23edo: Difference between revisions
Wikispaces>hstraub **Imported revision 240029907 - Original comment: ** |
Wikispaces>hstraub **Imported revision 240030021 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:hstraub|hstraub]] and made on <tt>2011-07-05 08: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-05 08:42:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240030021</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">=<span style="background-color: #000000; color: #009927; font-size: 109%;">23 tone equal temperament</span>= | <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">[[toc|flat]] | ||
=<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. | ||
| Line 51: | Line 55: | ||
//Allegro Moderato// by Easley Blackwood | //Allegro Moderato// by Easley Blackwood | ||
=Intervals= | |||
|| [[Degree]]s of 23-EDO || [[Cent]]s value || | || [[Degree]]s of 23-EDO || [[Cent]]s value || | ||
|| 0 || 0 || | || 0 || 0 || | ||
| Line 78: | Line 82: | ||
[[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"]] | ||
== == | == == | ||
=Commas= | |||
23 EDO tempers out the following commas. (Note: This assumes the val < 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). | 23 EDO tempers out the following commas. (Note: This assumes the val < 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). | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
| Line 90: | Line 94: | ||
||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= || | ||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= || | ||
=INSTRUMENTS= | |||
[[image:Icositriphonic_Bass.JPG width="594" height="216"]] | [[image:Icositriphonic_Bass.JPG width="594" height="216"]] | ||
//An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.// | //An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.// | ||
| Line 97: | Line 101: | ||
//An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.// | //An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.// | ||
=**23 tone [[Equal Modes]]:**= | |||
|| 10 10 3 || || | || 10 10 3 || || | ||
| Line 154: | Line 158: | ||
[[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 --><span style="background-color: #000000; color: #009927; font-size: 109%;">23 tone equal temperament</span></h1> | <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:WikiTextTocRule:18:&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:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#x23 tone equal temperament">23 tone equal temperament</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#INSTRUMENTS">INSTRUMENTS</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#x23 tone Equal Modes:">23 tone Equal Modes:</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Keyboards">Keyboards</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | ||
<!-- ws:end:WikiTextTocRule:28 --><br /> | |||
<br /> | |||
<br /> | |||
<!-- 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 /> | ||
| Line 199: | Line 207: | ||
<em>Allegro Moderato</em> by Easley Blackwood<br /> | <em>Allegro Moderato</em> by Easley Blackwood<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> | ||
| Line 349: | Line 357: | ||
</table> | </table> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:587:&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:587 --><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; | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->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 /> | ||
| Line 485: | Line 493: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt; | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="INSTRUMENTS"></a><!-- ws:end:WikiTextHeadingRule:10 -->INSTRUMENTS</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:588:&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:588 --><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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:589:&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:589 --><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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt; | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x23 tone Equal Modes:"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong>23 tone <a class="wiki_link" href="/Equal%20Modes">Equal Modes</a>:</strong></h1> | ||
<br /> | <br /> | ||
| Line 783: | Line 791: | ||
<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> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:590:&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:590 --><br /> | ||
<br /> | <br /> | ||
<!-- 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> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:591:&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:591 --></body></html></pre></div> | ||