Imagine yourself as an early astronomer. Your local ruler has been funding your research for several years, and now he wants some practical results. Your job: make a calendar. Which cycles are you going to include? What approximations are you going to make?
The following bibliography lists all sources consulted in preparing the article, as well as in compiling the feast days for the calendar applet. If you are interested in more detail about the general history of calendars and can read German, I strongly urge you to start with Ginzel, which despite its age remains indispensable. Another highly recommended work, which was published after I wrote the article, is Calendrical Calculations: The Millennium Edition, by Edward M. Reingold and Nachum Dershowitz (2001).
In principle, any astronomical cycle, e.g., the orbit of Venus or Mars, could be used to construct a calendar. In practice, very few societies bothered. These events were carefully recorded by astronomers, but only where these planets played an important role in religious observances (once again, see the Maya) were these events incorporated into the regular calendar.
Just as a year can be defined relative to the stars or the sun, so can a moon's orbital period. The length of time it takes the moon to complete one orbit around the Earth is 27.32166 days. From an Earth-bound observer's point of view, this is the time it takes the moon to return to the same place relative to the stars, and is called the sidereal month.
I wrote this applet back in 1998 to answer a question that was bugging me while I was plotting out a historical novel (which perhaps I'll finish some day, if I ever have time): what would the calendar have looked like at a particular date in the distant past? This isn't just a matter of calculating Easter and the feasts like Pentecost that depend on it. Saints' days change over time as new ones come along and old ones fall out of favor or are moved. Also, different regions may celebrate the same saint on a different day. Rather than simply look up things for the particular place and time I was dealing with, I decided to create a general-purpose solution.
An alternative to measuring the passage of the sun through a fixed point (equinox or solstice) would be to measure the appearance of a particularly prominent star or constellation, either just before sunrise or just after sunset. These events are called heliacal rising and setting and will yield a period that is fairly close to the mean tropical year.
If you are a farmer, an arbitrary period has its problems. Of particular interest is the best time to plant crops—an activity tied to the seasons, which are in turn linked to the earth's revolution around the sun. If all you have is an arbitrary cycle, it's much more difficult to tell just when you should plant. Some agricultural societies, therefore, have tried to link their calendar to the length of the time it takes the earth to rotate around the sun. Of course most agricultural societies have not known that the earth orbits around the sun.
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 calend
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 table below lists official adoption dates, with as much precision as I've been able to discover. Simply because the government told people to convert, however, does not mean they did so. Because of religiously inspired opposition to the conversion, both calendars were often in use in regions where there was a religiously mixed population.