An Arbitrary Cycle
The next simplest possibility for a calendar (although not necessarily for the people using it) is a cycle of days of arbitrary length. The calendar can proceed by simply counting days, over and over, ad infinitum. We have just such an arbitrary cycle in our week. Notice that the cycle of week days runs independently of our other cycles of month and year. Another example is the nundinae, an 8-day interval used in the Roman republic. An arbitrary cycle need not be quite so simple (the Maya have a 260-day count), but its advantage is that we need not bother adjusting our calendar to keep it in step with the irregular periods of the sun and the moon.