16808edo: Difference between revisions

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Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out 123201/123200 and1990656/1990625; in the 17-limit 194481/194480 and 336141/336140; in the 19-limit 43681/43680,89376/89375 and104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;16808edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 16808 division divides the octave into 16808 steps of size 0.0714 cents each. It is distinctly consistent and highly accurate through the 35 limit, and can be used as a measure of interval size (the &lt;a class="wiki_link" href="/jinn"&gt;jinn&lt;/a&gt;) for most intervals which occur in practice. It is a very, very strong 31-limit division, and both a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta peak&lt;/a&gt; and &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta integral&lt;/a&gt; tuning, and may also be a zeta gap edo, which someone with a large enough table of zeta zeros might check. In the 23, 29 and 31 limits it has the lowest logflat badness up until at least 200000; in the 19 limit it is beaten out by &lt;a class="wiki_link" href="/8539edo"&gt;8539edo&lt;/a&gt;, and in the 17 limit by &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/1506edo"&gt;1506edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3395edo"&gt;3395edo&lt;/a&gt; and &lt;a class="wiki_link" href="/7033edo"&gt;7033edo&lt;/a&gt;, but not 8539.&lt;br /&gt;

Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out 123201/123200 and1990656/1990625; in the 17-limit 194481/194480 and 336141/336140; in the 19-limit 43681/43680,89376/89375 and104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.&lt;br /&gt;

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