Lunar calendar
Encyclopedia
A lunar calendar is a calendar
that is based on cycles of the lunar phase
. A common purely lunar calendar is the Islamic calendar
or Hijri calendar. A feature of the Islamic calendar is that a year is always 12 months, so the months are not linked with the seasons and drift each solar year by 11 to 12 days. It comes back to the position it had in relation to the solar year approximately every 33 Islamic years. It is used mainly for religious purposes, and in Saudi Arabia
it is also used for commercial purposes. Because there are about twelve lunations (synodic months) in a solar year, this period (354.37 days) is sometimes referred to as a lunar year. The Hebrew calendar also uses a fixed ratio (12+7/19) so it will eventually drift, such that Passover would be in autumn.
s. That is, months reflect the lunar cycle, but then intercalary
months (e.g. "second Adar" in the Hebrew Calendar
) are added to bring the calendar year into synchronisation with the solar year. Some examples are the Chinese
and Hindu
calendars, and most calendar systems used in antiquity.
All these calendars have a variable number of months in a year. The reason for this is that a year is not evenly divisible by an exact number of lunation
s, so without the addition of intercalary
months the seasons would drift each year. This results in a thirteen-month year every two or three years.
Some lunar calendars are calibrated by annual natural events which are affected by lunar cycles as well as the solar cycle. An example of this is the lunar calendar of the Banks Islands
which includes three months in which the edible palolo worm
mass on the beaches. These events occur at the last quarter of the lunar month, as the reproductive cycle of the palolos is synchronised with the moon.
Even though the Gregorian calendar is in common and legal use, lunar calendars serve to determine traditional holidays in parts of the world such as China
, Japan
, Vietnam
, India
. Some examples include Chinese New Year
/Tết
(Vietnamese New Year) and Mid-Autumn Festival
/Chuseok
.
occurs in a particular time zone. For others, such as some Hindu calendars, each month begins on the day after the full moon or the new moon. Others were based in the past on the first sighting of a lunar crescent, such as the Hebrew calendar.
The average length of the synodic month is 29.530589 days. This requires the length of a month to be alternately 29 and 30 days (termed respectively hollow and full). The distribution of hollow and full months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed:
These fractions can be used in the construction of lunar calendars, or in combination with a solar calendar to produce a lunisolar calendar. The 49-month cycle was proposed as the basis of an alternative Easter computation
by Isaac Newton
around 1700. The tabular Islamic calendar
's 360-month cycle is equivalent to 24×15 months minus a correction of one day.
Calendar
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...
that is based on cycles of the lunar phase
Lunar phase
A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon, and Sun...
. A common purely lunar calendar is the Islamic calendar
Islamic calendar
The 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...
or Hijri calendar. A feature of the Islamic calendar is that a year is always 12 months, so the months are not linked with the seasons and drift each solar year by 11 to 12 days. It comes back to the position it had in relation to the solar year approximately every 33 Islamic years. It is used mainly for religious purposes, and in Saudi Arabia
Saudi Arabia
The Kingdom of Saudi Arabia , commonly known in British English as Saudi Arabia and in Arabic as as-Sa‘ūdiyyah , is the largest state in Western Asia by land area, constituting the bulk of the Arabian Peninsula, and the second-largest in the Arab World...
it is also used for commercial purposes. Because there are about twelve lunations (synodic months) in a solar year, this period (354.37 days) is sometimes referred to as a lunar year. The Hebrew calendar also uses a fixed ratio (12+7/19) so it will eventually drift, such that Passover would be in autumn.
Lunisolar calendars
Most lunar calendars are in fact lunisolar calendarLunisolar 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. That is, months reflect the lunar cycle, but then intercalary
Intercalation
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 calendars may require intercalations of both days and months.- Solar calendars :...
months (e.g. "second Adar" in the 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...
) are added to bring the calendar year into synchronisation with the solar year. Some examples are the Chinese
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...
and Hindu
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...
calendars, and most calendar systems used in antiquity.
All these calendars have a variable number of months in a year. The reason for this is that a year is not evenly divisible by an exact number of 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 without the addition of intercalary
Intercalation
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 calendars may require intercalations of both days and months.- Solar calendars :...
months the seasons would drift each year. This results in a thirteen-month year every two or three years.
Some lunar calendars are calibrated by annual natural events which are affected by lunar cycles as well as the solar cycle. An example of this is the lunar calendar of the Banks Islands
Banks Islands
The Banks Islands are a group of islands in northern Vanuatu.Together with the Torres Islands to the northwest, they make up the northernmost province of Torba. The group lies about north of Maewo, and includes Gaua and Vanua Lava, two of the 13 largest islands in Vanuatu...
which includes three months in which the edible palolo worm
Palolo worm
The palolo worm or Samoan palolo worm is a species of invertebrate in the Eunicidae family. They live in tropical coral reefs. Adults are about long and resemble spaghetti when viewed underwater.-Life cycle:...
mass on the beaches. These events occur at the last quarter of the lunar month, as the reproductive cycle of the palolos is synchronised with the moon.
Even though the Gregorian calendar is in common and legal use, lunar calendars serve to determine traditional holidays in parts of the world such as China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...
, Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
, Vietnam
Vietnam
Vietnam – sometimes spelled Viet Nam , officially the Socialist Republic of Vietnam – is the easternmost country on the Indochina Peninsula in Southeast Asia. It is bordered by China to the north, Laos to the northwest, Cambodia to the southwest, and the South China Sea –...
, India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
. Some examples include Chinese New Year
Chinese New Year
Chinese New Year – often called Chinese Lunar New Year although it actually is lunisolar – is the most important of the traditional Chinese holidays. It is an all East and South-East-Asia celebration...
/Tết
Tet
Tet can mean:*Tết or Tết Nguyên Đán, the Vietnamese new year**Tet Offensive, a military campaign that began in 1968*Têt in Roussillon, France*Equal temperament, abbreviated as 12-TET, 19-TET and so on...
(Vietnamese New Year) and Mid-Autumn Festival
Mid-Autumn Festival
The Mid-Autumn Festival , also known as the Moon Festival or Mooncake Festival or Zhongqiu Festival, is a popular lunar harvest festival celebrated by Chinese and Vietnamese people. A description of the festival first appeared in Rites of Zhou, a written collection of rituals of the Western Zhou...
/Chuseok
Chuseok
Chuseok , originally known as Hangawi , is a major harvest festival and a three-day holiday in Korea celebrated on the 15th day of the 8th month of the lunar calendar. Like many other harvest festivals, it is held around the Autumn Equinox...
.
Start of the lunar month
Lunar calendars differ as to which day is the first day of the month. For some lunar calendars, such as the Chinese calendar, the first day of a month is the day when an astronomical new moonNew moon
In astronomical terminology, the new moon is the lunar phase that occurs when the Moon, in its monthly orbital motion around Earth, lies between Earth and the Sun, and is therefore in conjunction with the Sun as seen from Earth...
occurs in a particular time zone. For others, such as some Hindu calendars, each month begins on the day after the full moon or the new moon. Others were based in the past on the first sighting of a lunar crescent, such as the Hebrew calendar.
Length of the lunar month
The length of a month orbit/cycle is difficult to predict and varies from its average value. Because observations are subject to uncertainty and weather conditions, and astronomical methods are highly complex, there have been attempts to create fixed arithmetical rules.The average length of the synodic month is 29.530589 days. This requires the length of a month to be alternately 29 and 30 days (termed respectively hollow and full). The distribution of hollow and full months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed:
- 29 / 1 (error: 1 day after about 2 months)
- 30 / 1 (error: 1 day after about 2 months)
- 59 / 2 (error: 1 day after about 33 months)
- 443 / 15 (error: 1 day after about 30 years)
- 502 / 17 (error: 1 day after about 70 years)
- 1447 / 49 (error: 1 day after about 3 millennia)
- 25101 / 850 (error: dependent on change of synodic month value)
- 765433 / 25920 (error: 1 day after about 16 millennia)
These fractions can be used in the construction of lunar calendars, or in combination with a solar calendar to produce a lunisolar calendar. The 49-month cycle was proposed as the basis of an alternative Easter computation
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....
by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
around 1700. The tabular Islamic calendar
Tabular 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...
's 360-month cycle is equivalent to 24×15 months minus a correction of one day.
See also
- Lunar phaseLunar phaseA lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon, and Sun...
- 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....
- 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...
- EpactEpactThe epact was originally defined as the age of the moon in days on January 1, and occurs primarily in connection with tabular methods for determining the date of Easter...