23edo: Difference between revisions
Wikispaces>guest **Imported revision 239938199 - Original comment: ** |
Wikispaces>hstraub **Imported revision 240028143 - 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:hstraub|hstraub]] and made on <tt>2011-07-05 08:19:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240028143</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">= | <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;white-space: pre-wrap ! important" class="old-revision-html">=<span style="background-color: #000000; color: #009927; font-size: 109%;">23 tone equal temperament</span>= | ||
23et, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. 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|46et]], 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 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes. | 23et, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. 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|46et]], 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 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes. | ||
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==**23 tone [[Equal Modes]]:**== | ==**23 tone [[Equal Modes]]:**== | ||
10 10 3 | |||
9 9 5 | || 10 10 3 || || | ||
8 8 7 | || 9 9 5 || || | ||
7 7 7 2 | || 8 8 7 || || | ||
7 2 7 7 | || 7 7 7 2 || || | ||
6 6 6 5 | || 7 2 7 7 || || | ||
6 5 6 6 | || 6 6 6 5 || || | ||
5 4 5 5 4 | || 6 5 6 6 || || | ||
5 4 5 4 5 | || 5 4 5 5 4 || [[3L 2s|3L 2s (father)]] || | ||
7 1 7 7 1 | || 5 4 5 4 5 || || | ||
7 1 7 1 7 | || 7 1 7 7 1 || || | ||
5 5 5 5 3 | || 7 1 7 1 7 || || | ||
5 3 5 5 5 | || 5 5 5 5 3 || [[4L 1s|4L 1s (bug)]] || | ||
|| 5 3 5 5 5 || || | |||
4 4 4 4 4 3 | 4 4 4 4 4 3 | ||
4 3 4 4 4 4 | 4 3 4 4 4 4 | ||
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[[image:Teclado_Icositrifónico.PNG width="567" height="297" caption="A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems"]]</pre></div> | [[image:Teclado_Icositrifónico.PNG width="567" height="297" caption="A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems"]]</pre></div> | ||
<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:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x23 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -- | <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:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x23 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="background-color: #000000; color: #009927; font-size: 109%;">23 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
23et, or 23-EDO, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents. 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">46et</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 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.<br /> | 23et, or 23-EDO, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents. 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">46et</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 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.<br /> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:372:&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:372 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Music-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Music-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h2> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Music-Commas-INSTRUMENTS"></a><!-- ws:end:WikiTextHeadingRule:10 -->INSTRUMENTS</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Music-Commas-INSTRUMENTS"></a><!-- ws:end:WikiTextHeadingRule:10 -->INSTRUMENTS</h3> | ||
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<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 /> | ||
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<!-- 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> | <!-- 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 /> | <br /> | ||
9 9 5<br /> | |||
8 8 7<br /> | |||
7 7 7 2<br /> | <table class="wiki_table"> | ||
7 2 7 7<br /> | <tr> | ||
6 6 6 5<br /> | <td>10 10 3<br /> | ||
6 5 6 6<br /> | </td> | ||
5 4 5 5 4<br /> | <td><br /> | ||
5 4 5 4 5<br /> | </td> | ||
7 1 7 7 1<br /> | </tr> | ||
7 1 7 1 7<br /> | <tr> | ||
5 5 5 5 3<br /> | <td>9 9 5<br /> | ||
5 3 5 5 5<br /> | </td> | ||
<td><br /> | |||
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<td>8 8 7<br /> | |||
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<td>7 7 7 2<br /> | |||
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<td>7 2 7 7<br /> | |||
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<td>6 6 6 5<br /> | |||
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<td>6 5 6 6<br /> | |||
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<td>5 4 5 5 4<br /> | |||
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<td><a class="wiki_link" href="/3L%202s">3L 2s (father)</a><br /> | |||
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<td>5 4 5 4 5<br /> | |||
</td> | |||
<td><br /> | |||
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<td>7 1 7 7 1<br /> | |||
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<td><br /> | |||
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<td>7 1 7 1 7<br /> | |||
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<td><br /> | |||
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<td>5 5 5 5 3<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br /> | |||
</td> | |||
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<td>5 3 5 5 5<br /> | |||
</td> | |||
<td><br /> | |||
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4 4 4 4 4 3<br /> | 4 4 4 4 4 3<br /> | ||
4 3 4 4 4 4<br /> | 4 3 4 4 4 4<br /> | ||
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<!-- 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> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Keyboards"></a><!-- ws:end:WikiTextHeadingRule:16 -->Keyboards</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Keyboards"></a><!-- ws:end:WikiTextHeadingRule:16 -->Keyboards</h1> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:376:&lt;img src=&quot;/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/567x297/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: 297px; width: 567px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/567x297/Teclado_Icositrif%C3%B3nico.PNG" alt="Teclado_Icositrifónico.PNG" title="Teclado_Icositrifónico.PNG" style="height: 297px; width: 567px;" /></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:376 --></body></html></pre></div> | ||