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 calendarA 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...
s may require intercalations of both days and months.
The solar
yearA year is the amount of time it takes the Earth to make one revolution around the Sun...
does not have a whole number of days (it's about 365.24 days), but a
calendar yearGenerally speaking, a calendar year begins on the New Year's Day of the given calendar system and ends on the day before the following New Year's Day. By convention, a calendar year consists of a natural number of days. To reconcile the calendar year with an astronomical cycle , certain years...
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 yearA 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 yearA leap year is a year containing one or more extra days in order to keep the calendar year synchronized with the astronomical or seasonal year....
of 366 days.
The
Decree of CanopusThe Decree of Canopus is a bilingual inscription-, written in three writing systems–Egyptian hieroglyphs, Egyptian Demotic, and Greek, on an ancient Egyptian memorial stone stele, the Stone of Canopus, a decree by the Egyptian priests honoring Pharaoh Ptolemy III Euergetes, Queen Berenice,...
, which was issued by the pharaoh Ptolemy III, Euergetes of
Ancient EgyptAncient Egypt was an ancient civilization of eastern North Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. The civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh, and...
in 239 BC, decreed a solar leap day system.
In the
Julian CalendarThe 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 CalendarThe 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 the calendar was named, on 24 February 1582 by the papal bull Inter gravissimas...
, 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.
The solar year does not have a whole number of
lunar monthIn lunar calendars, a lunar month is the time between two identical syzygies . There are many variations. In Middle-Eastern and European traditions, the month starts when the young crescent moon becomes first visible at evening after conjunction with the Sun 1 or 2 days before that evening...
s (it is about 12.37
lunationLunation is the mean time for one lunar phase cycle . It is on average 29.530589 days, or 29 days 12 hrs 44 mins & 3 secs...
s), so a lunisolar calendar must have a variable number of
monthThe month is a unit of time, used with calendars, which is approximately as long as some natural period related to the motion of the Moon; month and Moon are cognates. The traditional concept arose with the cycle of moon phases; such months are synodic months and last approximately 29.53 days...
s in a year. This is usually 12, but a 13th (an "intercalary" or "embolismic" month) is inserted every second or third year.
ISO 8601ISO 8601 is an international standard covering the exchange of date and time-related data. The standard is titled “Data elements and interchange formats — Information interchange — Representation of dates and times” and was issued by the International Organization for Standardization...
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 (
JulianThe 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...
,
GregorianThe 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 the calendar was named, on 24 February 1582 by the papal bull Inter gravissimas...
and
HebrewThe Hebrew calendar or Jewish calendar is a lunisolar calendar used by Jews, and in recent decades, by a growing number of Christians...
calendars), or determined by observation (
Iranian calendarThe Iranian calendar can refer to any in a succession of a set of calendars. They are used for over two millennia in Iran , Afghanistan and related societies....
).
The
International Earth Rotation and Reference Systems ServiceThe International Earth Rotation and Reference Systems Service , formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter and International Celestial Reference System ...
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 applies only to periods of 24 hours or longer.
See also
- Bahá'í calendar
The Bahá'í calendar, also called the Badí‘ calendar, used by the Bahá'í Faith, is a solar calendar with regular years of 365 days, and leap years of 366 days. Years are composed of 19 months of 19 days each, plus an extra period of "Intercalary Days"...
and Ayyám-i-HáAyyám-i-Há refers to a period of four or five intercalary days in the Bahá'í calendar, where Bahá'ís celebrate the Festival of Ayyám-i-Há...
- Chinese calendar
The Chinese calendar is lunisolar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures. It is often referred to as the Chinese calendar because it was first perfected by the Chinese around 500 BCE...
- Coptic calendar
The Coptic calendar, also called the Alexandrian calendar, is used by the Coptic Orthodox Church and still used in Egypt. This calendar is based on the ancient Egyptian calendar...
- Egyptian calendar
The ancient civil Egyptian calendar had a year that was 365 days long and was divided into 12 months of 30 days each, plus 5 extra days at the end of the year. The months were divided into 3 "weeks" of ten days each, an arrangement remarkably similar to the French Republican Calendar invented...
- Hebrew calendar
The Hebrew calendar or Jewish calendar is a lunisolar calendar used by Jews, and in recent decades, by a growing number of Christians...
- 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
The Iranian calendar can refer to any in a succession of a set of calendars. They are used for over two millennia in Iran , Afghanistan and related societies....
- Thai lunar calendar
The Thai lunar calendar is Thailand's version of the lunisolar Buddhist calendar used in the southeast Asian countries of Cambodia, Laos and Burma. Based on the third-century Surya Siddhanta Hindu calendar, these combine lunar and solar calendars for a nominal year of 12 months...
- Bengali calendar
The Bengali calendar or Bangla calendar is a traditional solar calendar used in Bangladesh and India's eastern states of West Bengal, Assam and Tripura. The year begins on Pôhela Baishakh, which falls on 14 April in Bangladesh and 15 April in India. In Assam, this corresponds to Bhaskar Era, named...
- Ethiopian calendar
The Ethiopian calendar , also called the Ge'ez calendar, is the principal calendar used in Ethiopia and also serves as the liturgical calendar for Christians in Eritrea belonging to the Eritrean Orthodox Tewahdo Church, Eastern Catholic Church and Lutheran Evangelical Church of Eritrea...