Editing Lunisolar calendar

{{Short description|Calendar with lunar month, solar year}}
{{Distinguish|text=[[Lunarsolar]]}}

[[File:Chinese Calendar(Daoguang 15).jpg|thumb|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 [[culture]]s, that combines monthly [[lunar cycle]]s with the [[solar year]]. As with all calendars which divide the year into months, there is an additional requirement that the year have a whole number of months (Moon cycles). The majority of years have twelve months but every second or third year is an [[embolismic month|embolismic year]], which adds a thirteenth [[Intercalation (timekeeping)|intercalary]], embolismic, or leap month.

Lunisolar calendars are [[lunar calendar]]s but, in contrast to purely lunar calendars such as the [[Islamic calendar]], have additional intercalation rules that reset them periodically into a rough agreement with the solar year and thus with the seasons.

==Examples==
The [[Chinese calendar|Chinese]], [[Buddhist calendar|Buddhist]], [[Burmese calendar|Burmese]], [[Assyrian calendar|Assyrian]],
[[Hebrew calendar|Hebrew]], [[Jain calendar|Jain]], traditional Nepali, [[Hindu calendar|Hindu]], [[Japanese calendar|Japanese]], [[Korean calendar|Korean]], [[Mongolian calendar|Mongolian]], [[Tibetan calendar|Tibetan]], and [[Vietnamese calendar|Vietnamese]] calendars (in the [[East Asian cultural sphere|East Asian Chinese cultural sphere]]), plus the ancient [[Hellenic calendars|Hellenic]], [[Coligny calendar|Coligny]], and [[Babylonian calendar]]s are all lunisolar. Also, some of the ancient [[Islamic calendar#Pre-Islamic calendar|pre-Islamic]] calendars in [[south Arabia]] followed a lunisolar system.<ref name="EI2-Tarikh">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.</ref> The Chinese, Coligny and
Hebrew{{efn|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).}} 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===
{{main|Chinese calendar}}[[File:Five Phases and Four Seasons Calendar.png|thumb|The Five Phases and Four Seasons of the traditional [[Chinese lunisolar calendar]], with English translation.]]

The [[Chinese calendar]] (華夏曆法) 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']), as movements of the sun (representing [[Yin Yang|Yang]]) and moon (representing Yin) are the references for the Chinese lunisolar calendar calculations.{{Citation needed|date=January 2023}} The Chinese lunisolar calendar is the origin of some variant calendars adopted by other neighboring countries, such as Vietnam and Korea. 

Together with astronomical, horological, and [[wikt:phenology|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,{{cn|date=March 2024}} 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&nbsp;BC – 771&nbsp;BC,  around 3000 years ago.<ref>{{Cite journal |title=Considering Chengzhou ("Completion of Zhou") and Wangcheng ("City of the King")  |last=Xu |first=Zhaofeng |journal=Chinese Archaeology |volume=8 |pages=172{{ndash}}177 |url=http://www.kaogu.cn/uploads/soft/Chinese%2520Archaeology/8/Considering%2520Chengzhou%2520('Completion%2520of%2520Zhou')%2520and%2520Wangcheng%2520('City%2520of%2520the%2520King').pdf |access-date=2023-09-20 |archive-url=https://web.archive.org/web/20150722225701/http://www.kaogu.cn/uploads/soft/Chinese%2520Archaeology/8/Considering%2520Chengzhou%2520('Completion%2520of%2520Zhou')%2520and%2520Wangcheng%2520('City%2520of%2520the%2520King').pdf |archive-date=2015-07-22 }}</ref> 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 western solar calendar is used together with the lunisolar calendar in China.

The most celebrated Chinese holidays, such as the [[Chinese New Year]] (華夏新年), [[Lantern Festival]] (元宵節), [[Mid-Autumn Festival]] (中秋節), and [[Dragon Boat Festival]] (端午節) 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 traditional calendar used the [[Sexagenary cycle|sexagenary]] cycle-based [[Chinese calendar correspondence table|''ganzhi'']] system's mathematically repeating cycles of [[Heavenly Stems]] and [[Earthly Branches]].{{cn|date=March 2024}}

==Movable feasts in the Christian calendars, related to the lunar cycle==
The [[Gregorian calendar]] (the world's most commonly used) is a solar one but the [[Western Christianity|Western Christian churches]] use a lunar-based algorithm to determine the [[date of Easter]] and consequent [[movable feast]]s.<ref>{{cite book | last = Richards | first = E. G. | date = 2013 | chapter = Calendars | title = Explanatory Supplement to the Astronomical Almanac | edition = 3rd | editor1-last = Urban | editor1-first = Sean | editor2-last = Seidelmann | editor2-first = P. Kenneth | publisher = University Science Books | location = Mill Valley, CA | isbn = 978-1-891389-85-6 |pages= 583, 592, §15.4}}</ref> 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 Christianity|Eastern Christian churches]] have a similar algorithm that is based on the [[Julian calendar]].

== Reconciling lunar and solar cycles ==

===Determining leap months===
{{More citations needed|section|date=July 2021}}
A [[tropical year]] is approximately 365.2422 [[mean solar day|days]] long and a [[synodic month]] is approximately 29.5306 days long,<ref>{{cite book | title=Explanatory Supplement to the Astronomical Almanac |year=1992 | editor=P. Kenneth Seidelmann |page=577 |url=https://archive.org/details/131123ExplanatorySupplementAstronomicalAlmanac/page/n302/mode/1up | quote=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)</ref> so a tropical year is approximately {{nowrap|365.2422 / 29.5306 ≈ 12.36826}} months long.  Because 0.36826 is between {{1/3}} and {{1/2}}, 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 {{frac|7|19}} (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.<ref>{{Cite web |first=R.H. |last=van Gent |date=July 2021  |url=https://webspace.science.uu.nl/~gent0113/babylon/babycal.htm |title=The Babylonian Calendar |publisher=Utrecht University}}</ref>

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{{snd}} the {{langnf|la|'''saltus lunae'''|leap of the moon}}{{snd}} 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|date=July 2021}}

The Buddhist and Hebrew calendars restrict the leap month to a single month of the year;{{citation needed|date=July 2021}} 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|date=July 2021}} 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|date=July 2021}}

===With uncounted time===
An alternative way of dealing with the fact that a solar year does not contain an integer number of [[lunar month]]s is by including uncounted time in a period of the year that is not assigned to a named month.<ref>{{ Citation | last = Nilsson | first = Martin P. | author-link = Martin P. Nilsson | date = 1920 | title = Primitive Time-Reckoning: A Study in the Origins and First Development of the Art of Counting Time among the Primitive and Early Culture Peoples | chapter = Calendar Regulation 1. The Intercalation | publisher = C. W. K. Gleerup | place = Lund | page = 240 | quote = 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.}}</ref> Some [[Coast Salish peoples]] used a calendar of this kind. For instance, the [[Sts'Ailes|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]].<ref>Suttles, Wayne P. ''Musqueam Reference Grammar'', UBC Press, 2004, p. 517.</ref>

== List of lunisolar calendars <span class="anchor" id="List of lunisolar calendars"></span> <!-- [[List of lunisolar calendars]] redirects here --> ==
The following is a list of lunisolar calendars sorted by family.
{{div col}}
* [[Babylonian calendar]] family &ndash; common use of the Metonic cycle
** [[Ancient Macedonian calendar]]
** [[Hebrew calendar]]
** [[Umma calendar]]
* [[Hindu calendar]] family &ndash; shared astronomical roots
** [[Vikram Samvat]]
** [[Buddhist calendar]]
** [[Burmese calendar]] ([[Pyu]] calendar)
*** [[Chula Sakarat]]
** [[Nepal Sambat]]
** [[Thai lunar calendar]]
** [[Vira Nirvana Samvat]] ([[Jain]] calendar)
<!-- The Bengali, Malayalam, Tamil, Tulu, Punjabi and Nanakshahi calendars are all solar calendar. Please do not add any of them. -->
* [[Chinese calendar]] family &ndash; years start on second new moon after winter solstice (save for leaps)
** [[Japanese calendar]]
** [[Korean calendar]]
** [[Mongolian calendar]]
** [[Tibetan calendar]]
** [[Vietnamese calendar]]
* Unclassified or independent
** [[Attic calendar]]
** A lunisolar calendar devised by [[Plethon]], né Georgios Gemistos, in his Book of Laws
** [[Egyptian calendar#Ptolemaic calendar|Ptolemic Egyptian calendar]]
** [[Inca Empire#Measures, calendrics and mathematics|Inca calendar]]
** [[Celtic calendar]], including [[Coligny calendar]]
** [[Muisca calendar]]
** [[Nisga'a#Calendar/life|Nisg̱a'a calendar]]
** [[Month#Eastern Ojibwe calendar|Old Eastern Ojibwe calendar]]
{{div col end}}

==See also==
*[[List of calendars]]
*{{anli|Callippic cycle}}
*[[Calendar reform]]
*{{anli|Nasi'}}
*Other non-solar calendars <!-- Please do not repeat calendars that are already described in the article -->
**[[Roman calendar]] (<!-- since 450 BC -->probably a lunisolar calendar with [[common year]]s of 355 days and [[leap year]]s of 378 days.)
**{{anli|Runic calendar}}

==Notes==
{{notelist}}

==References==
{{reflist}}

==Further reading==
* {{Cite book | last1 = Dershowitz | first1 = Nachum | author-link = Nachum Dershowitz | last2 = Reingold | first2 = Edward M. | author2-link = Edward M. Reingold  | date = 2008 | title = Calendrical Calculations |title-link= Calendrical Calculations | publisher = Cambridge University Press | location = Cambridge | isbn = 9780521885409 }}

==External links==
{{Commons category|Lunisolar calendars}}
*[http://aa.usno.navy.mil/faq/docs/calendars.php Introduction to Calendars] {{Webarchive|url=https://web.archive.org/web/20190613115330/https://aa.usno.navy.mil/faq/docs/calendars.php |date=2019-06-13 }}, US Naval Observatory, Astronomical Applications Department.
*[http://www.quadibloc.com/science/cal02.htm Luni-Solar Calendar]

{{Calendars}}
{{The Moon}}
{{Chronology}}

[[Category:Calendars]]
[[Category:Lunisolar calendars| ]]
[[Category:Phases of the Moon|*]]