The central problem all earthly calendar makers face is how to combine three intervals that have no common factor:

1. the time from sunrise to sunrise (the day)

2. the time it takes the moon to go from full to new to full again (the month)

3. the time it takes for a season to return (the year).

Because day, month, and year have no common factor, all calendars are approximations requiring periodic correction.

It doesn't take long for errors to accumulate. For example, suppose the year has 365 days. In 4 years, seasons will be 1 day off; in 100 years, 25 days; and in 730 years winter will arrive when summer used to. If we make the year 366 days, the seasons will reverse in only 244 years, but instead of winter coming later each year it will come earlier.

How well the calendar fit the solar year wasn't just of astronomical interest in pre-modern times. In regions with pronounced seasons, a farmer prospers who plants as early as possible but after the last killing frost. If the traditional date of the last killing frost shifts in relation to the equinoxes, something is wrong; an error of 25 days would be disastrous. To some of its users, wandering seasons negate the whole purpose of the calendar.

The day is the basic unit in all calendars, since it is very hard to legislate a change in the length of the day. Although the month obviously comes from the cycle of the moon's phases, one such cycle (a lunar month, or lunation) is about 29½ days. If the year is taken to be 12 lunar months, it will have 354 days, 11.4 days shorter than a solar year. Month and year have been reconciled in one of two ways:

One approach is to make the months longer than a lunar month, as our civil calendar does, or add an extra 11- or 12-day month. The date of the full moon then falls where it may, but in July it will always be summer (in the Northern Hemisphere).

The second approach keeps the lunar month (as, for example, the Islamic calendar does), so that the full moon falls on the same day of the month every month, but the relation between months and seasons changes each year.

Hunters and herders everywhere and cultures in the aseasonal tropics have often preferred calendars with accurate months (lunations), while planters in the temperate zones have gravitated toward accurate solar years.

Pages describing specific calendars:

Roman Julian Gregorian
Ethiopian Japanese Chinese
Hebrew Mayan French Republican
Islamic Iranian
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