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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A trivial temperament is something that fits the mathematical definition of "regular temperament", but is a unique, extreme case that people might be uncomfortable calling a "temperament". There are two kinds of trivial temperaments - JI, in which nothing is tempered, and '''OM''' temperament, in which everything is tempered. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-11 16:11:00 UTC</tt>.<br>
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| : The original revision id was <tt>300808992</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A trivial temperament is something that fits the mathematical definition of "regular temperament", but is a unique, extreme case that people might be uncomfortable calling a "temperament". There are two kinds of trivial temperaments - JI, in which nothing is tempered, and **OM** temperament, in which everything is tempered.
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| Just intonation is a codimension-0 "temperament", which means nothing is tempered. The set of commas that are tempered out is the set {1/1}, but that's still a set, so JI is still a regular temperament. There is an infinite family of these "temperaments", one for each subgroup of JI. The 2-limit version is the equal temperament [[1edo]]. The 3-limit version is the rank-2 temperament [[pythagorean]], which has all the properties of any other rank-2 temperament except that it tempers no commas. The 5-limit version is rank-3, and so on. The mapping for this temperament is an nxn identity matrix, with wedgies of <1|, <<1||, <<<1|||... . | | Just intonation is a codimension-0 "temperament", which means nothing is tempered. The set of commas that are tempered out is the set {1/1}, but that's still a set, so JI is still a regular temperament. There is an infinite family of these "temperaments", one for each subgroup of JI. The 2-limit version is the equal temperament [[1edo|1edo]]. The 3-limit version is the rank-2 temperament [[Pythagorean|pythagorean]], which has all the properties of any other rank-2 temperament except that it tempers no commas. The 5-limit version is rank-3, and so on. The mapping for this temperament is an nxn identity matrix, with wedgies of <1|, <<1||, <<<1|||... . |
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| **OM** temperament is the rank-0 temperament, in which every interval is a comma. Thus all notes are represented by the same note. This is different from 1edo because not even octaves exist; it could be described as 0edo. The mapping for this is the 0-val, <0 0 ... 0|.</pre></div>
| | '''OM''' temperament is the rank-0 temperament, in which every interval is a comma. Thus all notes are represented by the same note. This is different from 1edo because not even octaves exist; it could be described as 0edo. The mapping for this is the 0-val, <0 0 ... 0|. |
| <h4>Original HTML content:</h4>
| | [[Category:todo:link]] |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Trivial temperaments</title></head><body>A trivial temperament is something that fits the mathematical definition of &quot;regular temperament&quot;, but is a unique, extreme case that people might be uncomfortable calling a &quot;temperament&quot;. There are two kinds of trivial temperaments - JI, in which nothing is tempered, and <strong>OM</strong> temperament, in which everything is tempered.<br />
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| Just intonation is a codimension-0 &quot;temperament&quot;, which means nothing is tempered. The set of commas that are tempered out is the set {1/1}, but that's still a set, so JI is still a regular temperament. There is an infinite family of these &quot;temperaments&quot;, one for each subgroup of JI. The 2-limit version is the equal temperament <a class="wiki_link" href="/1edo">1edo</a>. The 3-limit version is the rank-2 temperament <a class="wiki_link" href="/pythagorean">pythagorean</a>, which has all the properties of any other rank-2 temperament except that it tempers no commas. The 5-limit version is rank-3, and so on. The mapping for this temperament is an nxn identity matrix, with wedgies of &lt;1|, &lt;&lt;1||, &lt;&lt;&lt;1|||... .<br />
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| <strong>OM</strong> temperament is the rank-0 temperament, in which every interval is a comma. Thus all notes are represented by the same note. This is different from 1edo because not even octaves exist; it could be described as 0edo. The mapping for this is the 0-val, &lt;0 0 ... 0|.</body></html></pre></div>
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