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Periods in a calendar (such as years and months) are usually, though not necessarily, synchronized with the cycle of the sun or the moon. The most common type of pre-modern calendar was the lunisolar calendar, a lunar calendar that occasionally adds one intercalary month to remain synchronised with the solar year over the long term.
The calendar in most widespread use today is the Gregorian calendar, introduced in the 16th century as a modification of the Julian calendar, which was itself a modification of the ancient Roman calendar. The term calendar itself is taken from calendae, the term for the first day of the month in the Roman calendar, related to the verb calare "to call out", referring to the ,,calling" of the new moon when it was first seen. Latin calendarium meant ,,account book, register" (as accounts were settled and debts were collected on the calends of each month). The Latin term was adopted in Old French as calendier and from there in Middle English as calender by the 13th century (the spelling calendar is early modern).
The course of the Sun and the Moon are the most evident forms of timekeeping, and the year and lunation were most commonly used in pre-modern societies worldwide as time units. Nevertheless, the Roman calendar contained very ancient remnants of a pre-Etruscan 10-month solar year. The first recorded calendars date to the Bronze Age, dependent on the development of writing in the Ancient Near East, the Egyptian and Sumerian calendars.
A larger number of calendar systems of the Ancient Near East becomes accessible in the Iron Age, based on the Babylonian calendar. This includes the calendar of the Persian Empire, which in turn gave rise to the Zoroastrian calendar as well as the Hebrew calendar.
A great number of Hellenic calendars develop in Classical Greece, and with the Hellenistic period also influence calendars outside of the immediate sphere of Greek influence, giving rise to the various Hindu calendars as well as to the ancient Roman calendar.
Calendars in antiquity were lunisolar, depending on the introduction of intercalary months to align the solar and the lunar years. This was mostly based on observation, but there may have been early attempts to model the pattern of intercalation algorithmically, as evidenced in the fragmentary 2nd-century Coligny calendar.
The Roman calendar was reformed by Julius Caesar in 45 BC. The Julian calendar was no longer dependent on the observation of the new moon but simply followed an algorithm of introducing a leap day every four years. This created a dissociation of the calendar month from the lunation.
The Islamic calendar is based on the prohibition of intercalation (nasi') by Muhammad, in Islamic tradition dated to a sermon held on 9 Dhu al-Hijjah AH 10 (Julian date: 6 March 632). This resulted in an observationally based lunar calendar shifting relative to the seasons of the solar year.
The first calendar reform of the early modern era was the Gregorian calendar, introduced in 1582 based on the observation of a long-term shift between the Julian calendar and the solar year.
There have been a number of modern proposals for reform of the calendar, such as the World Calendar, International Fixed Calendar, Holocene calendar, and, recently, the Hanke-Henry Permanent Calendar. Such ideas are mooted from time to time but fail to gain traction because of the loss of continuity, massive upheaval in implementation and religious objections.
A full calendar system has a different calendar date for every day. Thus the week cycle is by itself not a full calendar system; 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. 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 - 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 date system
Calendars with two levels of cycles:
year, month, and day - 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 - e.g., the ISO week date
Cycles can be synchronized with periodic phenomena:
Sun and Moon, Schedel's Nuremberg Chronicle, 1493
Lunar calendars are synchronized to the motion of the Moon (lunar phases); an example is the Islamic calendar.
Solar calendars are based on perceived seasonal changes synchronized to the apparent motion of the Sun; an example is the Persian calendar.
Lunisolar calendars are based on a combination of both solar and lunar reckonings; examples include the traditional calendar of China, the Hindu calendar in India, and the Hebrew calendar.
There are some calendars that appear to be synchronized to the motion of Venus, such as some of the ancient Egyptian calendars; synchronization to Venus appears to occur primarily in civilizations near the Equator.
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 acyclic 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.
Solar calendars assign a date to each solar day. 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. 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 mean solar day. Other types of calendar may also use a solar day.
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 don't vary much near the equator. It does, however, stay constant with respect to other phenomena, notably tides. An example is the Islamic calendar. Alexander Marshack, in a controversial reading, believed that marks on a bone baton (c. 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.
A lunisolar calendar is a lunar calendar that compensates by adding an extra month as needed to realign the months with the seasons. An example is the Hebrew calendar which uses a 19-year cycle.