Hebrew Month - Principles - Leap Years

Leap Years

The Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common (non-leap) years of 12 months and 7 are leap years of 13 months. To determine whether a Jewish year is a leap year, one must find its position in the 19-year Metonic cycle. This position is calculated by dividing the Jewish year number by 19 and finding the remainder. For example, the present Jewish year 5773 divided by 19 results in a remainder of 16, indicating that it is year 16 of the Metonic cycle. Since there is no year 0, a remainder of 0 indicates that the year is year 19 of the cycle. (See also Golden number (time).)

Years 3, 6, 8, 11, 14, 17, and 19 the Metonic cycle are leap years. To assist in remembering this sequence, some people use the mnemonic Hebrew word GUCHADZaT "גוחאדז"ט", where the Hebrew letters gimel-vav-het aleph-dalet-zayin-tet are used as Hebrew numerals equivalent to 3, 6, 8, 1, 4, 7, 9. The keviyah merely records whether the year is leap or common; פ for p'shutah, meaning simple and indicating a common year, and מ indicating a leap year.

Another memory aid notes that intervals of the major scale follow the same pattern as do Jewish leap years, with do corresponding to year 19 (or 0): a whole step in the scale corresponds to two common years between consecutive leap years, and a half step to one common year between two leap years. This connection with the major scale is more remarkable in the context of 19 equal temperament.

A mathematical way to determine leap year is to calculate the remainder using the following calculation: (7 × the Jewish year number + 1) / 19; if the remainder is less than 7, the year is a leap year. Also, rounding the result of (7 × the Jewish year number + 1) / 13 to the nearest whole number calculates a 0 for leap years and 1 for common years.