This section assembles empirical research and textual criticism on traditional Chinese calendrics, the 24 solar terms, the sexagenary (ganzhi) system, and ancient astronomical archives. By cross-referencing modern astrodynamic datasets with classic historical documents, these short essays trace the evolution of year-beginnings and calendar reforms. All materials strictly archive objective astronomical facts, completely excluding any astrological or divinatory interpretations.
This essay is about a calendar known almost entirely from a single sentence. The histories record that Qin Shi Huang, having unified the realm, adopted the 「颛顼历」, the Zhuanxu calendar, and fixed the head of the year at the tenth month; and that the Han took the same calendar over without change until the Taichu reform of 104 BCE. What the calendar itself looked like — how many days the year held, which months were long and which short, where the intercalary month was placed, which day began a month — the transmitted texts do not say. Excavated bamboo slips do. This piece sets the three textual statements against three groups of excavated calendar manuscripts: the calendar for the thirty-fourth year of Qin Shi Huang (213 BCE) from tomb no. 30 at Zhoujiatai in Jingzhou; the eighteen-slip calendar from tomb no. 247 at Zhangjiashan, running from the fifth year of Han Gaozu to the second year of Empress Lü (202–186 BCE); and the thirty-two-slip table from tomb no. 2 at Yinqueshan, for the first year of Yuanguang (134 BCE), which corrects an error carried for a thousand years by the Song Zizhi tongjian mulu. It explains why the intercalary month was called 「后九月」, the “latter ninth month”; sets out the Qin–Chu month-name concordance from the Shuihudi Rishu; and separates what the slips can be shown to support from what remains inference. Where a point is one view among others rather than a general one, it is labelled 【一说】 (one view). The piece is descriptive and carries no prediction.
Fig. 1 Bamboo slips of a Rishu (day-book) of the Qin-Han period, shown for reference; these are not the slips excavated at Fangmatan. Source: Wikimedia Commons, “Qin Rishu Bamboo Slips” (CC0) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Keywords: Zhuanxu calendar; 颛顼历; Qin calendar; early Han calendar; 后九月; intercalary month; bamboo slips; Zhoujiatai; Zhangjiashan; Yinqueshan; Shuihudi; Qin and Chu month names; Chinese calendrics
Fig. 2 The Mawangdui silk manuscripts. Silk manuscripts from Han tomb no. 3 at Mawangdui, Changsha. Related material shown for reference, not the Wuxing zhan or Tianwen qixiang zazhan themselves. Source: Wikimedia Commons，Mawangdui Silk Texts 1.JPG（Public domain） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Introduction
At the new year, the men of Qin celebrated in the tenth month.
This is written in the histories. When Qin Shi Huang unified the realm he used the 「颛顼历」, the Zhuanxu calendar; the head of the year was fixed at the tenth month, and the court’s congratulations were reckoned from the first day of that month. The Han took over and did not change it, and the calendar stayed in use down to the first year of Emperor Wu’s Taichu reign.
That one sentence is all the transmitted texts yield. What the calendar itself looked like cannot be seen. How many days the year held, which months were long and which short, where the intercalary month was placed, which day began a month — none of it.
Then, batch after batch, bamboo slips came out of tombs. One had the sexagenary day-signs for the whole of the thirty-fourth year of Qin Shi Huang copied out; one set the first days of the months, day by day, from the fifth year of Han Gaozu to the second year of Empress Lü; and one was made into a table, laid out on slips sixty-nine centimetres long.
Only now does the sentence on paper acquire something underneath it.
1. A name known only from paper
Take the name first.
The 「颛顼历」 is one of the 「古六历」, the six ancient calendars. These are the calendars attributed to Huangdi, Zhuanxu, the Xia, the Shang, the Zhou and the state of Lu, listed side by side in the Hanshu, 「Lüli zhi」. Of the six, the one actually taken up as the official calendar of a unified dynasty is the Zhuanxu.
How it was laid out, however, has always rested on indirect testimony. The old writers say it was a 「四分历」, a quarter-day calendar, with a year of three hundred and sixty-five and a quarter days. That number was worked out in the previous piece, on the gnomon: measure the winter-solstice shadow over four consecutive years, and the shadow comes back to its starting point after one thousand four hundred and sixty-one days; divide by four and there it is. The name 「四分历」 comes from that fraction.
The Huainanzi, 「Tianwen xun」, of the early Han adds a line:
反覆三百六十五度四分度之一而成一岁……天一以始建七十六岁，日月复以正月入营室五度无余分，名曰一纪。
Seventy-six years, and sun and moon come back to their places; this is called one 「纪」, one epoch. The Zhuanxu calendar rests on that single number.
But a number that can be derived on paper is not the same as the number the calendar officers of the day actually used. To establish that, one has to look at what they wrote down themselves.
2. The evidence on paper
Three statements, first, out of the transmitted texts.
The first is the Shiji, 「Qin Shihuang benji」:
始皇推终始五德之传，以为周得火德，秦代周德，从所不胜。方今水德之始，改年始，朝贺皆自十月朔。
「改年始」 means the head of the year was changed; 「朝贺皆自十月朔」 means the court’s congratulations were reckoned from the first day of the tenth month. Zhang Shoujie, commenting in the Tang, glosses the line:
周以建子之月为正，秦以建亥之月为正，故其年始用十月而朝贺。
The Zhou took the month of 建子 as the first month, the Qin took the month of 建亥 as the first month, and so the head of the year fell in the tenth month.
The second is the Shiji, 「Zhang Chengxiang liezhuan」. Zhang Cang, chancellor in the early Han, had served under the Qin as an imperial clerk, in charge of the palace books and of pitch-pipes and the calendar. When the Han was founded he put the new dynasty’s calendar in order:
张苍为计相时，绪正律历。以高祖十月始至霸上，因故秦时本以十月为岁首，弗革。
Liu Bang entered the passes in the tenth month and reached Bashang; Zhang Cang held that since the old Qin had taken the tenth month as the head of the year, it should not be altered. At the end of the same chapter Sima Qian appends a remark:
张苍文学律历，为汉名相，而绌贾生、公孙臣等言正朔服色事而不遵，明用秦之颛顼历，何哉？
Jia Yi and Gongsun Chen and others urged a reform of the calendar and of the first day of the month; Zhang Cang would hear none of it, and 「明用秦之颛顼历」, plainly used the Zhuanxu calendar of the Qin. This rhetorical question is one of the few appearances the Zhuanxu calendar makes in the Shiji.
The third is the Hanshu, 「Lüli zhi」. Ban Gu states the matter most fully:
「袭秦正朔」: the Qin’s reckoning was inherited. 「用《颛顼历》」: that is the calendar used. 「比于六历，疏阔中最为微近」: against the other five it is the crudest, and yet the closest of them to the actual sky. The last clause matters: used long enough, its first days of the month no longer fell on the new moon, the moon was still visible on the last day of a month, and the dates of the quarters were often wrong. This is the ground on which Emperor Wu afterwards reformed the calendar.
Three statements on paper, all pointing at one thing: Qin and the early Han used a calendar called the Zhuanxu, with the tenth month at the head of the year. How it was laid out, the texts still do not say.
3. The evidence from the ground: Qin
In the first half of 1993, at Guanjü township in the Shashi district of Jingzhou, Hubei, an archaeological team excavated a Qin tomb, numbered no. 30 at Zhoujiatai. Three hundred and eighty-seven bamboo slips were recovered from it.
Among them is a calendar manuscript, a copy of the sexagenary day-signs for the whole of the thirty-fourth year of Qin Shi Huang, that is, 213 BCE.
Its layout is a different matter from a modern wall calendar. The slips are a little over twenty-nine centimetres long, and a single slip is divided lengthwise into six sections, one section to a month. Six short months are copied first — the tenth, twelfth, second, fourth, sixth and eighth months, twenty-nine days each; then six long months — the eleventh, first, third, fifth, seventh and ninth, thirty days each. Short and long alternate the whole way down. At the end one further month is added, the 「后九月」, thirty days.
Twelve months plus one intercalary month come to three hundred and eighty-four days. In that year the extra month hung after the ninth.
The slips carry other characters besides. Alongside the day-signs there are scattered notes on the tomb occupant’s movements: on such a day he lodged at Jingling, on such a day at Jiangling, on such a day at Huangyou, on such a day he conducted business at Jingling; and in the first month there is an entry 「嘉平视事」. Researchers read these as the man’s journeys and his office work. A calendar manuscript, used as a notebook.
From the same tomb came a wooden tablet, with the first days of the months of the first year of Qin Er Shi (209 BCE) on its face, the day-signs of the twelfth month on its back, and characters of the sort 「廷赋所」 at the top. In the same batch of slips are the month-beginnings and month-lengths for the thirty-sixth and thirty-seventh years of Qin Shi Huang; the one for the thirty-sixth year carries a title after it, reading 「卅六年日」. People of that time gave their calendar manuscripts names.
4. The evidence from the ground: the early Han
At the end of 1983, at Zhangjiashan in Jiangling, Hubei, tomb no. 247 of the Han yielded a batch of bamboo slips. Eighteen of them, each twenty-three centimetres long, carried no original title; the editors gave them one and called them the 「历谱」, the Calendar Tables.
Eighteen slips, one to a year. Each, from top to bottom, gives the first days of the twelve months and of the intercalary month of that year. The first to the ninth are the fifth to the twelfth years of Han Gaozu (202 BCE onward); the tenth to the sixteenth are the first to the seventh years of Emperor Hui; the seventeenth and eighteenth are the first and second years of Empress Lü. The latest entry reaches the 「后九月」 of Empress Lü’s second year.
This is the earliest practical calendar manuscript of the early Western Han yet found. “Practical” is a word with weight: it is not a table computed by later men, but something copied down and used by people of the time.
Further on, in April 1972, tomb no. 2 of the Han at Yinqueshan in Linyi, Shandong. The calendar manuscript from this tomb is more carefully made than the two before it.
There are thirty-two slips, sixty-nine centimetres long, which on the Han foot is exactly three chi. The first slip records the year, the second the months, and from the third onward one day to a slip. Laid out, the thirty-two slips are a table.
It records thirteen months. From the tenth month, then the eleventh, the twelfth, the first … all the way to the ninth, with one more added at the end, the 「后九月」.
Find-spot
Date
Form
Content
Tomb no. 30, Zhoujiatai, Jingzhou, Hubei
34th year of Qin Shi Huang (213 BCE)
bamboo slips, one divided into six sections
sexagenary day-signs for the year, short and long months alternating, ending with a 后九月
Tomb no. 247, Zhangjiashan, Jiangling, Hubei
Han Gaozu 5 (202 BCE) to Empress Lü 2 (186 BCE)
eighteen bamboo slips, 23 cm long
one slip per year, the first days of the months given from top to bottom
Tomb no. 2, Yinqueshan, Linyi, Shandong
1st year of Yuanguang, Emperor Wu (134 BCE)
thirty-two bamboo slips, 69 cm long
a table read across, thirteen months, with calendar notes
The manuscript also carries calendar notes. Besides the days, the slips mark the 腊日, the winter solstice, the summer solstice, the beginning of spring and the beginning of autumn, along with the first, middle and last 伏, and a kind of day called 「反支」.
The most important thing about it is that it corrected an error. This manuscript records that the twelfth month and the first month of that year were both thirty days long, two long months running; the Song Zizhi tongjian mulu recorded them as short months. For more than a thousand years readers of history followed that book, and only after the slips came out was the reading put right.
The first slip carried a title whose characters are read in two ways; some read 「七年视日」, and the editors proposed a name of their own, the 「元光元年历谱」, the Calendar Tables for the First Year of Yuanguang. Emperor Wu’s 「建元」 reign had no seventh year: the seventh year of Jianyuan had in fact already changed the era, and was the first year of Yuanguang (134 BCE).
5. Where the 「后九月」 comes from
All three of the manuscripts above contain a 「后九月」, a “latter ninth month”. This month-name needs a word of its own.
The moon goes round in a little over twenty-nine and a half days, and twelve months come to about three hundred and fifty-four days; the sun goes round in a little over three hundred and sixty-five. The ten-odd days of difference, gathered over two or three years, make up a whole month. That month has to be inserted, and it is called the intercalary month.
Where to insert it differed from house to house. Under the Qin and in the early Han the intercalary month was put at the end of the year and called 「后九月」. The ancients had a name for the practice: 「归余于终」, returning the surplus to the end. The intercalation cycle of the quarter-day calendar was seven intercalary months in nineteen years.
Why should the end of the year be the ninth month? Because the head of the year was the tenth. The year began in the tenth month, so its end naturally fell in the ninth, and the extra month hung after the ninth; such a year had thirteen months.
The term 「后九月」 appears very early. Among the Shuihudi Qin slips there is a text called the 「编年纪」, which records major events year by year. Under the fifty-sixth year of King Zhao of Qin it has a single line:
五十六年，后九月，昭死。
King Zhao of Qin died in that year, and the month is given as the 「后九月」. The fifty-sixth year of King Zhao is 251 BCE. The month-name was already in use by then.
The Japanese scholar Kurihara Tomonobu saw the same thing in the order of entries in the Shiji, 「Qin benji」: under the forty-second year of King Zhao the tenth month is recorded before the ninth, and under the forty-eighth year the tenth month before the first. 【一说】 From this he inferred that taking the tenth month as the head of the year did not begin with the twenty-sixth year of Qin Shi Huang. Since the slips came out, that point has had physical objects alongside it.
6. Two sets of month names, Qin and Chu
What has been said so far concerns the months of Qin. But the lands the men of Qin conquered had belonged to other states. In Chu the months were called by another set of names.
In December 1975, a batch of bamboo slips came from tomb no. 11 of the Qin at Shuihudi in Yunmeng, Hubei. Among them, in the 「日书」, the Rishu, in its first recension, is a concordance of Qin and Chu month-names, month by month:
Qin month
Chu month
Qin month
Chu month
tenth
冬夕
fourth
七月
eleventh
屈夕
fifth
八月
twelfth
援夕
sixth
九月
first
刑夷
seventh
十月
second
夏
eighth
爨月
third
纺月
ninth
献马
The tenth month of Qin is called 冬夕 in Chu; the eleventh, 屈夕; the twelfth, 援夕. The names further down look even less like month-names: 刑夷, 纺月, 爨月, 献马.
These Chu month-names were not known to be month-names at all until recently. The inscription on the bells from Changtaiguan in Xinyang contains characters of the form 「屈栾」, which had never made sense; once the concordance appeared, it became clear that they were the month-names of Chu.
The table says one thing: Qin took the tenth month as the head of the year, but the months themselves still followed the Xia reckoning. The first month was still the first month; whichever month the handle of the Dipper pointed to at 建寅 was still called the first month. The difference between the months of Qin and of Chu lay exactly there.
7. Whose business the calendar is
The preceding sections have dealt with what can be seen on the slips. There is one more layer, written outside them.
Why did Qin take the tenth month as the head of the year? The Shiji, 「Qin Shihuang benji」, puts the reason in the virtue of the dynasty, not in the sky. The passage is about the virtue of Water: the Zhou had the virtue of Fire; the Qin replaced the Zhou, and so took the one that overcomes Fire, which is Water. At the beginning of the virtue of Water, therefore, 「改年始」, the head of the year was changed; therefore the court’s congratulations ran 「皆自十月朔」; therefore clothes and banners were 「皆上黑」; therefore 「数以六为纪」, the number six was made the measure.
Where the first day of the year is moved to is a posture; it tells the realm that the dynasty has changed from the ground up.
That the early Han did not change it was also a posture. Zhang Cang, putting the new dynasty’s calendar in order, kept the old Qin calendar on one hand and worked out the five virtues on the other, holding that the Han too had the virtue of Water, and therefore 「尚黑如故」, still honoured black as before. He took the whole Qin apparatus over as it stood. 【一说】 The doctrine of the Water virtue was later challenged in a special study, which argued that “the Qin used the virtue of Water” was an elaboration by later men. It is recorded here for what it is.
Politics aside, the calendrical facts can still be counted. The Zhuanxu calendar was in use from the year of Qin’s unification (221 BCE) to the reform of the calendar in the seventh year of Yuanfeng under Emperor Wu (104 BCE), a span of one hundred and seventeen years. From the founding of the Han to the reform, Ban Gu records 「汉兴百二岁矣」, a hundred and two years.
More than a century on one calendar, until the first days of the months no longer came out right and the full and waning moons were wrong, before the change was allowed.
8. What can be checked, and what is only inference
Looking back, the texts above ground and the objects below it together establish this much.
Qin and the early Han used a calendar called the Zhuanxu, with the tenth month at the head of the year. Three statements on paper and three groups of slips agree. The months of the year ran from the tenth to the ninth; the intercalary month was placed after the ninth and called the 「后九月」; the months alternated long and short, with one 后九月 added at the end. All this is visible on the Zhoujiatai and Yinqueshan manuscripts alike. The month-names of Qin and those of Chu are two different sets.
What cannot be checked should also be set out.
The slips are broken. The Zhoujiatai manuscript copies the thirty-fourth year; the same tomb holds month-beginnings for the thirty-sixth and thirty-seventh, so the years join up, but the gaps between them cannot be filled. The eighteen Zhangjiashan slips stop at the 「后九月」 of Empress Lü’s second year, and the stretch after that has to be picked up from other materials. Calendars in use in different places need not have been the same; within one batch of Qin slips there is more than one case of day-signs differing by a day, and some researchers hold that this is not necessarily a mistake but may reflect the priority of the calendars relied on.
What algorithm actually sits under the name “the Zhuanxu calendar” is likewise inference. The quarter-day year, the seven intercalations in nineteen years, the seventy-six-year epoch — these numbers can be read out of later literature; whether the copy in the hands of the calendar officers of the day was accurate, the slips say not a word.
The man in the tomb, copying out his calendar manuscript, most likely never thought of leaving it for people two thousand years later. He was writing down which day he travelled and which day he worked.
Note on the text
This is a popular exposition, and it makes no claim to original research. The calendrical facts cited rest on transmitted texts and on excavated material. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Chinese terms are left in their original characters where the word itself is the subject of the discussion.
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record.
References
[1] 史记 [Shiji]. Han.
[2] 汉书 [Hanshu]. Han.
[3] 淮南子 [Huainanzi]. Han.
[4] 湖北省荆州市周梁玉桥遗址博物馆. 关沮秦汉墓简牍 [Bamboo and Wooden Slips from the Qin and Han Tombs at Guanjü]. 北京: 中华书局, 2001.
[5] 张家山二四七号汉墓竹简整理小组. 张家山汉墓竹简〔二四七号墓〕 [Bamboo Slips from the Han Tomb at Zhangjiashan (Tomb 247)]. 北京: 文物出版社, 2001.
[6] 吴九龙. 银雀山汉简释文 [Transcriptions of the Han Bamboo Slips from Yinqueshan]. 北京: 文物出版社, 1985.
[7] 睡虎地秦墓竹简整理小组. 睡虎地秦墓竹简 [Bamboo Slips from the Qin Tomb at Shuihudi]. 北京: 文物出版社, 1990.
[8] 栗原朋信. 秦汉史の研究 [Kurihara Tomonobu, Studies in Qin and Han History]. 东京: 吉川弘文馆, 1960.
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
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You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the photographs of the excavated objects and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
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Fig. 1 The Dunhuang star chart. A Tang manuscript showing thirteen panels of stars and asterisms. A related star chart shown for reference, not the particular scroll discussed here. Source: Wikimedia Commons, “Dunhuang star map.jpg” (Public domain) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Abstract
Jupiter is called the Year Star (岁星) because it was used to reckon years. The ancients divided the celestial circuit into twelve equal parts, the twelve Jupiter stations (十二次), and the planet moves through roughly one station a year, so that a year could be named by the station it occupied. The Shiji, “Treatise on the Celestial Offices”, states flatly that the Year Star “completes the circuit in twelve years”, and for more than a thousand years this was taken as the standard. It is not correct. The note works through the arithmetic: the ancient figure of 30 7/16 degrees a year, times twelve, gives 365 1/4 degrees, which is internally consistent; but the modern value of 11.862 years leaves a surplus of 0.012 stations a year, and in about eighty to eighty-six years that surplus accumulates into a whole station — the Jupiter anomaly (超辰), the Year Star overstepping one station ahead of schedule. The note traces how the Zuo zhuan noticed the overstepping; how Liu Xin pinned it down and patched the Santong li with a rule of one overstep in 144 years, preserved in the Hanshu; how the difficulty of observation led the ancients to invent a mirror planet, Tai Sui (太岁), running one station a year in the opposite direction; and how the Yuanhe sifen li of 85 CE finally set Jupiter-based year reckoning aside for the stem-and-branch cycle. The note is descriptive; it contains no predictive claims.
Keywords: Jupiter; Year Star; twelve Jupiter stations; the Jupiter anomaly; Tai Sui; Jupiter-based year reckoning; Santong li; Yuanhe sifen li
Fig. 2 The Dengfeng observatory. Built under Guo Shoujing in the Yuan dynasty; the shadow-measuring terrace and the scale rule both survive. A related structure shown for reference, not an object discussed here. Source: Wikimedia Commons，Dengfeng Observatory.jpg（CC BY-SA 2.0） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
1. Why this star is called the Year Star
The Shiji, “Treatise on the Celestial Offices”, has a line that does not mince words: the Year Star 「十二岁而周天」 (“completes the circuit in twelve years”).
The line was written two thousand years ago, and for more than a thousand years afterwards the calendar-makers of every dynasty took it as their standard. But it is wrong.
Among the five planets, Jupiter’s pace is neither fast nor slow. Mercury goes round the sun more than four times a year, Venus rather more than once, Mars nearly twice; Jupiter takes more than eleven years, Saturn more than twenty-nine.
This rhythm of Jupiter’s makes it usable as a clock.
The ancients divided the celestial circuit from west to east into twelve equal parts, called the twelve Jupiter stations (十二次). Jupiter moves through roughly one station a year; whichever station it entered was recorded as “the year is in such-and-such a station”. The star took its name, the Year Star, from this.
The names of the twelve stations correspond to the twenty-eight lunar mansions:
Station
Twenty-eight mansions
Station
Twenty-eight mansions
Xingji
Dou, Niu
Chunshou
Jing, Gui
Xuanxiao
Nü, Xu, Wei
Chunhuo
Liu, Xing, Zhang
Juzi
Shi, Bi
Chunwei
Yi, Zhen
Jianglou
Kui, Lou
Shouxing
Jiao, Kang
Daliang
Wei, Mao, Bi
Dahuo
Di, Fang, Xin
Shishen
Zi, Shen
Ximu
Wei, Ji
The Shiji, “Treatise on the Celestial Offices”, gives the Year Star’s yearly course as 「岁行三十度十六分度之七」 (“it moves 30 and 7/16 degrees a year”).
Thirty degrees and seven sixteenths, times twelve, gives 365 degrees and a quarter. This is exactly the number of degrees in the celestial circuit as the ancients conceived it.
So in the ancients’ own arithmetic, “completes the circuit in twelve years” came out even, and nothing clashed.
2. But Jupiter does not travel on this scale
The ancients cut the celestial circuit into 365 and a quarter degrees in order to accommodate the sun — the sun moves one degree a day and completes the circuit in a year. Jupiter is not on this scale.
The modern measurement of Jupiter’s circuit round the sun is 11.862 years, about 4332.6 days. Converted to the twelve stations, Jupiter moves through 1.012 stations a year.
That is 0.012 of a station more than one.
This fraction is too small to measure in a single year. But it accumulates year by year.
3. After eighty years or so, it gives itself away
Once it has accumulated for about eighty years, it gives the game away. By then the surplus adds up to one whole station; that year the Year Star should move on to the next station, but it crosses over ahead of time.
The ancients gave this phenomenon a name: the Jupiter anomaly (超辰). The step it oversteps is called “overstepping one station” (超一辰).
How many years one overstep takes depends on which period value is used:
Value used
Years per overstep
the modern 11.862 years
85.9 years
the common 11.86 years
84.7 years
11.85657 years, computed in-house
82.7 years
All three figures are around eighty; the difference lies only in which period is taken. None is out of the way. The ancients did not know the number 11.86, but by comparing the texts they sensed that something was off.
The Zuo zhuan, under the twenty-eighth year of Duke Xiang, preserves a line: 「岁在星纪而淫于玄枵。」 (“The year is in Xingji, yet it trespasses into Xuanxiao.”) Xingji comes first, Xuanxiao after; the Year Star should have stayed in Xingji, yet it pushed forward into Xuanxiao. The word “trespass” (淫) speaks of overstepping the boundary.
Several hundred years later Liu Xin pinned the matter down. The Hanshu, “Treatise on Pitch Pipes and the Calendar”, preserves a verdict of his: 「三十二年，岁在星纪，距辛亥百四十五岁，盈一次矣。」 (“In the thirty-second year the year is in Xingji; a hundred and forty-five years from xin-hai, and one station has been exceeded.”)
The xin-hai in that sentence is the first day of the first month of the fifth year of Duke Xi. From that base point Liu Xin reckoned forward to the thirty-second year of Duke Zhao of Lu, a hundred and forty-five years, and the Year Star had overstepped a whole station. The sentence is the result of his reckoning year by year.
4. Liu Xin applied a patch
Having found it, he had to fix it.
Liu Xin, in the Santong li, gave the Year Star a new rule: one overstep in 144 years — that is, 145 stations travelled in 144 years.
The rule is preserved in the calendrical procedure of the Santong li in the Hanshu, “Treatise on Pitch Pipes and the Calendar”:
推岁所在，置上元以来，外所求年，盈岁数，除去之，不盈者以百四十五乘之，以百四十四为法。
(To reckon where the year lies: set down the years from the High Origin, excluding the year sought; subtract out the full number of years; multiply the remainder by 145, and take 144 as the divisor.)
In present-day terms: first multiply by 145, then divide by 144; the whole number obtained is called the “accumulated stations” (积次), the stations the Year Star has travelled; the remainder is called the “station remainder” (次余), this year’s fraction. Count from Xingji, and wherever the count lands is where it is.
This patch is a famous entry in the history of calendrics. Bian Shao of the Eastern Han, in a calendrical discussion, gave it two lines of assessment, preserved in the Xu Hanshu, “Treatise on Pitch Pipes and the Calendar”: 「百四十四岁一超次，与天相应，少有阙谬。」 (“One overstep in 144 years accords with heaven, and is rarely at fault.”)
Check it against the modern 11.86 years and there is an overstep every eighty-five years or so; Liu Xin said 144. The figure is not accurate.
Where it is worth remembering lies elsewhere: in the first calendar to be preserved whole in the histories, this was the first time anyone had written Jupiter’s fraction into the algorithm.
5. Tai Sui: making a false star to mark the years
The anomaly brought a further trouble, over the matter of “seeing”.
Where the Year Star ought to be, reckoned from the twelve stations, is a matter of calculation; where it actually is requires looking up. When the calculated and the seen fail to agree, the chain of year-reckoning loses a link.
So the ancients set up another star. This star does not appear in the sky; it moves as fast as the Year Star and in the opposite direction, one station a year through the twelve branch-stations.
This false star is called Tai Sui. In the Shiji, “Treatise on the Celestial Offices”, it is called “year yin” (岁阴); in the Huainanzi it is called “great yin” (太阴); later it was commonly called Tai Sui.
The Shiji, “Treatise on the Celestial Offices”, writes 「以摄提格岁：岁阴左行在寅，岁星右转居丑」 (“In a shetige year: the year yin moves left and is in yin, the Year Star turns right and rests in chou”), which is exactly this pair — the true star turning right, the false star moving left, one left and one right, mirror images of each other.
The twelve branch-stations Tai Sui travels are the twelve earthly branches. The twelve year-names of Tai Sui are shetige, danyan, zhixu, dahuangluo, dunzang, xieqia, tuntan, zuoe, yanmao, dayuanxian, kundun and chifenruo. The twelve year-names paired with the ten year-yang names make up the set in the Erya, “Explaining Heaven”.
Reckon the year-names by Tai Sui and there is no need to look up at any star; one simply counts on.
One point must be kept distinct. The Tai Sui spoken of here is the movement of that false star, a matter of calendrics; the “fleeting-year Tai Sui” of later fortune-telling borrows the same term for a different thing. The two Tai Sui must not be confused.
6. In the end, even the false star was discarded
Tai Sui year-reckoning shook off observation, but it went round the twelve branch-stations once every twelve years, and still needed adjusting when the anomaly came round.
The truly trouble-saving way was to switch to the stems and branches.
Ten heavenly stems paired with twelve earthly branches, sixty to a round, each turning in its own circle, looking at no star in the sky. Not relying on observation, it cannot be thrown out of phase by a star moving inaccurately; one need only count on, and it can be extended indefinitely.
In the second year of Yuanhe under Emperor Zhang of Han, 85 CE, the court promulgated the Yuanhe sifen li. With this calendar reform, Jupiter-based year reckoning was formally abolished and stem-and-branch year reckoning adopted.
From the Year Star to Tai Sui, and from Tai Sui to the stems and branches, this is a route of withdrawal: first the true star was watched to mark the years, then a false star was made to stand in, and at last even the false star was let go.
7. The number twelve has three origins
A year has twelve lunations; the twelve months together come to a little over 354 days, eleven days short of the tropical year, and the intercalary month makes up those eleven days. The direction of the Dipper’s handle divides the celestial circuit into twelve branch-stations as well — the direct origin of the branches’ month-establishment. Add the twelve Jupiter stations of the Year Star, and there are three routes.
Of the three, two can see the sky, and one reckons the months out. What finally settled the number twelve was, oddly enough, the unreliability of that star.
Closing
The ancients used Jupiter to mark the years because it moved steadily and one could see at a glance where it had got to. When it turned out not to be so steady, they switched to a false star; when the false star too gave trouble, they switched to the stems and branches.
Once the sixty-term cycle turns, it has nothing more to do with that Jupiter in the sky. The trouble piled up by eleven such fractions ends here.
What comes next asks an earlier question: what shape did the ancients take the sky to be.
A&Q
How many years does Jupiter actually take to go once round the sun?
Modern measurement gives 11.862 years, about 4332.6 days. The ancients reckoned it at twelve years, a difference of about fifty days a year.
What is the Year Star’s overstepping of a station?
Reckoned at twelve years to a circuit, the Year Star is taken to advance one of the twelve stations each year; Jupiter in fact moves slightly faster, by about 0.012 of a station a year. Once that has accumulated over about eighty years, the fraction makes up a whole station, and the Year Star crosses ahead of the station it ought to be in. The phenomenon is called the Jupiter anomaly (超辰).
How do the twelve stations correspond to the twenty-eight mansions?
The twelve stations divide the celestial circuit from west to east into twelve equal parts, each corresponding to one to three of the twenty-eight mansions. Xingji pairs with Dou and Niu, Xuanxiao with Nü, Xu and Wei, and so on down to Ximu with Wei and Ji.
When was Jupiter-based year reckoning abolished?
In the second year of Yuanhe under Emperor Zhang of Han, 85 CE, the Yuanhe sifen li was promulgated, abolishing Jupiter-based year reckoning and adopting stem-and-branch year reckoning.
Is the Tai Sui spoken of here the same as the “annual Tai Sui” of popular talk?
No. The Tai Sui of the calendar is the mirror of the Year Star, an imagined star running along the twelve branch-stations; the “annual Tai Sui” spoken of later borrows the same word for a different matter.
Note by Chujia Kuang
What is most worth remembering in this stretch of calendrical history is the three ways the ancients dealt with error. Finding the star inaccurate, they first mended the algorithm; when the algorithm could not be patched up, they made an obedient false star; when the false star too proved troublesome, they simply switched to the stems and branches, cut loose from the sky. Three steps on, the number twelve was kept, but the road it came by had changed its name.
About the author
Chujia Kuang (邝楚嘉), pen name Jiayan Yide (嘉言一得), is an independent researcher in Jieyang, Guangdong, devoted to archiving verifiable primary sources and calendar data.
This column writes about calendrics, solar terms, the stems and branches and orientation, and also about what he reads. The pen name 嘉言一得 comes from the 史记: 愚者千虑，必有一得, “the foolish man’s thousand thoughts must yield one gain”. Where something is written wrongly, corrections are welcome.
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record (木星走一圈不是十二年).
References
[1] Zuo zhuan [左传][M]. Pre-Qin period.
[2] Erya [尔雅][M]. Pre-Qin period.
[3] Sima Qian. Shiji [史记][M]. Western Han.
[4] Huainanzi [淮南子][M]. Western Han.
[5] Ban Gu. Hanshu [汉书][M]. Eastern Han.
[6] Sima Biao. Xu Hanshu [续汉书][M]. Western Jin.
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
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You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the excavated Qin and Han bamboo-slip photographs and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
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Stems and branches (干支) are usually met as a tool: they name the year in the four-pillar chart, mark the months, and divide the day into double-hours, and yet they are rarely explained in themselves. This note supplies that explanation. It begins with the two characters, which originally meant “trunk” and “branch” — the main stem of a tree and its bough — and with Cai Yong’s account, in the Yueling zhangju, of how the system was made to name days and months. The ten heavenly stems are then read in order as the life of a single plant, from the cracking of the shell (jia) to the storing of the seed (gui), with the source line for each step, chiefly from the Shiji, “Treatise on Pitch Pipes”, the Shuowen jiezi and the Shiming. The twelve earthly branches are read instead as the coming and going of qi, with zi in the eleventh month and wu at the summer solstice as its two pivots, and the Hanshu, “Treatise on Pitch Pipes and the Calendar”, stringing the twelve together. Two rules follow: yin and yang by odd and even position, the five phases by direction. The note explains why the branches carry two numberings that do not conflict, and why chen, xu, chou and wei are the four points of handover. It closes by dating the pairing of the branches with animals, from the Lunheng back to three excavated daybooks. The note is descriptive; it contains no predictive claims.
Fig. 1 A sexagenary table carved on an ox scapula (Jiaguwen Heji 37986), shown for reference; the bone was not excavated for the question discussed here. Source: Wikimedia Commons, “Heji 37986 Ganzhi table.jpg” (CC0) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Keywords: stems and branches; heavenly stems; earthly branches; yin and yang; five phases; zodiac animals; Lunheng; excavated daybooks
Fig. 2 The Dengfeng observatory. Built under Guo Shoujing in the Yuan dynasty; the shadow-measuring terrace and the scale rule both survive. A related structure shown for reference, not an object discussed here. Source: Wikimedia Commons，Dengfeng Observatory.jpg（CC BY-SA 2.0） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
1. The stem is the trunk, the branch is the bough
In the preceding ten notes the stems and branches have been used as a tool several times. They appear everywhere — in the year pillar, the month establishment, the double-hour — and not once have they been explained for what they are.
This is not a detour. The year is read from lichun, the month from the solar term, the hour from the sun. If the measuring rod has not first been aligned, the symbols will be of no use however well one knows them. Align the rod first; then learn the symbols.
Jia, yi, bing, ding — you can read them, you can write them; you learned them in primary school. You have probably also heard it said that jia, yi, bing, ding stand for “so on”, the equivalent of A, B, C, D.
They were not originally meant for ordering anything.
The two characters gan zhi (干支) were originally gan zhi (幹枝): the trunk of a tree and its boughs.
Cai Yong of the Eastern Han, in the Yueling zhangju, recorded where the system came from:
命大桡探五行之情，占斗纲所建，于是始作甲乙以名日，谓之干；作子丑以名月，谓之支。干支相配以成六旬。
(He charged Da Rao to investigate the disposition of the five phases, and to divine what the handle of the Dipper established; thereupon he first made jia and yi to name the days, calling them the stems; and made zi and chou to name the months, calling them the branches. Stems and branches were then paired to form the sixty-day cycle.)
The phrase “the Yellow Emperor charged Da Rao” in that sentence is legend, not history; it is safer to read it with the two words “it is said” prefixed.
The Shuowen jiezi glosses gan as 「筑墙端木也」 (“a pole set upright at the end of a wall under construction”), the post planted at each end when building a wall; it glosses zhi as 「去竹之枝也」 (“taking a branch from a bamboo”), the act of detaching a bamboo branch from the bamboo.
One is the main trunk, the other a side branch. Which is principal and which subordinate is fixed by the names themselves.
The Erya, “Explaining Heaven”, preserves an earlier set of names: the heavenly stems were called “year yang”, the earthly branches “year yin”. The names are out of use today, but they show that before the stems and branches became symbols they were first a way of giving names to time.
2. Ten characters, the life of one plant
Which ten characters are the ten heavenly stems?
Jia, yi, bing, ding, wu, ji, geng, xin, ren, gui.
Read in order, one after another, they tell the whole course of a plant from cracking its shell to setting its seed, and then to the seed’s return to storage.
Jia (甲) is breaking out of the shell. The Shiji, “Treatise on Pitch Pipes”, writes 「万物剖符甲而出也」 (“all things split their shell and come forth”); the Shuowen jiezi says 「从木，戴孚甲之象」 (“it follows the tree, with the appearance of bearing a shell”), pushing out with a shell on its head.
Yi (乙) is the crooked first growth. Shiji, “Treatise on Pitch Pipes”: 「万物生轧轧也。」 (“All things are born with a creaking.”) The Shuowen jiezi puts it vividly: 「象春草木冤曲而出，阴气尚强，其出乙乙也。」 (“Like the spring grasses and trees, which come out crooked and bent, the yin qi still strong, their coming out halting and slow.”) The yin qi still presses down; the tip of the shoot can only push out a little at a time.
Bing (丙) is growing stout and showing form. Shiji, “Treatise on Pitch Pipes” says 「阳道著明」 (“the way of yang becomes bright”); the Shuowen jiezi says 「万物成炳然」 (“all things become brilliant”). The shoot has opened out and the colour brightens.
Ding (丁) is growing firm and taking shape. Shiji, “Treatise on Pitch Pipes”: 「万物之丁壮也。」 (“The prime of all things.”)
Wu (戊) is luxuriance and density. The Shiming: 「戊，茂也。」 (“Wu means luxuriant.”)
Ji (己) is having form and being recordable. The Shiming says plainly: 「己，纪也，皆有定形可记识也。」 (“Ji means to record; all have a fixed form and can be recorded and known.”) The form is fixed and can be noted.
Geng (庚) is firm and drawing inward. The Shuowen jiezi: 「象秋时万物庚庚有实也。」 (“Like the autumn, when all things are geng geng and solid.”)
Xin (辛) is at the height of abundance and coming under constraint. The Shuowen jiezi: 「秋时万物成而熟。」 (“In autumn all things ripen and mature.”) At the time of harvest they also begin to be bound by the climate.
Ren (壬) is conceiving and nourishing. Shiji, “Treatise on Pitch Pipes”: 「壬之为言任也，阳气任养万物于下也。」 (“Ren means to bear; the yang qi bears and nourishes all things below.”) The new life is already conceived beneath.
Gui (癸) is closing and storing, awaiting sprouting. Shiji, “Treatise on Pitch Pipes”: 「癸之为言揆也，言万物可揆度。」 (“Gui means to measure; it says that all things can be measured.”) Put away, waiting to be measured again and to sprout again.
Read through the ten characters, and the life of a single plant has also run its course.
There is also a set of one-character mnemonics circulating online: jia-chai, yi-ya, bing-bing, ding-qiang, wu-mao, ji-ji, geng-geng, xin-xin, ren-ren, gui-kui. It is easy to remember, but it is a later summary, not the literal text of the Shiji, “Treatise on Pitch Pipes”. When quoting it, do not call it the original words of the Shiji.
3. The twelve branches speak of qi coming and going
The twelve earthly branches change the lens.
The heavenly stems speak of a single plant from birth to storage; the branches speak of when qi comes out and when it is pressed back. The Shiji, “Treatise on Pitch Pipes”, glosses zi: 「子者滋也，言万物滋于下也。」 (“Zi means to nourish; it says that all things are nourished below.”) Zi is in the eleventh month; the yang qi stirs underground.
By wu it has become 「阴阳交，故曰午」 (“yin and yang cross, and so it is called wu”). The Shuowen jiezi is clearer: 「啎也。五月，阴气午逆阳，冒地而出。」 (“To oppose. In the fifth month, the yin qi opposes the yang head-on and bursts up from the ground.”) The yin qi pushes upward and collides with the yang qi.
Zi and wu are the two pivots of the system. Zi is around the winter solstice, when the yang qi turns back from its deepest point; wu is around the summer solstice, when the yin qi counter-attacks from above.
The Hanshu, “Treatise on Pitch Pipes and the Calendar”, has a general outline that strings the twelve characters together:
孳萌于子，纽牙于丑，引达于寅，冒茆于卯，振美于辰，已盛于巳，咢布于午，昧薆于未，申坚于申，留孰于酉，毕入于戌，该阂于亥。
(In zi it multiplies and sprouts; in chou it knits its buds; in yin it draws forth and reaches out; in mao it pushes up its shoots; in chen it rouses its beauty; in si it is already at its height; in wu it puts forth its calyx; in wei it becomes dark and dense; in shen it extends and hardens; in you it stays and ripens; in xu it completes its entry; in hai it is enclosed and shut away.)
From zi, multiplying below, all the way to hai, which gathers all things into the kernel, and back again to zi.
4. Two rules: yin and yang by odd and even, the five phases by direction
The first rule is yin and yang; it is enough to count positions: the 1st, 3rd, 5th, 7th, 9th and 11th in the sequence are yang, the 2nd, 4th, 6th, 8th, 10th and 12th are yin.
The yang stems are jia, bing, wu, geng and ren; the yin stems are yi, ding, ji, xin and gui. The same for the branches: zi, yin, chen, wu, shen and xu are yang branches; chou, mao, si, wei, you and hai are yin branches.
The second rule is the assignment of the five phases. First remember a table; it is called the five phases: jia and yi pair with wood, bing and ding with fire, wu and ji with earth, geng and xin with metal, ren and gui with water. Why the five phases are five states of motion, and why they are ordered this way, is the subject of notes thirty-one and thirty-two.
Heavenly stems
Five phases
Direction
jia, yi
wood
east
bing, ding
fire
south
wu, ji
earth
centre
geng, xin
metal
west
ren, gui
water
north
The branches are assigned differently: two branches to each of the four directions — yin and mao belong to wood, si and wu to fire, shen and you to metal, hai and zi to water; chen, xu, chou and wei are separately assigned to earth and placed at the four corners.
There is a trap here: apply the stems’ scheme to the branches, and one begins by taking zi to be wood.
Zi belongs to water. The stems go two by two in a row; the branches take the four cardinal and four corner positions. The two arrangements are not the same thing.
5. Chen, xu, chou and wei: why both numberings are correct
The branches’ assignment to the five phases in fact has a second numbering. Both are correct and they do not clash.
One looks at what the character itself belongs to: yin and mao wood, si and wu fire, shen and you metal, hai and zi water, chen, xu, chou and wei earth. This is called the root qi (本气).
The other looks at what the group as a whole governs: yin, mao and chen belong to wood; si, wu and wei to fire; shen, you and xu to metal; hai, zi and chou to water; and chen, xu, chou and wei again to earth. Divided by direction, it is called the division by quarters (分方).
The difference arises only over the four characters chen, xu, chou and wei. Take chen: chen is the last character of spring; the wood qi has run to its end and the earth qi is beginning to hold sway, so chen itself belongs to earth; but it is still within the span of spring, and counted by group it still falls to the eastern wood.
There is a further point to state plainly, or the two will seem to contradict.
One rod measures qi. The wood qi appears in the month yin, is strongest in the month mao, and in the month chen gives way to earth.
The other rod measures phenomena (候), the visible state of things in the field. Though the first month is already established as yin, the cold is still heavy and the plants and trees do not stir; by the month mao the grass grows and the orioles fly; by the month chen they are luxuriant.
The two rods are half a beat apart: phenomena lags qi by about a month. So “wood is luxuriant only in the month chen” and “the wood qi gives way in the month chen” do not clash — one speaks of the wood in the field, the other of the qi on the board.
That chen, xu, chou and wei are the four special characters has its reason here: they are the points of handover where the qi has already turned and the phenomena have not yet caught up.
6. One character, three duties at once
The branches are closer to the ground than the stems, because they serve in three places at once.
First, marking the months. The first month is established as yin, the second as mao, on through the eleventh month established as zi and the twelfth as chou. This layer was set out fully in the earlier note on the head of the year.
Second, marking the hours. A day has twelve double-hours; the zi double-hour runs from eleven at night to one in the morning, the chou double-hour from one to three. This layer was listed in the earlier note on the ancient day.
Third, marking the years, paired with the zodiac animals. Zi-rat, chou-ox, yin-tiger, mao-rabbit, chen-dragon, si-snake, wu-horse, wei-goat, shen-monkey, you-rooster, xu-dog, hai-pig.
7. Pairing the twelve branches with animals was not yet fixed in the Qin and Han
Finally, something other accounts mostly do not discuss: when was the pairing of the twelve branches with animals fixed?
The earliest systematic record in the transmitted literature is Wang Chong’s Lunheng of the Eastern Han. The “Wushi” chapter writes:
寅，木也，其禽虎也。戌，土也，其禽犬也……子亦水也，其禽鼠也。午亦火也，其禽马也。
(Yin is wood, its animal the tiger. Xu is earth, its animal the dog. … Zi is also water, its animal the rat. Wu is also fire, its animal the horse.)
The “Wushi” chapter lists only eleven items, missing “chen-dragon”. “Chen is the dragon” appears in the Lunheng, “Yandu” chapter. Only the two chapters together make up the full twelve.
So is the Lunheng the earliest?
No. Excavated slips and tablets push the date back a good way.
In 1975, a batch of bamboo slips was unearthed from Qin tomb no. 11 at Shuihudi in Yunmeng, Hubei; the tomb’s occupant was buried in 217 BCE (the thirtieth year of the First Emperor of Qin). Among them, the “Daozhe” chapter of the Rishu pairs the branches with animals once over: zi-rat, chou-ox, yin-tiger, mao-rabbit, wu-deer, wei-horse, shen-huan, xu-old-sheep, hai-pig.
The Rishu of the Qin slips from Fangmatan in Tianshui, Gansu, unearthed in 1986, is another pairing; the Rishu of the Han slips from Kongjiapo in Suizhou, Hubei, buried in 142 BCE, is another again.
Set the three batches side by side and two things can be seen.
One is the date. The pairing of branches with animals existed at least by the Qin, some four hundred years earlier than the Lunheng.
The other is that it was “not yet fixed”. In the Qin slips wu pairs with the deer, not the horse; wei with the horse, not the goat; xu with the old sheep, not the dog. The same set of pairings was still shifting back and forth around the Qin–Han transition.
Chen Lianshan of Peking University has written an article devoted to sorting this out: the branch–animal pairings in these Rishu do not serve the same purpose as the later zodiac; they are used to infer the appearance of a thief and his hiding place, not to mark years. Strictly speaking, they should be called “day animals” (日肖) at that time, not yet “zodiac animals”.
By the Lunheng, the sequence of the twelve animals is basically the same as today’s. Using it to mark years and to pair with a person’s year of birth is later; how much later has no reliable dating conclusion at present.
Closing
The two characters gan zhi take one from the trunk of a tree and one from its bough. The ten heavenly stems are the life of a single plant; the twelve earthly branches are the coming and going of a single breath of qi. Each of the two sets has its own rule for fixing yin and yang, and each pairs with the five phases and the directions.
With this, the twenty-two symbols may be counted as fully known.
Knowing them fully is only the first step. Why these twenty-two characters are ordered as they are, and how they pull on one another, is three further long stretches still to come.
A&Q
How many heavenly stems and earthly branches are there, and what are they?
There are ten heavenly stems: jia, yi, bing, ding, wu, ji, geng, xin, ren and gui. There are twelve earthly branches: zi, chou, yin, mao, chen, si, wu, wei, shen, you, xu and hai. Together, twenty-two.
Why are the ten heavenly stems ordered jia, yi, bing, ding?
The order tells the life of a single plant: jia breaking its shell, yi the crooked first growth, bing showing its form, ding taking shape, all the way to gui, closing and storing away, waiting to sprout.
Is zi not of the wood phase?
Zi is water. Yin and mao are wood, si and wu fire, shen and you metal, hai and zi water, and chen, xu, chou and wei earth. To take zi for wood is usually to apply to the branches the stems’ arrangement of “two characters to one phase”.
In which book does the pairing of the twelve earthly branches with the zodiac animals first appear?
The earliest systematic record in the transmitted literature is Wang Chong’s Lunheng of the Eastern Han; its “Wushi” and “Yandu” chapters together make up the full twelve. But the Qin slips from Shuihudi, the Qin slips from Fangmatan and the Han slips from Kongjiapo are all earlier, pushing the date back at least to the Qin.
Is that pairing in the Qin slips the same as today’s?
No. In the “Daozhe” chapter of the Rishu from Shuihudi, wu pairs with the deer, wei with the horse and xu with the old sheep. The pairing was not yet fixed then, nor was its use the marking of years.
Note by Chujia Kuang
The twenty-two symbols are in fact only two kinds of thing: one kind shows how a plant grows, the other how a qi moves. Hold on to these two lines, and it serves far better than rote-memorising the five-phase pairings.
About the author
Chujia Kuang (邝楚嘉), pen name Jiayan Yide (嘉言一得), is an independent researcher in Jieyang, Guangdong, devoted to archiving verifiable primary sources and calendar data.
This column writes about calendrics, solar terms, the stems and branches and orientation, and also about what he reads. The pen name 嘉言一得 comes from the 史记: 愚者千虑，必有一得, “the foolish man’s thousand thoughts must yield one gain”. Where something is written wrongly, corrections are welcome.
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record (干支：从一棵树到二十二个字).
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the excavated Qin and Han bamboo-slip photographs and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
For the full terms of the licence, see: https://creativecommons.org Related articles
Fig. 1 A Chinese compass. A directional scale combined with a magnetic needle. A related instrument shown for reference; no original sinan has ever been excavated, and the modern object is a reconstruction, which this image does not stand in for. Source: Wikimedia Commons, “Antic chinese Compass.jpg” (Public domain) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Abstract
A Song-dynasty book, the Pingzhou ketan, records that the master of a seagoing ship watches the stars at night, the sun by day, and the compass only in overcast weather — the compass standing third. This note deals with the long stretch before the needle appeared, and with how people nevertheless fixed their directions. The core method, given in the Zhouli, “Kaogong ji”, is the gnomon: level the ground, set up a pole, draw a circle, and mark on the circumference the tip of the pole’s shadow at sunrise and again at sunset. The two points are left-right symmetric about the line of true north-south; joining them gives true east-west, and folding the line back to the pole gives true north-south, so that no direction need be known in advance. At night the pole star, the one place that barely moves, and the Dipper, a dial that turns, serve as rulers. The note then sets out the archaeological evidence — the Taosi observation structure in Shanxi and tomb 45 at Xishuipo in Henan — and traces the word “sinan” from a gnomon pole to a ladle-shaped object to the magnetised needle. It closes with the way orientation entered ritual and speech. The note is descriptive; it contains no predictive claims.
Keywords: direction-finding; gnomon; shadow measurement; pole star; the Dipper; sinan; magnetic declination; Taosi; Xishuipo
Fig. 2 The Dengfeng observatory. Built under Guo Shoujing in the Yuan dynasty; the shadow-measuring terrace and the scale rule both survive. A related structure shown for reference, not an object discussed here. Source: Wikimedia Commons，Dengfeng Observatory.jpg（CC BY-SA 2.0） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
1. One pole, one circle, two shadows
There is a Song-dynasty book called the Pingzhou ketan, by Zhu Yu, which records a rule observed aboard a seagoing ship:
舟师识地理，夜则观星，昼则观日，阴晦观指南针。
(The ship’s master knows the land: at night he watches the stars, by day he watches the sun, and in overcast weather he watches the compass.)
The ship’s navigator knows his way in three grades. At night he watches the stars, by day the sun, and only in overcast weather does the compass come round.
The compass comes third.
The point of importance here is this: on a Song-dynasty ship the compass was a substitute. In fine weather it was not needed.
A word on chronology first. This record comes from the eleventh or twelfth century, when the magnetic needle was already aboard ship. What follows concerns the earlier and much longer stretch, before the needle appeared, when people nonetheless fixed out east, west, north and south.
Begin with a passage in the Zhouli, “Kaogong ji”, section “Craftsmen”:
匠人建国，水地以县，置槷以县，眡以景。为规，识日出之景与日入之景，昼参诸日中之景，夜考之极星，以正朝夕。
(The craftsman establishes the state: he levels the ground by means of the plumb line, sets up the pole by means of the plumb line, and looks to the shadow. He draws a circle, marking the shadow at sunrise and the shadow at sunset, by day checking against the noon shadow, by night examining the pole star, and so corrects morning and evening.)
The words are few, but the unfamiliar characters are dense; each must be taken apart.
县 here is 悬, “to suspend”. A suspended cord gives a straight line, and water is used to test level. “To level the ground with a plumb line” is to make the ground flat.
槷 is read niè and is interchangeable with 臬; it is the gnomon, the pole set upright in the middle of level ground.
眡 is 视, “to look”. 景 is 影, “shadow”, the shadow of the sun.
为规 is to draw a circle with the pole as its centre. This step is the crux; without the circle there is nothing to compare the two shadows against.
The two characters 朝夕 are the most easily misread. They are not “morning and evening”. On “以正朝夕”, Zheng Xuan’s Han-dynasty commentary and Sun Yirang’s Qing-dynasty subcommentary are both explicit: to rectify zhao-xi is to rectify east and west.
Put together: level the ground, set up a pole, and draw a circle with the pole as centre. At sunrise mark the point where the tip of the pole’s shadow falls on the circumference; at sunset mark another.
The Zhoubi suanjing sets the method out more plainly:
其术曰：立正勾定之。以日始出，立表而识其晷；日入复识其晷。晷之两端相直者，正东西也；中折之指表者，正南北也。
(The method says: set up a true gnomon and fix it. At the first rising of the sun, set up the gnomon and mark its shadow; at sunset, mark the shadow again. The two ends of the shadows, joined straight, give true east and west; halved at the middle and pointed at the gnomon, they give true north and south.)
The moment the sun comes up, mark the shadow once; when it goes down, mark it again. Join the two ends of the two shadows, and that line is true east-west. Fold the line at its middle, and the midpoint so obtained, joined to the pole, is true north-south.
One pole, one circle, two marks a day. Direction comes out.
2. Why two shadows suffice
The reasoning is a single sentence: on the same day, the sun’s angle of illumination at sunrise and at sunset is the same.
The sun rises in the east and sets in the west; its light comes from directions that are symmetric between morning and evening. The tips of the two shadows are therefore left-right symmetric about the line of true north-south.
The axis of symmetry is true north-south.
The beauty of the matter: at no point does it require knowing any direction in advance. With a pole in hand and level ground underfoot, and two shadow marks a day, direction comes out of itself.
One thing must be explained. On the two days of the spring and autumn equinoxes the sun rises due east and sets due west; the pole’s shadow and the pole fall almost on the same east-west line, and the joining of the two ends does not hold. The Zhoubi suanjing also leaves a line: 冬至日加卯酉者……日不见矣, “on the day of the winter solstice at the hours mao and you … the sun is not seen”; there are days on which this cannot be measured at all.
So this must be done on chosen days, and repeated several times. It is not settled by a single measurement.
3. By day the sun, by night the stars
The second half of that passage in the Kaogong ji is 夜考之极星, “at night examine the pole star”. When the day’s work is done, the pole star is used at night to check it over.
The Huainanzi, “Qi su xun”, has a line, excellent:
夫乘舟而惑者，不知东西，见斗极则寤矣。
(One who is lost aboard a boat, not knowing east from west, on seeing the Dipper and the pole star at once understands.)
A person lost in direction aboard a boat, unable to tell east from west, at once understands on seeing the Dipper and the pole star.
Why can the pole star serve as true north? Because the earth’s axis points at it. All the stars in the sky turn through the night; only the pole star barely moves. To pick out one “unmoving” thing from a whole sky of “moving” ones is to obtain a fixed mark of direction.
One reminder here. The “pole star” spoken of today is today’s star. The celestial pole itself is also slowly moving, and the star nearest the pole two or three thousand years ago was not today’s. Hence the old books write “pole star” or “northern pivot” (北辰), which is a position, not the fixed name of a star. Behind this lies precession, which has a note of its own.
The Dipper, for its part, is the most serviceable ruler at night. The Shiji, “Treatise on the Celestial Offices”, says:
斗为帝车，运于中央，临制四乡。分阴阳，建四时，均五行，移节度，定诸纪，皆系于斗。
(The Dipper is the emperor’s chariot, revolving at the centre and governing the four quarters. The dividing of yin and yang, the establishing of the four seasons, the balancing of the five phases, the shifting of the measured degrees, the fixing of the several registers — all depend on the Dipper.)
The Dipper is the emperor’s chariot, revolving at the centre and governing the four quarters. Where the “centre” in the sky is, the four directions are thereby divided out.
The Yizhou shu, “Zhou yue jie”, also leaves a plainly written record: 斗柄建子，始昏北指, “the handle of the Dipper establishes 子; at dusk it points north”. At dusk the handle of the Dipper points north.
It must be made clear, though: the Dipper is not nailed in place pointing at one direction. The earth rotates, and it circles the celestial pole all night, so it is a dial that turns, and one must know when to look at it. The Dipper can also be used to fix the month, which is another matter, treated earlier.
4. Orientation was not reasoned out; it was dug up
What has been said above is all words on paper. Is there anything solid?
There is. And it is far earlier than paper.
At the Taosi site in Xiangfen, Linfen, Shanxi, the sacrificial area contains a structure numbered ⅡFJT1, roughly semicircular and covering about one thousand seven hundred and forty square metres. It takes the form of thirteen rammed-earth pillars enclosing twelve observation slots; the pillars stand at a radius of about ten point five metres from the centre, and the slots are mostly between fifteen and fifty centimetres wide, a width that roughly corresponds to the apparent diameter of the sun to the eye.
The use is this: a person stands at the fixed observation point at the centre and looks east, to see through which slot the sun passes as it rises over Mount Ta’er opposite. The slot is fixed; the sun moves. This reading is the excavators’ view, and voices of reservation are still heard in the field.
The structure as a whole faces south-east. Its method is precisely to use a fixed reference point to measure the direction of sunrise. From a large tomb of the middle Taosi period a painted wooden gnomon rule with graduations was also unearthed, the earliest physical example of a gnomon instrument so far found anywhere by archaeology.
He Nu, a researcher at the Institute of Archaeology of the Chinese Academy of Social Sciences, summed the whole thing up in four characters: 经天纬地, “to lay out the sky and weave the earth”. To lay out the sky is to fix the calendar and reverently to bestow the farming seasons; to weave the earth is to distinguish the directions and set the positions, to establish the centre and set up the pole.
The two characters “weave the earth” speak precisely of fixing direction.
An earlier site is at Puyang in Henan. Tomb 45 of the Xishuipo site, excavated in 1987, belongs to the Yangshao culture period, about six thousand five hundred years ago.
Researchers noticed one thing: four groups of remains — tomb 45 itself plus three subsidiary shell-mosaic features — are laid out strictly on the same meridian, evenly spaced, one group every twenty-five metres southward. On this basis it is judged that such an arrangement is no accident, and that the people of the time could already determine the meridian and used it to lay out the whole space.
The mosaics in the tomb are these: on the east side of the tomb occupant a dragon in shell, on the west side a tiger in shell; at the feet a triangular figure in shell, read as the Dipper, its handle laid out with two human shinbones. Researchers hold that two methods — setting up the gnomon to measure shadows, and observing the Dipper — are placed here together.
Taken together, these two sites show one thing: orientation was not an idea slowly groped toward. Six thousand five hundred years ago it was already set out precisely on the ground.
5. From a pole to a needle
Return to that order at the beginning. Before the compass, people relied on the pole, the shadow and the stars.
Where, then, do the two characters 司南 (sinan) come from?
Many do not know that it was not originally a magnetic spoon. The Han Feizi, “You du”, has a line:
故先王立司南，以端朝夕。
(Therefore the former kings set up the sinan, to rectify morning and evening.)
To rectify zhao-xi is to rectify east and west, the same sense as 以正朝夕 in the Kaogong ji. So the earliest “sinan” means a gnomon pole for measuring shadows.
The Guiguzi, “Mou pian”, says:
郑人之取玉也，必载司南之车，为其不惑也。
(When the men of Zheng went to fetch jade, they would carry a sinan cart, so as not to lose their way.)
When the men of Zheng went to gather jade, they carried a sinan on the cart, so as not to lose the way. By this point the sinan could be carried along.
By the Eastern Han, Wang Chong wrote in the Lunheng, “Shi ying pian”:
司南之杓，投之于地，其柢指南。
(The ladle of the sinan, set down on the ground, has its handle point south.)
By then the sinan was a ladle-shaped object which, set on the ground, has its handle pointing south. The character 杓 in this line is written 勺 in some editions.
After that comes magnetism. Shen Kuo of the Northern Song records an entry in the Mengxi bitan, chapter 24:
方家以磁石磨针锋，则能指南，然常微偏东，不全南也。
(The masters of methods rub the point of a needle with lodestone, and it can then point south; but it usually inclines slightly east, and does not point due south.)
Rub the tip of a needle with lodestone and the needle can point south, but it usually inclines slightly east, and does not point due south. Shen Kuo set down the three characters “inclines slightly east”, about four hundred years before Europeans discovered magnetic declination.
A single line now becomes clear:
Period
What direction was fixed by
Pre-Qin
Setting up the gnomon to measure shadows — one pole, two shadows
Warring States to Han
“Sinan” passes from gnomon pole to the name of an object
Northern Song
Artificially magnetised steel needles; Shen Kuo records magnetic declination
Song-Yuan and after
The magnetic needle goes aboard ship, fitted into the compass
The name changed, the instrument changed; the thing to be done was exactly the same — to fix direction.
6. Once orientation was fixed, it became a rule
Once direction was measured out, it did not stop at the level of measurement. It entered ritual, and it entered speech.
The Zhouyi, “Shuo gua”: 圣人南面而听天下，向明而治 (“The sage faces south to hear the affairs of the world, and governs facing the light.”). To face south is the sovereign’s position. In the Zhuangzi, “Dao zhi”, it becomes a set phrase altogether: 南面称孤, “facing south and calling oneself the lone one”.
The reverse is to face north. The Shiji, “Biographies of Li Yiji and Lu Jia”: 君王宜郊迎，北面称臣 (“Your Majesty should go out to the outskirts to meet him, and face north to call yourself his subject.”). To face north is the subject’s position.
Carriages have their own rules. The Shiji, “Biography of the Lord of Wei”: in going to meet Master Hou, 公子从车骑，虚左 (“the prince brought the carriage and outriders and left the left-hand seat empty”), leaving the left-hand seat vacant. To leave the left vacant is the highest respect. Hence the idiom 虚左以待, “to leave the left seat vacant in expectation”.
There is also the “host of the eastern road” (东道主, dongdaozhu). In the Zuozhuan, thirtieth year of Duke Xi, the state of Zheng lay east of Qin and was willing to entertain guests coming from the east, and so was called the host of the eastern road.
One point easily misunderstood must be made clear. “In the hall, facing south is the place of honour; indoors, facing east is the place of honour”; these are two different settings — deliberation in the hall and drinking indoors — and the rules differ. As for whether “left” or “right” ranks higher, the dynasties are not consistent.
A last word: 败北 (baibei, “to suffer defeat”).
The word has nothing to do with direction. 北 is an ancient form of 背, “back”. The Shuowen jiezi: 北，苝也，从二人相背 (“北 is 苝; it is formed from two people turning their backs to each other.”). When two armies fight, the defeated turn and run with their backs to the enemy, and so it is called baibei. Even if the beaten army runs all the way south, it is still called baibei.
Closing
Return to that pole.
The passage in the Kaogong ji does three things: level the ground, set up a pole, draw a circle. Then wait for sunrise, wait for sunset, and mark the shadow twice.
Once in the morning, once in the evening; join them into a line and it is east-west; fold it back at the middle to point at the pole, and it is north-south.
The Huainanzi says 见斗极则寤矣, “on seeing the Dipper and the pole star, one understands”; a lost person, seeing the Dipper and the pole star, at once understands. And before ever seeing the stars, people had already measured direction out with a pole.
East, west, north and south were not written on the ground to begin with. They were measured out by people with a pole, marking the shadow twice a day.
A&Q
Without a compass, how did the ancients fix east, west, north and south?
Set up a pole, draw a circle, mark the two shadow-tips at sunrise and at sunset. Join the two ends for true east-west; fold back from the middle toward the pole for true north-south. This is 以正朝夕 in the Zhouli, “Kaogong ji”.
Why are two shadow markings enough?
On the same day the sun’s angle of illumination at sunrise and at sunset is the same, and the two shadow-tips are left-right symmetric about the true north-south line. So no direction need be known in advance.
Was the “sinan” originally a magnetic spoon?
No. The Han Feizi, “You du”, says 立司南，以端朝夕; to rectify zhao-xi is to rectify east and west, and it means a gnomon pole for measuring shadows. Only with Wang Chong’s Lunheng, “Shi ying pian”, of the Eastern Han does 司南之杓 appear, a ladle-shaped object.
Who first recorded magnetic declination?
Shen Kuo. In the Mengxi bitan, chapter 24, he writes 常微偏东，不全南也, about four hundred years earlier than Europeans.
Does 败北 mean “to run north”?
No. 北 is an ancient form of 背, and the Shuowen jiezi says 从二人相背. A person defeated in battle runs with his back to the enemy, and so it is called baibei; whichever direction he runs, it is still called baibei.
Note by Chujia Kuang
One pole, one circle, two shadows a day: it looks crude, but the reasoning is deep. It does not require you first to know east, west, north and south; rather, it hands them to you. What is called a “sense of direction” today mostly means finding one’s way; direction as the ancients spoke of it was measured accurately first, and then used to fix ritual, position and cities. Once this level is established, later treatment of the earthly branches matched to directions, and of the three unions and three meetings, has a root.
About the author
Chujia Kuang (邝楚嘉), pen name Jiayan Yide (嘉言一得), is an independent researcher in Jieyang, Guangdong, devoted to archiving verifiable primary sources and calendar data.
This column writes about calendrics, solar terms, the stems and branches and orientation, and also about what he reads. The pen name 嘉言一得 comes from the 史记: 愚者千虑，必有一得, “the foolish man’s thousand thoughts must yield one gain”. Where something is written wrongly, corrections are welcome.
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record (没有指南针，古人怎么定方向).
[13] Zhu Yu. Pingzhou ketan [萍洲可谈][M]. Song dynasty.
[14] Shen Kuo. Mengxi bitan [梦溪笔谈][M]. Song dynasty.
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the excavated Qin and Han bamboo-slip photographs and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
For the full terms of the licence, see: https://creativecommons.org Related articles
