23edo: Difference between revisions

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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. 23edo is the 9th [[prime numbers|prime]] edo, following [[19edo]] and coming before [[29edo]].

=Music=  

//Allegro Moderato// by Easley Blackwood

=Commas=  

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&lt;strong&gt;&lt;em&gt;23-tET&lt;/em&gt;&lt;/strong&gt;, or &lt;strong&gt;&lt;em&gt;23-EDO&lt;/em&gt;&lt;/strong&gt;, is a tempered musical system which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony &lt;em&gt;(Icositrifonía)&lt;/em&gt;. It has good approximations for &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;, &lt;a class="wiki_link" href="/11_7"&gt;11/7&lt;/a&gt;, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. If to this subgroup is added the commas of &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, the larger 17-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*23 subgroup&lt;/a&gt; 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. 23edo is the 9th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;.&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Music&lt;/h1&gt;

&lt;em&gt;Allegro Moderato&lt;/em&gt; by Easley Blackwood&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Commas&lt;/h1&gt;