13 28 day months would get us a 364 day year. It's pretty close to the same. I think the Jewish calendar is lunar based, so there's precedent.
Discussion
Yes, the Romans fucked everything up.
Persian calendar is pretty awesome
Here we are, in September, the seventh month of the year. 🤦🏻♂️
In the old Roman Calendar, March 1st was new years day. September was the seventh month. The first of every month was the day after the new moon, and some years had Undecember as an 11 th month, with January being the 12 th month and February the 13 th month. January 1 st was the day after the first new noon after the winter solstice.
They started skipping Undecember and having January 1 st before the solstice because having 13 months was considered unlucky, and then the whole calender broke. Julius Caesar created the Julian Calender to fix it. It's been modified a few times over the past 2 millennia, and we technically don't use the Julian Calender anymore, but it is basically the same as the one we use.