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>2010-05-29 01:~~58:51~~ UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-29 02:01:10 UTC</tt>.<br>

: The original revision id was <tt>~~145584183~~</tt>.<br>

: The original revision id was <tt>145584295</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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===[[Schismatic family]]===

The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a [[microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.

The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a [[Microtempering|microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.

==Rank 3 temperaments==

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<br />

<h3 id="toc10"><a name="x-Meantone family-Schismatic family"></a><a class="wiki_link" href="/Schismatic%20family">Schismatic family</a></h3>

The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a <a class="wiki_link" href="/~~microtemperament~~">microtemperament</a> which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.<br />

The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a <a class="wiki_link" href="/Microtempering">microtemperament</a> which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.<br />

<br />

<h2 id="toc11"><a name="x-Rank 3 temperaments"></a>Rank 3 temperaments</h2>

@@ 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>2010-05-29 01:58:51 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-29 02:01:10 UTC</tt>.<br>
-: The original revision id was <tt>145584183</tt>.<br>
+: The original revision id was <tt>145584295</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 43: / Line 43: @@
 ===[[Schismatic family]]===
-The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a [[microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.
+The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a [[Microtempering|microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.
 ==Rank 3 temperaments==
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x-Meantone family-Schismatic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;a class="wiki_link" href="/Schismatic%20family"&gt;Schismatic family&lt;/a&gt;&lt;/h3&gt;
-  The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a &lt;a class="wiki_link" href="/microtemperament"&gt;microtemperament&lt;/a&gt; which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.&lt;br /&gt;
+  The schismatic family tempers out the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymas comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. The 5-limit version of the temperament is a &lt;a class="wiki_link" href="/Microtempering"&gt;microtemperament&lt;/a&gt; which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-Rank 3 temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Rank 3 temperaments&lt;/h2&gt;