic_Guitar.PNG" title="Icositriphonic_Guitar.PNG" style="height: 305px; width: 601px;" /><!-- ws:end:WikiTextLocalImageRule:652 --><br /> | ||
<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 /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:653:&lt;img src=&quot;/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/591x326/Teclado_Icositrif%C3%B3nico.PNG&quot; alt=&quot;A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems&quot; title=&quot;A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems&quot; style=&quot;height: 326px; width: 591px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/591x326/Teclado_Icositrif%C3%B3nico.PNG" alt="Teclado_Icositrifónico.PNG" title="Teclado_Icositrifónico.PNG" style="height: 326px; width: 591px;" /></td></tr><tr><td class="imageCaption">A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems</td></tr></table><!-- ws:end:WikiTextLocalImageRule:653 --><br /> | ||
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Chris Vaisvil made a do it yourself 23 edo electric guitar out of less than $50 of material. Here he is playing it.<br /> | Chris Vaisvil made a do it yourself 23 edo electric guitar out of less than $50 of material. Here he is playing it.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:654:&lt;img src=&quot;/file/view/playing.jpg/241873781/playing.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/playing.jpg/241873781/playing.jpg" alt="playing.jpg" title="playing.jpg" /><!-- ws:end:WikiTextLocalImageRule:654 --><br /> | ||
Here is a still shot of the completed instrument.<br /> | Here is a still shot of the completed instrument.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:655:&lt;img src=&quot;/file/view/complette.jpg/241873831/complette.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/complette.jpg/241873831/complette.jpg" alt="complette.jpg" title="complette.jpg" /><!-- ws:end:WikiTextLocalImageRule:655 --><br /> | ||
This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.<br /> | This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.<br /> | ||
<!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/youtube/K4iO7k152og?h=349&amp;w=560&quot; class=&quot;WikiMedia WikiMediaYoutube&quot; id=&quot;wikitext@@media@@type=&amp;quot;youtube&amp;quot; key=&amp;quot;K4iO7k152og&amp;quot; height=&amp;quot;349&amp;quot; width=&amp;quot;560&amp;quot;&quot; title=&quot;YouTube Video&quot;height=&quot;349&quot; width=&quot;560&quot;/&gt; --><iframe width="560" height="349" src="//www.youtube.com/embed/K4iO7k152og" frameborder="0" allowfullscreen></iframe><!-- ws:end:WikiTextMediaRule:1 --></body></html></pre></div> | <!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/youtube/K4iO7k152og?h=349&amp;w=560&quot; class=&quot;WikiMedia WikiMediaYoutube&quot; id=&quot;wikitext@@media@@type=&amp;quot;youtube&amp;quot; key=&amp;quot;K4iO7k152og&amp;quot; height=&amp;quot;349&amp;quot; width=&amp;quot;560&amp;quot;&quot; title=&quot;YouTube Video&quot;height=&quot;349&quot; width=&quot;560&quot;/&gt; --><iframe width="560" height="349" src="//www.youtube.com/embed/K4iO7k152og" frameborder="0" allowfullscreen></iframe><!-- ws:end:WikiTextMediaRule:1 --></body></html></pre></div> | ||