A Count of Days
The period which has generally been taken as basic for all calendars is the day (one alteration of light and darkness). To be more precise, the day to which we refer here is the solar day i.e., the length of time it takes the sun to reach the same spot in the sky again. Astronomers have traditionally used the sun's zenith, i.e. noon, as the reference point, because it can be most accurately measured, and because an entire night's observations can be recorded as occurring on a single day. The astronomers' practice differs from the current civil one (where the new day begins at midnight), as well as ancient civil practices, which began the next day either at sunrise or sunset. If you are willing to deal with large numbers, all you really need for a calendar is a linear count of days from some starting epoch.
Exactly such a count is often used by astronomers, the so-called Julian day, introduced by Joseph Scaliger in 1583. Julian Day 0 is defined as noon on Monday, January 1, 4713 B.C.E. (in the Julian Calendar). This strict day count is handy for comparing different calendar systems and making astronomical calculations, but rather awkward in ordinary life. It doesn't really help people know when to plant their crops or when to celebrate recurrent festivals. The only society to use something comparable to the Julian date in regular practice were the Classic Maya, but even they supplemented their so-called Long Count with other cycles of a more manageable variety.