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A calendar is a system of organizing days for social, religious, commercial or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. A date is the designation of a single, specific day within such a system. Periods in a calendar (such as years and months) are usually, though not necessarily, synchronized with the cycle of the sun or the moon. Many civilizations and societies have devised a calendar, usually derived from other calendars on which they model their systems, suited to their particular needs.
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 computerized systems, which can be set to remind the user of upcoming events and appointments.
A calendar can also mean a list of planned events, such as a court calendar.
The English word calendar is derived from the Latin word kalendae, which was the Latin name of the first day of every month.
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:
Calendars with two levels of cycles:
Cycles can be synchronized with periodic phenomena:
Very commonly a calendar includes more than one type of cycle, or has both cyclic and acyclic elements.
Many calendars incorporate simpler calendars as elements. For example, the rules of the Hebrew calendar depend on the seven-day week cycle (a very simple calendar), so the week is one of the cycles of the Hebrew 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 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.
There have been a number of proposals for reform of the calendar, such as the World Calendar, International Fixed Calendar, Holocene calendar, and, recently, the Hanke-Henry Permanent 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.
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.
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 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 was Year 18 of the Emperor Akihito.
An astronomical calendar is based on ongoing 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 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 calendar. The advantage of such a calendar is the ease of calculating when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore, even if the calendar is very accurate, its accuracy diminishes slowly over time, owing to changes in Earth's rotation. This limits the lifetime of an accurate arithmetic calendar to a few thousand years. After then, the rules would need to be modified from observations made since the invention of the calendar.
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.
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 to help people manage their personal schedules, time and activities, particularly when individuals have numerous work, school, and family commitments. People frequently use multiple systems, and may keep both a business and family calendar to help prevent them from overcommitting their time.
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.
Calendars in widespread use today include the Gregorian calendar, which is the de facto international standard, and is used almost everywhere in the world for civil purposes. Due to the Gregorian calendar's obvious connotations of Western Christianity, non-Christians and even some Christians sometimes replace the traditional era notations "AD" and "BC" ("Anno Domini" and "Before Christ") with "CE" and "BCE" ("Common Era" and "Before Common Era"). Even where there is a commonly used calendar such as the Gregorian calendar, alternative calendars may also be used, such as a fiscal calendar or the astronomical year numbering system.
The Islamic calendar, Muslim calendar or Hijri calendar is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to date events in most of the Muslim countries (concurrently with the Gregorian calendar), and used by Muslims everywhere to determine the proper day on which to celebrate Islamic holy days and festivals. The first year was the year during which the emigration of the Prophet Muhammad from Mecca to Medina, known as the Hijra, occurred. Each numbered year is designated either H for Hijra or AH for the Latin anno Hegirae (in the year of the Hijra). Being a purely lunar calendar, it is not synchronized with the seasons. With an annual drift of 11 or 12 days, the seasonal relation is repeated approximately each 33 Islamic years.
The Hijri-Shamsi calendar, also adopted by the Ahmadiyya Muslim Community, is based on solar calculations and is similar to the Gregorian calendar in its structure with the exception that the first year starts with Hijra.
The lunisolar Hindu calendars are some of the most ancient calendars of the world. The names of the twelve months are the same in most parts of India (because they are named in Sanskrit) though the spelling and pronunciation vary slightly and the first month of the year varies from one region to another depending upon past traditions. The standardized Indian national calendar based on Saka era with 78 CE as the start of the calendar is a lunar Hindu calendar used by the government together with Gregorian calendar. However, it is not used by the general public which widely uses the Vikrami lunar calendar Vikram Samvat with 56 BCE as the start of the calendar for religious activities and festivals. Vikram Samvat is also the official calendar in Nepal. A lunar month may have 29 or 30 days. All Hindu calendars have about 360 days and they insert an additional 13th month (by repeating a month twice in that year) every few years to synchronize with solar calendar. If the repeated month is, say, Chaitra, the repeated month is named Chaitra-2. In the next cycle, a month other than Chaitra will be repeated.
Eastern Christians of eastern Europe and western Asia used for a long time the Julian Calendar, that of the old Orthodox church, in countries like Russia. For over 1500 years, Westerners used the Julian Calendar as well.
While the Gregorian calendar is widely used in Israel's business and day-to-day affairs, the Hebrew calendar, used by Jews worldwide for religious and cultural affairs, also influences civil matters in Israel (such as national holidays) and can be used there for business dealings (such as for the dating of checks). The Chinese, Hebrew, Hindu, and Julian calendars are widely used for religious and/or social purposes. The Iranian (Persian) calendar is used in Iran and some parts of Afghanistan. The Ethiopian calendar or Ethiopic calendar is the principal calendar used in Ethiopia and Eritrea, with the Oromo calendar also in use in some areas. In neighboring Somalia, the Somali calendar co-exists alongside the Gregorian and Islamic calendars. In Thailand, where the Thai solar calendar is used, the months and days have adopted the western standard, although the years are still based on the traditional Buddhist calendar. Bahá'ís worldwide use the Bahá'í calendar.
A fiscal calendar generally means the accounting year of a government or a business. It is used for budgeting, keeping accounts and taxation. It is a set of 12 months that may start at any date in a year. The US government's fiscal year starts on 1 October and ends on 30 September. The government of India's fiscal year starts on 1 April and ends on 31 March. Small traditional businesses in India start the fiscal year on Diwali festival and end the day before the next year's Diwali festival.
In accounting (and particularly accounting software), a fiscal calendar (such as a 4/4/5 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 4 weeks (Sunday through Saturday), February has 4 weeks, March has 5 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 starts on a Monday, and ends on a Sunday. Week 1 is always the week that contains 4 January in the Gregorian calendar.
A calendar is also a physical device (often paper) (for example, a desktop calendar or a wall calendar). In a paper calendar one or two sheets 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 indicate the current date and weekday. This is the most common usage of the word.
In the USA Sunday is considered the first day of the week and so appears on the far left and Saturday the last day of the week appearing on the far right. In Britain the weekend may appear at the end of the week so the first day is Monday and the last day is Sunday. The US calendar display is also used in Britain.
It is common to display the Gregorian calendar in separate monthly grids of seven columns (from Monday to Sunday, or Sunday to Saturday depending on which day is considered to start the week — this varies according to country) and five to six rows (or rarely, four rows when the month of February contains 28 days beginning on the first day of the week), with the day of the month numbered in each cell, beginning with 1.
When working with weeks rather than months, a continuous format is sometimes more convenient, where no blank cells are inserted to ensure that the first day of a new month begins on a fresh row. Unlike with geographical maps, where many famous projections are known (such as the Mercator projection), the calendar projection is a matter of such triviality that no names for these exist in common circulation.
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