Chinese Luni-Solar Calendar

The traditional Chinese calendar is lunisolar: its months follow the moon, beginning at the new moon, while an intercalary month is added about every three years to keep the year in step with the sun and hold the solar terms in their seasons. An ordinary year of twelve months runs 353 to 355 days and a leap year of thirteen runs 383 to 385. Its most distinctive feature is the reckoning of years, months, days, and hours by the sexagenary cycle, the sixty combinations formed by pairing the ten Heavenly Stems with the twelve Earthly Branches, which also carry the familiar twelve-year animal zodiac. The calendar governs the Lunar New Year, the traditional festivals, and the almanac used to choose auspicious days. These are the features of the Chinese calendrical tradition, which also underlies the calendars of Korea, Vietnam, and elsewhere in East Asia.

The rule for inserting the intercalary month is fixed by astronomy rather than by a simple periodic count: a leap month is added whenever a lunar month contains no zhongqi, a major solar term, of the twenty-four that divide the solar year; because the solar terms average slightly longer than a lunar month, such a term-less month occurs roughly once every two to three years and is designated a repeat of the month before it, for example a second Fourth Month. This rule was formalised under the Han dynasty's Taichu calendar of 104 BCE and refined through successive imperial reforms, most recently the Shixian calendar introduced under Jesuit astronomical influence in 1645, which remains the algorithmic basis of the calendar's modern civil computation.

Every calendar in the world solves the same arithmetic problem, and there are only three solutions. A lunation is about 29.53 days and a tropical year about 365.2422 days, and the second is not a whole multiple of the first. A calendar can therefore follow the Moon and let its year drift against the sun, follow the sun and let its months lose contact with the Moon, or follow both and insert an extra month at intervals to keep them together.

The Chinese calendar takes the third path, and it is the most astronomically demanding of the major lunisolar systems because it fixes both the month and the intercalation by true positions rather than by a cycle. A month begins on the day of the astronomical new moon, so months are 29 or 30 days as the Moon actually runs, and the eleventh month is defined as the one containing the winter solstice.

Intercalation follows from the twenty-four solar terms rather than from a nineteen-year rule. A lunar month that contains none of the twelve major terms is declared a leap month and takes the number of the month before it, so a year can have thirteen months without any fixed schedule saying which years those are.

Running alongside all of this is the sexagenary cycle of ten stems and twelve branches, which names years, months, days and double hours and is independent of every astronomical quantity. The day count in particular has run without interruption since the Shang oracle bones, which makes it the longest continuously operating day count known and a check on Chinese historical chronology in its own right.