23edo: Difference between revisions
Wikispaces>hstraub **Imported revision 240037213 - Original comment: ** |
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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 09: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-05 09:55:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240037315</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">[[toc|flat]] | <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]] | ||
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=<span style="background-color: # | =<span style="background-color: #ffffff; 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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<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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#x23 tone equal temperament">23 tone equal temperament</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#x23 tone Equal Modes:">23 tone Equal Modes:</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#x23 tone equal temperament">23 tone equal temperament</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#x23 tone Equal Modes:">23 tone Equal Modes:</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
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<!-- 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: # | <!-- 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: #ffffff; color: #009927; font-size: 109%;">23 tone equal temperament</span></h1> | ||
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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 /> | ||