We have calendars based on the solar cycle, the lunisolar cycle, and the lunar cycle.
What if there was such a thing as a calendar based on the Martian synodic cycle.
We could create a calendar for Earth based on the number of orbits Mars completed around the Sun. It would be independent of the placement of seasons of Earth and would have nothing to do, but for fun, it would give the people some idea where the seasons on Mars on, though they are of no use other than educational on Earth.
What about a calendar based on the Martian sidreal cycle.
We could create a calendar for Earth based on the number of orbits Mars completed around the Sun. It would be independent of the placement of seasons of Earth and would have nothing to do, furthermore, it would have no regard for the seasons for Mars.
Which one would you prefer?
Let's create the Martian Synodic Calendar of Earth since we're used to a calendar with seasons even though they're for seasons on Mars.
Each Martian Synodic Year is 686.97258 for most estimates. Every 73 years, one at 36 and another 37 years after that, there would have to be 686 days in the calendar instead of the normal 687 days or the calendar would be fast by one day every 36 and a half years, or two for every 73 years on average.
I would create 24 months for the Martian Calendar, using the names of months other than those used in the Gregorian calendar in order to reduce confusion. For a 687 day year, 15 of the months would be of 29 days while the remaining nine would be 28 days. For a 686 day year, one of the 29-day months would be reduced to 28 days.
The placement of the 28 and 29 month days would have a pattern that has a few rules: no more than three months in a row with 29 days, no two months in a row has 28 days, and the first and last months of the year have 29 days.
For the 24 months, the sequence for the Martian Calendar of Earth would be for months 1-18: 29, 28, 29, 28, 29, 28, 29, 29, 28, 29, 28, 29, 29, 28, 29, 29, 28, 29.
For month 19, it would have 29 days except during years 36, 73 and if there is an emergency year in the future when it would have to be redued to 28 days for those reverse-leap years.
For months 20-24: 29, 28, 29, 28 and 29.
This calendar would be for amusement for celebrity birthday nerds who could use the Martian Calendar dates (with date, month and year) translated from the Gregorian Calendar dates (with date, month and year) and see which celebrities share the same birthdate on the Martian Calendar of Earth.
The trick is to line up the first years of the reckoning with both calendars so that the years line up.
When Pope Gregory XIII modified the Julian-1 Calendar to correct the number of days to line up the seasons and to correct the day Easter should be observed, he used the year 325, when the First Council of Nicaea on July 4, 325 A.D. established rules on when to celebrate Easter, effective in the year 326 A.D. To create the Martian Calendar of Earth for the Christian Era, they would have to line up the year zero of the Martian calendar of Earth with the year 1 B.C. of the Julian-1 calendar because most people thought Jesus Christ was born in 1 B.C.
Some people could use other reckonings, such as: