16808edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 557205531 - Original comment: ** |
Wikispaces>hearneg **Imported revision 626564653 - 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: | : This revision was by author [[User:hearneg|hearneg]] and made on <tt>2018-02-18 02:54:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>626564653</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 (the [[jinn]]) for most intervals which occur in practice. It is a very, very strong 31-limit division, and | <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 (the [[jinn]]) for most intervals which occur in practice. It is a very, very strong 31-limit division, and a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]], [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral]] and zeta gap tuning. 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]]. | ||
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. | 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. | ||
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16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.</pre></div> | 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.</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"><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 (the <a class="wiki_link" href="/jinn">jinn</a>) for most intervals which occur in practice. It is a very, very strong 31-limit division, and | <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>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 (the <a class="wiki_link" href="/jinn">jinn</a>) for most intervals which occur in practice. It is a very, very strong 31-limit division, and a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak</a>, <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral</a> and zeta gap tuning. 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>.<br /> | ||
<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. 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.<br /> | 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.<br /> | ||
<br /> | <br /> | ||
16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which <a class="wiki_link" href="/22edo">22edo</a> and <a class="wiki_link" href="/764edo">764edo</a> are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.</body></html></pre></div> | 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which <a class="wiki_link" href="/22edo">22edo</a> and <a class="wiki_link" href="/764edo">764edo</a> are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.</body></html></pre></div> | ||
Revision as of 02:54, 18 February 2018
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author hearneg and made on 2018-02-18 02:54:08 UTC.
- The original revision id was 626564653.
- 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 (the [[jinn]]) for most intervals which occur in practice. It is a very, very strong 31-limit division, and a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]], [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral]] and zeta gap tuning. 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]]. 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. 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.
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 (the <a class="wiki_link" href="/jinn">jinn</a>) for most intervals which occur in practice. It is a very, very strong 31-limit division, and a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak</a>, <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral</a> and zeta gap tuning. 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>.<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. 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.<br /> <br /> 16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which <a class="wiki_link" href="/22edo">22edo</a> and <a class="wiki_link" href="/764edo">764edo</a> are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.</body></html>