# Calendopaedia - Lunar Calendars

### The Lunar Year

Most calendars are based on the solar year.
Solar years have the disadvantage of not being easily observable. Many years
of observations are required to fix them with any significant degree of
accuracy. On the other hand, the phases of the Moon -- and the first
visibility after the new moon in particular -- are very easy and quick to
observe. Therefore, the first calendars defined a lunar year, usually
consisting of 12 synodic months. A synodic month is the interval from one new
moon to the next and lasts 29.530588 days. This is equivalent to 29 days,
12 hours, 44 minutes and 2.9 seconds. Since for practical reasons a
month should contain an integer number of days, most calendars alternated
between months of 29 and 30 days, respectively. A year made out of six
months of each type has 354 days and is thus too short by 0.3672 days as
compared with a true lunar year. Therefore lunar calendars have to insert one leap day
about every third year to keep in step with the moon phases. A pure lunar
calendar is not synchronous with the seasons and after 16 years will put
the winter in the summer and vice versa. Over a period of 32 years it will
cycle through a complete year.

### The Luni-Solar Year

A luni-solar year is the attempt to combine the phases of the moon and the
seasons into one calendar. This is possible if leap months are inserted.
Several schemes were used in history. The best known solution was found by
the Greek Meton in the year 432 BC but apparently was known to other cultures
before. The Metonic cycle encompasses a total of 235 months of which 125 are
*full* (i.e. they have 30 days) and 110 are `hollow' (having 29 days). The
months are combined into 12 normal years with 12 months each and 7 leap years
with 13 months each. The cycle covers 6940 days whereas 225 synodic months
sum up to 6939.688 days and 19 tropical years to 6939.602 days. The difference
in motion between Sun and Moon amounts to only 0.0866 days so that eclipses
repeat in the Metonic cycle with high accuracy.

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