Maybe,Maybe I did some quick math nothing perfect

365/7/12=4.34. This is the standard year. You can see that if you maintain a 7 day week, you get more than 4 weeks in a months, but not quite 5

For 13 months the maths is 365/7/13=4.01. Waaay closer to 4.

However 13 is prime.so splitting the year into parts would be impossible. Quarterly reports would be impossible since you can't have all quarters be the same amount of days