Intercalation
Encyclopedia
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
s may require intercalations of both days and months.
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 only 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
of 365 days, an extra day ("leap day" or "intercalary day") about every four years, causing a leap year
to have 366 days (Julian
, Gregorian
and Indian national calendar
s).
The Decree of Canopus
, which was 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
successfully 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 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
and French Republican calendar
s), but a sixth epagomenal day is intercalated every four years in some (Coptic, Ethiopian and French Republican calendars). The Bahá'í calendar
includes four epagomenal days, with a fifth intercalary day matching the pattern of intercalation in the Gregorian calendar.
s (it is about 12.37 lunation
s), so a lunisolar calendar must have a variable number of month
s in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" 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 calendar
s). The Buddhist calendar
adds both an intercalary day and month on a usually regular cycle.
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.
can insert or remove leap seconds from the last day of any month (June and December are preferred). These are sometimes described as intercalary, although the word intercalation strictly applies only to periods of 24 hours or longer.
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.
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...
s may require intercalations of both days and months.
Solar calendars
The solar or tropical yearTropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
does not have a whole number of days (it is about 365.24 days), but a calendar year
Calendar year
Generally 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 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, causing a leap year
Leap year
A leap year is a year containing one extra day in order to keep the calendar year synchronized with the astronomical or seasonal year...
to have 366 days (Julian
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
, Gregorian
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
and Indian national calendar
Indian national calendar
The Indian national calendar is the official civil calendar in use in India. It is used, alongside the Gregorian calendar, by The Gazette of India, news broadcasts by All India Radio, and calendars and communications issued by the Government of India.The term may also ambiguously refer to the...
s).
The Decree of Canopus
Decree of Canopus
The Decree of Canopus is a bilingual inscription in two languages, and in three scripts. It was written in three writing systems: Egyptian hieroglyphs, Egyptian Demotic, and Greek, on an ancient Egyptian memorial stone stele, the Stone of Canopus...
, which was issued by the pharaoh Ptolemy III, Euergetes of Ancient Egypt
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...
in 239 BC, decreed a solar leap day system; an Egyptian leap year was not adopted until 25 BC, when the Roman Emperor Augustus
Augustus
Augustus ;23 September 63 BC – 19 August AD 14) is considered the first emperor of the Roman Empire, which he ruled alone from 27 BC until his death in 14 AD.The dates of his rule are contemporary dates; Augustus lived under two calendars, the Roman Republican until 45 BC, and the Julian...
successfully instituted a reformed Alexandrian calendar.
In the Julian calendar
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
, as well as in the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
, 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 calendar
The ancient civil Egyptian calendar had a year that was 360 days long and was divided into 12 months of 30 days each, plus five extra days at the end of the year. The months were divided into three weeks of ten days each...
, Coptic
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...
, Ethiopian
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 Church, Eastern Catholic Church and Lutheran Evangelical Church of Eritrea...
and French Republican calendar
French Republican Calendar
The French Republican Calendar or French Revolutionary Calendar was a calendar created and implemented during the French Revolution, and used by the French government for about 12 years from late 1793 to 1805, and for 18 days by the Paris Commune in 1871...
s), but a sixth epagomenal day is intercalated every four years in some (Coptic, Ethiopian and French Republican calendars). The Bahá'í calendar
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"...
includes four epagomenal days, with a fifth intercalary day matching the pattern of intercalation in the Gregorian calendar.
Lunisolar calendars
The solar year does not have a whole number of lunar monthLunar month
In 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 one or two 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 days 12 hours 44 minutes and 3 seconds...
s), so a lunisolar calendar must have a variable number of month
Month
A month is a unit of time, used with calendars, which was first used and invented in Mesopotamia, as a 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...
s in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" 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
Metonic cycle
In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...
(Hebrew calendar
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
and in the determination of Easter
Computus
Computus is the calculation of the date of Easter in the Christian calendar. The name has been used for this procedure since the early Middle Ages, as it was one of the most important computations of the age....
) or using calculations of lunar phases (Hindu lunisolar
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. Nepali calendar, Bengali calendar, Malayalam calendar, Tamil calendar, Telugu calendar, Kannada...
and Chinese calendar
Chinese calendar
The Chinese calendar is a lunisolar calendar, 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 as well...
s). The Buddhist calendar
Buddhist calendar
The Buddhist calendar is used on mainland Southeast Asia in the countries of Thailand, Cambodia, Laos, Burma and Sri Lanka in several related forms. It is a lunisolar calendar having months that are alternately 29 and 30 days, with an intercalated day and a 30-day month added at regular intervals...
adds both an intercalary day and month on a usually regular cycle.
Lunar calendar
The tabular Islamic calendarTabular Islamic calendar
The Tabular Islamic 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 arithmetic rules rather than by observation or astronomical calculations...
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.
Leap seconds
The International Earth Rotation and Reference Systems ServiceInternational 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 reference frame standards, notably through its Earth Orientation Parameter and International Celestial Reference System ...
can insert or remove leap seconds from the last day of any month (June and December are preferred). These are sometimes described as intercalary, although the word intercalation strictly applies only to periods of 24 hours or longer.
Other uses
ISO 8601ISO 8601
ISO 8601 Data elements and interchange formats – Information interchange – Representation of dates and times is an international standard covering the exchange of date and time-related data. It was issued by the International Organization for Standardization and was first published in 1988...
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.
See also
- Bahá'í calendarBahá'í calendarThe 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-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... - Celtic calendarCeltic calendarThe 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, and festivals....
- Chinese calendarChinese calendarThe Chinese calendar is a lunisolar calendar, 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 as well...
- Coptic calendarCoptic calendarThe 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 calendarEgyptian calendarThe ancient civil Egyptian calendar had a year that was 360 days long and was divided into 12 months of 30 days each, plus five extra days at the end of the year. The months were divided into three weeks of ten days each...
- Hebrew calendarHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
- Hindu calendarHindu calendarThe 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. Nepali calendar, Bengali calendar, Malayalam calendar, Tamil calendar, Telugu calendar, Kannada...
- Islamic calendarIslamic calendarThe Hijri calendar , also known as the Muslim calendar or Islamic calendar , is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to date events in many Muslim countries , and used by Muslims everywhere to determine the proper day on which to celebrate Islamic...
- Iranian calendarIranian calendarThe Iranian calendars or sometimes called Persian calendars are a succession of calendars invented or used for over two millennia in Greater Iran...
- Thai lunar calendarThai lunar calendarThe Thai lunar calendar , or Dai calendar , Tai calendar, is Thailand's version of the lunisolar Buddhist calendar used in the southeast Asian countries of Cambodia, Laos and Burma, for calculating lunar-regulated holy days...
- Bengali calendarBengali calendarThe Bengali calendar or Bangla calendar is a solar and sidereal Hindu calendar used by the Bengali people. It is used in the eastern Indian states of West Bengal, Assam and Tripura and in Bangladesh...
- Ethiopian calendarEthiopian calendarThe 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 Church, Eastern Catholic Church and Lutheran Evangelical Church of Eritrea...