Faces of the Moon
See also: earthquakes and the moon, new corn moon, cycles of the moon.
In attempting to measure the Cycles of the Phases of the Moon, several longer scales of measure have been discovered. Curiously, the larger the span of time, the more accurate the measure, as if approaching a limit.
Metonic Cycle:
235 Lunations = 19 years = 6, 940 days
Calliptic Cycle:
940 lunations = 76 years = 27, 259 days
Hipparchic Cycle:
3, 760 lunations -1 day = 304 years -1 day = 111, 035 days
The Chinese Calendar inserts a 13th lunar month to account for the difference between the lunar year and the solar year, about 11 days.
7 leap months in 19 years
144 leap months in 391 years