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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>2015-08-22 20:06:38 UTC</tt>.<br>
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| : The original revision id was <tt>557183763</tt>.<br>
| | 14348edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit [[relative error]] than any lower equal temperaments aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that, it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]], which has to do with its higher limit capability—it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond. The only inconsistent interval pair in the [[69-odd-limit]] is ([[31/29]], [[58/31]]) with 50.2% relative error. Thus the full [[67-limit]] interpretation using the patent val is obvious, though it may be preferable to omit either prime [[29/1|29]] or [[31/1|31]]. |
| : 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>
| | An edo of similar size with full consistency to a very high limit ([[57-odd-limit]]) is [[20567edo]]. |
| <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 14348 division divides the octave into 14348 equal parts of 0.083635 cents each. It is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from [[7033edo|7033]]. It is also distinctly consistent in the 29 limit, and has a lower 23-limit relative error than any lower division aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that it is a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak edo]]. It factors as 2^2 * 17 * 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all divisors.</pre></div>
| | === Prime harmonics === |
| <h4>Original HTML content:</h4>
| | {{Harmonics in equal|14348|columns=11}} |
| <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>14348edo</title></head><body>The 14348 division divides the octave into 14348 equal parts of 0.083635 cents each. It is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from <a class="wiki_link" href="/7033edo">7033</a>. It is also distinctly consistent in the 29 limit, and has a lower 23-limit relative error than any lower division aside from <a class="wiki_link" href="/2460edo">2460</a>, <a class="wiki_link" href="/8269edo">8269</a>, <a class="wiki_link" href="/8539edo">8539</a> and <a class="wiki_link" href="/11664edo">11664</a>. Besides all that it is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak edo</a>. It factors as 2^2 * 17 * 211, so <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/68edo">68</a> and <a class="wiki_link" href="/422edo">422</a> are all divisors.</body></html></pre></div>
| | {{Harmonics in equal|14348|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 14348edo (continued)}} |
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| | === Subsets and supersets === |
| | 14348 factors into primes as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all subsets. |