Tour of regular temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-24 00:59:30 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-24 01:01:53 UTC</tt>.<br>

: The original revision id was <tt>~~231242432~~</tt>.<br>

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=Regular temperaments=

A rank r [[http://en.wikipedia.org/wiki/Regular_temperament|regular temperament]] in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An [[abstract regular temperament]] can be defined in various ways, for instance by giving a set of [[comma|commas]] tempered out by the temperament, or a set of r independent vals defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the [[comma pump examples|comma pumps]] of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example i the pump I-vii-IV-ii-V-I of meantone temperament.

A rank r [[http://en.wikipedia.org/wiki/Regular_temperament|regular temperament]] in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An [[abstract regular temperament]] can be defined in various ways, for instance by giving a set of [[comma|commas]] tempered out by the temperament, or a set of r independent [[Vals and Tuning Space|vals]] defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the [[comma pump examples|comma pumps]] of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example is the pump I-vii-IV-ii-V-I of meantone temperament.

=[[edo|Equal temperaments]]=

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<h1 id="toc0"><a name="Regular temperaments"></a>Regular temperaments</h1>

<br />

A rank r <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow">regular temperament</a> in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperament</a> can be defined in various ways, for instance by giving a set of <a class="wiki_link" href="/comma">commas</a> tempered out by the temperament, or a set of r independent vals defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the <a class="wiki_link" href="/comma%20pump%20examples">comma pumps</a> of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example i the pump I-vii-IV-ii-V-I of meantone temperament.<br />

A rank r <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow">regular temperament</a> in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperament</a> can be defined in various ways, for instance by giving a set of <a class="wiki_link" href="/comma">commas</a> tempered out by the temperament, or a set of r independent <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">vals</a> defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the <a class="wiki_link" href="/comma%20pump%20examples">comma pumps</a> of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example is the pump I-vii-IV-ii-V-I of meantone temperament.<br />

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<h1 id="toc1"><a name="Equal temperaments"></a><a class="wiki_link" href="/edo">Equal temperaments</a></h1>

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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>2011-05-24 00:59:30 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-24 01:01:53 UTC</tt>.<br>
-: The original revision id was <tt>231242432</tt>.<br>
+: The original revision id was <tt>231242832</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 10: / Line 10: @@
 =Regular temperaments=
-A rank r [[http://en.wikipedia.org/wiki/Regular_temperament|regular temperament]] in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An [[abstract regular temperament]] can be defined in various ways, for instance by giving a set of [[comma|commas]] tempered out by the temperament, or a set of r independent vals defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the [[comma pump examples|comma pumps]] of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example i the pump I-vii-IV-ii-V-I of meantone temperament.
+A rank r [[http://en.wikipedia.org/wiki/Regular_temperament|regular temperament]] in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An [[abstract regular temperament]] can be defined in various ways, for instance by giving a set of [[comma|commas]] tempered out by the temperament, or a set of r independent [[Vals and Tuning Space|vals]] defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the [[comma pump examples|comma pumps]] of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example is the pump I-vii-IV-ii-V-I of meantone temperament.
 =[[edo|Equal temperaments]]=
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 &lt;br /&gt;
-A rank r &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow"&gt;regular temperament&lt;/a&gt; in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An &lt;a class="wiki_link" href="/abstract%20regular%20temperament"&gt;abstract regular temperament&lt;/a&gt; can be defined in various ways, for instance by giving a set of &lt;a class="wiki_link" href="/comma"&gt;commas&lt;/a&gt; tempered out by the temperament, or a set of r independent vals defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the &lt;a class="wiki_link" href="/comma%20pump%20examples"&gt;comma pumps&lt;/a&gt; of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example i the pump I-vii-IV-ii-V-I of meantone temperament.&lt;br /&gt;
+A rank r &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow"&gt;regular temperament&lt;/a&gt; in a particular tuning may be defined by giving r multiplicatively independent real numbers, which can be multiplied together to produce the intervals attainable in the temperament. An &lt;a class="wiki_link" href="/abstract%20regular%20temperament"&gt;abstract regular temperament&lt;/a&gt; can be defined in various ways, for instance by giving a set of &lt;a class="wiki_link" href="/comma"&gt;commas&lt;/a&gt; tempered out by the temperament, or a set of r independent &lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;vals&lt;/a&gt; defining the mapping of the temperament. A characteristic feature of any temperament tempering out a comma are the &lt;a class="wiki_link" href="/comma%20pump%20examples"&gt;comma pumps&lt;/a&gt; of the comma, which are a sequence of harmonically notes or chords which return to their starting point when tempered, but which would not do so in just intonation. An example is the pump I-vii-IV-ii-V-I of meantone temperament.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Equal temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;a class="wiki_link" href="/edo"&gt;Equal temperaments&lt;/a&gt;&lt;/h1&gt;