Calendar
A calendar is a method used for keeping time on a scale of years. The term calendar can refer to either the rules for calculating the length of years, months, and holidays, or to record-keeping devices which show the relations between days, weeks, months, and years.
Most societies on earth have created calendars to keep track of time, and to predict annual occurrences, such as the start of seasons. Many calendars are divided into 12 months which approximate the cycle of the moon's apparent revolution about the earth. Calendars which attempt to maintain the length of each year equivalent to one tropical year are solar calendars, calendars which maintain the length of each year as an integral number of lunar months, but attempt to maintain the average length of year as one tropical year are luni-solar calendars, while calendars which are based on an integral number of lunar months and do not keep synchronized with the solar year are lunar calendars.
The lunar month is about 29.53 days long, and thus 12 lunar months are about 354.37 days. 235 lunar months are almost exactly 19 solar years long, with an excess of about 0.86 days. This coincidence forms the basis of the Metonic cycle and of several calendars.
Julian calendar
The Julian calendar was commissioned by Julius Caesar probably in 48 BC. It was developed by Roman astronomers and instituted in 46 BC by adding 90 days to the pre-Roman calendar in order to realign it with the tropical year. The first regular Julian year was 45 BC. The Julian year is normally 365 days long, with a leap day inserted every fourth year to adjust for the fractional day, making the average length of the year 365.25 days long. As the tropical year is approximately 365.2422 days long, this will result in the calendar year gaining about one day in 128 years, resulting in calendar drift.
When the Julian calendar was adopted, the equinoxes and solstices occurred on March 25, June 25, September 25, and December 25. When the formula for determining the date of Easter was adopted at the Council of Nicaea in 325 AD, the vernal equinox was on March 21, and that date was set as the base of the calculation of Easter.
Gregorian calendar
In the Gregorian calendar used by most countries for legal purposes, the year is normally 365 days long, with a leap day inserted periodically to adjust for the fractional day. A leap day is inserted in every year whose number is divisible by 4, unless the year is also divisible by 100 but not 400. Years with the leap day are called leap years Thus 1896 and 1904 were leap years, but 1900 was not; however, 1996, 2000, and 2004 are all leap years. This correction adjusts the year to be 365.2425 days long. As the tropical year is approximately 365.2422 days long, this will result in the calendar year gaining about one day in 3300 years. Various proposals have been made to adjust for the anomaly, but none have become official.
When the Gregorian calendar was adopted, an adjustment was made to return the vernal equinox to March 21, to allow the formula for the date of Easter to be based on the actual vernal equinox.
French republican calendar
The French republican calendar was adopted by the French National Convention in 1793. The calendar was based on the Gregorian calendar, except that it started on the day of the autumnal equinox, the months were regularlized to consist of 30 days divided into three 10-day weeks each, with an additional 5 or 6 days to make up the difference. There were proposals to adopt a regular pattern of leap years similar to the Gregorian Calendar, with an addition of dropping one leap day every 4000 years; however, such proposals were not adopted, and the astronomical basis of the beginning of the year was retained.
Maya Calendar
The Maya calendar was based on a variety of cycles, including a 13-day and 20-day cycle which combined for a 260-day ceremonial "year" called the Tzolkin, and a 365-day year, called Haab, which had no compensation for the extra quarter-day in the solar cycle. The Tzolkin and Haab cycle in a 52-Haab cycle, and thus every date within a 52-Haab cycle could be uniquely identified by the combination of its Haab date and its Tzolkin date. This was considered sufficient for most people, as 52 years was longer than the average lifespan.
Hebrew calendar
The traditional Hebrew or Jewish calendar is a luni-solar calendar based on the Metonic cycle. In a cycle of 19 years, 7 years have 13 lunar months, while the remaining 12 have 12 lunar months. Each month begins on the date of the new moon, with some minor adjustments made for keeping certain holy days off certain days of the week. In the period before the destruction of the Temple in Jerusalem in 70 CE, the calendar was based on astronomical observations. After that time, rule-based systems for calculating the details of the calendar were adopted. The final version of the rules were described by Maimonides in 1178 CE, and have been maintained by Jewish communities around the world since that time.
Islamic calendar
The Islamic calendar is a purely lunar calendar, with 12 months in each year, each beginning on the date of the new moon. As a result of the Islamic year averaging just over 354 days, the beginning of the year, and all dates fixed in the Islamic calendar, rotate through the solar year (and against solar calendars) in a cycle about 33 (solar) years long.