Some brief notes on what a calendar is, how they are made, and why they are used

The calendar is such a familiar object that we seldom reflect on what it means, and how it came to be. My interest was aroused by Ms Westrheim's charming book, and these are a few thoughts that came to mind.

Probably most fundamental calendar is a count of days, like a prisoner's tally on the dungeon wall. Whether a day begins at sunset, sunrise, midnight or noon, the number of days between two events can be determined without error, so long as one stays in the same place and sober. Each day is pretty much like the last, with the sun rising in the east, and then setting in the west, either obviously or behind the weather. A calendar that is a pure count of days is the Julian Day, named by the chronologist Scaliger after his son. Day 1 was sometime in 4713 BC, and we are now up in the millions, but this count is reliable, and the best way to find the time between two events. The Julian Day is divided decimally, and begins at noon at Greenwich. It is the least confusing way to identify a particular day.

Priests rely on regular services for the extraction of money, goods or food from their communities, and for the appeasement of the spirits with blood and supplication to the accompaniment of fire, preaching and dancing. These activities could occur daily, but this is a bit too frequently to go over well, so some longer period is better. The moon repeats its cycle of phases every 29.5 days, and since it is a mysterious heavenly object, it is ideal for religious observances. Religious observances can be coordinated with the phases of the moon, and time divided into months (moonths), each month beginning when the thin crescent of the new moon is seen in the twilight. This is a beautiful enough sight anyway to lend class to the observance.

The month can then be divided into days, which now are more memorable by being part of the longer cycle, and certain things are done on certain days. On the 1st, we feast. On the 7th, we fast, on the 12th we sacrifice a virgin to the river, and on the 20th we give a pig to the priests. The problem is that the month is not an integral number of days. This only worries the orderly mind, which wants some fixed number of days so the future can be precisely planned. One solution, which is actually used, is to alternate months of 29 and 30 days, which only slowly gets out of register with the moon.

What happens when we are in the evening of the 30th day of some month, and the new crescent is not seen as it should be? Well, we could start the month anyway, or we could add a day, called an intercalary day, hoping to see the crescent the next evening. Both methods have been used, but the latter is the most popular with the precise minds. This day we can make a holiday, or the occasion for an extra gift to the priests, or a day for athletic contests or drinking.

There is another great and very obvious cycle, the year. The observant note that the sun moves northward and southward, through the equinoxes and solstices, as the cycle of nature in the temperate latitudes takes place. For an agricultural socie ty, this cycle is of practical importance. Besides, it is also a good impetus for religious observances, such as feeding blood to the sun so it will not go too far south and leave the world dark. The efficacy of such rites was obvious, since the sun turned around as soon as they took place. The year is about 365.24 days long, or 12.4 lunations, unfortunately. The cycles of day, month and year do not mesh evenly.

One alternative is simply to neglect the year, and base the calendar so that it stays in step with the moon, using an intercalary day now and again. 12 months are arbitrarily defined to be a year. This gives about a 354-day year, which is 11 days short of a real year. In about 33 years, the months would go completely through the seasons. People who don't do much agriculture are happy with such a calendar, which is called lunar.

If you can't do this, several shifts are possible. First, you can insert 11 extra days in every year, and devote them to a general festival or something. Or, you can insert a whole month every two or three years, as necessary, to keep the months in register with the seasons. King Numa Pompilius' calendar of 713 BC was of the latter type, with 12 lunar months every year, and extra months thrown in now and then. It replaced Romulus's calendar of 10 months and only 303 days which began on 1 March, and gave the ordinal names to the months (September, October, etc.) from the order they had in that calendar. These compromise calendars are termed luni-solar.

With good astronomy, it is perceived that the sun makes an annual journey through the stars on the path called the ecliptic. Of course, the average person can't see the stars and the sun at the same time, so this takes a degree of scientific sophistication. One can divide the ecliptic into 12 segments of 30° each, the signs of the Zodiac. The passage of the sun through each segment is a zodiacal month. These months are not equal in length. Those of the winter are shorter than average, and those of the summer longer than average. It is possible to design a calendar with, say, 12 months of arbitrary but unvarying lengths that correspond roughly with the sun's residence in each sign. The Egyptians logically took 30 days in each month, making 360 days in the year. Such a calendar is solar. The Egyptian year, being a little short, moved through the seasons slowly in a 72-year cycle. Since the actual year was of importance to them--it timed the rise of the Nile--5 intercalary days were added to get an alternative 365-day year. This ran through the seasons only once in 1520 years or so. Since events were dated not only by these calendars, but also by the heliacal rising of Sirius, the differences allow precise calibration of Egyptian dates, something not possible anywhere else. Egyptians had little interest in the moon's phases, since their religion was tied to the year and the Nile.

The Julian Calendar lengthened some of the months to give a 365-day year without intercalary days, and in addition added an intercalary day every fourth year, now 29 February, to give an average 365.25 day year. The longer months were placed in the summer because the sun's movement through the stars is slower in these months. A further correction of omitting the extra day on even century years, except every 400 years, keeps the calendar in close synchronization with the seasons. This is the Gregorian Calendar, but the difference from the Julian is piddling. No great scientific insight was necessary to devise this correction. This calendar, which is now all but universally used for civil purposes, is a purely solar calendar. It is possible to convert from Julian Day to Gregorian Day, and vice-versa, easily by a mathematical process any computer can easily carry out.

The week is a purely arbitrary grouping of days, mainly to give names to the days for convenience. Weeks go on oblivious of any astronomical happenings. The day of the week can be found from the Julian Day by simply dividing by 7. The Chinese week was five days, named for the five Chinese elements. The revolting French had a 10-day week. The revolting Russians had a 5-day week with a month of 6 weeks at first, then a 6-day week with 5 weeks in a month later. The Mayas and Aztecs used 13-day and 20-day divisions simultaneously.

It requires some intelligence to work out a system of arranging and naming days to stay in step with the moon and sun, but no more science than simply counting days. Errors will become evident after the passage of a sufficient interval of time. The lazy will merely intercalate days as necessary, the clever will think up formulas for adding the extra days in advance. No extra precision of measurement is necessary.

Because a calendar system counts years or days from some early date does not mean that the calendar existed at that date. Any calendar can be extrapolated backwards to create a proleptic calendar for expressing dates before the calendar actually existed. The Julian Day starts in 4713 BC, but no one could have known it at the time, since the Julian Day was not devised until the 17th century.


M. Westrheim, Calendars of the World (Oxford: One World Publishing, 1993).

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Composed by J. B. Calvert
Created 4 July 2000
Last revised