|
|
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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|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 EDO lists|zeta peak]], [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|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|8539edo]], and in the 17 limit by [[72edo|72edo]], [[1506edo|1506edo]], [[3395edo|3395edo]] and [[7033edo|7033edo]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : 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>626564653</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>
| |
| <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 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. |
|
| |
|
| 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|22edo]] and [[764edo|764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns. |
| <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 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></pre></div>
| |