Definitions for "Metonic cycle"
A period of 19 years which almost exactly equals 235 synodic months.  The Hebrew calendr is based on the Metonic cycle and has 7 years with 13 months and 12 years with 12 months.
" Cycle métonique" A period of almost 19 years (i.e.235 lunations) created by the Athenian astronomer Meton (5th century BC), to obtain a period in which new and full Moon recur on the same day.
The 19 year cycle wherein the conjunctions of the Sun and Moon begin to appear progressively in the zodiac in the same places as in the previous cycle. Discovered by Meton of Athens. This is the cycle whereby the solar and lunar calendars can be approximately synchronised.