Full Moon Cycle and The Year
Formulated in another way: the full moon cycle is the period that it takes the Sun to return to the perigee of the Moon's orbit (as seen from the Earth). So it is a kind of "perigee year", similar to the eclipse year which is the time for the Sun to return to the ascending node of the Moon's orbit on the ecliptic.
Why does a full moon cycle last almost 14 lunations rather than just the 12.37 lunations of a year? This would be the case, if the moon's orbit kept a constant orientation with respect to the stars, but the tidal effect of the Sun causes the orbit to precess over a cycle just under 9 years. In that time, the number of full moon cycles passed becomes one less than the number of sidereal years passed.
Hence the full moon cycle can be defined such that the lunar precession cycle is the beat period of the full moon cycle and sidereal year. See lunar precession.
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