Intercalary Month

Overview

An intercalary month (also called an embolismic or leap month) is an additional month inserted into a lunisolar calendar to correct the drift between the calendar year and the solar year. A 12-month lunar year is approximately 354 days, about 11 days shorter than the solar year of roughly 365.2422 days. Without periodic corrections, the months would gradually shift out of alignment with the seasons.

The Metonic Cycle

In 432 BCE, the Athenian astronomer Meton introduced into the Greek calendar the relationship that 19 solar years correspond almost exactly to 235 lunar months. Babylonian astronomers had already been using the same relationship since the late 6th century BCE. Based on this 19-year cycle, 7 intercalary months are inserted over the span of 19 years. The Hebrew calendar applies the 19-year cycle as a fixed rule, while the Chinese agricultural calendar and the traditional Japanese calendar determine intercalations from astronomical calculation and so arrive at roughly the same frequency. The specific rules for which month receives the intercalation vary by system - in the Chinese calendar, the intercalary month is the one that contains no major solar term (zhongqi).

Modern Relevance

Although the Gregorian calendar is now the international standard, intercalary months still affect cultural events across East Asia. The date of Lunar New Year shifts each year because months begin on the day of the new moon and intercalary months are added on top of that cycle. For software handling traditional calendar dates, the existence of intercalary months means the "month" value can reach 13, a case that must be accounted for in date libraries and validation logic.