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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>2011-03-26 07:16:00 UTC</tt>.<br>
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| : The original revision id was <tt>214167738</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">The //148 equal division// divides the octave into 148 equal parts of 8.108 cents each. It provides the [[optimal patent val]] for 11-limit [[Diaschismic family|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping <148 235 344 416| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[80edo]] for the 12&56 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead.
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| 148 = 4 * 37, with divisors 2, 4, 37, 74.</pre></div>
| | 148edo's closest fifth is on the very sharp side, 3.45 cents sharp of just. With better approximations of [[9/1|9]], [[11/1|11]], [[15/1|15]], [[17/1|17]], and [[21/1|21]], it commends itself as a 2.9.15.21.11.17 [[subgroup]] system. |
| <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>148edo</title></head><body>The <em>148 equal division</em> divides the octave into 148 equal parts of 8.108 cents each. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit <a class="wiki_link" href="/Diaschismic%20family">echidnic temperament</a>, the 10&amp;46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the <a class="wiki_link" href="/patent%20val">patent val</a> tempers out 686/675 and 1029/1024, but an alternative mapping &lt;148 235 344 416| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of <a class="wiki_link" href="/80edo">80edo</a> for the 12&amp;56 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. <br />
| | The 5-limit [[patent val]] still makes sense, and it tempers out [[2048/2025]], making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val| 148 235 344 '''416''' }} (148d) with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7-, 13-, 17- and 19-limit [[bidia]], the 68 & 80 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for [[echidnic]], the 46 & 102 temperament, in the 11-limit, and the 148f val is an excellent tuning for echidnic in the 13- and 17-limit. |
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| 148 = 4 * 37, with divisors 2, 4, 37, 74.</body></html></pre></div> | | === Harmonics === |
| | {{Harmonics in equal|148|columns=9}} |
| | {{Harmonics in equal|148|columns=9|start=10|title=Approximation of odd harmonics in 148edo (continued)}} |
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| | === Subsets and supersets === |
| | Since 148 = 4 × 37, 148edo has subset edos {{EDOs| 2, 4, 37, and 74 }}. |
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| | [[Category:Echidnic]] |
| | [[Category:Bidia]] |