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Intercalation is the insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendar
Lunisolar calendar

A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will predict the constellation near which the full moo...
s may require intercalations of both days and months.

The solar year
Year

A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. By extension, this can be applied to any planet: for example, a "Martian year" is the time in which Mars completes its own orbit....
 does not have a whole number of days (it's about 365.24 days), but a calendar year
Calendar year

According to the Gregorian calendar, the calendar year begins on January 1 and ends on December 31.Generally speaking, a calendar year begins on the New Year of the given calendar system and ends on the day before the following New Year's day....
 must have a whole number of days. The only way to reconcile the two is to vary the number of days in the calendar year.

In solar calendars, this is often done by adding to a common year
Common year

A common year is a common type of calendar year. It has exactly 365 days and so is not a leap year. More generally, it is a calendar year without intercalation....
 of 365 days, an extra day (leap day or intercalary day) about every four years: this makes a leap year
Leap year

A leap year is a year containing one or more extra days in order to keep the calendar year synchronized with the astronomical year or seasonal year....
 of 366 days.

The Decree of Canopus
Decree of Canopus

The Decree of Canopus is the trilingual inscription, written in three writing systems–Egyptian hieroglyphs, Demotic , and Greek language, on an ancient Egyptian memorial stone stele, the Stone of Canopus, a decree by the Egyptian priests honoring Pharaoh Ptolemy III Euergetes, Queen Berenice, wife of Ptolemy III, and Princess Berenice ....
, which was issued by the pharaoh Ptolemy III, Euergetes of Ancient Egypt
Ancient Egypt

Ancient Egypt was an Ancient history civilization in eastern North Africa, concentrated along the lower reaches of the Nile in what is now the modern nation of Egypt....
 in 239 BC, decreed a solar leap day system.

In the Julian Calendar
Julian calendar

The Julian calendar, a reform of the Roman calendar, was introduced by Julius Caesar in 46 BC, and came into force in 45 BC . It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year, known at least since Hipparchus....
 as well as in the Gregorian Calendar
Gregorian calendar

The Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom it was named, on 24 February 1582 by the papal bull Inter gravissimas....
 that improved it, intercalation is done by adding an extra day to February in each leap year.






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Intercalation is the insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendar
Lunisolar calendar

A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will predict the constellation near which the full moo...
s may require intercalations of both days and months.

The solar year
Year

A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. By extension, this can be applied to any planet: for example, a "Martian year" is the time in which Mars completes its own orbit....
 does not have a whole number of days (it's about 365.24 days), but a calendar year
Calendar year

According to the Gregorian calendar, the calendar year begins on January 1 and ends on December 31.Generally speaking, a calendar year begins on the New Year of the given calendar system and ends on the day before the following New Year's day....
 must have a whole number of days. The only way to reconcile the two is to vary the number of days in the calendar year.

In solar calendars, this is often done by adding to a common year
Common year

A common year is a common type of calendar year. It has exactly 365 days and so is not a leap year. More generally, it is a calendar year without intercalation....
 of 365 days, an extra day (leap day or intercalary day) about every four years: this makes a leap year
Leap year

A leap year is a year containing one or more extra days in order to keep the calendar year synchronized with the astronomical year or seasonal year....
 of 366 days.

The Decree of Canopus
Decree of Canopus

The Decree of Canopus is the trilingual inscription, written in three writing systems–Egyptian hieroglyphs, Demotic , and Greek language, on an ancient Egyptian memorial stone stele, the Stone of Canopus, a decree by the Egyptian priests honoring Pharaoh Ptolemy III Euergetes, Queen Berenice, wife of Ptolemy III, and Princess Berenice ....
, which was issued by the pharaoh Ptolemy III, Euergetes of Ancient Egypt
Ancient Egypt

Ancient Egypt was an Ancient history civilization in eastern North Africa, concentrated along the lower reaches of the Nile in what is now the modern nation of Egypt....
 in 239 BC, decreed a solar leap day system.

In the Julian Calendar
Julian calendar

The Julian calendar, a reform of the Roman calendar, was introduced by Julius Caesar in 46 BC, and came into force in 45 BC . It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year, known at least since Hipparchus....
 as well as in the Gregorian Calendar
Gregorian calendar

The Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom it was named, on 24 February 1582 by the papal bull Inter gravissimas....
 that improved 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 calendar, years whose number is evenly divisible by 100 but not 400, were exempted in order to improve accuracy. Thus, 2000 was the first century year in 400 years to be a leap year.

The solar year does not have a whole number of lunar month
Lunar month

In lunar calendars, a lunar month is the time between two identical syzygy . There are many variations. In Middle-Eastern and European traditions, the month starts when the new moon becomes first visible at evening after Astronomical conjunction with the Sun 1 or 2 days before that evening ....
s (it is about 12.37 lunation
Lunation

Lunation is the mean time for one lunar phase cycle .  It is on average 29.530589 days, or 29 d 12 h 44 min 3 s.  The length of this cycle is linked to many phenomena in nature....
s), so a lunisolar calendar must have a variable number of month
Month

The month is a unit of time, used with calendars, which is approximately as long as some natural Orbital period related to the motion of the Moon; month and Moon are cognates....
s in a year. This is usually 12 months, but a 13th month (an intercalary or embolismic month) is added to the year every two or three years.

ISO 8601
ISO 8601

ISO 8601 is an international standard for calendar date and time representations issued by the International Organization for Standardization . Specifically, the standard is titled "Data elements and interchange formats ? Information interchange ? Representation of dates and times"....
 includes a specification for a 52-week year. Any year that has 53 Thursdays has 53 weeks; this extra week may be regarded as intercalary.

The determination of whether a year has intercalation may be calculated (Julian
Julian calendar

The Julian calendar, a reform of the Roman calendar, was introduced by Julius Caesar in 46 BC, and came into force in 45 BC . It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year, known at least since Hipparchus....
, Gregorian
Gregorian calendar

The Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom it was named, on 24 February 1582 by the papal bull Inter gravissimas....
 and Hebrew
Hebrew calendar

The Hebrew calendar or Jewish calendar is a lunisolar calendar used by Jews, now predominantly for religious purposes. It is used to reckon the Jewish New Year and dates for Jewish holidays, and also to determine appropriate Torah reading of Torah portions, Yahrzeits , and daily Psalm reading, among many ceremonial uses....
 calendars), or determined by observation (Iranian calendar
Iranian calendar

The Iranian calendar or Solar Hejri is an astronomical solar calendar and one of the longest chronological records in history and is currently used in Iran and Afghanistan as the main official calendar....
).

The International Earth Rotation and Reference Systems Service
International Earth Rotation and Reference Systems Service

The International Earth Rotation and Reference Systems Service , formerly the International Earth Rotation Service, is the body responsible for maintaining global time and Frame of reference standards, notably through its Earth Orientation Parameter and International Celestial Reference System groups....
 can insert or remove leap seconds from the calendar up to twice a year, these are sometimes described as intercalary although the word intercalation strictly only applies to time periods of 24 hours or longer.

See also

  • Bahá'í calendar
    Bahá'í calendar

    The Bah?'? calendar, also called the Bad? calendar, used by the Bah?'? Faith, is a solar calendar with regular years of 365 days, and leap years of 366 days....
     and Ayyám-i-Há
    Ayyám-i-Há

    Ayy?m-i-H? refers to a period of four or five intercalary days in the Bah?'? calendar, where Bah?'? Faith celebrate the Festival of Ayy?m-i-H?....
  • Chinese calendar
    Chinese calendar

    The Chinese calendar is lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. This measure of time was first introduced by the Babylonians ....
  • Hebrew calendar
    Hebrew calendar

    The Hebrew calendar or Jewish calendar is a lunisolar calendar used by Jews, now predominantly for religious purposes. It is used to reckon the Jewish New Year and dates for Jewish holidays, and also to determine appropriate Torah reading of Torah portions, Yahrzeits , and daily Psalm reading, among many ceremonial uses....
  • Hindu calendar
    Hindu calendar

    The Hindu calendar used in ancient times has undergone many changes in the process of regionalization, and today there are several regional Indian calendars, as well as an Indian national calendar....
  • Islamic prohibition of intercalation
  • Iranian calendar
    Iranian calendar

    The Iranian calendar or Solar Hejri is an astronomical solar calendar and one of the longest chronological records in history and is currently used in Iran and Afghanistan as the main official calendar....
  • Thai lunar calendar
    Thai lunar calendar

    The Thai lunar calendar is Thailand's version of the lunisolar calendar Buddhist calendar used in the southeast Asian countries of Cambodia, Laos and Myanmar....
  • Bengali calendar
    Bengali calendar

    The Bengali calendar or Bangla calendar is a traditional solar calendar calendar used in Bangladesh and India's eastern states of West Bengal, Assam and Tripura....
  • Ethiopian calendar
    Ethiopian calendar

    The Ethiopian calendar , also called the Ge'ez calendar, is the principal calendar used in Ethiopia and is also the liturgical year of Christians in Eritrea belonging to the Eritrean Orthodox Tewahdo Church, Eastern Catholic Church of Eritrea and Lutheran ....