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## 1. The Egyptian calendar

The Egyptian calendar was developed in the Egypt of the pharaos, so long ago that we don't know when exactly, but probably 4000 or more years ago. The Egyptian calendar was a solar calendar.

Already around the year −2150, the Egyptians divided the night (from sundown till sunup) into twelve equal parts, which were therefore shorter in the summer than in the winter: so-called unequal hours. A corresponding division of the daytime (between sunrise and sunset) is not known from before −1450. A division of a full day and night together into 24 equal hours is known from a text from about −1350 [Stephenson, p. 2] and has found its way into our time keeping.

There is an ancient document that claims that the Egyptian calendar year contained 365 days from the end of the 17th dynasty of pharaos (around −1500), but had only 360 days before then [Verbrugghe, pp. 156, 179]. With a 360-day calendar year, the start of the year would have moved through all seasons in only about 70 years, and with a year of always 365 days it takes about 1460 years. That latter period is now referred to as a Sothis period, but it was apparently of no importance in ancient Egypt itself.

When the Romans conquered Egypt around AD 30, they enforced the use of a leap year every four years, which made the Egyptian calendar stay in step (as far as the length of the calendar year goes) with the Julian calendar then in use in Rome itself. The Egyptian calendar after the adoption of the leap year rule is called the Alexandrian calendar. The first day of the Alexandrian calendar is always around 29 August on the Julian calendar.

Every Egyptian calendar year contained 12 months. Those months and their lengths are mentioned in the following table.

Table 1: Months of the Egyptian Calendar

month days
1 Thoth 30
2 Phaophi 30
3 Athyr 30
4 Choiak 30
5 Tybi 30
6 Mecheir 30
7 Phamenoth 30
8 Pharmuthi 30
9 Pachon 30
10 Payni 30
11 Epiphi 30
12 Mesore 30
(epagomenai) 5

The names in the table are those mentioned by Claudius Ptolemaeus in his Almagest (from around AD 150) [Toomer]. Every Egyptian calendar year has the same number of days (365), and so does every month (30 days), with 5 extra days at the end of the year (called epagomenai by the ancient Greeks) to complete the year. With these rules, the Egyptian calendar was very easy to use, and was used also outside of Egypt, by astronomers, from the ancient Greeks (such as Claudius Ptolemaeus around AD 150) through the end of the Middle Ages, around 400 years ago. Copernicus still used the Egyptian calendar!

## 2. The Babylonian calendar

The Babylonian calendar was used in ancient Mesopotamia (nowadays Iraq and its surroundings). The origin of this calendar is hidden in great age, probably around 3000 years ago. The Babylonian calendar was a lunisolar calendar with 12 or 13 months a year that each had 29 or 30 days. The months of the Babylonian calendar are listed in the following table.

Table 2: Months of the Babylonian Calendar

month
1 Nisannu
2 Ajjaru
3 Simanu
4 Duuzu
5 Abu
6 Ululu
Ululu Ⅱ (embolismic month)
7 Tashritu
8 Arahsamnu
9 Kislimu
10 Tebetu
11 Shabatu

Embolismic months were inserted after Ululu or Adaru. A new day started at sunset, and a new month at the first appearance of the yound crescent Moon after New Moon. The beginning of the year was always around the beginning of spring in the northern hemisphere.

At the latest around the year −750 (in the Julian proleptic calendar) the Babylonians divided a full day into twelve equal parts ("double hours"), which were each divided into 30 equal parts. Babylonian arithmetic was based on the number 60, and that's where our division of an hour into 60 minutes and a minute into 60 seconds comes from [Stephenson, p. 2].

At first, the beginning of months and years was determined by observations, but after a while periods and rules were discovered with which the lunar phases, and so the beginning of months, could be reasonably accurately predicted. From about the year −400 the calendar was based on fixed rules, themselves based on the close connection between 235 synodical months and 19 tropical years. The city of Babylon was deserted and forgotten after about AD 100, and eventually the Babylonian calendar also got out of use. When Islam spread across the area around AD 650, the associated Islamic calendar gained prominence, which is of a quite different type. The Babylonian calendar still lives on to some degree in the Jewish calendar, which follows almost the same rules and has very similar names for the months.

## 3. The Greek calendars

The Greeks in ancient times used both equal and unequal hours [Stephenson, p. 3]. Each Greek city-state had its own calendar, with its own names for the months, and inserting embolistic months into the local calendar had more to do with local politics than with the desire for a regular predictable calendar. Because of this, our knowledge of the exact correspondence between dates on ancient Greek calendars and dates on other calendars is very limited.

## 4. The Julian calendar

The oldest Roman calendar (used from perhaps as early as the year −700 on the Julian proleptic calendar) was a lunar calendar, with in the beginning perhaps only 10 months in each calendar year, though that isn't very clear. The year then started with the month of March, and September through December were then the 7th through 10th months, and their names suggest (septem = 7, octo = 8, novem = 9, decem = 10). July was then still called Quintilis (quit = 5), and August was called Sextilis (sext = 6). Eventually (or perhaps soon) January and February appeared at the end of the calendar year.

Around −450, the calendar changed to become a lunisolar one, by occasional insertion of an embolistic month of 22 or 23 days just after the feast of the Terminalia on 23 February. The remaining days of February followed after the embolistic month. The insertion of the embolistic month happened so haphazardously that the calendar year came to be very much out of step with the seasons. In that time, March, May, Quintilis and October each had 31 days, February had 28, and the remaining months had 29, which yields a total of 355 days.

To get the calendar back into line with the seasons, Julius Caesar, the leader of the Roman Empire at the time, inserted several extra months into the year −45, which made that year 445 days long. Caesar changed the calendar, starting with the year we now refer to as −44, to a solar calendar of 365 days a year, by adding a couple of days to certain months: January, Sextilis, and December got 2 days extra to end up with 31, and April, June, September, and November gained 1 day to end up with 30. Caesar had the year officially start with January, which apparently had been the case already unofficially for a while. He also decreed that each fourth year should get an extra day inserted where the embolistic months used to be inserted, between 23 and 24 February [Censorinus], [van Wijk, p. 51]. With the Roman way of inclusive counting, the extra day was the sixth one before the end of February, and was called the bissextile day (the "second sixth" day). It is possible that Caesar learned the advantages of a regular predictable calendar during a lengthy visit to Egypt in −45.

Historians have determined that the year −44 was not a leap year. In honor of Caesar, the Senate of Rome decided to rename the month of Quintilis to Julius (July), but Caesar did not live to see the first month of July, because he was assassinated on the 15th day (the Ides) of the preceding March (of the year −43). After the death of Caesar, the Romans mistakenly counted every third year a leap year instead of the intended every fourth year, so that the calendar quickly got out of step with the seasons again. Caesar's successor, Emperor August, fixed this mistake by not having any leap years for a decade or so, so that from the year AD 8 at the latest the Julian calendar was once again on the track laid out by Caesar. In honor of Emperor August, the month of Sextilis was renamed to Augustus (August). The history of the lengths, names, and places of the months is illustrated by the following table (based on a description by the late Roman author Censorinus [Censorinus] [van Wijk, p. 51]).

Table 3: Months of the Julian Calendar

around −450 from −44 later English
11 ianuarius 29 1 31 January
12 februarius 28 2 February
1 mars 31 3 March
2 aprilis 29 4 30 April
3 maius 31 5 May
4 iunius 29 6 30 June
5 quintilis 31 7 iulius July
6 sextilis 29 8 31 augustus August
7 september 29 9 30 September
8 october 31 10 October
9 november 29 11 30 November
10 december 29 12 31 December
355 365

The Romans used a very different way from us for naming days of the month. For an example of the Roman way of dating, see the Roman Calendar Example Page.

The Julian calendar was used without interruption until 1582, when Pope Gregory XIII made some changes that modified the calendar (at first only in the Catholic areas, later also elsewhere) into the Gregorian calendar.

On 17 August 2010 it will be 750,000 days since the death of Julius Caesar.

## 5. The French revolutionary calendar

The French revolutionary calendar was used in France after the French Revolution, from 24 November 1793 until 1 January 1806 (when Napoléon Bonaparte had become the leader of the French people), and again from 6 until 23 May 1871 (on the Gregorian calendar). Each year began at the autumnal equinox (the one in what we call September) and contained 12 months of 30 days each, followed by 5 (or 6) days that were not part of any month. The names of the months were: Vendémiaire, Brumaire, Frimaire, Nivôse, Pluviôse, Ventôse, Germinal, Floréal, Prairial, Messidor, Thermidor, and Fructidor, and the 5 or 6 month-less days that followed were together called the jours sansculottides. Each month was divided into three periods of 10 days (called décades), of which the last day was a day of rest. The workers weren't happy about this, because on the Gregorian calendar they had had a day of rest every 7th day.

The epoch of the calendar (1 Vendémiaire of year 1) coincided with the autumnal equinox of 1793 on the Gregorian calendar. At first, leap years were determined by the rule that the autumnal equinox must fall on 1 Vendémiaire, but this led to problems to predict when exactly future years would begin, so it was suggested to use a set of Gregorian-like leap year rules, but the calendar was abolished before those rules came into effect [Dershowitz].

## 6. The Central American calendars

The peoples of Anahuac (Central America) used many different calendars before they were conquered by the Spaniards in the 16th century, but those calendars were all based on the same pattern, which we'll explain here based on the Tikan calendars of the Maya.

The calendars of Anahuac had a period of 20 days (called venteina by the Spaniards; the local name is not known anymore) with a name for each day. The names of the days of the venteina used in the Tikal calendar were: Imix, Ik, Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Etz'nab, Cauac and Ahau. The calendars also had a period of 13 days (called trecena by the Spaniards) in which each day had a number. These two cycles were run at the same time, such that after a day 6 Ik followed a day 7 Akbal, and then 8 Kan. A particular designation for a day in this system returned after 260 days, which period was called tzolkin in the language of Yucatan.

At the same time, there was also a year of 365 days, divided into 18 months of 20 days each, plus a 19th month of only 5 days. Each day in each month got a number (starting in the Tikal calendar with number 0, not 1), such that after day 0 Pop followed 1 Pop, and then 2 Pop. The names of the months in the Tikal calendar were: Pop, Uo, Zip, Zot'z, Tzec, Xul, Yaxkin, Mol, Ch'en, Yax, Zac, Ceh, Mac, Kankin, Muan, Pax, Kayab, Cumku and Uayeb. This system is now sometimes called the haab. With this year of 365 days, the calendar was a solar calendar.

A particular year was not identified by a number, but (usually) by the identification of the first day of the year in the tzolkin. If, for example, a particular year started with day 6 Ik, then the year was also called 6 Ik. The next year would then be 7 Manik, with the number one greater because 365 days equals 28 trecenas plus one day, and the month five positions further beause of the five extra days at the end of the year. The following year would then be 8 Eb, and the years after that 9 Caban and 10 Ik, and so on.

The calendars of Anahuac did not have leap years, so the calendar year ran out of step with the seasons by about 1 day each 4 years, just like the Egyptian calendar. A given day was usually identified by its positions in both the tzolkin and the haab cycles, for example 6 Ik 2 Pop, which was followed by 7 Akbal 3 Pop. After 52 calendar years of each 365 days a particular tzolkin-haab combination would come again. This period was called the hunab and is now called the calendar round, or even the Mayan century.

Besides these two cycles, the peoples of Anahuac also used the so-called Long Count, with several cycles that each consisted of a number of smaller cycles. The cycles and their lengths were:

 1 kin =  1 day 1 uinal =  20 kin =  20 days 1 tun =  18 uinal =  360 days 1 katun =  20 tun =  7 200 days (about 20 years) 1 baktun =  20 katun =  144 000 days (about 394 years) 1 may =  13 katun =  1 872 000 days (about 5125 years) 1 pictun =  20 baktun =  2 880 000 days (about 7885 years) 1 calabtun =  20 pictun =  57 600 000 days (about 157 700 years) 1 kinchiltun =  20 calabtun =  1 152 000 000 days (about 3 154 004 years) 1 alautun =  20 kinchiltuns = ` 23 040 000 000 days (about 63 080 082 years)

Only the first five of these units of time were usually used in the Long Count. After 13 baktun = 20 may, the main cycle of the Long Count was complete and a new one would start. Each date was indicated by its (numbered) position in all cycles, starting with the baktun and then down to the kin. The numbers started at 0. A complete date specification consisted of the positions of the day in the Long Count, the tzolkin, and the haab.

The first day of the Long Coun, the epoch, was 0.0.0.0.0 4 Ahau 8 Cumku. With which day on the Julian proleptic calendar does that correspond? After the conquest of Central America by the Spaniards, many of the documents of the indigenous peoples were destroyed by the conquerors, and many local customs (such as the local calendars) were suppressed if the new masters felt they were not suitable. Because of this, the exact correspondence between the calendars of Anahuac (and especially the Long Count) and the calendars of the Spaniards (Julian/Gregorian) has been lost. Investigators of this question have proposed dates between the years of −3632 and −2593 of the Julian proleptic calendar. Nowadays most experts agree that 6 September −3113 (Julian proleptic; Julian day 584,283) is the correct one, as proposed in 1950 by Thompson.

A date, for example chiseled into a building or statue, was usually given in the tzolkin and haab. Sometimes the Long Count was also included, but sometimes it was not. If there's no Long Count, then the date is ambiguous even in its own calendar, because then the same combination recurs every 52 calendar years. For example, there's a Maya inscription (in the "Leyden Plaque" [Edmonson, p. 32]) that lists the date (after translation into the Tikal calendar) 1 Eb 0 Yaxkin. This date occurred most recently on 8 August 1983, and every 18,980 days before that. Which one is the correct one? Fortunately, the Long Count is also given, as 8.14.3.1.12, and that corresponds (assuming the Thompson correlation) with 14 September, AD 320.

1 January 2000 corresponded to 12.19.6.15.2 11 Ik 10 Kankin. The Long Count of 0.0.0.0.0 recurs on 21 December 2012, but that date can still be distinguished from the epoch because the tzolkin-haab designation of the coming 0.0.0.0.0 is 4 Ahau 3 Kankin, and the epoch was 0.0.0.0.0 4 Ahau 8 Cumku. The first time that 0.0.0.0.0 4 Ahau 8 Cumku comes again is in the year 34,302.

## 7. The Gaulish Calendar

Our knowledge of the Gaulish calendar is almost entirely based on the "Calendar of Coligny" that describes five years, probably dates to the 1st century AD, and was found in 1897 near Coligny in France. This Gaulish calendar was a lunisolar calendar with 12 or 13 months per year. The names and lengths of the months are displayed in the following table. (It is of course possible that the names or even the whole calendar was different in other regions or times.)

Name Days
Ciallos 0/30
1 Samon 30
2 Dumann 29
3 Riuros 30
4 Anagantios 29
5 Ogron 30
6 Cutios 30
Ciallos 0/30
7 Giamon 29
8 Simiuisonn 30
9 Equos 29
10 Elembiu 29
11 Edrin 30
12 Cantios 29

The month Ciallos was an embolistic month that was inserted before Samon once every five years, and between Cutios and Giamon 2.5 years later. This Gaulish calendar therefor had an embolistic month every 2.5 years. This gave the calendar year a length of 354 or 384 days, with an average length of 366 days. To keep in step with the seasons in the long run, an embolistic month needed to be dropped once in a while, but how and when this happened is not known.

It is not clear at what phase of the Moon each month began. Some people think it was at Full Moon, others at New Moon, and yet others at First Quarter. The Celts counted a full day as a night and the following day. Modern Western calendars count days, but the Celts counted nights (as in "fortnight" for a period of 14 days).

It is not entirely clear in which time of year each month of the Gaulish calendar fell. Many people think that the Gaulish month of Samon roughly corresponds with the modern Irish month of Samhainn (November), but John Bonsing gives convincing arguments [Bonsing] that there is no reasonable proof for the Samon - Samhainn connection, that modern Samhainn in fact corresponds to the Gaulish month of Giamon, and that the beginning of the Gaulish year (with the month Samon or the preceding embolistic month of Ciallos) corresponds to about the middle of the modern month of May.