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:~~mbattaglia1~~|~~mbattaglia1~~]] and made on <tt>2011-09-05 22:08:45 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-05 22:42:53 UTC</tt>.<br>

: The original revision id was <tt>~~251021756~~</tt>.<br>

: The original revision id was <tt>251031282</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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===[[Pythagorean family]]===

The Pythagorean family tempers out the Pythagorean comma, |-19 12 0>. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate

The Pythagorean family tempers out the Pythagorean comma, |-19 12 0>. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate chains of 12-equal, offset from one another justly tuned 5/4.

chains of 12-equal, offset from one another justly tuned 5/4.

===[[Apotome family]]===

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<br />

<h3 id="toc18"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Pythagorean family"></a><a class="wiki_link" href="/Pythagorean%20family">Pythagorean family</a></h3>

The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate~~<br />~~

The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate chains of 12-equal, offset from one another justly tuned 5/4.<br />

chains of 12-equal, offset from one another justly tuned 5/4.<br />

<br />

<h3 id="toc19"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Apotome family"></a><a class="wiki_link" href="/Apotome%20family">Apotome family</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:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-05 22:08:45 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-05 22:42:53 UTC</tt>.<br>
-: The original revision id was <tt>251021756</tt>.<br>
+: The original revision id was <tt>251031282</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 79: / Line 79: @@
 ===[[Pythagorean family]]===
-The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate
+The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate chains of 12-equal, offset from one another justly tuned 5/4.
-chains of 12-equal, offset from one another justly tuned 5/4.
 ===[[Apotome family]]===
@@ Line 353: / Line 352: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments--Pythagorean family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;&lt;a class="wiki_link" href="/Pythagorean%20family"&gt;Pythagorean family&lt;/a&gt;&lt;/h3&gt;
-  The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&amp;gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate&lt;br /&gt;
+  The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&amp;gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. Temperaments in this family tend to have a period of 1/12th octave, and the 5-limit compton temperament can be thought of generating as two duplicate chains of 12-equal, offset from one another justly tuned 5/4.&lt;br /&gt;
-chains of 12-equal, offset from one another justly tuned 5/4.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments--Apotome family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;&lt;a class="wiki_link" href="/Apotome%20family"&gt;Apotome family&lt;/a&gt;&lt;/h3&gt;