16808edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2014-05-22 13:20:18 UTC.
- The original revision id was 510644832.
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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>