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, incorporating 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 some 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 Chinese, Buddhist, Burmese, Assyrian, Hebrew, Jain and Kurdish as well as the traditional Nepali, Hindu, 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 [lower-alpha 1] 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.

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 [ citation needed ] 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.[ citation needed ] The Chinese lunisolar calendar is believed to be the origin of some variant calendars used in other neighboring countries, such as Vietnam and Korea.

The traditional calendar calendars used the sexagenary cycle-based ganzhi system's mathematically repeating cycles of Heavenly Stems and Earthly Branches.[ citation needed ] Together with astronomical, horological, and phenological observations, definitions, measurements, and predictions of years, months, and days were refined. Astronomical phenomena and calculations emphasized especially the efforts to mathematically correlate the solar and lunar cycles from the perspective of the earth,[ citation needed ] which however are known to require some degree of numeric approximation or compromise.

The earliest record of the Chinese lunisolar calendar was in the Zhou dynasty (1050 BC – 771 BC, around 3000 years ago. [2] 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 calendar in the Yuan dynasty, and the Daming calendar in the Ming dynasty, etc. Starting in 1912, the solar calendar is used together with the lunar calendar in China.

The most celebrated Chinese holidays, such as Spring Festival (Chunjie, 春節), also known as the Chinese New Year, Lantern Festival (元宵節), Mid-Autumn Festival (中秋節), Dragon Boat Festival (端午節), and Qingming Festival (清明節) are all based upon the Chinese lunisolar calendar. In addition, 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.

The Gregorian calendar (the world's most commonly used) is a solar one but the Western Christian churches use a lunar-based algorithm to determine the date of Easter and consequent movable feasts. [3] Briefly, the date is determined with respect to the ecclesiastical full moon that follows the ecclesiastical equinox in March. (These events are almost, but not quite, the same as the actual astronomical observations.) The Eastern Christian churches have a similar algorithm that is based on the Julian calendar.

Reconciling lunar and solar cycles

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 (about 0.3684211): 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]

Intercalation of leap months is frequently controlled by the "epact", which is the difference between the lunar and solar years (approximately 11 days). 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  the saltus lunae ( Latin for 'leap of the moon')  which 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 Metonic cycle states that 7 of 19 years will contain an additional intercalary month and those years are numbered: 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 sorted by family.

See also


  1. 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 about 365.2468 days is intermediate between the tropical year (about 365.2422 days) and the sidereal year (about 365.2564 days).

Related Research Articles

<span class="mw-page-title-main">Calendar</span> 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 and 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.

<span class="mw-page-title-main">Chinese calendar</span> Lunisolar calendar from China

The traditional Chinese calendar is a lunisolar calendar, combining the solar, lunar, and other cycles for various social and religious purposes. More recently, in China and Chinese communities the Gregorian calendar has been adopted and adapted in various ways, and is generally the basis for standard civic purposes, but incorporating traditional lunisolar holidays. However, there are many types and subtypes of the Chinese calendar, partly reflecting developments in astronomical observation and horology, with over a millennium plus history. The major modern form is the Gregorian calendar-based official version of the Mainland China, although diaspora versions are also notable in other parts of China and Chinese-influenced cultures; however, aspects of the traditional lunisolar calendar remain popular, including the association of the twelve animals of the Chinese Zodiac in relation to months and years.

<span class="mw-page-title-main">Hebrew calendar</span> Lunisolar calendar used for Jewish religious observances

The Hebrew calendar, also called the Jewish calendar, is a lunisolar calendar used today for Jewish religious observance and as an official calendar of Israel. It determines the dates of Jewish holidays and other rituals, such as yahrzeits and the schedule of public Torah readings. 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 days or months.

A leap year is a calendar year that contains an additional day compared to a common year. The 366th day is added to keep the calendar year synchronised with the astronomical year or seasonal year. Since astronomical events and seasons do not repeat in a whole number of days, calendars having a constant number of days each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting ("intercalating") an additional day—a leap day—or month—a leap month—into some years, the drift between a civilization's dating system and the physical properties of the Solar System can be corrected.

<span class="mw-page-title-main">Lunar calendar</span> 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 on the solar year. The most widely observed purely lunar calendar is the Islamic calendar. A purely lunar calendar is distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation – such as by insertion of a leap month. The details of when months begin vary 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 of months arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days, making for roughly 12.37 such months in one Earth year. 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.

<span class="mw-page-title-main">Metonic cycle</span> 19-year pattern in lunisolar calendars

The Metonic cycle or enneadecaeteris is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 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.

<span class="mw-page-title-main">New moon</span> First lunar phase, the definition varies

In astronomy, the new moon is the first lunar phase, when the Moon and Sun have the same ecliptic longitude. At this phase, the lunar disk is not visible to the naked eye, except when it is silhouetted against the Sun during a solar eclipse.

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 types of calendar are lunar calendar and lunisolar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of the Moon phase.

The Hindu calendar, also called Panchanga, is one of various lunisolar calendars that are traditionally used in the Indian subcontinent and Southeast Asia, with further regional variations for social and Hindu religious purposes. They adopt a similar underlying concept for timekeeping based on sidereal year for solar cycle and adjustment of lunar cycles in every three years, but differ in their relative emphasis to moon cycle or the sun cycle and the names of months and when they consider the New Year to start. Of the various regional calendars, the most studied and known Hindu calendars are the Shalivahana Shaka found in the Deccan region of Southern India and the Vikram Samvat (Bikrami) found in Nepal and the North and Central regions of India – both of which emphasize the lunar cycle. Their new year starts in spring. In regions such as Tamil Nadu and Kerala, the solar cycle is emphasized and this is called the Tamil calendar and Malayalam calendar and these have origins in the second half of the 1st millennium CE. A Hindu calendar is sometimes referred to as Panchangam (पञ्चाङ्गम्), which is also known as Panjika in Eastern India.

<span class="mw-page-title-main">Date of Easter</span> Calculation of its date

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. 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 covers practices with ancient roots as people created and used various methods to keep track of days and larger divisions of time. Calendars commonly serve both cultural and practical purposes and are often connected to astronomy and agriculture.

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.

<span class="mw-page-title-main">Babylonian calendar</span> Lunisolar calendar

The Babylonian calendar was a lunisolar calendar used in Mesopotamia from around the second millennium BCE until the Seleucid Era, and it was specifically used in Babylon from the Old Babylonian Period until the Seleucid Era. The civil lunisolar calendar was used contemporaneously with an administrative calendar of 360 days, with the latter used only in fiscal or astronomical contexts. The lunisolar calendar descends from an older Sumerian calendar used in the 4th and 3rd millennia BCE.

The Buddhist calendar is a set of lunisolar calendars primarily used in Tibet, Cambodia, Laos, Myanmar, India, Sri Lanka, Thailand and Vietnam as well as in Malaysia and Singapore and by Chinese populations 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 lunar calendar and by the Thai solar calendar.

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.


  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. Xu, Zhaofeng. "Considering Chengzhou ("Completion of Zhou") and Wangcheng ("City of the King")" (PDF). Chinese Achaeology. 8: 172–177. Archived from the original (PDF) on 2015-07-22. Retrieved 2023-09-20.
  3. Richards, E. G. (2013). "Calendars". In Urban, Sean; Seidelmann, P. Kenneth (eds.). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, CA: University Science Books. pp. 583, 592, §15.4. ISBN   978-1-891389-85-6.
  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. van Gent, R.H. (July 2021). "The Babylonian Calendar". Utrecht University.
  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.

Further reading