LunarClock.org have devised a clock and calendar for the moon. Apparently, this was necessary because of the moon’s rotation and length of day is different than the Earth’s (or something like that). Anyway, the site’s FAQ gives some explanation.
1. What is the Lunar Calendar and why do I need one?
The Lunar Calendar is designed to be used by colonists of the Moon, and it differs from the one we use here on Earth. Unless you live on the Moon, you don’t really need one, but you can support the idea anyway. Who, knows? Perhaps you will live on the Moon in the future, or your children might. You can read the details on how this calendar works.