What advantages would a Martian calendar have over an Earth calendar?
Since a Martian calendar is based on the length of a Martian year, it will keep time with the Martian seasons. An Earth calendar cannot. Furthermore, there are several deficiencies in the Gregorian calendar. For instance, each year and each month begins on a different day of the week, and on the whims of Roman autocrats, days were removed from February and given to July and August. There have been various plans to correct these defects over the past several centuries, but social inertia has doomed attempts to reform the calendar. On Mars we have the opportunity to create a calendar that has a much more rational structure than the Gregorian calendar.