15edt: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 12:15:56 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 14:11:38 UTC</tt>.<br>

: The original revision id was <tt>~~250619028~~</tt>.<br>

: The original revision id was <tt>250637172</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>

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=Properties=

The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15> in the 5-limit, which is tempered out by [[19edo]] but has an [[optimal patent val]] of [[303edo]]. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&123, which has a mapping [<1 0 0 0|, <0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of

The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each, corresponding to 9.464 edo. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15> in the 5-limit, which is tempered out by [[19edo]] but has an [[optimal patent val]] of [[303edo]]. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&123, which has a mapping [<1 0 0 0|, <0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of 126.773, very close to 15edt.

126.773, very close to 15edt.

=Intervals of 15edt=

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<br />

<h1 id="toc1"><a name="Properties"></a>Properties</h1>

The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15&gt; in the 5-limit, which is tempered out by <a class="wiki_link" href="/19edo">19edo</a> but has an <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> of <a class="wiki_link" href="/303edo">303edo</a>. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&amp;123, which has a mapping [&lt;1 0 0 0|, &lt;0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of ~~<br />~~

The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each, corresponding to 9.464 edo. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15&gt; in the 5-limit, which is tempered out by <a class="wiki_link" href="/19edo">19edo</a> but has an <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> of <a class="wiki_link" href="/303edo">303edo</a>. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&amp;123, which has a mapping [&lt;1 0 0 0|, &lt;0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of 126.773, very close to 15edt.<br />

126.773, very close to 15edt.<br />

<br />

<h1 id="toc2"><a name="Intervals of 15edt"></a>Intervals of 15edt</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 12:15:56 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 14:11:38 UTC</tt>.<br>
-: The original revision id was <tt>250619028</tt>.<br>
+: The original revision id was <tt>250637172</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>
@@ Line 11: / Line 11: @@
 =Properties=
-The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15&gt; in the 5-limit, which is tempered out by [[19edo]] but has an [[optimal patent val]] of [[303edo]]. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&amp;123, which has a mapping [&lt;1 0 0 0|, &lt;0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of
+The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each, corresponding to 9.464 edo. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15&gt; in the 5-limit, which is tempered out by [[19edo]] but has an [[optimal patent val]] of [[303edo]]. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&amp;123, which has a mapping [&lt;1 0 0 0|, &lt;0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of 126.773, very close to 15edt.
-.773, very close to 15edt.
 =Intervals of 15edt=
@@ Line 49: / Line 48: @@
   &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Properties&lt;/h1&gt;
-The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15&amp;gt; in the 5-limit, which is tempered out by &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; but has an &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; of &lt;a class="wiki_link" href="/303edo"&gt;303edo&lt;/a&gt;. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&amp;amp;123, which has a mapping [&amp;lt;1 0 0 0|, &amp;lt;0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of  &lt;br /&gt;
+The 15 equal division of 3, the tritave, divides it into 15 equal parts of 126.797 cents each, corresponding to 9.464 edo. It has 5 and 13 closely in tune, but does not do so well for 7 and 11, which are quite sharp. It tempers out the comma |0 22 -15&amp;gt; in the 5-limit, which is tempered out by &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; but has an &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; of &lt;a class="wiki_link" href="/303edo"&gt;303edo&lt;/a&gt;. As a 3.5.13 subgroup system, it tempers out 2197/2187 and 3159/3125. In the 7-limit it tempers out 375/343 and 6561/6125, and in the 11-limit, 81/77, 125/121 and 363/343. 15edt is related to the 2.3.5.13 subgroup temperament 19&amp;amp;123, which has a mapping [&amp;lt;1 0 0 0|, &amp;lt;0 15 22 35|], where the generator, an approximate 27/25, has a POTE tuning of 126.773, very close to 15edt.&lt;br /&gt;
-.773, very close to 15edt.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals of 15edt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals of 15edt&lt;/h1&gt;