1395edo: Difference between revisions

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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>2015-08-15 17:11:19 UTC</tt>.<br>
 
: The original revision id was <tt>556739689</tt>.<br>
1395edo is a strong higher-limit system, being a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. However, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.
: The revision comment was: <tt></tt><br>
 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The 1395 division divides the octave into 1395 steps of 0.8602 cents each. It is a strong higher-limit system, being a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak, integral and gap edo]]. The patent val is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]], though it is only consistent through the 21 limit, due to 23 being all of 0.3 cents flat. A comma basis for the 19 limit is 2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635 and 14875/14872.</pre></div>
=== Prime harmonics ===
<h4>Original HTML content:</h4>
{{Harmonics in equal|1395|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">&lt;html&gt;&lt;head&gt;&lt;title&gt;1395edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 1395 division divides the octave into 1395 steps of 0.8602 cents each. It is a strong higher-limit system, being a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta peak, integral and gap edo&lt;/a&gt;. The patent val is the first one after 311 with a lower 37-limit &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt;, though it is only consistent through the 21 limit, due to 23 being all of 0.3 cents flat. A comma basis for the 19 limit is 2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635 and 14875/14872.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Harmonics in equal|1395|columns=11|start=12|title=Approximation of prime harmonics in 1395edo (continued)}}
 
=== Subsets and supersets ===
Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.