calendar

Standard units and cycles

The basic unit of computation in a calendar is the day. Although days are now measured from midnight to midnight, this has not always been so. Astronomers, for instance, from about the 2nd century ce until 1925, counted days from noon to noon. In earlier civilizations and among primitive peoples, where there was less communication between different settlements or groups, different methods of reckoning the day presented no difficulties. Most primitive tribes used a dawn-to-dawn reckoning, calling a succession of days so many dawns, or suns. Later the Babylonians, Jews, and Greeks counted a day from sunset to sunset, whereas the day was said to begin at dawn for the Hindus and Egyptians and at midnight for the Romans. The Teutons counted nights, and from them the grouping of 14 days called a fortnight is derived.

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There was also great variety in the ways in which the day was subdivided. In Babylonia, for example, the astronomical day was divided differently than the civil day, which, as in other ancient cultures, was composed of “watches.” The length of the watches was not constant but varied with the season, the day watches being the longer in summer and the night watches in the winter. Such seasonal variations in divisions of the day, now called seasonal or temporal hours, became customary in antiquity because they corresponded to the length of the Sun’s time above the horizon, at maximum in summer and at minimum in winter. Only with the advent of mechanical clocks in western Europe at the end of the 13th century did seasonal (unequal) hours become inconvenient.

Most early Western civilizations used 24 seasonal hours in the day—12 hours of daylight and 12 of darkness. This was the practice of the Greeks, the Sumerians and Babylonians, the Egyptians, and the Romans—and of Western Christendom so far as civil reckoning was concerned. The church adopted its own canonical hours for reckoning daily worship: there were seven of these—matins, prime, terce, sext, none, vespers, and compline—but in secular affairs the system of 24 hours held sway. This number, 2 × 12, or 24, was derived in Babylonia from the Sumerian sexagesimal method of reckoning, based on gradations of 60 (5 × 12 = 60) rather than on multiples of 10. In Babylonia, for most purposes, both daylight and night were divided into three equal watches, and each watch was subdivided into half- and quarter-watches. Babylonian astronomers, perhaps in preference to the variable civil system, divided every day into 12 equal units, called bēru, each of which was subdivided into 30 gesh. The oldest known astronomical texts are from the Old Babylonian period, but this dual system may be attributable to earlier Sumerian society.

Once the day is divided into parts, the next task is to gather numbers of days into groups. Among primitive peoples, it was common to count moons (months) rather than days, but later a period shorter than the month was thought more convenient, and an interval between market days was adopted. In West Africa some tribes used a four-day interval; in central Asia five days was customary; the Assyrians adopted five days and the Egyptians 10 days, whereas the Babylonians attached significance to the days of the lunation that were multiples of seven. In ancient Rome, markets were held at eight-day intervals; because of the Roman method of inclusive numeration, the market day was denoted nundinae (“ninth day”) and the eight-day week an inter nundium.

The seven-day week may owe its origin partly to the four (approximately) seven-day phases of the Moon and partly to the Babylonian belief in the sacredness of the number seven, which was probably related to the seven planets. Moreover, by the 1st century bce the Jewish seven-day week seems to have been adopted throughout the Roman world, and this influenced Christendom. The names in English of the days of the week are derived from Latin or Anglo-Saxon names of gods.

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The month is based on the lunation, that period in which the Moon completes a cycle of its phases. The period lasts approximately 29 1/2 days, and it is easy to recognize and short enough for the days to be counted without using large numbers. In addition, it is very close to the average menstrual period of women and also to the duration of cyclic behavior in some marine creatures. Thus, the month possessed great significance and was often the governing period for religious observances, of which the dating of Easter is a notable example. Most early calendars were, essentially, collections of months, the Babylonians using 29- and 30-day periods alternately, the Egyptians fixing the duration of all months at 30 days, with the Greeks copying them, and the Romans in the Julian calendar having a rather more complex system using one 28-day period with the others of either 30 or 31 days.

The month is not suitable for determining the seasons, for these are a solar, not lunar, phenomenon. Seasons vary in different parts of the world. In tropical countries there are just the rainy and dry periods, but elsewhere there are successions of wider changes. In Egypt the annual flooding of the Nile was followed by seeding and then harvest, and three seasons were recognized; but in Greece and other more northern countries there was a succession of four seasons of slightly different lengths. However many there seemed to be, it was everywhere recognized that seasons were related to the Sun and that they could be determined from solar observations. These might consist of noting the varying length of the midday shadow cast by a stick thrust vertically into the ground or follow the far more sophisticated procedure of deducing from nocturnal observations the Sun’s position against the background of the stars. In either case the result was a year of 365 days, a period incompatible with the 29 1/2-day lunation. To find some simple relationship between the two periods was the problem that faced all calendar makers from Babylonian times onward.

A number of non-astronomical natural signs have also been used in determining the seasons. In the Mediterranean area such indications change rapidly, and Greek poet Hesiod (c. 800 bce) mentions a wide variety: the cry of migrating cranes, which indicated a time for plowing and sowing; the time when snails climb up plants, after which digging in vineyards should cease; and so on. An unwitting approximation to the tropical year may also be obtained by intercalation, using a simple lunar calendar and observations of animal behavior. Such an unusual situation grew up among the Yami fishermen of Botel Tobago Island (Lan Yü, Taiwan). They use a calendar based on phases of the Moon, and sometime about March—the precise date depends on the degree of error of their lunar calendar compared with the tropical year—they go out in boats with lighted flares. If flying fish appear, the fishing season is allowed to commence, but if the lunar calendar is too far out of step with the seasons, the flying fish will not rise. Fishing is then postponed for another lunation, which they insert in the lunar calendar, thus having a year of 13 instead of the usual 12 lunations.