A lunar calendar is a calendar that is based on cycles of the lunar 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 solar year by 11 to 12 days, 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.
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.
Some lunar calendars are calibrated by annual natural events which are affected by lunar cycles as well as the solar cycle. An example of this is the lunar calendar of the Banks Islands which includes three months in which the edible palolo worm mass on the beaches. These events occurs at the last quarter of the lunar month, as the reproductive cycle of the palolos is synchronised with the moon.
Start of the lunar month
Lunar calendars differ as to which day is the first day of the month. For some lunar calendars, such as the Chinese calendar, the first day of a month is the day when an astronomical new moon appears in a particular time zone. For others, such as some Hindu calendars, each month begins at full moon. Others were based in the past on the first sighting of a lunar crescent, such as the Hebrew calendar.
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 requires the length of a month to be 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:
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