16808edo: Difference between revisions

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**Imported revision 510633818 - Original comment: **
 
Wikispaces>genewardsmith
**Imported revision 510644832 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-22 12:38:22 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-22 13:20:18 UTC</tt>.<br>
: The original revision id was <tt>510633818</tt>.<br>
: The original revision id was <tt>510644832</tt>.<br>
: The revision comment was: <tt></tt><br>
: 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>
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>
<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 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 for most intervals which occur in practice. It is both a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak]] and [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral]] 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 [[8539edo]], and in the 17 limit by [[72edo]], [[1506edo]], [[3395edo]] and [[7033edo]].</pre></div>
<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 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 for most intervals which occur in practice. It is both a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak]] and [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral]] 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 [[8539edo]], and in the 17 limit by [[72edo]], [[1506edo]], [[3395edo]] and [[7033edo]], but not 8539.
 
Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404.</pre></div>
<h4>Original HTML content:</h4>
<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 for most intervals which occur in practice. It is 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;.&lt;/body&gt;&lt;/html&gt;</pre></div>
<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 for most intervals which occur in practice. It is 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;
&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. 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 13:20, 22 May 2014

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2014-05-22 13:20:18 UTC.
The original revision id was 510644832.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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 for most intervals which occur in practice. It is both a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak]] and [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral]] 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 [[8539edo]], and in the 17 limit by [[72edo]], [[1506edo]], [[3395edo]] and [[7033edo]], but not 8539.

Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404.

Original HTML content:

<html><head><title>16808edo</title></head><body>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 for most intervals which occur in practice. It is both a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak</a> and <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral</a> 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 <a class="wiki_link" href="/8539edo">8539edo</a>, and in the 17 limit by <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/1506edo">1506edo</a>, <a class="wiki_link" href="/3395edo">3395edo</a> and <a class="wiki_link" href="/7033edo">7033edo</a>, but not 8539.<br />
<br />
Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404.</body></html>