what could be simpler?

I got yet another wacky idea for a Martian calendar. Start with 24 months of 28 days each. Drop one day from every seventh month (so that a given month is short in one year out of seven), and add one day every 48 years. The result is longer than the mean tropical year by one day in 6176 years.

An analogous calendar for Earth: start with 12 months of 30 days, add 3 days to every 7 months (so the cycle is 30 30 31 30 31 30 31), and add one day every ten years; this is long by one day in 219130 years.

to balance a calendar

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 smaller dot represents the sometimes-missing day in the variable 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?