Calendar

A calendar is a system for naming periods of time, typically days. These names are known as calendar dates. The dates may be based on the perceived motion of astronomical objects. A calendar is also a physical device (often paper) that illustrates the system (for example, a desktop calendar) — this is the most common usage of the word.

Other calendar types

Complete and incomplete calendars

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, which 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.

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Pragmatic, theoretical and mixed calendars

Calendars may be pragmatic, theoretical, or mixed.

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A pragmatic calendar is one that is based on observation; examples are the religious Islamic calendar and the old religious Jewish calendar in the time of the Second Temple. 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 that working out when a particular date would occur is difficult.

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A theoretical calendar is one that is based on a strict set of rules; an example is the current 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.

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A mixed calendar combines the features of both pragmatic and theoretical calendars. Mixed calendars usually begin as theoretical calendars, but are adjusted pragmatically

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when some type of asynchrony becomes apparent; the shift from the Julian to the Gregorian calendar is such an example.

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The Gregorian calendar, as a final example, is complete, solar, and mixed.

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