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 01:01:53 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-24 01:03:02 UTC</tt>.<br>

: The original revision id was <tt>~~231242832~~</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 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.

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 sequences of harmonically related 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>

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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 />

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 sequences of harmonically related 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 01:01:53 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-24 01:03:02 UTC</tt>.<br>
-: The original revision id was <tt>231242832</tt>.<br>
+: The original revision id was <tt>231243010</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 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.
+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 sequences of harmonically related 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;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Regular temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Regular temperaments&lt;/h1&gt;
 &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;
+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 sequences of harmonically related 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;