Kodak used to operate on this 13 month calendar. When I asked someone who used to work there, she was shocked that I knew about it and said that it was the best thing about working there. The original plan that this calendar is based on called for a liminal day between years for New Year's Day with 2 days for leap years
The Jews recognized this and their calendar runs akin to it (https://www.timeanddate.com/date/jewish-leap-year.html), but with 7 "leap months" occurring over the course of 19 years. Of course, then they fuck it up with extra or fewer days to keep certain holidays from falling on certain days of the week. You win some, you lose some.
Fuck it. No-one is this thread can seem to agree, so I'm making a unilateral declaration that from here on out, all units of time except for the second are abolished, and we just use unix time for everything. You have until 1699217619s to make the switch.
I've never been a fan of this idea, it doesn't go far enough and further makes things less symmetric/divisible. I say we use 6-day weeks, 5 weeks per month, 12 months per year, and an inter-calary holiday week of 5-6 days. A six day week means 4 days working, 2 days rest, and that can be staggered more easily/equitably assuming work needs full coverage in a week. We start the new year on the Spring Equinox because it's generally more pleasant.
For bonus points, we switch to base-12 (or dozenal) in our numbering system because after the transition it's a much easier system to deal with as far as division and multiplication is concerned (e.g. 1/4 would be .3 instead of .25, 1/3 is .4 instead of .333..., 1/2 is .6, etc.).
Octember it will be after October. The names will be just as incorrect as they have been for way too long but if anyone wanted the names and order to correspond to their own meaning it would have been fixed by now.
Before we get too crazy, let's consider for a second the importance of 12 in units of measure. It shows up in time: minute, second, length (imperial ft), and I'm sure many other places.
The benefit is it's evenly divisible by 2, 3, and 4. How would we define seasons with 13 months?
Starting the week on a Monday is psych warfare on the working class and pretty fucked up to begin with. Starting it on Sunday was the Church's idea... Start every week for the future of humanity on a Saturday and get your dessert first.