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:~~igliashon~~|~~igliashon~~]] and made on <tt>2011-07-16 17:15:03 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-25 16:21:49 UTC</tt>.<br>

: The original revision id was <tt>~~241605067~~</tt>.<br>

: The original revision id was <tt>242785079</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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Although the concept of regular temperament is centuries old and predates much of modern mathematics, members of the Yahoo! Alternative Tuning List have developed a particular form of numerical "short-hand" for describing the properties of temperaments. The most important of these are vals and commas, which any student of the modern regular temperament paradigm should become familiar with as a first order of business. These concepts are rather straight-forward and require very little math to understand.

Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an "optimal" tuning for the generator. The two most frequently used forms of optimization are POTE ("Pure-Octave Tenney-Euclidean") and TOP ("Tenney OPtimal", or "Tempered Octaves, Please"). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.

Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an "optimal" tuning for the generator. The two most frequently used forms of optimization are POTE ("Pure-Octave Tenney-Euclidean") and [[Top tuning|TOP]] ("Tenney OPtimal", or "Tempered Octaves, Please"). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.

=[[edo|Equal temperaments]]=

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Although the concept of regular temperament is centuries old and predates much of modern mathematics, members of the Yahoo! Alternative Tuning List have developed a particular form of numerical &quot;short-hand&quot; for describing the properties of temperaments. The most important of these are vals and commas, which any student of the modern regular temperament paradigm should become familiar with as a first order of business. These concepts are rather straight-forward and require very little math to understand.<br />

<br />

Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an &quot;optimal&quot; tuning for the generator. The two most frequently used forms of optimization are POTE (&quot;Pure-Octave Tenney-Euclidean&quot;) and TOP (&quot;Tenney OPtimal&quot;, or &quot;Tempered Octaves, Please&quot;). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.<br />

Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an &quot;optimal&quot; tuning for the generator. The two most frequently used forms of optimization are POTE (&quot;Pure-Octave Tenney-Euclidean&quot;) and <a class="wiki_link" href="/Top%20tuning">TOP</a> (&quot;Tenney OPtimal&quot;, or &quot;Tempered Octaves, Please&quot;). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.<br />

<br />

<h1 id="toc3"><a name="Equal temperaments"></a><a class="wiki_link" href="/edo">Equal temperaments</a></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:igliashon|igliashon]] and made on <tt>2011-07-16 17:15:03 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-25 16:21:49 UTC</tt>.<br>
-: The original revision id was <tt>241605067</tt>.<br>
+: The original revision id was <tt>242785079</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 22: / Line 22: @@
 Although the concept of regular temperament is centuries old and predates much of modern mathematics, members of the Yahoo! Alternative Tuning List have developed a particular form of numerical "short-hand" for describing the properties of temperaments. The most important of these are vals and commas, which any student of the modern regular temperament paradigm should become familiar with as a first order of business. These concepts are rather straight-forward and require very little math to understand.
-Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an "optimal" tuning for the generator. The two most frequently used forms of optimization are POTE ("Pure-Octave Tenney-Euclidean") and TOP ("Tenney OPtimal", or "Tempered Octaves, Please"). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.
+Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an "optimal" tuning for the generator. The two most frequently used forms of optimization are POTE ("Pure-Octave Tenney-Euclidean") and [[Top tuning|TOP]] ("Tenney OPtimal", or "Tempered Octaves, Please"). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.
 =[[edo|Equal temperaments]]=
@@ Line 294: / Line 294: @@
 Although the concept of regular temperament is centuries old and predates much of modern mathematics, members of the Yahoo! Alternative Tuning List have developed a particular form of numerical &amp;quot;short-hand&amp;quot; for describing the properties of temperaments. The most important of these are vals and commas, which any student of the modern regular temperament paradigm should become familiar with as a first order of business. These concepts are rather straight-forward and require very little math to understand.&lt;br /&gt;
 &lt;br /&gt;
-Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an &amp;quot;optimal&amp;quot; tuning for the generator. The two most frequently used forms of optimization are POTE (&amp;quot;Pure-Octave Tenney-Euclidean&amp;quot;) and TOP (&amp;quot;Tenney OPtimal&amp;quot;, or &amp;quot;Tempered Octaves, Please&amp;quot;). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.&lt;br /&gt;
+Another recent contribution to the field of temperament is the concept of optimization, which can take many forms. The point of optimization is to minimize the difference between a temperament and JI by finding an &amp;quot;optimal&amp;quot; tuning for the generator. The two most frequently used forms of optimization are POTE (&amp;quot;Pure-Octave Tenney-Euclidean&amp;quot;) and &lt;a class="wiki_link" href="/Top%20tuning"&gt;TOP&lt;/a&gt; (&amp;quot;Tenney OPtimal&amp;quot;, or &amp;quot;Tempered Octaves, Please&amp;quot;). Optimization is rather mathematically-intensive, but it is seldom (if ever) left as an exercise to the reader; most temperaments are presented here in their optimal forms.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Equal temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/edo"&gt;Equal temperaments&lt;/a&gt;&lt;/h1&gt;