The 581 equal division divides the octave into 581 equal steps of 2.065 cents each. It is a very strong 19- and 23-limit system, uniquely consistent to the 25-limit. It tempers out 2401/2400 in the 7-limit, 3025/2025, 19712/19683, 151263/151250 in the 11-limit, and 2080/2079, 4096/4095, 4225/4224, 6656/6655 and 10648/10647 in the 13-limit. It supports and gives a good tuning for the 41&229 microtemperament, which has a neutral thirds generator. It is the first division after 270 with a lower 19-limit relative error, and the first past 311 with a lower 23-limit relative error, and not until 1578 do we reach a lower 23-limit relative error.