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Have you heard the joke that old-school/Catskill Jewish comedians love to tell about the timing of the Jewish holidays? The punch line revolves around the idea that the Jewish holidays are never “on time.” They are either “early” or “late.”  Compare the starting dates of Rosh Hashanah, Chanukah, and Pesach/Passover for the last two years. Rosh Hashanah 2015 started on September 13^th (“early”), and in 2016 it will start on October 2^nd (“late”.) Chanukah 2015 started on December 6^th (“early”) and it will start on December 24^th this year (“late”.) Pesach 2015 started on April 3^rd (“early”.) This year, 2016, it will start on April 22^nd (“late”.) Why does the timing of Jewish holidays vary from year to year?

 Jewish holidays are “fixed.” Each year they occur on the same day of the same Hebrew month. For example, Passover always starts at nightfall on the 15^th of Nissan. The Jewish calendar is based on three astronomical phenomena: the rotation of the Earth about its axis (a day); the revolution of the moon about the Earth (a month); and the revolution of the Earth about the sun (a year). These three phenomena are independent of each other, so there is no direct correlation between them. On average, the moon revolves around the Earth in about 29½ days. The Earth revolves around the sun in about 365¼ days, that is, about 12.4 lunar months.

The civil calendar used by most of the world has abandoned any correlation between the moon cycles and the month, arbitrarily setting the length of months to 28, 30 or 31 days. The Jewish calendar, however, coordinates all three of these astronomical phenomena. Months are either 29 or 30 days, corresponding to the 29½-day lunar cycle. Years are either 12 or 13 months, corresponding to the 12.4 month solar cycle. .

The problem with strictly lunar calendars is that there are approximately 12.4 lunar months in every solar year, so a 12-month lunar calendar is about 11 days shorter than a solar year and a 13-month lunar calendar is about 19 days longer than a solar year. The months drift around the seasons on such a calendar. On a 12-month lunar calendar, the month of Nissan, which is supposed to occur in the spring, would occur 11 days earlier in the season each year, eventually occurring in the winter, then the fall, then the summer, and then the spring again. With a 13-month lunar calendar, the same thing would happen in the other direction, and faster.

To compensate for this drift, the Jewish calendar uses a 12-month lunar calendar with an extra month occasionally added. The month of Nissan occurs 11 days earlier each year for two or three years, and then jumps forward 30 days, balancing out the drift. In ancient times, this month was added by observation: the Sanhedrin observed the conditions of the weather, the crops and the livestock, and if these were not sufficiently advanced to be considered "spring," then the Sanhedrin inserted an additional month into the calendar to make sure that Passover would occur in the spring.

A year with 13 months is referred to in Hebrew as Shanah Me'uberet, literally: a pregnant year. In English, we commonly call it a leap year. The additional month is known as Adar I, Adar Rishon (first Adar) or Adar Alef. The extra month is inserted before the regular month of Adar (known in such years as Adar II, Adar Sheini or Adar Beit). Adar I 5776 starts on March 10^th 2016 and Adar II starts on April 11^th 2016. Purim falls on March 23^rd 2016 and is celebrated during Adar I (the 14^th of Adar I.)

In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations. This calendar, still in use, standardized the length of months and the addition of months over the course of a 19 year cycle, so that the lunar calendar realigns with the solar years. Adar I is added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the cycle.

The current cycle began in the Jewish year 5758 (the year that began October 2, 1997). If you are musically inclined, you may find it helpful to remember this pattern of leap years by reference to the major scale: for each whole step there are two regular years and a leap year; for each half-step there is one regular year and a leap year. This is easier to understand when you examine the keyboard illustration below and see how it relates to the leap years above.

In addition, Yom Kippur should not fall adjacent to Shabbat, because this would cause difficulties in coordinating the fast with Shabbat, and Hoshanah Rabbah should not fall on Saturday because it would interfere with the holiday's observances. A day is added to the month of Cheshvan or subtracted from the month of Kislev of the previous year to prevent these things from happening.