Lunisolar calendar

A lunisolar calendar is a sophisticated system used by many cultures to track time. It combines the monthly cycles of the moon with the solar year. Most calendars divide a year into months based on lunar cycles. However, a purely lunar calendar can drift away from the solar seasons. To prevent this, lunisolar calendars use specific rules to stay in sync with the sun. This balance allows people to track both the phases of the moon and the changing seasons.

The need for this system comes from a mathematical gap between the sun and moon. A tropical year lasts approximately 365.2422 days. A single synodic month, which is one lunar cycle, lasts about 29.5306 days. If you multiply twelve lunar months, the total is much shorter than a full solar year. To fix this, these calendars use intercalation. This process adds an extra month, known as an intercalary or embolismic month, to certain years. Most years have twelve months, but an extra thirteenth month is added every second or third year.

One famous way to manage these extra months is the Metonic cycle. This cycle was applied by the Babylonians in the late sixth century BCE. It relies on a 19-year period that includes seven leap months. These leap months occur in years 3, 6, 8, 11, 14, 17, and 19 of the cycle. The Hebrew and Julian calendars both use this specific sequence. Astronomers often use a value called the epact to control this. The epact is the difference between the lunar and solar years, which is about 11 days. By incrementing this value each year, the calendar can decide exactly when to add a month.

Different lunisolar calendars track different celestial movements. Some, like the Chinese and Hebrew calendars, track the tropical year. This helps them stay aligned with the seasons on Earth. Others, such as the Buddhist and Hindu calendars, track the sidereal year. This means they track the position of the full moon among the constellations. Because of these different goals, the timing of leap months can vary. For example, the Chinese and Hindu calendars use the true apparent motion of the sun. This means their leap months do not usually happen near perihelion, when the sun's apparent speed is fastest.

The Chinese lunisolar calendar is one of the most well-known examples. It is often called an agricultural or farming calendar. It also refers to the movements of the sun as Yang and the moon as Yin. The earliest records of this system date back to the Zhou dynasty, between 1050 BC and 771 BC. Over thousands of years, many versions evolved through different dynasties. These include the Qin, Han, Tang, Yuan, and Ming calendars. While China began using the Western solar calendar in 1912, the lunisolar system remains vital for culture.

This calendar system deeply influences many traditions and celebrations. The most famous Chinese holidays are based on these lunar and solar cycles. These include the Chinese New Year, the Lantern Festival, the Mid-Autumn Festival, and the Dragon Boat Festival. The Chinese zodiac is also a classification scheme based on this calendar. It assigns an animal to each year in a repeating twelve-year cycle. Even the popular concept of Heavenly Stems and Earthly Branches comes from this mathematical system.

Lunisolar principles appear in many other cultures and even in religious traditions. The Hebrew, Buddhist, Burmese, and Japanese calendars all use lunisolar methods. Other examples include the ancient Babylonian, Assyrian, and Hellenic calendars. Even some ancient pre-Islamic calendars in south Arabia followed this system. Interestingly, some Western Christian churches use a lunar-based algorithm to find the date of Easter. They look for the ecclesiastical full moon that follows the March equinox. This shows how many different systems try to reconcile the moon and the sun to organize human life.