Calendar change in the Qin and Han periods

The Qin inheritance

Qin began the year with the tenth lunar month, and early Han government initially retained this arrangement. The numbered months therefore ran from month 10 through months 11 and 12, followed by months 1 to 9. Month numbering and the point at which the year number changed were separate conventions.

Calendar reform also had political meaning. Qin associated its rule with Water in the five-phase system and adopted black as an official colour. Han debates over the dynasty's place in this succession connected the calendar, ceremonial colours and legitimate rule. Changing the year boundary could express the establishment of a new order, even while much of the inherited method of calculation remained in use.

The calendar had to coordinate lunar months with the seasonal year. Twelve lunar months are shorter than a seasonal year, so additional months were needed at intervals. Officials also required a sequence of month beginnings and daily designations for their records. Deciding when the administrative year began was only one part of this larger task.

The Taichu reform

Emperor Wu's Taichu reform of 104 BCE established month 1, traditionally associated with the beginning of spring, as the start of the year. Taichu also became the name of a new reign era. The reform's astronomical framework developed into the Santong system associated with Liu Xin, whose procedures survive in the Hanshu, or History of the Former Han. This later formulation incorporates developments beyond the original reform.

The project brought together different kinds of expertise. Tang Du worked on the heavens, Luoxia Hong performed calendrical calculations, and Deng Ping's method was selected after rival proposals were examined. Observing equipment and comparisons between predictions and celestial phenomena helped the court decide which method to authorize.

Calculations needed an epoch: a defined starting point from which elapsed days and astronomical cycles could be counted. Aligning a new moon, winter solstice and a particular cyclical day at an ideal epoch had symbolic as well as computational appeal. The resulting procedures had to connect the Sun's seasonal cycle, the Moon's phases and the continuous count of days.

The Taichu–Santong tradition used a mean lunar month of 29 days plus 43/81 of a day, approximately 29.530864 days. Repeated addition of this mean interval supplied a calculated sequence of new moons. These were mean new moons calculated at uniform intervals. Later methods allowed for the uneven motions of the Sun and Moon when assigning month beginnings.

A nineteen-year framework reconciled the lunar and seasonal cycles. Nineteen ordinary twelve-month years contain 228 months. Adding seven leap months gives 235 lunar months, close to nineteen seasonal years. This cycle provided a practical scheme for intercalation, though later calendars did not all retain a fixed nineteen-year pattern.

Han reform continued with the Eastern Han Sifen calendar, which entered official use in 85 CE. Its name, meaning “quarter remainder,” refers to the quarter-day component of its year length.

The Sifen calendar used a year of 365¼ days. Its adoption revised the numerical relationship between months and years while retaining a lunisolar structure. Even small differences in a mean interval could accumulate over repeated calculations.

Excavated records

Bamboo and wooden documents preserve dates from the working life of Qin and Han administration. A dated entry may combine a reign year, lunar month and day name from the Ganzhi, or stem-and-branch cycle. Some records also give the numbered lunar day or identify a leap month. These details help reconstruct the calendar actually used for the document.

A pairing of a numbered lunar day with its cyclical name provides an internal check. Counting backward through the sixty-day cycle gives the name of the month's first day. Dates from successive months can then help establish month lengths. Because the cycle repeats every sixty days, a day name alone cannot determine an absolute date.

Excavated records also help test the calendrical accounts preserved in the Shiji, or Records of the Grand Historian, and the Hanshu. A discrepancy may arise from a copied character, an uncertain reading or an incorrect reconstruction of month beginnings and leap months. This is why a complete early calendar cannot always be recovered by applying one later formula backward. The original month and day designations remain essential to the chronology.