23edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 575541907 - Original comment: ** |
Wikispaces>Nickname2 **Imported revision 583021901 - 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:Nickname2|Nickname2]] and made on <tt>2016-05-13 08:21:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>583021901</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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DMS value ||= Approximate | DMS value ||= Approximate | ||
Ratios* ||= Armodue | Ratios* ||= Armodue | ||
Notation || | Notation || Notes || | ||
|| 0 || 0 ||= 1/1 ||= 1 || | || 0 || 0 ||= 1/1 ||= 1 || || | ||
|| 1 || 52.1739 | || 1 || 52.1739 | ||
15°39'8" ||= 33/32, 34/33 ||= 2b || | 15°39'8" ||= 33/32, 34/33 ||= 2b || || | ||
|| 2 || 104.3478 | || 2 || 104.3478 | ||
31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# || | 31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# || Less than 1-cent off 17/16 || | ||
|| 3 || 156.5217 | || 3 || 156.5217 | ||
47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 || | 47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 || || | ||
|| 4· || 208.6957 | || 4· || 208.6957 | ||
62°36'31" ||= 9/8, 44/39 ||= 3b || | 62°36'31" ||= 9/8, 44/39 ||= 3b || || | ||
|| 5 || 260.8696 | || 5 || 260.8696 | ||
78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# || | 78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# || || | ||
|| 6 || 313.0435 | || 6 || 313.0435 | ||
93°54'47" ||= 6/5 ||= 3 || | 93°54'47" ||= 6/5 ||= 3 || Much better at approximating 6/5 than 12-EDO || | ||
|| 7· || 365.2174 | || 7· || 365.2174 | ||
109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b || | 109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b || || | ||
|| 8 || 417.3913 | || 8 || 417.3913 | ||
125°13'3* ||= 14/11, 33/26 ||= 3# || | 125°13'3* ||= 14/11, 33/26 ||= 3# || Practically just approximation of 14/11 || | ||
|| 9 || 469.5652 | || 9 || 469.5652 | ||
140°52'10" ||= 21/16, 17/13 ||= 4 || | 140°52'10" ||= 21/16, 17/13 ||= 4 || || | ||
|| 10· || 521.7391 | || 10· || 521.7391 | ||
156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 || | 156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 || || | ||
|| 11 || 573.913 | || 11 || 573.913 | ||
172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b || | 172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b || || | ||
|| 12 || 626.087 | || 12 || 626.087 | ||
187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# || | 187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# || || | ||
|| 13· || 678.2609 | || 13· || 678.2609 | ||
204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 || | 204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 || Great generator for Hornbostel temperament. || | ||
|| 14 || 730.4348 | || 14 || 730.4348 | ||
219°7'50" ||= 32/21, 26/17 ||= 7b || | 219°7'50" ||= 32/21, 26/17 ||= 7b || || | ||
|| 15 || 782.6087 | || 15 || 782.6087 | ||
234°46'57" ||= 11/7, 52/33 ||= 6# || | 234°46'57" ||= 11/7, 52/33 ||= 6# || || | ||
|| 16· || 834.7826 | || 16· || 834.7826 | ||
251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 || | 251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 || || | ||
|| 17 || 886.9565 | || 17 || 886.9565 | ||
266°5'13" ||= 5/3 ||= 8b || | 266°5'13" ||= 5/3 ||= 8b || || | ||
|| 18 || 939.1304 | || 18 || 939.1304 | ||
282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# || | 282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# || || | ||
|| 19· || 991.3043 | || 19· || 991.3043 | ||
297°23'29" ||= 16/9, 39/22 ||= 8 || | 297°23'29" ||= 16/9, 39/22 ||= 8 || || | ||
|| 20 || 1043.4783 | || 20 || 1043.4783 | ||
313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b || | 313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b || || | ||
|| 21 || 1095.6522 | || 21 || 1095.6522 | ||
328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# || | 328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# || || | ||
|| 22 || 1147.8261 | || 22 || 1147.8261 | ||
344°40'52" ||= 33/17, 64/33 ||= 9 || | 344°40'52" ||= 33/17, 64/33 ||= 9 || || | ||
|| 23·· || 1200 | || 23·· || 1200 | ||
360° ||= 2/1 ||= 1 || | 360° ||= 2/1 ||= 1 || || | ||
*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | *based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x23 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="font-size: 1.4em;">Intervals</span></h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x23 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="font-size: 1.4em;">Intervals</span></h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:816:&lt;a href=&quot;/Harmony%20of%2023edo&quot;&gt;&lt;img src=&quot;/file/view/Ciclo%20Icositrifon%C3%ADa.png/390051610/491x490/Ciclo%20Icositrifon%C3%ADa.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 490px; width: 491px;&quot; /&gt;&lt;/a&gt; --><a href="/Harmony%20of%2023edo"><img src="/file/view/Ciclo%20Icositrifon%C3%ADa.png/390051610/491x490/Ciclo%20Icositrifon%C3%ADa.png" alt="Ciclo Icositrifonía.png" title="Ciclo Icositrifonía.png" style="height: 490px; width: 491px;" /></a><!-- ws:end:WikiTextLocalImageRule:816 --><br /> | ||
<br /> | <br /> | ||
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<td style="text-align: center;">Armodue<br /> | <td style="text-align: center;">Armodue<br /> | ||
Notation<br /> | Notation<br /> | ||
</td> | |||
<td>Notes<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | |||
<td><br /> | |||
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<td style="text-align: center;">2b<br /> | <td style="text-align: center;">2b<br /> | ||
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<td><br /> | |||
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</td> | </td> | ||
<td style="text-align: center;">1#<br /> | <td style="text-align: center;">1#<br /> | ||
</td> | |||
<td>Less than 1-cent off 17/16<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
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</td> | </td> | ||
<td style="text-align: center;">3b<br /> | <td style="text-align: center;">3b<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">2#<br /> | <td style="text-align: center;">2#<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
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</td> | </td> | ||
<td style="text-align: center;">3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | |||
<td>Much better at approximating 6/5 than 12-EDO<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">4b<br /> | <td style="text-align: center;">4b<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
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</td> | </td> | ||
<td style="text-align: center;">3#<br /> | <td style="text-align: center;">3#<br /> | ||
</td> | |||
<td>Practically just approximation of 14/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | |||
<td><br /> | |||
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</td> | </td> | ||
<td style="text-align: center;">5<br /> | <td style="text-align: center;">5<br /> | ||
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<td style="text-align: center;">6b<br /> | <td style="text-align: center;">6b<br /> | ||
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<td style="text-align: center;">5#<br /> | <td style="text-align: center;">5#<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | |||
<td>Great generator for Hornbostel temperament.<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">7b<br /> | <td style="text-align: center;">7b<br /> | ||
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<td style="text-align: center;">6#<br /> | <td style="text-align: center;">6#<br /> | ||
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<td style="text-align: center;">7<br /> | <td style="text-align: center;">7<br /> | ||
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<td style="text-align: center;">8b<br /> | <td style="text-align: center;">8b<br /> | ||
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<td style="text-align: center;">7#<br /> | <td style="text-align: center;">7#<br /> | ||
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<td style="text-align: center;">8<br /> | <td style="text-align: center;">8<br /> | ||
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<td style="text-align: center;">9b<br /> | <td style="text-align: center;">9b<br /> | ||
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<td style="text-align: center;">8#<br /> | <td style="text-align: center;">8#<br /> | ||
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<td><br /> | |||
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<td style="text-align: center;">9<br /> | <td style="text-align: center;">9<br /> | ||
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<td style="text-align: center;">1<br /> | <td style="text-align: center;">1<br /> | ||
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The chart below shows some of the <a class="wiki_link" href="/MOSScales">Moment of Symmetry (MOS)</a> modes of <a class="wiki_link" href="/Mavila">Mavila</a> available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:<br /> | The chart below shows some of the <a class="wiki_link" href="/MOSScales">Moment of Symmetry (MOS)</a> modes of <a class="wiki_link" href="/Mavila">Mavila</a> available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:817:&lt;img src=&quot;/file/view/23edoMavilaMOS.jpg/288679838/23edoMavilaMOS.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/23edoMavilaMOS.jpg/288679838/23edoMavilaMOS.jpg" alt="23edoMavilaMOS.jpg" title="23edoMavilaMOS.jpg" /><!-- ws:end:WikiTextLocalImageRule:817 --><br /> | ||
<br /> | <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 /> | 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 /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:14 -->Books</h1> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:14 -->Books</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:818:&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:818 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc7"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:16 -->Instruments</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc7"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:16 -->Instruments</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:819:&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:819 --><br /> | ||
<em>An Icositriphonic 8-string Guitar. 23-ED2 Guitar by Ron Sword.</em><br /> | <em>An Icositriphonic 8-string Guitar. 23-ED2 Guitar by Ron Sword.</em><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:820:&lt;img src=&quot;/file/view/Icositriphonic_Bass.JPG/206711470/640x193/Icositriphonic_Bass.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 193px; width: 640px;&quot; /&gt; --><img src="/file/view/Icositriphonic_Bass.JPG/206711470/640x193/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 193px; width: 640px;" /><!-- ws:end:WikiTextLocalImageRule:820 --><br /> | ||
<em>An Icositriphonic P-Bass. 23-ED2 Bass by Tútim Dennsuul Wafiil.</em><br /> | <em>An Icositriphonic P-Bass. 23-ED2 Bass by Tútim Dennsuul Wafiil.</em><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:821:&lt;img src=&quot;/file/view/Icositriphonic%20Gitar%201.png/358559595/640x216/Icositriphonic%20Gitar%201.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 216px; width: 640px;&quot; /&gt; --><img src="/file/view/Icositriphonic%20Gitar%201.png/358559595/640x216/Icositriphonic%20Gitar%201.png" alt="Icositriphonic Gitar 1.png" title="Icositriphonic Gitar 1.png" style="height: 216px; width: 640px;" /><!-- ws:end:WikiTextLocalImageRule:821 --><br /> | ||
<em>An Icositriphonic 'Hendrix' TravelGuitar. 23-ED2 'Gitar' by Tútim Dennsuul Wafiil.</em><br /> | <em>An Icositriphonic 'Hendrix' TravelGuitar. 23-ED2 'Gitar' by Tútim Dennsuul Wafiil.</em><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:822:&lt;img src=&quot;/file/view/Icositritar%201.png/358559793/640x271/Icositritar%201.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 271px; width: 640px;&quot; /&gt; --><img src="/file/view/Icositritar%201.png/358559793/640x271/Icositritar%201.png" alt="Icositritar 1.png" title="Icositritar 1.png" style="height: 271px; width: 640px;" /><!-- ws:end:WikiTextLocalImageRule:822 --><br /> | ||
<em>The 'Icositritar', 23-ED2 5-string Acoustic Guitar by Tútim Dennsuul Wafiil.</em><br /> | <em>The 'Icositritar', 23-ED2 5-string Acoustic Guitar by Tútim Dennsuul Wafiil.</em><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:823:&lt;img src=&quot;/file/view/Teclado%20Icositrif%C3%B3nico.PNG/390051980/607x323/Teclado%20Icositrif%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 323px; width: 607px;&quot; /&gt; --><img src="/file/view/Teclado%20Icositrif%C3%B3nico.PNG/390051980/607x323/Teclado%20Icositrif%C3%B3nico.PNG" alt="Teclado Icositrifónico.PNG" title="Teclado Icositrifónico.PNG" style="height: 323px; width: 607px;" /><!-- ws:end:WikiTextLocalImageRule:823 --><br /> | ||
<em>An illustrative image of a 23-ED2 Keyboard</em><br /> | <em>An illustrative image of a 23-ED2 Keyboard</em><br /> | ||
<br /> | <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 /> | 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:824:&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:824 --><br /> | ||
Here is a still shot of the completed instrument.<br /> | Here is a still shot of the completed instrument.<br /> | ||
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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 /> | ||
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