OK, it breaks the assumption that quarters are a whole number of months.
12 is a handy number of months to have in the year. 12 is divisible by 2, 3, 4, and 6. Not by 5, but you can't have everything (unless we had 60 months of 6 or 7 days each... let's not go there).
13 is prime.
I think not bothering with months at all would be better than having a 13 month year.