3125edo

The 3125 equal division of the octave divides it into 5^5 = 3125 equal parts of exactly 0.384 cents each. It is notable for being an extremely strong 7-limit system, being the first equal division past 171edo with a lower relative error. It is also distinctly consistent through the 15 odd limit. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and 117440512/117406179 are tempered out- it should be noted this EDO is so far the only EDO confirmed to have been known for tempering out 117440512/117406179 prior to the discovery of its significance as the difference between a stack of five 33/32 quartertones and one 7/6 subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

The fact that 3125 = 5^5 makes curious notations possible based on the symmetric base 5 positional number system, by converting the number to base 5 with digits {-2, -1, 0, 1, 2}.