18edo: Difference between revisions
Wikispaces>igliashon **Imported revision 139215305 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 139248063 - 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:xenwolf|xenwolf]] and made on <tt>2010-05-04 03:23:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>139248063</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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<span style="font-size: 14px; line-height: 21px;">**Relationship to Other EDOs** </span> | <span style="font-size: 14px; line-height: 21px;">**Relationship to Other EDOs** </span> | ||
18-EDO, aka the "third-tone" system, is related to 12-tET by the whole-tone scale (which is 6-EDO), since 18=6*3 and 12=6*2; hence a 12-tET "whole tone" is divided into 3 equal parts in 18-EDO. Since 18=9*2, 18-EDO contains two sets of 9-EDO, offset from each other by a third-tone. 18-EDO is related to 13-EDO, 21-EDO, 23-EDO, and 28-EDO in that all are "Father" temperaments (they temper out 16/15--the difference between a major third and perfect fourth). It is related to 11-EDO, 15-EDO, 25-EDO, and 29-EDO in that they are all "Amity" temperaments ("Amity" is derived from the acronym of "Acute Minor Thirds", meaning a minor third sharper than 6/5 but still flatter than a neutral third). | 18-EDO, aka the "third-tone" system, is related to [[12edo|12-tET]] by the whole-tone scale (which is [[6edo|6-EDO]]), since 18=6*3 and 12=6*2; hence a 12-tET "whole tone" is divided into 3 equal parts in 18-EDO. Since 18=9*2, 18-EDO contains two sets of [[9edo|9-EDO]], offset from each other by a third-tone. 18-EDO is related to [[13edo|13-EDO]], [[21edo|21-EDO]], [[23edo|23-EDO]], and [[28edo|28-EDO]] in that all are [[Father Temperament|"Father" temperaments]] (they temper out 16/15--the difference between a major third and perfect fourth). It is related to [[11edo|11-EDO]], [[15edo|15-EDO]], [[25edo|25-EDO]], and [[19edo|29-EDO]] in that they are all [[Amity Temperament|"Amity" temperaments]] ("Amity" is derived from the acronym of "Acute Minor Thirds", meaning a minor third sharper than 6/5 but still flatter than a neutral third). | ||
==Useful Moment-of-Symmetry Scales== | ==Useful Moment-of-Symmetry Scales== | ||
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<span style="font-size: 14px; line-height: 21px;"><strong>Relationship to Other EDOs</strong> </span><br /> | <span style="font-size: 14px; line-height: 21px;"><strong>Relationship to Other EDOs</strong> </span><br /> | ||
18-EDO, aka the &quot;third-tone&quot; system, is related to 12-tET by the whole-tone scale (which is 6-EDO), since 18=6*3 and 12=6*2; hence a 12-tET &quot;whole tone&quot; is divided into 3 equal parts in 18-EDO. Since 18=9*2, 18-EDO contains two sets of 9-EDO, offset from each other by a third-tone. 18-EDO is related to 13-EDO, 21-EDO, 23-EDO, and 28-EDO in that all are &quot;Father&quot; temperaments (they temper out 16/15--the difference between a major third and perfect fourth). It is related to 11-EDO, 15-EDO, 25-EDO, and 29-EDO in that they are all &quot;Amity&quot; temperaments (&quot;Amity&quot; is derived from the acronym of &quot;Acute Minor Thirds&quot;, meaning a minor third sharper than 6/5 but still flatter than a neutral third).<br /> | 18-EDO, aka the &quot;third-tone&quot; system, is related to <a class="wiki_link" href="/12edo">12-tET</a> by the whole-tone scale (which is <a class="wiki_link" href="/6edo">6-EDO</a>), since 18=6*3 and 12=6*2; hence a 12-tET &quot;whole tone&quot; is divided into 3 equal parts in 18-EDO. Since 18=9*2, 18-EDO contains two sets of <a class="wiki_link" href="/9edo">9-EDO</a>, offset from each other by a third-tone. 18-EDO is related to <a class="wiki_link" href="/13edo">13-EDO</a>, <a class="wiki_link" href="/21edo">21-EDO</a>, <a class="wiki_link" href="/23edo">23-EDO</a>, and <a class="wiki_link" href="/28edo">28-EDO</a> in that all are <a class="wiki_link" href="/Father%20Temperament">&quot;Father&quot; temperaments</a> (they temper out 16/15--the difference between a major third and perfect fourth). It is related to <a class="wiki_link" href="/11edo">11-EDO</a>, <a class="wiki_link" href="/15edo">15-EDO</a>, <a class="wiki_link" href="/25edo">25-EDO</a>, and <a class="wiki_link" href="/19edo">29-EDO</a> in that they are all <a class="wiki_link" href="/Amity%20Temperament">&quot;Amity&quot; temperaments</a> (&quot;Amity&quot; is derived from the acronym of &quot;Acute Minor Thirds&quot;, meaning a minor third sharper than 6/5 but still flatter than a neutral third).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Useful Moment-of-Symmetry Scales</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Useful Moment-of-Symmetry Scales</h2> | ||