3600edo

The 3600 equal division divides the octave into 3600 equal parts of exactly 1/3 of a cent each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps. It also has the advantage of expressing the steps of 72edo in whole numbers. Aside from its relationship to cents, it is of interest as a system supporting ennealimmal temperament, tempering out the ennealimma, |1 -27 18>, in the 5-limit and (with the patent val) 2401/2400 and 4375/4374 in the 7-limit. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. Via the val <3600 5706 8359 10106 12453 13318|, 3600edo also supports hemiennealimmal temperament.

Divisors

The divisors of 3600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, and 1800.

...because the prime factorization is

$3600=2^{4}\cdot 3^{2}\cdot 5^{2}$