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Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. [1] Lunisolar calendars may require intercalations of days or months.
The solar or tropical year does not have a whole number of days (it is about 365.24 days), but a calendar year must have a whole number of days. The most common way to reconcile the two is to vary the number of days in the calendar year.
In solar calendars, this is done by adding an extra day ("leap day" or "intercalary day") to a common year of 365 days, about once every four years, creating a leap year that has 366 days (Julian, Gregorian and Indian national calendars).
The Decree of Canopus, issued by the pharaoh Ptolemy III Euergetes of Ancient Egypt in 239 BC, decreed a solar leap day system; an Egyptian leap year was not adopted until 25 BC, when the Roman Emperor Augustus instituted a reformed Alexandrian calendar.
In the Julian calendar, as well as in the Gregorian calendar, which improved upon it, intercalation is done by adding an extra day to February in each leap year. In the Julian calendar this was done every four years. In the Gregorian, years divisible by 100 but not 400 were exempted in order to improve accuracy. Thus, 2000 was a leap year; 1700, 1800, and 1900 were not.
Epagomenal [2] days are days within a solar calendar that are outside any regular month. Usually five epagomenal days are included within every year (Egyptian, Coptic, Ethiopian, Mayan Haab' and French Republican Calendars), but a sixth epagomenal day is intercalated every four years in some (Coptic, Ethiopian and French Republican calendars).
The Solar Hijri calendar, used in Iran, is based on solar calculations and is similar to the Gregorian calendar in its structure, and hence the intercalation, with the exception that its epoch is the Hijrah. [3]
The Bahá'í calendar includes enough epagomenal days (usually 4 or 5) before the last month (علاء, ʿalāʾ) to ensure that the following year starts on the March equinox. These are known as the Ayyám-i-Há.
The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37 lunations), so a lunisolar calendar must have a variable number of months per year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" month or "embolismic" month every second or third year. Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year Metonic cycle (Hebrew calendar and in the determination of Easter) or using calculations of lunar phases (Hindu lunisolar and Chinese calendars). The Buddhist calendar adds both an intercalary day and month on a usually regular cycle.
In principle, lunar calendars do not employ intercalation because they do not seek to synchronise with the seasons, and the motion of the moon is astronomically predictable. But religious lunar calendars rely on actual observation.
The Lunar Hijri calendar, the purely lunar calendar observed by most of Islam, depends on actual observation of the first crescent of the moon and thus has no intercalation. Each month still has either 29 or 30 days, but due to the variable method of observations employed, there is usually no discernible order in the sequencing of 29- or 30-day month lengths. Traditionally, the first day of each month is the day (beginning at sunset) of the first sighting of the hilal (crescent moon) shortly after sunset. If the hilal is not observed immediately after the 29th day of a month (either because clouds block its view or because the western sky is still too bright when the moon sets), then the day that begins at that sunset is the 30th. [4]
The tabular Islamic calendar, used in Iran, has 12 lunar months that usually alternate between 30 and 29 days every year, but an intercalary day is added to the last month of the year 12 times in a 33-year cycle. Some historians also linked the pre-Islamic practice of Nasi' to intercalation.
The International Earth Rotation and Reference Systems Service can insert or remove leap seconds from the last day of any month (June and December are preferred). These are sometimes described as intercalary. [5]
ISO 8601 includes a specification for a 52/53-week year. Any year that has 53 Thursdays has 53 weeks; this extra week may be regarded as intercalary.
The xiuhpōhualli (year count) system of the Aztec calendar had five intercalary days after the eighteenth and final month, the nēmontēmi , in which the people fasted and reflected on the past year.
A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a physical record of such a system. A calendar can also mean a list of planned events, such as a court calendar, or a partly or fully chronological list of documents, such as a calendar of wills.
The Hijri calendar, or Arabic calendar also known in English as the Muslim calendar and Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to determine the proper days of Islamic holidays and rituals, such as the annual fasting and the annual season for the great pilgrimage. In almost all countries where the predominant religion is Islam, the civil calendar is the Gregorian calendar, with Syriac month-names used in the Levant and Mesopotamia but the religious calendar is the Hijri one.
The Julian calendar is a solar calendar of 365 days in every year with an additional leap day every fourth year. The Julian calendar is still used as a religious calendar in parts of the Eastern Orthodox Church and in parts of Oriental Orthodoxy as well as by the Amazigh people.
A leap year is a calendar year that contains an additional day compared to a common year. The 366th day is added to keep the calendar year synchronised with the astronomical year or seasonal year. Since astronomical events and seasons do not repeat in a whole number of days, calendars having a constant number of days each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting ("intercalating") an additional day—a leap day—or month—a leap month—into some years, the drift between a civilization's dating system and the physical properties of the Solar System can be corrected.
A lunar calendar is a calendar based on the monthly cycles of the Moon's phases, in contrast to solar calendars, whose annual cycles are based on the solar year. The most widely observed purely lunar calendar is the Islamic calendar. A purely lunar calendar is distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation – such as by insertion of a leap month. The details of when months begin vary from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.
A lunisolar calendar is a calendar in many cultures, incorporating lunar calendars and solar calendars. The date of lunisolar calendars therefore indicates both the Moon phase and the time of the solar year, that is the position of the Sun in the Earth's sky. If the sidereal year is used instead of the solar year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In some cases ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.
A month is a unit of time, used with calendars, that is approximately as long as a natural phase cycle of the Moon; the words month and Moon are cognates. The traditional concept of months arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days, making for roughly 12.37 such months in one Earth year. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth–Sun line, are still the basis of many calendars today and are used to divide the year.
The Metonic cycle or enneadecaeteris is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar.
The Roman calendar was the calendar used by the Roman Kingdom and Roman Republic. Although the term is primarily used for Rome's pre-Julian calendars, it is often used inclusively of the Julian calendar established by the reforms of the Dictator Julius Caesar and Emperor Augustus in the late 1st century BC.
A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar. The main other types of calendar are lunar calendar and lunisolar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of the Moon phase.
The ancient Egyptian calendar – a civil calendar – was a solar calendar with a 365-day year. The year consisted of three seasons of 120 days each, plus an intercalary month of five epagomenal days treated as outside of the year proper. Each season was divided into four months of 30 days. These twelve months were initially numbered within each season but came to also be known by the names of their principal festivals. Each month was divided into three 10-day periods known as decans or decades. It has been suggested that during the Nineteenth Dynasty and the Twentieth Dynasty the last two days of each decan were usually treated as a kind of weekend for the royal craftsmen, with royal artisans free from work.
The epact used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January. Its principal use is in determining the date of Easter by computistical methods. It varies from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.
The history of calendars covers practices with ancient roots as people created and used various methods to keep track of days and larger divisions of time. Calendars commonly serve both cultural and practical purposes and are often connected to astronomy and agriculture.
Calendar reform or calendrical reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design.
The Babylonian calendar was a lunisolar calendar used in Mesopotamia from around the second millennium BCE until the Seleucid Era, and it was specifically used in Babylon from the Old Babylonian Period until the Seleucid Era. The civil lunisolar calendar was used contemporaneously with an administrative calendar of 360 days, with the latter used only in fiscal or astronomical contexts. The lunisolar calendar descends from an older Sumerian calendar used in the 4th and 3rd millennia BCE.
The Ethiopian calendar, or Ge'ez calendar is the official state civil calendar of Ethiopia and serves as an unofficial customary cultural calendar in Eritrea, and among Ethiopians and Eritreans in the diaspora. It is also an ecclesiastical calendar for Ethiopian Christians and Eritrean Christians belonging to the Orthodox Tewahedo Churches, Eastern Catholic Churches, and Eastern Protestant Christian P'ent'ay Churches. The Ethiopian calendar is a solar calendar that has much in common with the Coptic calendar of the Coptic Orthodox Church of Alexandria and Coptic Catholic Church, but like the Julian calendar, it adds a leap day every four years without exception, and begins the year on 11 or 12th of September in the Gregorian calendar. A gap of seven to eight years between the Ethiopian and Gregorian calendars results from an alternative calculation in determining the date of the Annunciation.
The Buddhist calendar is a set of lunisolar calendars primarily used in Tibet, Cambodia, Laos, Myanmar, Bangladesh, India, Sri Lanka, Thailand and Vietnam as well as in Malaysia and Singapore and by Chinese populations for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunar calendar and by the Thai solar calendar.
Mesori is the twelfth month of the ancient Egyptian and Coptic calendars. It is identical to Nahase in the Ethiopian calendar.
The intercalary month or epagomenal days of the ancient Egyptian, Coptic, and Ethiopian calendars are a period of five days in common years and six days in leap years in addition to those calendars' 12 standard months, sometimes reckoned as their thirteenth month. They originated as a periodic measure to ensure that the heliacal rising of Sirius would occur in the 12th month of the Egyptian lunar calendar but became a regular feature of the civil calendar and its descendants. Coptic and Ethiopian leap days occur in the year preceding Julian and Gregorian leap years.
The Burmese calendar is a lunisolar calendar in which the months are based on lunar months and years are based on sidereal years. The calendar is largely based on an older version of the Hindu calendar, though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with the Metonic cycle's near tropical years by adding intercalary months and days at irregular intervals.
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