270edo
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- This revision was by author xenwolf and made on 2011-06-27 16:06:11 UTC.
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The 270 equal division divides the octave into 270 equal parts of 4.4444 cents each. It is a very strong [[13-limit]] system, distinct and consistent through the 15 odd limit, and is the thirteenth [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. In the [[5-limit]] it tempers out the [[ennealimma]], |1 -27 18>, the [[vulture comma]], |24 -21 4>, and the vishnuzma or semisuper comma, |23 6 -14>. In the [[7-limit]] it tempers out 2401/2400 and 4375/4374, so that it supports ennealimmal temperament, the wizma, 420175/419904 and the landscape comma, 250047/250000. In the [[11-limit]], it tempers out 5632/5625, 3025/3024 and 9801/9800. Finally in the 13-limit it tempers out 676/675, 1001/1000, 1716/1715 and 2080/2079, making it an [[The Archipelago|archipelago]] tuning, and the optimal patent val for some of the archipelago temperaments.
== Divisors ==
270 is a highly composite number, with divisors 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90 and 135, and some of these form the periods of the period and generators for some of rank two temperaments 270 supports; these include [[Ragismic microtemperaments#Ennealimmal|ennealimmal]], hemiennealimmal and [[The Archipelago#Rank two temperaments|decitonic]].
The prime factorization of 270 is
[[math]]
270 = 2 \cdot 3^{3} \cdot 5
[[math]]Original HTML content:
<html><head><title>270edo</title></head><body>The 270 equal division divides the octave into 270 equal parts of 4.4444 cents each. It is a very strong <a class="wiki_link" href="/13-limit">13-limit</a> system, distinct and consistent through the 15 odd limit, and is the thirteenth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a>. In the <a class="wiki_link" href="/5-limit">5-limit</a> it tempers out the <a class="wiki_link" href="/ennealimma">ennealimma</a>, |1 -27 18>, the <a class="wiki_link" href="/vulture%20comma">vulture comma</a>, |24 -21 4>, and the vishnuzma or semisuper comma, |23 6 -14>. In the <a class="wiki_link" href="/7-limit">7-limit</a> it tempers out 2401/2400 and 4375/4374, so that it supports ennealimmal temperament, the wizma, 420175/419904 and the landscape comma, 250047/250000. In the <a class="wiki_link" href="/11-limit">11-limit</a>, it tempers out 5632/5625, 3025/3024 and 9801/9800. Finally in the 13-limit it tempers out 676/675, 1001/1000, 1716/1715 and 2080/2079, making it an <a class="wiki_link" href="/The%20Archipelago">archipelago</a> tuning, and the optimal patent val for some of the archipelago temperaments.<br />
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<!-- ws:start:WikiTextHeadingRule:1:<h2> --><h2 id="toc0"><a name="x-Divisors"></a><!-- ws:end:WikiTextHeadingRule:1 --> Divisors </h2>
270 is a highly composite number, with divisors 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90 and 135, and some of these form the periods of the period and generators for some of rank two temperaments 270 supports; these include <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">ennealimmal</a>, hemiennealimmal and <a class="wiki_link" href="/The%20Archipelago#Rank two temperaments">decitonic</a>. <br />
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The prime factorization of 270 is<br />
<br />
<!-- ws:start:WikiTextMathRule:0:
[[math]]<br/>
270 = 2 \cdot 3^{3} \cdot 5<br/>[[math]]
--><script type="math/tex">270 = 2 \cdot 3^{3} \cdot 5</script><!-- ws:end:WikiTextMathRule:0 --></body></html>