A Martian year is 668.6 Martian days; that’s 3.4 less than 24×28. I asked myself, how should the short months be arranged for best ‘balance’? I ran all combinations and this is it:
The three big dots represent the missing days in short months; the small dot represents the sometimes-missing day in leap month; and the diamond, slightly left of center, is the center of gravity of the dots.
Then I thought, what if I were designing a calendar for a world where the number of days in a year is 5¼ off from a multiple of 12?
I wondered what the point of balancing months in a solar calendar was (as opposed to a lunar calendar that wants each day to start at new moon), but I realized it would make sense to distribute monthly wages evenly. I also wonder why you’d want months on the Mars to be around 28 days.
A Martian year is 22+ Earth-months. Most Martian calendar proposals use 24 months because 24 is a highly composite number.
By the way, see also http://www.quadibloc.com/science/cal05.htm