540edo: Difference between revisions
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== Theory == | == Theory == | ||
Since 540 = 2 × 270 and 540 = 45 × 12, it contains [[270edo]] and [[12edo]] as subsets, both belonging to [[The Riemann Zeta Function and Tuning #Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]]. It is [[enfactored]] in the 13-limit, with the same tuning as 270edo, but it makes for a reasonable 17- and 19-limit system, and perhaps beyond. It is, however, no longer [[consistent]] in the [[15-odd-limit]], all because of [[15/13]] being 1.14 cents sharp of just. | Since 540 = 2 × 270 and 540 = 45 × 12, it contains [[270edo]] and [[12edo]] as subsets, both belonging to [[The Riemann Zeta Function and Tuning #Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]]. It is [[enfactoring|enfactored]] in the 13-limit, with the same tuning as 270edo, but it makes for a reasonable 17- and 19-limit system, and perhaps beyond. It is, however, no longer [[consistent]] in the [[15-odd-limit]], all because of [[15/13]] being 1.14 cents sharp of just. | ||
=== Prime harmonics === | === Prime harmonics === | ||
Revision as of 22:46, 13 January 2022
The 540 equal divisions of the octave (540edo), or the 540(-tone) equal temperament (540tet, 540et), divides the octave in 540 equal steps of about 2.22 cents each.
Theory
Since 540 = 2 × 270 and 540 = 45 × 12, it contains 270edo and 12edo as subsets, both belonging to the zeta peak edos, zeta integral edos and zeta gap edos sequences. It is enfactored in the 13-limit, with the same tuning as 270edo, but it makes for a reasonable 17- and 19-limit system, and perhaps beyond. It is, however, no longer consistent in the 15-odd-limit, all because of 15/13 being 1.14 cents sharp of just.
Prime harmonics
Script error: No such module "primes_in_edo".
Divisors
540 is a very composite number. The prime factorization of 540 is 22 × 33 × 5. Its divisors are 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, and 270.