Overview
Key data
| Item | Detail |
|---|---|
| Year head (doujian) | Zhuanxu: jian-hai; Huangdi, Zhou, Lu: jian-zi; Yin: jian-chou; Xia: jian-yin |
| Type | Quarter-remainder calendar |
| Tropical year | 365¼ days |
| Synodic month | 29 + 499/940 days |
| Intercalation | Seven in nineteen years |
The six and their year heads
According to the Han shu the six are, in order, Huangdi, Zhuanxu, Xia, Yin, Zhou and Lu. Their astronomical values are nearly identical; the real difference lies in which month begins the year.
Zhuanxu begins with the tenth month; Huangdi, Zhou and Lu with the eleventh; Yin with the twelfth; Xia with the first.
Why “quarter-remainder”
All six take 365¼ days for the tropical year — the denominator contains four, hence the name. The synodic month is 29 + 499/940 days, and seven intercalations in nineteen years reconcile solar and lunar reckoning. The scheme matches the Greek Metonic cycle, and was the common basis of pre-Qin calendrical work.
The three zheng
Which month heads the year differed by dynasty. The doctrine of the three zheng takes zi as the heavenly, chou as the earthly and yin as the human. The Shiji records:
A quotation
This doctrine is not unassailable. The linguist Wang Li rejected it, noting that though the Qin moved the year head to jian-hai, it still did not call the tenth month the “first,” and the seasonal pairing stayed with the Xia. The year head is one thing, the first month another, and the seasonal pairing a third.
Antiquity and date of composition
The six take the names of Huangdi, Zhuanxu, Xia, Yin, Zhou and Lu, but do not come from those ages. The Song shu says:
A further quotation
Zu Chongzhi held the same view. Zhang Peiyu’s chronological tables place the epochs of all six in the Warring States, Huangdi’s around the third century BCE. The “six ancient calendars” were thus mostly the work of Warring States and Qin calendrists adopting ancient names.
Survival
The originals are long lost. Zhuanxu’s has Qin bamboo slips in support; the other five survive only in fragments in the Han shu and the Kaiyuan Zhanjing, from which their outlines can be reconstructed.
Compiled and arranged by Chujia Kuang.