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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-10 17:59:32 UTC</tt>.<br>
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| : The original revision id was <tt>187246847</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">162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.
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| The non-patent val <162 257 377| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, <162 257 377 455| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic family|diaschismic]]. In the 11-limit <162 257 377 455 561| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</pre></div> | | Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]]. |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>162edo</title></head><body>162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536. <br />
| | The non-patent val {{val| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val| 162 257 '''377''' 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val| 162 257 '''377''' 455 '''561''' }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val| 162 257 '''377''' 455 '''561''' '''600''' }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning. |
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| The non-patent val &lt;162 257 377| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit <a class="wiki_link" href="/Diaschismic%20family">diaschismic</a>. In the 11-limit &lt;162 257 377 455 561| tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.</body></html></pre></div>
| | === Prime harmonics === |
| | {{Harmonics in equal|162}} |
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| | === Subsets and supersets === |
| | Since 162 factors into {{factorization|162}}, 162edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 27, 54, and 81 }}. |