270edo
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 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 archipelago tuning, and the optimal patent val for some of the archipelago temperaments.
Divisors[edit]
270 is a very 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 ennealimmal, hemiennealimmal and decitonic.
The prime factorization of 270 is
Here may be found a table of 270edo intervals.