Calendar

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A calendar is a system for naming periods of time, typically days. These names are known as calendar dates. Cycles in a calendar are often synchronised with the perceived motion of astronomical objects.

A calendar is also a physical device (often paper). This is the most common usage of the word. Other similar types of calendars can include computerised systems, which can be set to remind the user of upcoming events and appointments.

As a subset, 'calendar' is also used to denote a list of particular set of planned events (for example, court calendar).

Calendar systems[]

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 days from a reference day. This applies for the Julian day. Virtually the only possible variation is using a different reference day, 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, more commonly, 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, and the Hebrew calendar
year, week, and weekday - e.g. the ISO week date

Cycles can be synchronised with periodic phenomena:

A lunar calendar is synchronized to the motion of the Moon (lunar phases); an example is the Islamic calendar.
A solar calendar is based on perceived seasonal changes synchronized to the apparent motion of the Sun without taking the lunar cycles into account; an example is the Persian 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. A lunisolar calendar is synchronized both to the motion of the Moon and to the apparent motion of the Sun; an example is the Jewish calendar.

Many calendars incorporate simpler calendars as elements. For example, the rules of the Jewish calendar depend on the seven-day week cycle (a very simple calendar), so the week is one of the cycles of the Jewish calendar. It is also common to operate two calendars simultaneously, usually providing unrelated cycles, and the result may also be considered a more complex calendar. For example, the Gregorian calendar has no inherent dependence on the seven-day week, but in Western society the two are used together, and calendar tools indicate both the Gregorian date and the day of week.

The week cycle is shared by various calendar systems (although the significance of special days such as Friday, Saturday, and Sunday varies). Systems of leap days usually do not affect the week cycle. The week cycle was not even interrupted when 10, 11, 12, or 13 dates were skipped when the Julian calendar was replaced by the Gregorian calendar by various countries.

Solar calendars[]

Days used by solar calendars[]

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.

Calendar reform[]

See the main article on Calendar reform

There have been a number of proposals for reform of the calendar, such as the World Calendar, International Fixed Calendar, Symmetry454 Calendar, and Sol 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.

Lunar calendars[]

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. It does, however, stay constant with respect to other phenomena, notably tides. A lunisolar calendar is a lunar calendar that compensates by adding an extra month as needed to realign the months with the seasons. Examples are the Jewish calendar, which bases its intercalation of months on the 19-year Metonic cycle, and the Chinese calendar, which is an observational calendar with a set of rules regarding when to insert leap months.

Lunar calendars are believed to be the oldest calendars invented by mankind. Cro-Magnon people are claimed to have invented one around 32,000 BC.

Fiscal calendars[]

A fiscal calendar (such as a 5/4/4 calendar) 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 to do this (the ISO week). The ISO week runs Monday through Sunday and Week 1 is always the week that contains January 4 Gregorian.

Calendar subdivisions[]

Nearly all calendar systems group consecutive days into "months" and also into "years". In a solar calendar a year approximates Earth's tropical year (that is, the time it takes for a complete cycle of seasons), traditionally used to facilitate the planning of agricultural activities. In a lunar calendar, the month approximates the cycle of the moon phase. Consecutive days may be grouped into other periods such as the week.

Because the number of days in the tropical year is not a whole number, a solar calendar must have a different number of days in different years. This may be handled, for example, by adding an extra day (29 February) in leap years. The same applies to months in a lunar calendar and also the number of months in a year in a lunisolar calendar. This is generally known as intercalation. Even if a calendar is solar, but not lunar, the year cannot be divided entirely into months that never vary in length.

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. Many cultures use different baselines for their calendars' starting years. For example, the year in Japan is based on the reign of the current emperor--2006 would be Year 18 of the Emperor Akihito.

Other calendar types[]

Accuracy Types[]

Calendars have different ways of maintaining accuracy. Either they can refer directly to observations or just use an arithmetic rules.

An astronomical calendar 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 pragmatic 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.

An arithmetic 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 as a rule-based or theoretical calendar. The advantage of such a calendar is the ease of working out when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore, even if the calendar is very accurate, its accuracy perishes slowly over time owing to the slowing of Earth's rotation and the gradual changes in the length of the tropical year and the synodic month. 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.

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.

Uses[]

The primary practical use of a calendar is to identify days: to be informed about and/or to agree on a future event and to record an event that has happened. Days may be significant for civil, religious or social reasons. For example, a calendar provides a way to determine which days are religious or civil holidays, which days mark the beginning and end of business accounting periods, and which days have legal significance, such as the day taxes are due or a contract expires. Also a calendar may, by identifying a day, provide other useful information about the day such as its season.

Calendars are also used as part of a complete timekeeping system: date and time of day together specify a moment in time. In the modern world, written calendars are no longer an essential part of such systems, as the advent of accurate clocks has made it possible to record time independently of astronomical events.

Physical calendars[]

A calendar is also a physical device (often paper) (for example, a desktop calendar); one sheet can show a single day, a week, a month, or a year. If a sheet is for a single day, it easily shows the date and the weekday. If a sheet is for multiple days it shows a conversion table to convert from weekday to date and back. With a special pointing device, or by crossing out past days, it may show what the current date and weekday is. This is the most common usage of the word.

The sale of physical calendars has been restricted in some countries, and given as a monopoly to universities and national academies. Examples include the Prussian Academy of Sciences and the University of Helsinki, which had a monopoly on the sale of calendars in Finland until the 1990s.

Calendars in computing[]

30 Boxes
Active calendar
hCalendar
iCalendar
Calendrical software
Calendrical algorithms

Sources[]

Calendrical Calculations; Nachum Dershowitz and Edward M. Reingold; Cambridge University Press, 1997; ISBN 0-521-56474-3; Book Info; Online Calculator
Mapping Time, the calendar and its history; E G Richards; Oxford University Press, 1998; ISBN 0-19-850413-6
A comparative Calendar of the Iranian, Muslim Lunar, and Christian Eras for Three Thousand Years; Ahmad Birashk; Mazda Publishers, 1993; ISBN 0-939214-95-4
The Comprehensive Hebrew Calendar; Arthur Spier; Feldheim Publishers, 1986; ISBN 0-87306-398-8
High Days and Holidays in Iceland; Árni Björnsson; Mál og menning, 1995; ISBN 9979-3-0802-8
Explanatory Supplement to the Astronomical Almanac; P. Kenneth Seidelmann, ed.; University Science Books, 1992; ISBN 0-935702-68-7; Chapter 12: Calendars by L. E. Doggett
Sun, Moon, and Sothis; Lynn E. Rose; Kronos Press, 1999; ISBN 0-917994-15-9