The Hebrew calendar's leap months follow a rhythm older than the calendar's fixed form: the nineteen year lunisolar cycle. The underlying fact is astronomical. Nineteen solar years and two hundred thirty five lunar months agree with each other to within about two hours, so a calendar that adds a thirteenth month in seven years out of every nineteen keeps its months on the moon and its festivals in their seasons at the same time. Babylonian astronomers standardised intercalation on this cycle by the fifth century BCE, and the Athenian astronomer Meton published it in 432 BCE, which is why the West calls it the Metonic cycle.
The fixed Hebrew calendar embeds it directly: years three, six, eight, eleven, fourteen, seventeen and nineteen of each cycle receive the added month of Adar, and the pattern repeats without observation or decree. The same nineteen year rhythm reached Christian timekeeping through the computus, where the golden number, a year's position in the cycle, located the paschal moon for the date of Easter. Babylonian astronomy yielded a second great period relation, the saros of two hundred twenty three months, after which eclipses repeat; it governs eclipse prediction rather than any calendar, and the two cycles together are the deep arithmetic under this part of the atlas. Neither has an entry of its own by design: they are rhythms, and they live where they are used.