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Intercalation or embolism in timekeeping is the insertion of a
leap day February 29, also known as leap day or leap year day, is a date added to leap year A leap year (also known as an intercalary year or wikt:bissextile, bissextile year) is a calendar year that contains an additional day (or, in the case of ...
,
week A week is a time unit equal to seven days. It is the standard time period used for cycles of rest days in most parts of the world, mostly alongside—although not strictly part of—the Gregorian calendar. In many languages, the days of the we ...
, or month into some
calendar year A calendar is a system of organizing days. This is done by giving names to periods of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, ...
s to make the
calendar 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 calendar date, date is the designation of a single, specific day within such a system. A calendar is also ...

calendar
follow the seasons or moon phases.
Lunisolar calendar A lunisolar calendar is a calendar 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 calendar date, date is the designation of a single, specific day ...
s may require intercalations of both days and months.


Solar calendars

The solar or
tropical year A tropical year (also known as a solar year or tropical period) is the time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past ...
does not have a whole number of days (it is about 365.24 days), but a
calendar year A calendar is a system of organizing days. This is done by giving names to periods of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, ...
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 to a
common year A common year is a calendar year A calendar is a system of organizing days. This is done by giving names to periods of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in ...
of 365 days, an extra day ("leap day" or "intercalary day") about every four years, causing a
leap year A leap year (also known as an intercalary year or wikt:bissextile, bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) added to keep the calendar year synchronized with the astron ...

leap year
to have 366 days ( Julian, Gregorian and
Indian national calendar The Indian national calendar, sometimes called the Saka calendar, is used, alongside the Gregorian calendar, by ''The Gazette of India'', in news broadcasts by All India Radio and in calendars and communications issued by the Government of India. ...

Indian national calendar
s). The
Decree of CanopusThe Decree of Canopus is a trilingual inscription in three scripts, which dates from the Ptolemaic period of ancient Egypt Ancient Egypt was a civilization of Ancient history, ancient North Africa, concentrated along the lower reaches of th ...
, which was issued by the pharaoh
Ptolemy III Euergetes egy, Iwaennetjerwysenwy Sekhemankhre Setepamun#Clayton06, Clayton (2006) p. 208 , predecessor = Ptolemy II , successor = Ptolemy IV , nebty = ''ḳn nḏtj-nṯrw jnb-mnḫ-n-tꜢmrj'Qen nedjtinetjeru inebmenekhentamery''The bra ...

Ptolemy III Euergetes
of
Ancient Egypt Ancient Egypt was a civilization  A civilization (or civilisation) is a that is characterized by , , a form of government, and systems of communication (such as ). Civilizations are intimately associated with additional char ...

Ancient Egypt
in 239 BCE, decreed a solar leap day system; an Egyptian leap year was not adopted until 25 BC, when the Roman Emperor
Augustus Caesar Augustus (23 September 63 BC19 August AD 14) was the first Roman emperor The Roman emperor was the ruler of the Roman Empire during the imperial period (starting in 27 BC). The emperors used a variety of different titles through ...

Augustus
successfully instituted a reformed Alexandrian calendar. In the
Julian calendar The Julian calendar, proposed by Julius Caesar Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman Roman or Romans usually refers to: *Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century B ...
, as well as in the
Gregorian calendar The Gregorian calendar is the calendar 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 calendar date, date is the designation of a single, speci ...
, 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 days are days within a solar calendar that are outside any regular month. Usually five epagomenal days are included within every year (
Egyptian Egyptian describes something of, from, or related to Egypt. Egyptian or Egyptians may refer to: Nations and ethnic groups * Egyptians, a national group in North Africa ** Egyptian culture, a complex and stable culture with thousands of years of r ...
,
Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group mainly in the area of modern Egypt but also in Sudan and Libya * Coptic language, a Northern Afro-Asiatic language spoken in Egypt until at least the 17th century * Coptic alphabet, th ...
,
Ethiopian Ethiopians are the native inhabitants of Ethiopia, as well as the global diaspora of Ethiopia. Ethiopians constitute Ethiopians#Component Ethnicities, several component ethnic groups, many of which are closely related to ethnic groups in neighb ...
, Mayan Haab' and
French Republican Calendar The French Republican calendar (french: calendrier républicain français), also commonly called the French Revolutionary calendar (), was a calendar A calendar is a system of organizing days. This is done by giving names to periods of ...
s), but a sixth epagomenal day is intercalated every four years in some (Coptic, Ethiopian and French Republican calendars). The Bahá'í calendar includes enough epagomenal days (usually 4 or 5) before the last month (, ''ʿalāʾ'') to ensure that the following year starts on the
March equinox The March equinox or northward equinox is the equinox An equinox is traditionally defined as the time when the plane In mathematics, a plane is a flatness (mathematics), flat, two-dimensional surface (mathematics), surface that extends ...
. These are known as the
Ayyám-i-Há Ayyám-i-Há refers to a period of intercalary day 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. Lunisolar calendars may re ...
.


Lunisolar calendars

The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37
lunation In lunar calendar A lunar calendar is a calendar 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 calendar date, date is the designation of a sing ...
s), so a lunisolar calendar must have a variable number of
month A month is a unit of time, used with calendars, that is approximately as long as a natural orbital period of the Moon; the words ''month'' and ''Moon'' are cognates. The traditional concept arose with the cycle of Moon phases; such lunar months ("l ...
s in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" or "embolismic" month every second or third year (see
blue moon A blue moon is an additional full moon The full Moon of 22 October 2010, as seen through a ecliptic latitude (or northern lunar standstill">lunistice), so the southern lunar craters, craters are especially prominent and cast shadows visibl ...

blue moon
). Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year
Metonic cycle For example, by the 19-year Metonic cycle, the full moon repeats on or near Christmas day between 1711 and 2300. A small horizontal libration is visible comparing their appearances. A red color shows full moons that are also lunar eclipses. The ...

Metonic cycle
(
Hebrew calendar The Hebrew calendar ( Hebrew: , ), also called Jewish calendar, is a lunisolar calendar used today for Jewish religious observance, and as an official calendar of the state of Israel Israel (; he, יִשְׂרָאֵל; ar, إِس ...
and in the determination of Easter) or using calculations of lunar phases (
Hindu lunisolar
Hindu lunisolar
and
Chinese calendar The traditional Chinese calendar (officially known as the Agricultural Calendar [], Former Calendar [], Traditional Calendar [] or Yin Calendar []), is a lunisolar calendar which reckons years, months and days according to astronomical pheno ...
s). The Buddhist calendar adds both an intercalary day and month on a usually regular cycle.


Lunar calendars

The
tabular Islamic calendar The Tabular Islamic calendar (an example is the Fatimid or Misri calendar) is a rule-based variation of the Islamic calendar. It has the same numbering of years and months, but the months are determined by arithmetical rules rather than by obser ...
usually has 12 lunar months that alternate between 30 and 29 days every year, but an intercalary day is added to the last month of the year 11 times within a 30-year cycle. Some historians also linked the pre-Islamic practice of Nasi' to intercalation. The
Solar Hijri calendar The Solar Hijri calendar ( fa, گاه‌شماری هجری خورشیدی, gāhshomāri-ye hejri-ye khorshidi; ps, لمريز لېږدیز کلیز, lamrez legdez kalhandara) is a solar calendar and one of the various ancient Iranian calendars. ...
are based on solar calculations and is similar to the Gregorian calendar in its structure, and hence the intercalation, with the exception that the year date starts with the
Hegira Hegira () is a medieval Latin transliteration of the Arabic word meaning "departure" or "migration", among other definitions. Alternative transliterations of the word include Hijra or Hijrah. The word is commonly used to refer to the journey ...
.


Leap seconds

The
International Earth Rotation and Reference Systems Service The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time Time is the indefinite continued sequence, progress of existence and ...
can insert or remove
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise solar tim ...

leap second
s from the last day of any month (June and December are preferred). These are sometimes described as intercalary.leap second by Merriam-Webster OnLine
/ref>


Other uses

ISO 8601 ISO 8601 is an international standard An international standard is a technical standard A technical standard is an established norm (social), norm or requirement for a repeatable technical task which is applied to a common and repeated use of rule ...
includes a
specification A specification often refers to a set of documented requirements to be satisfied by a material, design, product, or service. A specification is often a type of technical standard A technical standard is an established norm (social), norm or require ...
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 The Aztec or Mexica calendar is the calendar, calendrical system used by the Aztecs as well as other Pre-Columbian era, Pre-Columbian indigenous peoples of Mexico, peoples of central Mexico. It is one of the Mesoamerican calendars, sharing the bas ...

Aztec calendar
had five intercalary days after the eighteenth and final month, the '' nēmontēmi'', in which the people reflect on the past year and do fasting.


See also

*
Lunisolar calendar A lunisolar calendar is a calendar 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 calendar date, date is the designation of a single, specific day ...
*
Egyptian Egyptian describes something of, from, or related to Egypt. Egyptian or Egyptians may refer to: Nations and ethnic groups * Egyptians, a national group in North Africa ** Egyptian culture, a complex and stable culture with thousands of years of r ...
,
Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group mainly in the area of modern Egypt but also in Sudan and Libya * Coptic language, a Northern Afro-Asiatic language spoken in Egypt until at least the 17th century * Coptic alphabet, th ...
, and Ethiopian calendars *
Iranian calendar The Iranian calendars or Iranian chronology ( fa, گاه‌شماری ایرانی, ''Gāh-Šomāri-ye Irāni'') are a succession of calendars invented or used for over two millennia in , also known as Persia. One of the longest chronological re ...
*
Islamic calendar The Hijri calendar ( ar, ٱلتَّقْوِيم ٱلْهِجْرِيّ '), also known as the Lunar Hijri calendar and (in English) as the Islamic, Muslim or Arabic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 o ...
*
Celtic calendar The Celtic calendar is a compilation of pre-Christian Celtic systems of timekeeping, including the Gaulish Coligny calendar, used by Celtic countries to define the beginning and length of the day, the week, the month, the seasons, quarter days, a ...
*
Thai lunar calendarThe Thai lunar calendar ( th, ปฏิทินจันทรคติ, , , literally, ''Specific days according to lunar norms''), or Tai calendar, is a lunisolar A lunisolar calendar is a calendar A calendar is a system of organizing day ...
*
Bengali calendar The Bengali Calendar or Bangla Calendar ( bn, বঙ্গাব্দ , , Baṅgābda) is a luni-solar calendar A lunisolar calendar is a calendar in many culture Culture () is an umbrella term which encompasses the social behavior and Nor ...
*
Igbo calendar The Igbo calendar () is the traditional calendar system of the Igbo people from present-day Nigeria Nigeria (), officially the Federal Republic of Nigeria, is a country in West Africa. It borders Niger in Niger–Nigeria border, the north, ...
*
World Calendar #REDIRECT World Calendar#REDIRECT World Calendar The World Calendar is a proposed reform Reform ( lat, reformo) means the improvement or amendment of what is wrong, corrupt, unsatisfactory, etc. The use of the word in this way emerges in the late 1 ...

World Calendar
*
Intercalated Games The Intercalated Olympic Games were to be a series of ''International Olympic Games'' halfway between what is now known as the Games of the Olympiad. This proposed series of games, intercalated in the Olympic Games cycle, was to always be held i ...


References

{{Time measurement and standards Calendars Units of time