Lunisolar calendar

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Record of the Chinese lunisolar calendar for 1834, 1835, and 1836 during the Qing Dynasty under the Daoguang Emperor's Reign (Dao Guang Shi Si Nian ,Dao Guang Shi Wu Nian ,Dao Guang Shi Liu Nian ) Chinese Calendar(Daoguang 15).jpg
Record of the Chinese lunisolar calendar for 1834, 1835, and 1836 during the Qing Dynasty under the Daoguang Emperor's Reign (道光十四年,道光十五年,道光十六年)

A lunisolar calendar is a calendar in many cultures, combining lunar calendars and solar calendars. The date of Lunisolar calendars therefore indicates both the Moon phase and the time of the solar year, that is the position of the Sun in the Earth's sky. If the sidereal year (such as in a sidereal solar calendar) is used instead of the solar year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.


The Five Phases and Four Seasons of the traditional Chinese lunisolar calendar, with English translation. Five Phases and Four Seasons Calendar.png
The Five Phases and Four Seasons of the traditional Chinese lunisolar calendar, with English translation.
1729 Japanese calendar, which used the Jokyo calendar procedure, published by Ise Grand Shrine Jokyo-reki.jpg
1729 Japanese calendar, which used the Jōkyō calendar procedure, published by Ise Grand Shrine

Their months are based on the regular cycle of the Moon's phases. So lunisolar calendars are lunar calendars with – in contrast to them – additional intercalation rules being used to bring them into a rough agreement with the solar year and thus with the seasons.

The main other type of calendar is a solar calendar.


The Buddhist, Burmese, Assyrian, Hebrew, Hindu, Jain and Kurdish as well as the traditional Chinese, Japanese, Korean, Mongolian, Tibetan, and Vietnamese calendars (in the East Asian Chinese cultural sphere), plus the ancient Hellenic, Coligny, and Babylonian calendars are all lunisolar. Also, some of the ancient pre-Islamic calendars in south Arabia followed a lunisolar system. [1] The Chinese, Coligny and Hebrew [2] lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon. The Tibetan calendar was influenced by both the Chinese and Buddhist calendars. The Germanic peoples also used a lunisolar calendar before their conversion to Christianity.

Chinese lunisolar calendar

The Chinese calendar or Chinese lunisolar calendar is also called Agricultural Calendar [農曆; 农历; Nónglì; 'farming calendar'], or Yin Calendar [陰曆; 阴历; Yīnlì; 'yin calendar']), based on the concept of Yin Yang and astronomical phenomena, as movements of the sun, moon, Mercury, Venus, Mars, Jupiter and Saturn (known as the seven luminaries) are the references for the Chinese lunisolar calendar calculations.

The earliest record of the Chinese lunisolar calendar is the Zhou Dynasty (1050 BC – 771 BC). Throughout history, the Chinese lunisolar calendar had many variations and evolved with different dynasties with increasing accuracy, including the "six ancient calendars" in the Warring States Period, the Qin calendar in the Qin Dynasty, the Han calendar or the Taichu calendar in the Han Dynasty and Tang Dynasty, the Shoushi calenar in the Yuan Dynasty, and the Daming calendar in the Ming Dynasty, etc. Starting 1912, the solar calendar is used together with the lunar calendar in China.

The most celebrated Chinese holidays, like the Spring Festival, or the Chinese New Year, Lantern Festival, Mid-Autumn Festival, Dragon Boat Festival, Qingming Festival, etc. are all based on the Chinese lunisolar calendar. And the popular Chinese zodiac is a classification scheme based on the Chinese calendar that assigns an animal and its reputed attributes to each year in a repeating twelve-year cycle.

Moveable feasts in the Gregorian calendar

The solar Gregorian calendar uses the Computus [3] to determine the date of Easter and other moveable feasts with respect to both lunar and solar events.

Islamic calendar

The Islamic calendar is a lunar calendar of exactly 12 months, but not a lunisolar calendar because its date is not related to the Sun; Its solar counterpart is the Solar Hijri calendar, which is used in Iran and Afghanistan. The civil versions of the Julian and Gregorian calendars are solar, because their dates do not indicate the Moon phase – however, both the Gregorian and Julian calendars include undated lunar calendars that allow them to calculate the Christian celebration of Easter, so both are lunisolar calendars in that respect.

Determining leap months

A tropical year is approximately 365.2422 days long and a synodic month is approximately 29.5306 days long, [4] so a tropical year is approximately 365.2422 / 29.5306 ≈ 12.36826 months long. Because 0.36826 is between 13 and 12, a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years. More precisely, 0.36826 is quite close to 719 ≈ 0.3684211 and several lunisolar calendars have 7 leap months in every cycle of 19 years (called a 'Metonic cycle'). The Babylonians applied the 19-year cycle in the late sixth century BCE. [5]

A tropical year is longer than 12 lunar months and shorter than 13 of them. The arithmetical equation 12 × 12 + 7 × 13 = 235 allows it to be seen that a combination of 12 'short' years (12 months) and 7 'long' years (13 months) will be equal to 19 solar years. Intercalation of leap months is frequently controlled by the "epact", which is the difference between the lunar and solar years (approximately 11 days). The Metonic cycle, used in the Hebrew calendar and the Christian ecclesiastical calendars, adds seven months during every nineteen-year period.[ citation needed ] The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12. This adjustment, the saltus lunae, causes the epacts to repeat every 19 years. When the epact reaches 30 or higher, an intercalary month is added and 30 is subtracted. The intercalary years are numbers 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence.[ citation needed ]

The Buddhist and Hebrew calendars restrict the leap month to a single month of the year;[ citation needed ] the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true apparent motion of the Sun,[ citation needed ] their leap months do not usually occur within a couple of months of perihelion, when the apparent speed of the Sun along the ecliptic is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.[ citation needed ]

With uncounted time

An alternative way of dealing with the fact that a solar year does not contain an integer number of lunar months is by including uncounted time in a period of the year that is not assigned to a named month. [6] Some Coast Salish peoples used a calendar of this kind. For instance, the Chehalis began their count of lunar months from the arrival of spawning chinook salmon (in Gregorian calendar October), and counted 10 months, leaving an uncounted period until the next chinook salmon run. [7]

List of lunisolar calendars

The following is a list of lunisolar calendars:

See also


  1. F.C. De Blois, "TAʾRĪKH": I.1.iv. "Pre-Islamic and agricultural calendars of the Arabian peninsula", The Encyclopaedia of Islam, 2nd edition, X:260.
  2. The modern Hebrew calendar, since it is based on rules rather than observations, does not exactly track the tropical year, and in fact the average Hebrew year of ~365.2468 days is intermediate between the tropical year (~365.2422 days) and the sidereal year (~365.2564 days).
  3. Richards 2013, p. 583, 592, §15.4.
  4. P. Kenneth Seidelmann, ed. (1992). Explanatory Supplement to the Astronomical Almanac. p. 577. For convenience, it is common to speak of a lunar year of twelve synodic months, or 354.36707 days. (which gives a mean synodic month as 29.53059 days or 29 days 12 hours 44 minutes and 3 seconds)
  5. "The Babylonian Calendar".
  6. Nilsson, Martin P. (1920), "Calendar Regulation 1. The Intercalation", Primitive Time-Reckoning: A Study in the Origins and First Development of the Art of Counting Time among the Primitive and Early Culture Peoples, Lund: C. W. K. Gleerup, p. 240, The Lower Thompson Indians in British Columbia counted up to ten or sometimes eleven months, the remainder of the year being called the autumn or late fall. This indefinite period of unnamed months enabled them to bring the lunar and solar year into harmony.
  7. Suttles, Wayne P. Musqueam Reference Grammar, UBC Press, 2004, p. 517.

Related Research Articles

Calendar System for organizing the days of year

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 date is the designation of a single, specific day within such a system. A calendar is also a physical record of such a system. A calendar can also mean a list of planned events, such as a court calendar or a partly or fully chronological list of documents, such as a calendar of wills.

Chinese calendar Lunisolar calendar from China

The traditional Chinese calendar, is a lunisolar calendar which identifies years, months, and days according to astronomical phenomena. In China, it is defined by the Chinese national standard GB/T 33661–2017, "Calculation and Promulgation of the Chinese Calendar", issued by the Standardization Administration of China on May 12, 2017.

Hebrew calendar Lunisolar calendar used for Jewish religious observances

The Hebrew calendar, also called Jewish calendar, is a lunisolar calendar used today for Jewish religious observance, and as an official calendar of the state of Israel. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits, and daily Psalm readings, among many ceremonial uses. In Israel, it is used for religious purposes, provides a time frame for agriculture, and is an official calendar for civil holidays, alongside the Gregorian calendar.

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 require intercalations of both days and months.

A leap year is a calendar year that contains an additional day added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have a constant number of days in each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting an additional day or month into some years, the drift between a civilization's dating system and the physical properties of the Solar System can be corrected. A year that is not a leap year is a common year.

Lunar calendar Calendar based on the phases of the Moon

A lunar calendar is a calendar based on the monthly cycles of the Moon's phases, in contrast to solar calendars, whose annual cycles are based only directly on the solar year. The most commonly used calendar, the Gregorian calendar, is a solar calendar system that originally evolved out of a lunar calendar system. A purely lunar calendar is also distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation. The details of when months begin varies from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.

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 ("lunations") are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth–Sun line, are still the basis of many calendars today, and are used to divide the year.

Metonic cycle Span of 235 lunar months close to 19 solar years

The Metonic cycle or enneadecaeteris is a period of approximately 19 years after which the phases of the moon recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic lunar months is just 1 hour, 27 minutes and 33 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar.

A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar. The main other type of calendar is a lunar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of the Moon phase.

Date of Easter Calculation of the date of Easter

As a moveable feast, the date of Easter is determined in each year through a calculation known as computus. Easter is celebrated on the first Sunday after the Paschal full moon, which is the first full moon on or after 21 March. Determining this date in advance requires a correlation between the lunar months and the solar year, while also accounting for the month, date, and weekday of the Julian or Gregorian calendar. The complexity of the algorithm arises because of the desire to associate the date of Easter with the date of the Jewish feast of Passover which, Christians believe, is when Jesus was crucified.

The epact, used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January. Its principal use is in determining the date of Easter by computistical methods. It varies from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.

The history of calendars, that is, of people creating and using methods for keeping track of days and larger divisions of time, covers a practice with ancient roots.

Calendar reform or calendrical reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design.

Babylonian calendar

The Babylonian calendar was a lunisolar calendar with years consisting of 12 lunar months, each beginning when a new crescent moon was first sighted low on the western horizon at sunset, plus an intercalary month inserted as needed by decree. The calendar is based on a Sumerian predecessor preserved in the Umma calendar of Shulgi.

The Buddhist calendar is a set of lunisolar calendars primarily used in mainly South and Southeast Asian countries such as Cambodia, Laos, Sri Lanka, Myanmar and Thailand as well as in Chinese populations of Malaysia and Singapore for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunisolar calendar and by the Thai solar calendar.

Vikram Samvat or Bikram Sambat and also known as the Vikrami calendar, is the historical Hindu calendar used in the Indian subcontinent. It is the official calendar of Nepal. In India it is used in several states. The traditional Vikram Samvat calendar, as used in India, uses lunar months and solar sidereal years. The Nepali Bikram Sambat introduced in 1901 AD, also uses a solar sideral year.

The Ancient Macedonian calendar is a lunisolar calendar that was in use in ancient Macedon in the 1st millennium BCE. It consisted of 12 synodic lunar months, which needed intercalary months to stay in step with the seasons. By the time the calendar was being used across the Hellenistic world, seven total embolimoi were being added in each 19 year Metonic cycle. The names of the ancient Macedonian Calendar remained in use in Syria even into the Christian era.

The Burmese calendar is a lunisolar calendar in which the months are based on lunar months and years are based on sidereal years. The calendar is largely based on an older version of the Hindu calendar, though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with the Metonic cycle's near tropical years by adding intercalary months and days at irregular intervals.

Chula Sakarat or Chulasakarat is a lunisolar calendar derived from the Burmese calendar, whose variants were in use by most mainland Southeast Asian kingdoms down to the late 19th century. The calendar is largely based on an older version of the Hindu calendar though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with Metonic cycle's tropical years by adding intercalary months and intercalary days on irregular intervals.

Nisan-years is an ancient calendar system used around Mesopotamia. Its beginning was from the prehistorical era. Ever since Mesopotamia had historical writings, even before the First Babylonian dynasty of Hammurabi, its calendar used the Nisan-years.