Tour of regular temperaments: 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>2012-06-~~11 13~~:58:12 UTC</tt>.<br>

: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2012-07-01 14:01:18 UTC</tt>.<br>

: The original revision id was <tt>~~344462398~~</tt>.<br>

: The original revision id was <tt>349367170</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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This tempers out the mirkwai comma, |0 3 4 -5> = 16875/16807, a no-twos comma (ratio of odd numbers.)

===[[Quince clan]]===

This tempers out quince, the no-threes comma |-15 0 -2 7> = 823543/819200.

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===[[Septisemi temperaments]]===

These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/4 with 7/4.

These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4.

===[[Mint temperaments]]===

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These temper out |6 3 -1 -3> = 1728/1715, the orwellisma.

===[[Octagar temperaments]]===

Octagar temperaments temper out the octagar comma, |5 -4 3 -2> = 4000/3969.

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<br />

<h3 id="toc50"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Clans-Quince clan"></a><a class="wiki_link" href="/Quince%20clan">Quince clan</a></h3>

This tempers out quince, the no-threes comma |-15 0 -2 7&gt; = 823543/819200.<br />

<br />

<h1 id="toc51"><a name="Temperaments for a given comma"></a>Temperaments for a given comma</h1>

<br />

<h3 id="toc52"><a name="Temperaments for a given comma--Septisemi temperaments"></a><a class="wiki_link" href="/Septisemi%20temperaments">Septisemi temperaments</a></h3>

These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/4 with 7/4.<br />

These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4.<br />

<br />

<h3 id="toc53"><a name="Temperaments for a given comma--Mint temperaments"></a><a class="wiki_link" href="/Mint%20temperaments">Mint temperaments</a></h3>

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<br />

<h3 id="toc60"><a name="Temperaments for a given comma--Octagar temperaments"></a><a class="wiki_link" href="/Octagar%20temperaments">Octagar temperaments</a></h3>

Octagar temperaments temper out the octagar comma, |5 -4 3 -2&gt; = 4000/3969.<br />

<br />

<h3 id="toc61"><a name="Temperaments for a given comma--Hemifamity temperaments"></a><a class="wiki_link" href="/Hemifamity%20temperaments">Hemifamity temperaments</a></h3>

@@ 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>2012-06-11 13:58:12 UTC</tt>.<br>
+: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2012-07-01 14:01:18 UTC</tt>.<br>
-: The original revision id was <tt>344462398</tt>.<br>
+: The original revision id was <tt>349367170</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 177: / Line 177: @@
 This tempers out the mirkwai comma, |0 3 4 -5&gt; = 16875/16807, a no-twos comma (ratio of odd numbers.)
 ===[[Quince clan]]===
 This tempers out quince, the no-threes comma |-15 0 -2 7&gt; = 823543/819200.
@@ Line 183: / Line 183: @@
 ===[[Septisemi temperaments]]===
-These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/4 with 7/4.
+These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4.
 ===[[Mint temperaments]]===
@@ Line 206: / Line 206: @@
 These temper out |6 3 -1 -3&gt; = 1728/1715, the orwellisma.
 ===[[Octagar temperaments]]===
 Octagar temperaments temper out the octagar comma, |5 -4 3 -2&gt; = 4000/3969.
@@ Line 550: / Line 550: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc50"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Quince clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;&lt;a class="wiki_link" href="/Quince%20clan"&gt;Quince clan&lt;/a&gt;&lt;/h3&gt;
-This tempers out quince, the no-threes comma |-15 0 -2 7&amp;gt; = 823543/819200.&lt;br /&gt;
+ This tempers out quince, the no-threes comma |-15 0 -2 7&amp;gt; = 823543/819200.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc51"&gt;&lt;a name="Temperaments for a given comma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;Temperaments for a given comma&lt;/h1&gt;
   &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc52"&gt;&lt;a name="Temperaments for a given comma--Septisemi temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;&lt;a class="wiki_link" href="/Septisemi%20temperaments"&gt;Septisemi temperaments&lt;/a&gt;&lt;/h3&gt;
-  These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/4 with 7/4.&lt;br /&gt;
+  These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc53"&gt;&lt;a name="Temperaments for a given comma--Mint temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;&lt;a class="wiki_link" href="/Mint%20temperaments"&gt;Mint temperaments&lt;/a&gt;&lt;/h3&gt;
@@ Line 579: / Line 579: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc60"&gt;&lt;a name="Temperaments for a given comma--Octagar temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;&lt;a class="wiki_link" href="/Octagar%20temperaments"&gt;Octagar temperaments&lt;/a&gt;&lt;/h3&gt;
-Octagar temperaments temper out the octagar comma, |5 -4 3 -2&amp;gt; = 4000/3969.&lt;br /&gt;
+ Octagar temperaments temper out the octagar comma, |5 -4 3 -2&amp;gt; = 4000/3969.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc61"&gt;&lt;a name="Temperaments for a given comma--Hemifamity temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;&lt;a class="wiki_link" href="/Hemifamity%20temperaments"&gt;Hemifamity temperaments&lt;/a&gt;&lt;/h3&gt;