Calendar

== Systems ==
[[Image:Universal Calendar including a meton cycle.svg|350px|thumb|A universal calendar, combining different calendars]]

A full calendar system has a different calendar date for every day.<ref>{{Cite book |last=Onlineverdan |url=https://books.google.com/books?id=f3uMDwAAQBAJ&newbks=0&printsec=frontcover&pg=SA10-PA6&dq=A+full+calendar+system+has+a+different+calendar+date+for+every+day&hl=vi |title=APTITUDE & REASONING for GATE & ESE 2020 |publisher=Infinity Educations |isbn=978-81-940294-3-4 |pages=10-6 |language=en}}</ref><ref>{{Cite book |last=Jain |first=Hemant |url=https://books.google.com/books?id=G4yEDwAAQBAJ&newbks=0&printsec=frontcover&pg=SA8-PA5&dq=A+full+calendar+system+has+a+different+calendar+date+for+every+day&hl=vi |title=RRB Junior Engineer (2019) - MATHEMATICS for 1st STAGE CBT |date=2019-01-21 |publisher=Infinity Educations |isbn=978-81-939356-9-9 |pages=8-5 |language=en}}</ref> Thus the week cycle is by itself not a full calendar system;<ref>{{Cite book |last=Jain |first=Hemant |url=https://books.google.com/books?id=G4yEDwAAQBAJ&newbks=0&printsec=frontcover&pg=SA8-PA5&dq=Thus+the+week+cycle+is+by+itself+not+a+full+calendar+system&hl=vi |title=RRB Junior Engineer (2019) - MATHEMATICS for 1st STAGE CBT |date=2019-01-21 |publisher=Infinity Educations |isbn=978-81-939356-9-9 |pages=8-5 |language=en}}</ref> neither is a system to name the days within a year without a system for identifying the years.

The simplest calendar system just counts time periods from a reference date.<ref>{{Cite book |last=Jain |first=Hemant |url=https://books.google.com/books?id=G4yEDwAAQBAJ&newbks=0&printsec=frontcover&pg=SA8-PA6&dq=The+simplest+calendar+system+just+counts+time+periods+from+a+reference+date.&hl=vi |title=RRB Junior Engineer (2019) - MATHEMATICS for 1st STAGE CBT |date=2019-01-21 |publisher=Infinity Educations |isbn=978-81-939356-9-9 |pages=8-6 |language=en}}</ref> This applies for the [[Julian day]] or [[Unix Time]]. Virtually the only possible variation is using a different reference date, in particular, one less distant in the past to make the numbers smaller. Computations in these systems are just a matter of addition and subtraction.

Other calendars have one (or multiple) larger units of time.

Calendars that contain one level of cycles:
* week and weekday&nbsp;– this system (without year, the week number keeps on increasing) is not very common
* year and ordinal date within the year, e.g., the [[ISO 8601#Ordinal dates|ISO 8601 ordinal date system]]

Calendars with two levels of cycles:
* year, month, and day&nbsp;– most systems, including the [[Gregorian calendar]] (and its very similar predecessor, the [[Julian calendar]]), the [[Islamic calendar]], the [[Solar Hijri calendar]] and the [[Hebrew calendar]]
* year, week, and weekday&nbsp;– e.g., the [[ISO week date]]

Cycles can be synchronized with periodic phenomena:
[[File:Sun and Moon Nuremberg chronicle.jpg|250px|thumbnail|right|[[Sun]] and [[Moon]], Schedel's Nuremberg Chronicle, 1493]]
* [[Lunar calendar]]s are synchronized to the motion of the Moon ([[lunar phase]]s); an example is the Islamic calendar.
* [[Solar calendar]]s are based on perceived [[seasonal year|seasonal]] changes synchronized to the apparent motion of the Sun; an example is the [[Persian calendar]].
* [[Lunisolar calendar]]s are based on a combination of both solar and lunar reckonings; examples include the [[Chinese calendar|traditional calendar of China]], the [[Hindu calendar]] in India and Nepal, and the Hebrew calendar.
* The week cycle is an example of one that is not synchronized to any external phenomenon (although it may have been derived from lunar phases, beginning anew every month).

Very commonly a calendar includes more than one type of cycle or has both cyclic and non-cyclic elements.

Most calendars incorporate more complex cycles.   For example, the vast majority of them track years, months, weeks and days.   The seven-day week is practically universal, though its use varies. It has run uninterrupted for millennia.{{sfn|Zerubavel | 1985}}

===Solar===
{{main|Solar calendar}}

Solar calendars assign a ''date'' to each [[solar time|solar day]].<ref>{{Cite web |title=Introduction to Calendars |url=https://aa.usno.navy.mil/faq/calendars |access-date=2024-03-12 |website=aa.usno.navy.mil}}</ref> A day may consist of the period between [[sunrise]] and [[sunset]], with a following period of [[night]], or it may be a period between successive events such as two sunsets.<ref>{{Cite book |url=https://books.google.com/books?id=drMzAQAAMAAJ&newbks=0&printsec=frontcover&pg=PA983&dq=A+day+may+consist+of+the+period+between+sunrise+and+sunset,+with+a+following+period+of+night&hl=vi |title=The Jurist |date=1861 |publisher=S. Sweet |pages=983 |language=en}}</ref><ref>{{Cite book |last=Oxossi |first=Diego de |url=https://books.google.com/books?id=FN11EAAAQBAJ&newbks=0&printsec=frontcover&pg=PT37&dq=A+day+may+consist+of+the+period+between+sunrise+and+sunset,+with+a+following+period+of+night&hl=vi |title=Sacred Leaves: A Magical Guide to Orisha Herbal Witchcraft |date=2022-07-08 |publisher=Llewellyn Worldwide |isbn=978-0-7387-6721-5 |language=en}}</ref> The length of the interval between two such successive events may be allowed to vary slightly during the year, or it may be averaged into a [[solar time|mean solar day]]. Other types of calendar may also use a solar day.

The Egyptians appear to have been the first to develop a solar calendar,<ref>{{Cite web |title=Solar calendar {{!}} Ancient Egypt, Mayan, Aztec {{!}} Britannica |url=https://www.britannica.com/science/solar-calendar |access-date=2024-03-12 |website=www.britannica.com |language=en}}</ref> using as a fixed point the annual sunrise reappearance of the Dog Star—[[Sirius]], or Sothis—in the eastern sky, which coincided with the annual flooding of the Nile River.<ref>{{Cite book |url=https://books.google.com/books?id=mXsoAQAAIAAJ&newbks=0&printsec=frontcover&dq=The+Egyptians+appear+to+have+been+the+first+to+develop+a+solar+calendar,&q=The+Egyptians+appear+to+have+been+the+first+to+develop+a+solar+calendar,&hl=vi |title=The New Encyclopædia Britannica: Micropædia |date=1991 |publisher=Encyclopædia Britannica |isbn=978-0-85229-529-8 |pages=941 |language=en}}</ref><ref>{{Cite book |last=Lawson |first=Russell M. |url=https://books.google.com/books?id=kwTHEAAAQBAJ&newbks=0&printsec=frontcover&pg=PT179&dq=The+Egyptians+appear+to+have+been+the+first+to+develop+a+solar+calendar,&hl=vi |title=Science in the Ancient World: From Antiquity through the Middle Ages |date=2021-09-23 |publisher=Bloomsbury Publishing USA |isbn=979-8-216-14241-6 |language=en}}</ref><ref>{{Cite book |last=Muntz |first=Charles |url=https://books.google.com/books?id=VGHODQAAQBAJ&newbks=0&printsec=frontcover&pg=PT16&dq=The+Egyptians+appear+to+have+been+the+first+to+develop+a+solar+calendar,&hl=vi |title=Diodorus Siculus and the World of the Late Roman Republic |date=2017-01-02 |publisher=Oxford University Press |isbn=978-0-19-064901-2 |language=en}}</ref> They built a calendar with 365 days, divided into 12 months of 30 days each, with 5 extra days at the end of the year. However, they didn't include the extra bit of time in each year, and this caused their calendar to slowly become inaccurate.<ref>{{Cite web |title=Solar calendar &#124; chronology &#124; Britannica |url=https://www.britannica.com/science/solar-calendar}}</ref>

===Lunar===
{{Main|Lunar calendar}}
Not all calendars use the solar year as a unit. A lunar calendar is one in which days are numbered within each [[lunar phase]] cycle.  Because the length of the [[lunar month]] is not an even fraction of the length of the [[tropical year]], a purely lunar calendar quickly drifts against the seasons, which do not vary much near the equator.  It does, however, stay constant with respect to other phenomena, notably [[tide]]s. An example is the [[Islamic calendar]].
Alexander Marshack, in a controversial reading,<ref>James Elkins, ''[https://books.google.com/books?id=5Ku6YdWurMgC&pg=PA63&lpg=PA63 Our beautiful, dry, and distant texts]'' (1998) 63ff.</ref> believed that marks on a bone baton ({{Circa|25,000 BC}}) represented a lunar calendar. Other marked bones may also represent lunar calendars. Similarly, Michael Rappenglueck believes that marks on a 15,000-year-old cave painting represent a lunar calendar.<ref>{{cite news |url=http://news.bbc.co.uk/2/hi/science/nature/975360.stm |title=Oldest lunar calendar identified |work=BBC News |date=16 October 2000 |access-date=14 March 2013 |archive-date=11 February 2021 |archive-url=https://web.archive.org/web/20210211233146/http://news.bbc.co.uk/2/hi/science/nature/975360.stm |url-status=live }}</ref>

===Lunisolar===
A [[lunisolar calendar]] is a lunar calendar that compensates by adding an extra month as needed to realign the months with the seasons. Prominent examples of lunisolar calendar are [[Hindu calendar]] and [[Buddhist calendar]] that are popular in [[South Asia]] and [[Southeast Asia]]. Another example is the Hebrew calendar, which uses a [[metonic cycle|19-year cycle]].