Lunar calendar

Lunar calendar

A lunar calendar is a calendar that is based on cycles of the moon phase. The only widely used purely lunar calendar is the Islamic calendar or Hijri calendar, whose year always consists of 12 lunar months. A feature of a purely lunar year, on the Islamic calendar model, is that the calendar ceases to be linked to the seasons, and drifts each year by 11 days (or 12 days in case of leap year), and comes back to the position it had in relation to the solar year approximately every 33 Islamic years. It is used predominantly for religious purposes. In Saudi Arabia it is also used for commercial purposes.

Most lunar calendars, except the Hijri, are in fact lunisolar calendars. That is, months are kept on a lunar cycle, but then intercalary months are added to bring the lunar cycles into synchronisation with the solar year.

Because there are about twelve lunations (synodic months) in a solar year, this period (354.37 days) is sometimes referred to as a lunar year.

Lunisolar calendars

Most lunar calendars are, in fact, lunisolar; such as the Chinese, Hebrew, and Hindu calendars, and most calendar systems used in antiquity.

All these calendars have a variable number of months in a year. The reason for this is that a year is not evenly divisible by an exact number of lunations, so without the addition of intercalary months the seasons would drift each year. This results in a thirteen-month year every two or three years.

Start of the lunar month

Lunar calendars differ as to which day is the first day of the year.

For some lunar calendars, such as the Chinese calendar, the first day of a month is the day when an eclipse moon appears in a particular time zone.

Many other lunar calendars are based on the first sighting of a lunar crescent.

Length of the lunar month

The length of a month orbit/cycle is difficult to predict and varies from its average value. Because observations are subject to uncertainty and weather conditions, and astronomical methods are highly complex, there have been attempts to create fixed arithmetical rules.

The average length of the synodic month is 29.530589 days. This means the length of a month is alternately 29 and 30 days (termed respectively hollow and full). The distribution of hollow and full months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed:

   29 /   1   (error: 1 day after about  2 months)
   30 /   1   (error: 1 day after about  2 months)
   59 /   2   (error: 1 day after about 33 months)
  443 /  15   (error: 1 day after about 30 years)
  502 /  17   (error: 1 day after about 70 years)
 1447 /  49   (error: 1 day after about 3 millennia)
25101 / 850 (error: dependent on change of synodic month value}

These fractions can be used in the construction of lunar calendars, or in combination with a solar calendar to produce a lunisolar calendar. The 49-month cycle was proposed as the basis of an alternative Easter computation by Isaac Newton around 1700 . The tabular Islamic calendar's 360-month cycle is equivalent to 24×15 months minus a correction of one day.

Old English 13-month lunar year

In England, a calendar of thirteen months of 28 days each, plus one extra day, known as "a year and a day" was still in use up to Tudor times. This would be a hybrid calendar that had substituted regular weeks of seven days for actual quarter-lunations, so that one month had exactly four weeks, regardless of the actual moon phase. The "lunar year" is here considered to have 364 days, resulting in a solar year of "a year and a day".

As a religious tradition, the thirteen-month years survived among European peasants for more than a millennium after the adoption of the Julian Calendar and now the Gregorian Calendar.

The "Edwardian" (probably Edward II, late 13th or early 14th century) ballad of Robin Hood for example has "How many merry months be in the year? / There are thirteen, I say ...", amended by a Tudor editor to "...There are but twelve, I say....". Robert Graves in the introductions to Greek Myths comments on this with "Thirteen, the number of the sun's death-month, has never lost its evil reputation among the superstitious."

Even in the late 20th century, British financial institutions were still administering lunar mortgages, requiring an annual adjustment.

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