The word calendar is also used to describe the physical device (often paper) for using the system (for example, desktop calendar), and also a particular set of planned events (for example, court calendar).
Nearly all calendar systems use a unit colloquially called "year" that approximates Earth's tropical year (that is, the time it takes for a complete cycle of seasons) to facilitate the planning of agricultural activities. Many calendars also have a time unit called "month" based on the moon phase in the sky; a lunar calendar is one in which days are numbered within each moon phase cycle. Because the length of the lunar month does not fit as an exact divisor of the length of the tropical year, a purely lunar calendar quickly drifts against the seasons. A lunisolar calendar is a lunar calendar that compensates by adding an extra month as needed to realign the months with the seasons.
In the Roman Empire, the year-based Julian calendar was adopted. It numbers days within months that are longer than the lunar cycle, so it is not convenient for tracking phases of the moon, but it does a better job tracking the seasons. Unfortunately, Earth's tropical year is not an exact multiple of days either (it is approximately 365.2422 days), so it too slowly drifted out of sync with the seasons. For such reasons, the Gregorian calendar was later adopted by most of the Western? starting in 1582, eventually spreading to be the dominant calendar currently in use in the world.
Cultures may define other units of time, such as the week, for the purpose of scheduling regular activities that do not easily coincide with months or years.
There have been a number of proposals for reform of the calendar, such as the World calendar or Perpetual calendar. The United Nations considered adopting such a reformed calendar for a while in the 1950s, but these proposals have lost most of their popularity.
Even where there is a commonly used calendar such as the Gregorian calendar, alternate calendars may also be used, such as a Fiscal calendar.
One example of an alternate calendar is a Fiscal calendar, which might be a 5/4/4 calendar, which fixes each month at a specific number of weeks to facilitate comparisons from month to month and year to year. January always has exactly 5 weeks (Sunday through Saturday), February has 4 weeks, March has 4 weeks, etc. Note that this calendar will normally need to add a 53rd week to every 5th or 6th year, which might be added to December or might not be, depending on how the organization uses those dates. There exists an international standard way doing this (the ISO week). The ISO week runs Monday through Sunday and Week 1 is always the week that contains January 4 Gregorian.
Calendar systems: Gregorian calendar, Julian calendar, Roman calendar, Chinese calendar, Hebrew calendar, Islamic calendar, [Mayan calendar]?, Fiscal calendar ...
A moment is a very small piece of time (how much doesn't matter, so long as it is smaller than the smallest piece of time of interest). A day is a collection of moments; usually, a day is about 24 hours long. A date is the name of a day, according to some naming convention. A calendar is a naming convention for days.
Calendars may be either complete or incomplete. Complete calendars provide a way of naming each consecutive day, while incomplete calendars do not. The early Roman calendar, that had no way of designating the days of the winter months other than to lump them together as "winter" is an example of an incomplete calendar, while the Gregorian calendar is an example of a complete calendar.
Calendars in use on Earth are most frequently lunar, solar?, luni-solar or arbitrary. A lunar calendar is synchronized to the motion of the Moon; an example is the Islamic calendar. A solar calendar is synchronized to the motion of the Sun; an example is the [Persian calendar]?. A luni-solar calendar is synchronized to the motions of both the Moon and the Sun; an example is the Jewish calendar. An arbitrary calendar is not synchronized to either the Moon or the Sun; an example is the [Julian date]? used by astronomers. 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.
Calendars may be pragmatic, theoretical, or mixed.
A pragmatic calendar is one that is based on observation; an example is the religious Islamic calendar. Such a calendar is also referred to as an observation-based or astronomical calendar. The advantage of such a calendar is that it is perfectly and perpetually accurate. The disadvantage is working out when a particular date would occur.
A theoretical calendar is one that is based on a strict set of rules; an example is the Jewish calendar. Such a calendar is also referred to a rule-based or arithmetical calendar. The advantage of such a calendar is the ease of working out when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore if the calendar is very accurate, its accuracy perishes slowly over time owing to changes in Earth's rotation. This limits the lifetime of an accurate theoretical calendar to a few thousand years. After then, the rules would need to be modified from observations made since the invention of the calendar, resulting in a mixed calendar.
A mixed calendar combines the features of both pragmatic and theoretical calendars. Mixed calendars usually begin as theoretical calendars, but are adjusted pragmatically when some type of asynchrony becomes apparent; the shift from the Julian to the Gregorian calendar is such an example.
The Gregorian calendar, as a final example, is complete, solar, and mixed.
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