We’re all used to a 12-month calendar, and we just deal with the fact that there are different number of days in different months, and that February doesn’t have the same number of days every year. That’s pretty crazy, right?
Some people certainly thought so, and that’s why the 13-month international fixed calendar was proposed. In the international fixed calendar, there are 13 months, which each have 28 days. It is an example of a perennial calendar, as every date always occurs on the same weekday. You may have noted that 13 times 28 is only 364, so you do need an extra day. In the international fixed calendar, there is an extra day called “Sol” between the months of June and July. Leap years are handled just as in our usual Gregorian calendar.
Before World War II, there was a big debate about adopting the international fixed calendar, and two of its big proponents was Kodak founder George Eastman, and Eastman–Kodak used the international calendar from 1928 until 1989.
(Thanks to investigator Karen Kustedjo for bringing this to our attention.)
Other calendars: Investigator Carlos Gershenson informs us that there are Mesoamerican calendars that consist of 20 months of 18 days, plus five or six “dead” days (in which everybody apparently got drunk).