|
|
| (25 intermediate revisions by 8 users not shown) |
| Line 1: |
Line 1: |
| <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>2015-08-18 10:54:16 UTC</tt>.<br>
| | |
| : The original revision id was <tt>556880431</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | 3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral, and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}. |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | |
| <h4>Original Wikitext content:</h4>
| | === Prime harmonics === |
| <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 **3395** division divides the octave into 3395 equal steps of 0.35346 cents each. It is an extremely strong 17- and 19-limit system, and a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]].</pre></div>
| | {{Harmonics in equal|3395|columns=11}} |
| <h4>Original HTML content:</h4>
| | |
| <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>3395edo</title></head><body>The <strong>3395</strong> division divides the octave into 3395 equal steps of 0.35346 cents each. It is an extremely strong 17- and 19-limit system, and a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak, integral and gap edo</a>. It has a lower 17-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any edo until <a class="wiki_link" href="/7033edo">7033</a>, and a lower 19-limit relative error than any edo until <a class="wiki_link" href="/8269edo">8269</a>.</body></html></pre></div>
| | === Subsets and supersets === |
| | Since 3395 factors into {{factorization|3395}}, 3395edo has subset edos 5, 7, 35, 97, 485, and 679. |
| | |
| | == Regular temperament properties == |
| | 3395edo has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br />per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br />ratio* |
| | ! Temperaments |
| | |- |
| | | 1 |
| | | 2319\3395 |
| | | 819.676 |
| | | 55115776/34328125 |
| | | [[Genojacobin]] |
| | |- |
| | | 35 |
| | | 1409\3395<br />(51\3395) |
| | | 498.027<br />(18.026) |
| | | 4/3<br />(?) |
| | | [[Bromine]] |
| | |- |
| | | 97 |
| | | 1409\3395<br />(9\3395) |
| | | 498.027<br />(3.181) |
| | | 4/3<br />(?) |
| | | [[Berkelium]] |
| | |} |
| | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct |
| | |
| | [[Category:Jacobin]] |
| | [[Category:Quartismic]] |