13 months improves some things, but it does not work well for 4 seasons. There are two definitions of seasons. In the simpler one, they start March 1, June 1,

13 months improves some things, but it does not work well for 4 seasons. There are two definitions of seasons. In the simpler one, they start March 1, June 1, September 1, and December 1. (In the other, they are truer to astronomy and start about 20 days later.) With 13 months in a year, that would be a lot messier. Since there is symmetry to the year, it makes sense to divide it into a number of pieces that works well with that symmetry. 12 pieces makes sense because it's a multiple of 4. If you look at the length of days as a function of year, it resembles a sine wave. You wouldn't create a unit of angular measurement where one full circle is 13 units. (You'd have trig identities like sin(x+13/4)=cos(x)!) There would be similar disadvantages if you divided a year into 13 pieces.