Several times in history, the calendar has changed. For example, in 1752 in England, September skipped from the 2nd to the 14th as they finally moved to the Gregorian calendar. The beginning of the year was changed from March 25 to January 1. At other points, new months have been added.
What does such a change mean to your characters if they live through it? Do they notice? Do they rail against it? Or maybe you have a character pushing for a new way of tracking time. If so, why, and who doesn't like it?