Overview

The use of a calendar is to measure time for the purpose of actual business and to record historical events. Calendars are also used to determine days of festivities or natural events (like solar eclipses), and to prognosticate auspicious or non-auspicious days. The calendars of all cultures are based on astronomical phenomena like the movement of the moon, the “movement” of the sun, and those of planets and starry constellations. The traditional Chinese calendar is a combination of a solar calendar (based on the “position” of the sun and the resultant seasonal phenomena) and a lunar calendar (following the lunar phases).

The "peasant calendar" (nongli 農曆), also called "old calendar" (jiuli 舊曆) or "Chinese calendar" (Zhongli 中曆) is the traditional calendar used in China before the official introduction of the Western calendar in 1912. It is still widely used among the people, especially in Hong Kong, Taiwan and among Chinese overseas communities, mainly for traditional holidays and festivities, and for the determination of auspicious days and hours. The peasant calendar divides the year into 24 so-called solar terms (ershisi jieqi 二十四節氣) whose names indicate agricultural activities and the phaenology of the nature like daxue 大雪 "Heavy snow", shuangjiang 霜降 "Hoar frost descends", or Jingzhe 驚蟄 "Excited insects". This traditional calendar is allegedly in use since the Xia period 夏 (17th-15th cent. BCE), and therefore also called the "Xia calendar" (Xiali 夏曆). The oldest records on the Chinese calendar are to be found in the book Xia xiaozheng 夏小正. Because of the great importance of the moon for the calculation of this calendar, it is also known under the name of "Yin, i.e. moon or lunar, calendar" (yinli 陰曆). The course of the months is stringently geared to the new moon phase, and therefore it is necessary to make from time to time use of an intercalary month (runyue 閏月) to cover the leap to the solar calendar that increments in the course of time. A year with an intercalary month is called runnian 閏年. The "peasant calendar" is therefore in fact a luni-solar calendar (modern term yinyangli 陰陽曆), and not a purely lunar calendar.

The first month is called zhēngyuè (!) 正月, but the other months are given regular numbers, like eryue 二月 "second month", sanyue 三月 "third month", and to son. Each month begins at midnight on the day when the lunar path (baijing 白經) and the solar path (huangjing 黃經) fall together. This day is called the "first day" (chuyi 初一), the second chu'er 初二, the third chusan 初三, and so on, but from the tenth day on the syllable chu is dropped and instead the word ri "day" is added, like shiri 十日 "the tenth", shiyiri 十一日 "the eleventh". There are "long months" (dayue 大月) with a length of 30 days, and "small months" (xiaoyue 小月) with a length of 29 days, in such a combination over the year that the real length of a month of 29.53059 days is met on average. This results in a length of the lunar year of 354 of 355 days, which makes for a leap of around between 10 and 12 days to the solar year.

An intercalary month has therefore to be inserted alternately all two or three years, which makes for an average (called runzhou 閏周 "intercalary cycle") of seven intercalary months (called zhangrun 章閏 "full set of intercalary months") in a period of 19 years (zhangsui 章歲 "full set of years"). This is because the length of 19 years is very close to the exact length of 235 lunar months, as already observed in the Four-Parts Calendar (sifen li 四分曆) from the Warring States period 戰國 (5th cent.-221 BCE) . At which time in the year an intercalary month is inserted, depends on the 24 solar terms and the general conditions to be expected during that time. Unlike in the Western calendar, where the intercalary day is always February 29th, the Chinese lunar calendars knows intercalary months throughout the year (except months during which the so-called zhongqi 中氣 solar terms occur: yushui 雨水, chunfen 春分, guyu 穀雨, xiaoman 小滿, xiazhi 夏至, dashu 大暑, chushu 處暑, qiufen 秋分, shuangjiang 霜降, xiaoxue 小雪, dongzhi 冬至, and dahan 大寒), for instance, the "intercalary (month after the) third month" (run sanyue 閏三月). The ancient "intercalary cycle" method was still not very perfect, and was therefore ameliorated by Zhao Fei 趙{非+欠} who lived in the small empire of Northern Liang 北涼 (398-439) during the Sixteen States period 十六國 (300~430) and defined the intercalary cycle as 221 intercalary months in 600 years. Zu Chongzhi 祖沖之 of the Liu-Song period 劉宋 (420-479) used a relationship of 144 intercalary months in 391 years, which is more accurate that the method of Zhao Fei. Li Chunfeng's 李淳風 Linde Calendar 麟德曆 from the Linde reign-period 麟德 (664-665) of the Tang period 唐 (618-907) was the last calendar in which the intercalary cycle had to be fixed anew.

The beginning of the first month of the traditional peasant calendar is oriented towards the winter solstice, that is the date on which the day is shortest and the night longest (December 21 according to the Western Calendar). The New Year's Day (yuandan 元旦) of the traditional Chinese calendar was (and is), the day of the second newmoon following the winter solstice. The oldest calendar of China was the so-called Xia calendar 夏曆. During the Xia period the beginning of the year was on the first day of the first month (zhengyue chuyi 正月初一), during the Shang period 商 (17th-11th cent. BCE) the first day of the twelfth month of the Xia calendar, during the Zhou period 周 (11th cent.-221 BCE) on the first day of the eleventh month of the Xia calendar, and during the Qin 秦 (221-206 BCE) and the early Han 漢 (206 BCE-220 CE), on the first day of the tenth month. During the calendar reform (the introduction of the Taichu calendar 太初曆) under Emperor Wu 漢武帝 (r. 141-87 BCE) of the Han dynasty the beginning of the calendric year was shifted back to the first day of the first month of the Xia calendar, which is valid until today.

Chronology

Time is measured with the help of several methods. Besides units also known in the Western calendar (seasons, months, weeks and hours), the traditional Chinese calendar makes use of several more concepts, namely the 24 solar terms (ershisi jieqi 二十四節氣), the sexagenarian cycle (a combination of the ten signs or characters called Celestial Stems and the twelve signs known as Terrestrial Branches), and the Jupiter year.

Dynasties

In Western historiography the history of mankind (which begins with the existence of written sources) is divided into the three ages of Antiquity (ca. 600 BCE–600 CE), the Middle Ages (ca. 600–1500), and the Modern Age. Marxist theoreticians divided history into the age of the slaveholder society (corresponding to Antiquity), the age of feudalism (ca. 600-1750), and the age of capitalism. This socio-economical approach is also important for the People's Republic of China where Marxist theoreticians had and still have problems to transfer this model on Chinese history. They see the end of the age of feudalism in the Xinhai Revolution 辛亥革命 from 1911 and the phase of capitalism from 1912 to the "liberation" of 1949. A similar tripartite timeline like the Antiquity-Middle Age-Modern Age model which pretends a kind of intellectual and scientific progress, does not exist in traditional Chinese historiography. Western sinologists see the Chinese age of Antiquity (the "Golden Age" that served as a model for later times) as the time from 1200 BCE to ca. 300 CE, that of the Middle Ages (the "Dark Age" of equestrian warriors) from 300-900 CE, and the Modern Age (with a great progress in technology and fundamental changes in the social structure) as beginning with the Song dynasty.

Instead, history was in China traditionally divided into dynastic cycles, in which a ruling family or dynasty sees its rise and victory over a predecessor (mostly because of its military, but also moral superiority, and therefore being selected as "sons of Heaven", see Heaven), an apogee of cultural, economic and military (seen in territorial expansion) success, and a downfall due to corruption among the officialdom and depravity of the ruling house. The concept of the dynastic cycle focuses on the political history of the dynasty itself and neglects factual changes in the power structure, the administrative system, society, economy and the material and intellectual culture. Chinese history therefore seems to be an everlasting "revolution" (in the astronomical sense) of ups and downs of ruling families that sometimes were able to unify the whole territory of China, and sometimes failed to do so, with the result that China was divided into several empires or states. Still today, biographies persons begin with an indication of the dynasty under which he or she lived.

While the Egyptian dynasties are counted with numbers, the Chinese dynasties are given names. Most of these names are derived from a territory over which a dynastic founder was the master before becoming emperor. The name of the Han dynasty 漢 (206 BCE-220 CE), for instance, is derived from the name of a river in a region (Hanzhong 漢中) over which Liu Bang 劉邦, the dynastic founder, was made king. Similarly, the Wei dynasty 魏 (220-265) has its name derived from the kingdom of Wei, over which Cao Cao 曹操, the father of the first emperor of the dynasty (Cao Pi 曹丕), had ruled. The names of the dynasties (chao 朝, literally "the place to be faced", i.e. the court) are at the same time the name of their empire (guo 國). The Han dynasty (Han chao 漢朝) ruled over the Han empire, and the Tang dynasty 唐 (618-907) over the Tang empire. Through history, therefore, "China" was known with many different names, changing with the access of a new dynasty. The Japanese even continued to name China "Tang" (Tō) after the downfall of that dynasty. The last three imperial dynasties named themselves with mottos, namely Yuan 元 (1279-1368) "the (new) Origin", Ming 明 (1368-1644) "the Brilliant", and Qing 清 (1644-1911) "the Pure".

There are not a few cases in which fresh emperors chose a name for their dynasty that had already been used. In order to discern these dynasties and their empires, historians used suffixes (like geographic terms, time words, or family names), like the Southern Qi 南齊 (479-502) and the Northern Qi 北齊 (550-577), the Liu-Song 劉宋 (420-479) and the (Great) Song 宋 (960-1279), the Cao-Wei 曹魏 and the Later 後魏 or Northern Wei 北魏 (386-534). These suffixes are also used to discern between distinctive phases in a dynasty's life cycle, like Western Zhou 西周 (11th cent.-770 BCE) and Eastern Zhou 東周 (770-221 BCE), Western 西漢 or Former Han 前漢 (206 BCE-8 CE) and Eastern 東漢 or Later Han 後漢 (25-220 CE), Western 西晉 (265-316) and Eastern Jin 東晉 (317-420), Northern Song 北宋 (960-1126) and Southern Song 南宋 (1127-1279). In all these cases, the dynasty had been forced to move its capital to another place as a consequence of a drastic political incidence (invasion by "barbarians" or re-founding of the dynasty after inner turmoils).
The name of the dynasty is (unlike in Europe, like Tudor, Bourbon or Hapsburg) not identical to the family name of the ruling house (the family Liu 劉 constituted the Han dynasty, the family Li 李 the Tang, and the rulers of the Song dynasty had the family name Zhao 趙). The only exception is the short-lived Chen dynasty 陳 (557-589), whose founder had the family name Chen, but the name of the dynasty has been chosen because its founder Chen Baxian 陳霸先 had been king of Chen before adoptiong the title of emperor. The names of the dynasties are also used to designate the time during which they ruled. The Han ruled during the Han period (Han dai 漢代), and the Qing during the Qing period (Qing dai 清代).

This method is problematic during those times during which several dynasties shared "China" among themselves. During the Three Empires period 三國 (220-280), for instance, the three dynasties Wei, Shu 蜀 (221-263) and Wu 吳 (222-280) were ruling simultaneously over different parts of "China". It is therefore not appropriate to speak of the Wu period or the Shu period. Historians disputed about which of the three dynasties was the righteous successor of the Han, and chose the Wei dynasty. The Three Empires period can therefore be identical with the Wei period, but the Wei dynasty was ended before the last of the Three Empires, Wu, was conquered by the Wei's successor, the Jin dynasty. Similar instances or parallel ruling houses are the Southern and Northern dynasties period 南北朝 (300~600, with a group of dynasties following each other in the south, and several realms in the north that ruled over different parts of northern China), the Five Dynasties period 五代 (907-960, with five dynasties ruling consecutively over the north and ten states ruling over various parts of southern China), and the Song period. The Song period is actually an exception from the former cases because the Song ruled only over central and southern China, while the north was occupied by the Liao empire 遼 (907-1125), and then the Jin empire 金 (1115-1234), and the northwest by the Western Xia empire 西夏 (1038-1227). There is no overarching term for this period of time like "Southern and Northern Dynasties". The three dynasties ruling over the north were of non-Chinese origin (Khitans, Jurchens and Tanguts), just like the Yuan dynasty that was founded by the Mongols and ruled over the whole of China.

Reign-Periods

Because there is no fix year in Chinese history to which the calendar is related to (like the birth year of Jesus Christ, Mohammed's escape of Medinah, or the "creation of the world"), the actual ordinal year of an emperor's reign (the reign-period or era) or that of his reign mottos (nianhao 年號) were used to indicate a year. Before and in the first decades of the Han period 漢 (206 BCE-220 CE), there were still no reign mottos. Years were therefore indicated by the length of a ruler's reign, like Jingwang shisan nian 敬王十三年 "thirteenth year of King Jing's (the king of Zhou, r. 520-476 BCE) reign", or Wendi san nian 文帝三年 "third year of Emperor Wen's (emperor of the Han dynasty, r. 180-157 BCE) reign". It is important to note that the first year of a reign-period was not that in which the emperor acceded to the throne, but the next one, after the first New Year had passed. This was an expression of filial piety towards the late king or emperor. King Jing of the Zhou dynasty, for instance, acceded to the throne in 520 BCE, but his first year of reign (Jingwang yuannian 敬王元年) was 519 BCE. The first year of a reign or reign-period (period under a certain motto) is called yuannian 元年, the others are regularly counted (ernian 二年, sannian 三年 etc.).

The first introduction of a new reign era was inaugurated in 163 BCE under Emperor Wen 漢文帝 (r. 180-157 BCE) who declared this year as Houyuan yuannian 後元元年 "First year of the later Origin". His successor, Emperor Jing 漢景帝 (r. 157-141 BCE), inaugurated two new reigns, Zhongyuan 中元 "Middle Origin" (this name might have been given retrospectively) in 149 BCE, and Houyuan 後元 "Later Origin" in 143 BCE. His son, Emperor Wu 漢武帝 (r. 141-87 BCE), was the first who chose a motto for the first full year of his reign, namely Jianyuan 建元 "Establishment of a (new) origin", in 140 BCE. Six years later he chose the reign motto Yuanguang 元光 "Brilliance of the origin", which lasted for another six years. Emperor Wu's reign mottos were also the first whose names had a meaningful slogan. During his whole reign from 141 to 87 BCE he made use of eleven reign mottos. From then on all emperors made use of reign mottos, and even usurpers or counter-emperors used to proclaim a reign under new auspices. Liu Yu 劉豫, Emperor of Qi 齊 (r. 1130-1137), for instance, chose the motto Fuchang 阜昌 "Brilliance of Qufu 曲阜" (Qufu was the home town of Confucius that was located in Liu Yu's small empire), and the usurper Li Zicheng 李自成, who proclaimed himself Emperor of Dashun 大順 (r. 1644-1645), the motto Yongchang 永昌 "Everlasting brightness". President Yuan Shikai 袁世凱 made himself emperor on January 1, 1916 (forced to resign on April 24) and chose the reign motto Hongxian 洪憲 "All-Embracing Constitution".

Most reign mottos are two syllables or words long, but during the Song period 宋 (960-1279) some four-syllable mottos were chosen like Taiping xingguo 太平興國 "Flourishing of the State under the Great Peace" (976-983), Dazhong xiangfu 大中祥符 "Auspicious Omen of the Great Centre" (1008-1016) or Jianzhong jingguo 建中靖國 "Pacified State Established in the Middle" (1101). Some mottos were fashionable during certain times, like the words chun 淳 "pure" and you 祐 "heavenly assistance" that are almost exlusively used by the Song dynasty.

To make identification by a reign motto easier, the mottos were rarely used more than once through Chinese history. Yet there are some exception, like the motto Yong'an 永安 "Everlasting Peace" that was used by the Wu dynasty 吳 (258-263), the Jin dynasty 晉 (304), the statelet of Northern Liang 北涼 (401-411), the Northern Wei dynasty 北魏 (528-529) and the Western Xia 西夏 (1098-1100).

There are two basic problems with this method. The first is that if a ruler was not accepted as the legal sovereign or during times of political division, several mottos (and therefore also different calendars with different years) were used at the same time. During the Eastern Zhou period 東周 (770-221 BCE) it was not only the king of Zhou who ruled by his own calendar, but each of the regional rulers counted the length of his own rule as an instrument of measuring years. This makes it very complicate to identify a year during that time, and leads easily to errors. One example might highlight this complexity.
The Western year 477 BCE was the ...

43th year of King Jing of Zhou 周敬王

16th year of Duke Ai of Lu 魯哀公

4th year of Duke Ping of Qi 齊平公

35th year of Duke Ding of Jin 晉定公

14th year of Duke Dao of Qin 秦悼公

12th year of King Hui of Chu 楚惠王

40th year of Duke Jing of Song 宋景公

1st year of Lord Qi of Wei 衛君起

14th year of Marquis Cheng of Cai 蔡成侯

24th year of Duke Sheng of Zheng 鄭聲公

16th year of Duke Xian of Yan 燕獻公

the 19th year of King Fucha of Wu 吳王夫差

Similar, but less extreme cases occurred during the Three Empires period 三國 (220-280), the Southern and Northern Dynasties 南北朝 (300~600) period, the Five Dynasties period 五代 (907-960), and the period of the Song 宋 (960-1279), Liao 遼 (907-1125) and Jin 金 (1115-1234) dynasties.

Table xx. Parallel reign-mottos of the Three Empires

Wei 魏	Shu 蜀	Wu 吳
Huangchu 黃初 (220-226)	Zhangwu 章武 (221-222)	Huangwu 黃武 (222-228)
	Jianxing 建興 (223-237)
Taihe 太和 (227-232)
		Huanglong 黃龍 (229-231)
		Jiahe 嘉禾 (232-237)
Qinglong 青龍 (233-236)
Jingchu 景初 (237-239)
	Yanxi 延熙 (238-257)	Chiwu 赤烏 (238-250)
Zhengshi 正始 (240-248)
Jiaping 嘉平 (249-253)
		Taiyuan 太元 (251)
		Shenfeng 神鳳 (252)
		Jianxing 建興 (252-253)
Zhengyuan 正元 (254-255)		Wufeng 五鳳 (254-255)
Ganlu 甘露 (256-259)		Taiping 太平 (256-257)
	Jingyao 景耀 (258-262)	Yong'an 永安 (258-263)
Jingyuan 景元 (260-263)
	Yanxing 炎興 (263)
Xianxi 咸熙 (264-265)		Yuanxing 元興 (264)
		Ganlu 甘露 (265)

Most emperors before the Ming period 明 (1368-1644) changed their reign mottos several times during their reign the counting of years began anew. The change of a reign motto is indicated by the word gaiyuan 改元 "change to a new first year". Such a change could be made during the course of a year and was sometimes effected just in the middle of a current year, and not necessarily with the beginning of a new calendric year. Empress Wu Zetian 武則天 (r. 684-690) was most notorious for this practice because reign mottos, expressing a style of rule or an auspicious omen supporting the reign, played an important role in her legitimization. Yet also other rulers used to play this game. On the day eryue yimao 二月乙未 ([30th day of the] second month, with the cyclical signs yi and mao) of the sixth year of the Xianqing reign-period 顯慶 (i. e. April 4, 661 CE) Emperor Gaozong 唐高宗 (r. 649-683) changed the reign motto to Longshuo 龍朔, and the first year of this reign began on sanyue bingshen 三月丙申 ([1st day of the] third month, with the cyclical signs bing and shen), with the new moon. During his more than thirty-years-long reign he changed his motto no less than fourteen times, and Empress Wu Zetian, who was factual emperor for slightly less than five years, had four reign mottos, on average one for each year. The opposite paradigm was Emperor Xuanzong 唐玄宗 (r. 711-755), who ruled even longer, but only proclaimed three reign mottos, the longest, Kaiyuan 開元 (713-741), lasting for 29 years.

From the Ming period on there were only very few occasions that the reign motto was changed by one emperor. Emperor Yingzong 明英宗 (r. 1435-1449) of the Ming chose a new motto when he came back to the throne in 1456; and Huang Taiji, the khan of the Jurchens, who had two mottos, the second of which was chosen in 1636 because he renamed his dynasty from (Later) Jin 後金 to Qing 清 (1644-1911). During the Ming and Qing periods each emperor had practically only one reign motto. For this reason the emperors of these two dynasties are usually not called with their posthumous title (like Wendi 文帝 or Wudi 武帝) or their temple name (like Taizong 太宗 or Taizu 太祖), but with their reign motto (e.g. the Wanli Emperor 萬曆帝, the Guangxu Emperor 光緒帝). Among these, the Jiajing Emperor 嘉靖帝 (r. 1521-1566) ruled for 45 years, the Wanli Emperor for 48 years, the Kangxi Emperor 康熙帝 (r. 1661-1722) for 61 years, and the Qianlong Emperor 乾隆帝 (r. 1735-1796) for 60 years. In Western literature, the era names are often used to refer to emperor, like "Emperor Kangxi". Reign periods were sometimes abbreviated and joint to expressions signifying two or three reign-period, like Kang-Yong-Qian 康雍乾 for the reign-periods Kangxi, Yongzheng 雍正 (1723-1735), and Qianlong, or Dao-Xian 道咸 for the the decades of the reign-periods Daoguang 道光 (1821-1850) and Xianfeng 咸豐 (1851-1861).

A particular problem with chronology is that the first reign motto of a sovereign was only chosen for the new year after the accession of the throne, as an expression of piety towards the predecessor. This means that Kaiyuan yuannian 開元元年 (year 713 CE) was the first year with the reign motto Kaiyuan "Opening the Origin", but already the second calendric year in which Emperor Xuanzong 唐玄宗 (r. 712-755) of the Tang ruled. For the Qing period, this means that the Kangxi reign-period lasted from xxx 1662 to 1722, but the Kangxi Emperor ruled from 5 Feb 1661 to 20 Dec 1722.

To make things even more complex, the New Year begins in China according to the lunar calendar which is somewhat later than in the Western calendar. The four to eight weeks of difference in the beginning of the year have to be taken into account when converting traditional Chinese years into Western years. It is therefore not quite correct to say that the year Yongzheng yimao 雍正乙卯 was 1735 (the 13th year of the Yongzheng reign-period, with the cyclical signs yi and mao), but the year yimao (and the 13th year with the reign motto Yongzheng) reached from 24 Jan 1735 to 11 Feb 1736, while the Yongzheng Emperor had already died on October 8, 1735, and his son took over official functions on October 16, the first day of the ninth lunar month. For the reason of convenience, this small overlapping of the Western and Chinese calendar is often neglected when indicating years only, even if this leads to errors in dates.

This can be very confusing because one year can be referred to by several different reign mottos, like the year 692 that was the third year with the reign motto Tianshou 天授 "Celestial instruction", yet in the fourth month (approx. May-Jun) the reign motto Ruyi 如意 "As we wish" was chosen, and in the ninth month (approx. Oct-Nov) the motto Changshou 長壽 "Longevity". Similarly confusing is a period of time when several dynasties reigned China. The year 1066, for example, was the third year with the reign motto Zhiping 治平 "Ruling to peace" in the Northern Song empire, the second year with the reign motto Xianyong 咸雍 "Everything in harmony" in the Liao empire and the fourth year with the reign motto Gonghua 拱化 "Towards an all-embracing [policy]" in the Western Xia empire. The change of the reign motto was called gaiyuan 改元 "change over to a (new) beginning". When a new emperor mounted the throne it was common that the reign motto of his predecessor (in most cases, the new emperor's father) was retained until the first day of the next year. Such a proclamation was often combined with a great amnesty (dashe 大赦).

The counting of years by reign mottos was also known in Vietnam and is still in use in Japan (because it is the only one of the East Asian countries where still an emperor exists). The reign motto of the retired Japanese emperor Akihito 明仁 (r. 1989-2019) was Heisei 平成 "Outbalanced Completion", and Bảo Đại 保大 "Protection of Grandness" (1926-1945) was the reign motto of the last emperor of Vietnam (while his personal name was Nguyễn Phúc Thiển 阮福晪). The Manchu rulers of the Qing dynasty chose two reign mottos, one in Chinese, and one in Manchurian. The names are not in all cases literal translations of each other. XXX

After the foundation of the Republic in late 1911 it was decided to rename the year 1912 into the first year of the Republic (Minguo yuannian 民國元年). With this decision, the traditional Chinese method of counting years was retained, while the official luni-solar calendar itself was replaced by the Western calendar, at least in public. After 1949, the Republican government in Taiwan retained the "reign-motto" method and still uses it today, side by side with the Western year.

Reign mottos are also inscribed on coins, instead of using the idealized portraits of rulers, like in the West. A common inscription of a very common and widespread coins was, for instance, Kaiyuan tongbao 開元通寶 "Circulating wealth from the Kaiyuan reign-period (713-741)".

Years

The beginning of time periods in the Chinese calendar is always tied to the new moon (shuo 朔). Each month in the lunar calendar thus begins with a new moon (black and invisible), just like the year begins at the point of time when Yin (inactive, hidden, dark) prevails over nature. The problem for ancient astronomers was that the velocity of the moon on its path around the earth is not constant (like all celestial bodies, the moon follows an elliptic path on which it moves quicker in the parts of its orbit that are closer to the earth) and therefore the length of time between one new moon and the next are not exactly the same. A long-term middle value of this length is called the "lunar month" (shuowangyue 朔望月) or "leveled month" (pingshuo 平朔), and the calculation method is called "fixing (the date of the) new moon" (dingshuo 定朔). xxx

Table x. The Ten-Years Cycle of the Ten Celestial Stems (shi tiangan 十天干)

no.	stem	astrological names
1	甲 jia	閼逢 efeng, 焉逢 yanfeng
2	乙 yi	旃蒙 zhanmeng, 端蒙 duanmeng
3	丙 bing	柔兆 rouzhao, 遊兆 youzhao
4	丁 ding	強圉 qiangyu, 彊梧 qiangwu
5	戊 wu	著雍 zhuyong, 祝犁 zhuli
6	己 ji	屠維 tuwei, 徒維 tuwei
7	庚 geng	上章 shangzhang, 商橫 shangheng
8	辛 xin	重光 chongguang
9	壬 ren	玄黓 xuanyi, 橫艾 heng'ai
10	癸 gui	昭陽 zhaoyang, 尚章 shangzhang
The ten Celestial Stems, constituting the first part of the sixty cyclical designations of years, with their astrological names. The cycle of these years is independant from historical events and runs permanently.

Each year bears the designation of a combination of two cyclical signs, namely the 10 Celestial Stems (shi tiangan 十天干) of the Ten-Years Cycle and the 12 Terrestrial Branches (shi'er dizhi 十二地支) which are combined to a cycle of 60 (with only the first half of all possible combinations used). In popular belief each year represents one of twelve animals, whose character is ascribed to all persons born in that year. This "zodiac" (which has nothing to do with starry constellations like in the West) is connected to the twelve Terrestrial Branches, which are always in the second position of the cyclical combination. This means that all years with the cyclical combinations jiazi 甲子, bingzi 丙子, wuzi 戊子, gengzi 庚子, and renzi 壬子 are "years of the rat". There are many helpful tools in the internet to show which year corresponds to which animal. In translations the animal cycle is often preferred because it is easier to comprehend for a Westerner than a detailed explanation of the the clumsy combination of the two stem and branches cycles.

Table x+1. The Twelve Years of the Jupiter Cycle or Twelve Terrestrial Branches (shi'er dizhi 十二地支)

no.	branch	animal	astronomical names
1	子 zi	鼠 shu rat, mouse	困敦 kundun
2	丑 chou	牛 niu ox, cow	赤奮若 chifenruo
3	寅 yin	虎 hu tiger	攝提格 shetige
4	卯 mao	兔 tu rabbit	單閼 dan'e
5	辰 chen	龍 long dragon	執徐 zhixu
6	巳 si	蛇 she snake	大荒落 dahuangluo, 大芒落 damangluo
7	午 wu	馬 ma horse	敦牂 dunzang
8	未 wei	羊 yang sheep, ram	協洽 xieqia, 汁洽 zhiqie
9	申 shen	猴 hou monkey	涒灘 tuntan, 苪漢 binghan
10	酉 you	雞 ji cock, roaster	作噩 zuo'e, 作鄂 zuo'e
11	戌 xu	狗 gou or 犬 quan dog	閹茂 yanmao, 淹茂 yanmao
12	亥 hai	豬 zhu pig, boar	大淵獻 dayuanxian
Designation of years by the twelve Terrestrial Branches, the animal zodiac, and their astronomical names. The Branches are combined with the Ten Stems to a cycle of sixty years. While the Ten Stems represent a decade of years, the Twelve Branches constitute a "dodecade" of years. As can be seen from the existence of astronomical names, they are derived from the stations of the planet Jupiter during its twelve-years-long phase of XXX.

In combination with a reign motto, years are often indicated by rendering the cyclical combination (a method called ganzhi jinian fa 干支紀年法), like Daoguang renchen 道光壬辰 "the year with the cyclical combination renchen 壬辰 during the Daoguang reign-period (1821-1850)", i.e. 1832, or dingchou nian 丁丑年 or dingchou sui 丁丑歲 "during the year with the cyclical combination dingchou". The latter example can only be exactly determined if the historical context of the statement is known, because every sixty years, the cyclical combinations repeat. The year dingchou might be 1877, 1937 or 1997.

Apart from the animal cycle and the cyclical combinations, Chinese literature makes use of several alternative designations for years that are partially astronomical, partially colloquial, and some also poetic. The astronomical designations for the twelve Terrestrial Branches are derived from the names of the station of the planet Jupiter (suixing 歲星) in its twelve-year cycle around the sun. For each year of the Jupiter cycle, there are designations that probably originate in Indian astronomy. According to this method (called suixing jinian fa 歲星紀年法), the year with the cyclical combination jiayin 甲寅, for instance, is called efeng shetige 閼逢攝提格.

There were historically three different points of time when the calendric year began, known as san zheng 三正 "three first-months". These were the New Year of the Xia Calendar (Xiazheng 夏正), that of the Yin or Shang Calendar (>Yinzheng 殷正), and that of the Zhou Calendar (Zhouzheng 周正). These beginnings of the year were defined as the time when the star Antares (dahuoxing 大火星, modern name Xinxiu er 心宿二) was to be seen at dawn. During the Xia period, this was the beginning of the third astronomical month (yin 寅 XXX), during the Shang period that of the fourth , and during the Zhou period that of the fifth month. The first month of the Xia calendar therefore corresponded to the twelfth month of the Yin/Shang, and to the eleventh month of the Zhou calendar. The consecutive change of the beginning of the year under these three dynasties was called the "Three connected (calendars)" (santong 三統) and was described in the explanation Santong shuo 三統說 XXX. The historians Wang Tao 王韜, Zhu Wenxin 朱文鑫 and Shinzō Shinjō 新城新藏 have found out that the theory of these three changes was only developed during the Spring and Autumn or the Warring States period, and can not be proved by historical evidence. Qian Caocong 錢寶琮 is of the opinion that these were regional calendars used by the peoples of the Xia, Shang and Zhou, and not official calendars of the three dynasties.

Months

The months of the calendar are normally counted with numbers, barring the first month of the year which is called zhēngyuè (!) 正月. The other months are given regular numbers, like eryue 二月 "second month", sanyue 三月 "third month", and so son. Intercalary months (runyue 閏月) are to be found in nine among a cycle of seventeen years. They serve to cover the leap of the lunar calendar to the solar calendar that increments in the course of time.

The Chinese lunar calendars knows intercalary months throughout the year, except months during which the so-called zhongqi 中氣 solar terms occur: yushui 雨水, chunfen 春分, guyu 穀雨, xiaoman 小滿, xiazhi 夏至, dashu 大暑, chushu 處暑, qiufen 秋分, shuangjiang 霜降, xiaoxue 小雪, dongzhi 冬至, and dahan 大寒). The name of the intercalary months depends on the preceding month, for instance, the "intercalary (month after the) third month" (run sanyue 閏三月). The sequence of the months is therefore sanyue, run sanyue, siyue. There are short months with 29 days and long months with 30 days.

It is important to note that the number-counted months of the luni-solar calendar (whose year begins between late January and late February) are not identical to the astronomical months whose cycle begins in December XXX. The names of these months are that of the cycle of the twelve Terrestrial Branches. There are furthermore colloquial and poetic names for each of the twelve months.

According to the beliefs of correlative thinking each month is related to a cardinal direction, a type of wind, a musical pitch pipe, and one of 28 starry constellations, with which the planet Jupiter culminates in the course of the year.

The Twelve Months and Their Cosmic Relations
no.	branch	constellations (boundaries overlapping)	direction, mythological animal, seasonal wind	pitch pipe
1	子 zi	東壁 Dongbi 營室 Yingshi	North; winter; xuanwu 玄武 "Black Warrior"; Guangmo wind 廣莫風	黃鍾 huangzhong
2	丑 chou	危 Wei 虛 Xu 須女 Xunü		大呂 dalü
3	寅 yin	牽牛 Qianniu 建星 Jianxing 箕 Ji	Tiaofeng wind 條風	泰蔟 taicu
4	卯 mao	尾 Wei 心 Xin 房 Fang	East; spring; qinglong 青龍 "Green Dragon"; Mingshu wind 明庶風	夾鍾 jiazhong
5	辰 chen	氐 Di 亢 Hang 角 Jiao		姑洗 guxian
6	巳 si	軫 Chen 翼 Ji 七星 Qixing	Qingming wind 清明風	中呂 zhonglü
7	午 wu	張 Zhang 注 Zhu	South; summer; zhuque 朱雀 "Vermilion Bird"; Jingfeng wind 景風	蕤賓 ruibin
8	未 wei	弧 Hu 狼 Lang		林鍾 linzhong
9	申 shen	罰 Fa 參 Shen	Liangfeng wind 涼風	夷則 yize
10	酉 you	濁 Zhuo 留 Liu	West; autumn; baihu 白虎 "White Tiger"; Changhe wind 閶闔風	南呂 nanlü
11	戌 xu	胃 Wei 婁 Lou 奎 Kui		無射 wuyi
12	亥 hai	東壁 Dongbi	Buzhou wind 不周風	應鍾 yingzhong
Designation of the astronomical months according to the twelve Terrestrial Branches. XXX according to the books XXX.

All three calendric months of one season are given designations that are also used in the field of family relationships, namely mengchun 孟春 "oldest month of spring", zhongchun 仲春 "middle month of spring", and jichun 季春 "smallest month of spring", and so on. The astronomical occurrences, the phaenology of nature, and the work of the farmers during each month of the year is described in early texts like the Xia xiaozheng 夏小正 "Small calendar of the Xia" (today a chapter of the semi-Classic Da Dai Liji 大戴禮記) or Yueling 月令 "Proceedings of Government in the different months" (today a chapter of the Confucian Classic Liji 禮記). About the first month, for example, it is said that the star Ju 鞠 appears. At the beginning of dusk the constellation Shen 參 culminates. The tail of the Northern Dipper points downwards. At that time is favourable wind. It is necessary that there is thunder in the first month. The husbandman goes out as soon as the snow is melting. The frost fades, and people remove the remaining dirt. The hibernate animals wake up, the wild goose appears in the northern villages, the pheasant cries excitedly, the fish appear and brake the ice, in the gardens sprouts the leek, the voles come out, the otters offer fish, the eagles behave like turtledoves. The willows push, the plums, abricots and peaches begin to flower, nodules cover the herb gao 縞, and the chicks breed and feed (transl. according to Grynpas). In the last month of spring, the sun is in the constellation Wei 胃, the constellation culminating at dusk being Qixing 七星, and that culminating at dawn Qianniu 牽牛. Rainbows begin to appear. In this month the influences of life and growth are fully developed; and the warm and genial airs diffuse themselves. The rains of the season will be coming down, and the waters beneath will be swelling up. The Elaeococca begins to flower. Moles are transformed into quails. Duckweed begins to grow. The crooked shoots are all put forth, and the buds are unfolded (transl. Legge).
The important ancient history Chunqiu 春秋 "Spring and Autumn Annals" is called so because the entries in this chronicle list the seasons, the months, and the days. This method was so impressive that it gave its name to a whole age, the Spring and Autumn period 春秋 (770-5th cent. BCE).

Weeks and Days

Months are today divided into three ten-day weeks (xun 旬). The first week is called shangxun 上旬, the second or middle zhongxun 中旬, and the last xiaxun 下旬. Yet traditionally the weeks have nothing to do with the lunar months directly, but are a sub-unit of the sexagenary cycle of 60 days, six weeks constituting one cycle. The days of weeks were therefore counted with the help of the ten celestial stems (jia 甲, yi 乙, bing 丙, ... gui 癸). The weeks run through the year, independently of the beginning of months and the solar year. Unlike the Western calendric weeks, they are not related to the beginning of a year and overlap the boundaries of the months and the beginning of a new year. For example, the traditional Chinese year in 2009 began on January 26 on the day with the cyclical combination xinwei 辛未, the year 2010 on February 14 with the combination yiwei 乙未, 2011 on February 3 and with the combination jichou 己丑.
The term xun 旬 is also used to denote a decade of life, for instance, qi xun 七旬 "seventy years (of life)".
The Western seven-day week was introduced in China in 1912, although it was known long before under the name qiyao 七曜 "seven illuminators" already during the Tang period 唐 (618-907) and earlier, when it came to China by Buddhist transmission. The Chinese names for the days of the seven-days week changed over time. The earliest reference to the qiyao days is to be found in Fan Ning's 范甯 commentary to the Classic Guliangzhuan 穀梁傳 from the Eastern Jin period 東晉 (317-420). The oldest detailed description of the idea behind the seven-day week, and their names in foreign languages, is to be found in the Buddhist calendric treatise Xiuyao lijing 宿曜曆經 (Tripitaka 1299, full title Wenshushili Pusa ji zhuxian suo shuo jixiong shiri shan'e xiuyao jing 文殊師利菩薩及諸仙所說吉凶時日善惡宿曜經, translated from Sanskrit by the monk Bukong 不空).
Each day was related to one "star" or its deity, similar to the Western week (Wednesday as the day of Wotan, or martedì as the day of God Mars). These were sun, moon, the the five visible planets Mars, Mercury, Jupiter, Venus and Saturn. In Chinese translation the names of the five planets were replaced by the five elements correlating to them (see Five Agents), namely fire for Mars, water for Mercury, Wood for Jupiter, metal for Venus, and Earth for Saturn, so that Sunday was riyaori 日曜日 "sun-day", Monday yueyaori 月曜日 "moon-day", Tuesday huoyaori 火曜日 "fire-day", etc. This system is still in use in Japan and Korea (nichiyōbi, getsuyōbi, kayōbi etc. in Japanes, and ilyoil, wolyoil, hwayoil etc. in Korean). In more recent times (early 20th century?) the term yaori 曜日 became obsolete and was replaced by a system that centered more on Sunday, the day of the Lord, while the other days were counted with numbers. There are two terms for "day" in this system, namely xingqi 星期 (an ancient name for the qixi festival 七夕 on the 7th day of the 7th lunar month) and libai 禮拜 "ritual prayer". The latter term clearly shows Christian influence. Sunday is xingqi tian 星期天 or libai tian 禮拜天 (in the People's Republic rather qingqi ri 星期日, to avoid the word tian 天 "Heaven"), Monday xingqi yi 星期一 or libai yi 禮拜一, etc. A rarely seen system of counting days calls Sunday zhuri 主日 "Day of the Lord", Monday zhanli er 瞻禮二 "Ritual observation two" (because according to Catholic day counting Sunday is the first day of the week), etc. It is also used in Vietnam, where Monday is called chủ nhật 主日, Monday ngày thứ hai "day number two" (Vietamese words) etc. This system leads to some confusion because Saturday is called zhanli qi 瞻禮七 "Ritual observation seven" (as the last day of the week), while the secular system calls it xingqi liu 星期六 "star-period six" and the Protestant system libai liu 禮拜六 "Ritual prayer six".
In some printed calendars the term zhou 週 "cycle" is used as a word for "week", and the days are called: Sunday zhouri 週日, Monday zhouyi 週一, etc.
An example of a traditional date looks either like Xuantong san nian ba yue shijiu ri 宣統三年八月十九日 "Nineteenth day of the eight lunar month of the third year of the Xuantong reign-period" (i.e. October 10th, 1911), or bayue guichou 八月癸丑 "eight month, day with the cyclical combination guichou".

Hours

The traditional Chinese day was divided into twelve hours ("double-hours" from the Western perspective, in Chinese shi 時). They do not begin at midnight, but the point of midnight is just in the middle of the mid-night hour, the "hour of the rat". The popular names of the twelve hours are that of twelve animals that are also used for the twelve-year cycle. More scholary, the hours are termed with the names of the twelve Terrestrial Branches. The expression mao shi 卯時 means, the time between 5 to 7 AM, or "the hour of the rabbit". The animal designations are preferred by Westerners when referring to Chinese time, but rarely used in Chinese. Two of the terrestrial branches are still known in modern time designations, namely zi 子 in ziye 子夜 "midnight", and wu 午 in the terms shangwu 上午 "before noon", zhongwu 中午 "high noon", xiawu 下午 "afternoon" and wufan 午飯 "lunch" etc. Quite famous is also the exterior gate of the imperial palace, the Wumen 午門 that was located to the south (the direction of midday).
In ancient times the hours were announced publicly from the drumtower (gulou 鼓樓) in each larger city. Belltowers (zhonglou 鐘樓) served to announce the morning, as well as the death of an emperor or an inimical attack.

The Twelve Double-Hours (shi'er shichen 十二時辰)
no.	branch	animal	hour
1	子 zi	鼠 shu rat, mouse	2300-0100
2	丑 chou	牛 niu ox, cow	0100-0300
3	寅 yin	虎 hu tiger	0300-0500
4	卯 mao	兔 tu rabbit	0500-0700
5	辰 chen	龍 long dragon	0700-0900
6	巳 si	蛇 she snake	0900-1100
7	午 wu	馬 ma horse	1100-1300
8	未 wei	羊 yang sheep, ram	1300-1500
9	申 shen	猴 hou monkey	1500-1700
10	酉 you	雞 ji cock, roaster	1700-1900
11	戌 xu	狗 gou or 犬 quan dog	1900-2100
12	亥 hai	豬 zhu pig, boar	2100-2300
Designations of hours by the twelve Terrestrial Branches, the animal names for these hours (popular in the West), and the corresponding time from 11 PM on.

The Twenty-four Solar Terms

The 24 Solar Terms (ershisi jieqi 二十四節氣) are periods of time during which certain phaenological events take place, particularly the arrival of seasons, the growth and withering of plants, high points in temperature and precipitation, and cycles in the life of insects and other animals. The term jieqi literally means "nodes of energy" and refers to the growing and declining energy (qi 氣) of Yin and Yang in the course of the year. The year begins at the point in which Yin (the less energetic) prevails and Yang (the more energetic) just begins to rise again. This point can either be around the winter solstice (dongzhi 冬至 "winter has arrived"), or when spring visibly begins. Because of this ambiguous definition, the beginning of the year was not always defined in the same way in earlier times. Some authors translate jieqi as "mini-seasons", with a length of two weeks. They are related to the solar year because it is the sun that influences the "energy" on earth, and not the moon, whose appearance and movement determines the calendar.
There are two different types of jieqi, namely the twelve proper jieqi, and the twelve zhongqi 中氣 "middle energies". They alternate with each other. These designations might have origined during the Warring States period 戰國 (5th cent.-221 BCE) and are first mentioned in full in the chapter Tianwen xun 天文訓 "On the patterns of Heaven" in the book Huainanzi 淮南子.
The solar terms were originally examined with the help of a gnomon (guibiao 圭表) whose shadow can be used to determine the hour of the day (by the position of the shadow in the segment of a circle), but also, by the changing length of the shadow over the months, the process of the year. This is most easy at those points of time when the shadow is shortest (xiazhi 夏至 "summer has arrived") and longest (dongzhi 冬至 "winter has arrived"). The time in-between those occurrences was divided into twelve parts with eleven further points of time that each initiated the beginning of a "mini-season". Each of these twelve segments was passed two times a year. The beginning point of the season dongzhi was seen as the beginning of the solar year (the point when the Yang energy is lowest), and the point xiazhi (the Yang energy being strongest) as the medium point of it. During the solar terms chunfen 春分 and qiufen 秋分 the vernal and autumnal equinoxes occur. The term qingming 清明 is also known otherwise because it is the time when the Qingming Festival or tomb-sweeping festival (qingmingjie 清明節) takes place. It might be well to recall the fact that the solar terms are part of the lunar year and therefore begin with the Chinese new year.
This gnomon method is called "balancing the energy (terms)" (pingqi 平氣). Each of the twelve months of the year includes one jieqi point and one zhongqi point (marking the beginning of a term), for instance, the solar term lichun 立春 as the jieqi and the term yushui 雨水 as the zhongqi. In some cases it can be that one month includes only one of the solar terms because the solar terms operate with the solar year, and the months with the shorter lunar year. With the introduction of the Taichu Calendar 太初曆 during the mid-Former Han period 前漢 (206 BCE-8 CE) the rule was therefore established that a jieqi term might occur in the second half of a month and the first half of the following, and a zhongqi term only in the frame of one month. Should there in any case be a month without a zhongqi term, this month is then made an intercalary month of the foregoing month.
A reform of this method was undertaken during the Sui period 隋 (581-618). The astronomer Zhang Zixin 張子信 had become aware that the "velocity of the sun" is not the same at each time of the year (because the earth moves on a slightly elliptic orbit and is quicker in those stretches where it is closer to the sun). In 604 therefore Liu Chuo 劉焯 created the Huangji Calendar 皇極曆, in which the course of the sun along the "Yellow Path" (the ecliptic of the sun) is divided into 24 segments of equal size. Each solar term begins at the point of time at which the sun enters the particular segment. This new method was called "fixation of energy (terms)" (dingqi 定氣). Both methods continued to be used, the old one for the calendar in daily use, the new for the scholarly calculation of the method. Only during the Qing period 清 (1644-1911) the old pingqi method was finally abolished.

The Twenty-Four Solar Terms (shi'er jieqi 十二節氣)
solar term	meaning	approximate date of beginning
立春 Lichun	"Spring begins"	Feb 5
雨水 Yushui 中	"Rain water"	Feb 19
驚蟄 Jingzhe	"Excited insects"	Mar 5
春分 Chunfen 中	"Vernal partition" (Vernal equinox)	Mar 20
清明 Qingming	"Clear and bright"	Apr 5
穀雨 Guyu 中	"Grain rains"	Apr 20
立夏 Lixia	"Summer begins"	May 5
小滿 Xiaoman 中	"Grain starts filling"	May 21
芒種 Mangzhong	"Grain in ear"	June 6
夏至 Xiazhi 中	"Summer arrives" (Summer solstice)	June 21
小暑 Xiaoshu	"Slight heat"	July 7
大暑 Dashu 中	"Great heat"	July 23
立秋 Lichun	"Autumn begins"	Aug 7
處暑 Chushu 中	"Limit of heat"	Aug 23
白露 Bailu	"White dew"	Sep 8
秋分 Qiufen 中	"Autumnal partition" (Autumnal equinox)	Sep 23
寒露 Hanlu	"Dold dew"	Oct 8
霜降 Shuangjiang 中	"Hoar frost descends"	Oct 23
立冬 Lidong	"Winter begins"	Nov 7
小雪 Xiaoxue 中	"Little snow"	Nov 22
大雪 Daxue	"Heavy snow"	Dec 7
冬至 Dongzhi 中	"Winter arrives" (Winter solstice)	Dec 21
小寒 Xiaohan	"Little cold"	Jan 6
大寒 Dahan 中	"Severe cold"	Jan 21
The twenty-four solar terms (two-week intervals) and their approximate time of beginning. The symbol 中 signifies the zhongqi terms, whose beginning can not fall in an intercalary month.

Source: Liu Jinyi 劉金沂 (1980). "Ershisi jieqi 二十四節氣", in: Zhongguo da baike quanshu 中國大百科全書, Tianwenxue 天文學, Beijing/Shanghai: Zhongguo da baike quanshu chubanshe, p. 69.

Celestial Stems and Terrestrial Branches and the Sexagenary Cycle

The sexagenarian cycle is a combination of the signs of two cycles, namely that of the Ten Celestial Stems (shi tiangan 十天干) and that of the Twelve Terrestrial Branches (shi'er dizhi 十二地支). It was in use from at least the Shang period 商 (17th-11th cent. BCE), but the date of its introduction is not known. The cycle is used to count years and covers approximately one human lifetime, namely sixty years. It is not joined to any political or cultural occurrence (like the birth of Jesus Christ or Mohammed's flight to Medina). After sixty years, the cycle begins anew. The sexagenery cycle is applied to count year and days, and therefore six times covers the time period of a (lunar) year (6 * 60 = 360), or approximately once the lifetime of a man (sixty years). The twelve branches are also used to count months and the hours of a day ("double-hours" from the Western perspective). The ten stems are also generally used to count, for instance, chapters or volumes of a book, or like numbers in a list (up to ten). During the Xia 夏 (17th - 15th cent. BCE) and the Shang periods the temple names of kings included a number of the Ten Stems, like Tai Kang 太康 (or Tai Geng 太庚) and Kong Jia 孔甲 of the Xia and, much more regularly, Shang Jia 上甲, Bao Yi 報乙, Bao Ding 報丁 and Bao Bing 報丙 of the Shang. The rules of this pattern are still not sufficiently explained.

The Ten Celestial Stems (shi tiangan 十天干) no. stem 1 甲 jia 2 乙 yi 3 丙 bing 4 丁 ding 5 戊 wu 6 己 ji 7 庚 geng 8 辛 xin 9 壬 ren 10 癸 gui	The Twelve Terrestrial Branches (shi'er dizhi 十二地支) no. branch 1 子 zi 2 丑 chou 3 寅 yin 4 卯 mao 5 辰 chen 6 巳 si 7 午 wu 8 未 wei 9 申 shen 10 酉 you 11 戌 xu 12 亥 hai
The Sixty Cyclical Combinations 1 甲子 2 乙丑 3 丙寅 4 丁卯 5 戊辰 6 己巳 7 庚午 8 辛未 9 壬申 10 癸酉 11 甲戌 12 乙亥 13 丙子 14 丁丑 15 戊寅 16 己卯 17 庚辰 18 辛巳 19 壬午 20 癸未 21 甲申 22 乙酉 23 丙戌 24 丁亥 25 戊子 26 己丑 27 庚寅 28 辛卯 29 壬辰 30 癸巳 31 甲午 32 乙未 33 丙申 34 丁酉 35 戊戌 36 己亥 37 庚子 38 辛丑 39 壬寅 40 癸卯 41 甲辰 42 乙巳 43 丙午 44 丁未 45 戊申 46 己酉 47 庚戌 48 辛亥 49 壬子 50 癸丑 51 甲寅 52 乙卯 53 丙辰 54 丁巳 55 戊午 56 己未 57 庚申 58 辛酉 59 壬戌 60 癸亥

The first unit or "number" of the sexagenarian cycle is the cyclical combination jiazi 甲子, the last combination is guihai 癸亥. Each day and each year are given one of the sixty "numbers" in the predefined sequence, and after sixty units, the cycle begins with the first "number" again. Because of its cyclical character the sixty combinations can only be used to indicate years within a time frame of one generation (when counting years), or three months (when counting days).
In practice, therefore, they are combined with the reign mottos of emperors, for instance, Yongzheng yimao 雍正乙卯, meaning the year with the cyclical combination yimao 乙卯 during the Yongzheng reign-period, i.e. 1735. This kind of naming years is often to be found in the late imperial period, when emperors only chose one single reign motto, and was even used in the twentieth century, as can be seen in the designations of important political events, like the reform movement of 1898 (wuxu bianfa 戊戌變法 "constitutional change during the wuxu year") of 1898 or the Revolution of 1911 (xinhai geming 辛亥革命 "Revolution of the xinhai year"). Today, the cyclical characters of the year are still indicated on calendars and are also used by artists, particularly calligraphers, to indicate the year in which their work was created.
When used for days, it is necessary to combine the cyclical characters with the month, or at least the season, in order to avoid confusion. Today, this method is not any more used in daily life.
The twelve Terrestrial Branches were also used to count double-hours (shi 時, shichen 時辰) and months (yue 月). The first of the characters, zi 子, corresponds to the Western hours 2300 to 0100 (11 PM to 1 AM), the second, chou 丑, to the double-hour between 0100 to 0300 (1 to 3 AM). In order to count months, the cyclical character zi is used to designate the month in which the winter solstice (dongzhi 冬至) occurs.

Source: Chen Jiujin 陳久金 (1980). "Ganzhi 干支", in: Zhongguo da baike quanshu 中國大百科全書, Tianwenxue 天文學, Beijing/Shanghai: Zhongguo da baike quanshu chubanshe, p. 83.

The Jupiter Cycle

It was observed in oldest times that the planet Jupiter (modern name muxing 木星) accidentally "revolves" around the earth in a timespan (the sidereal period) of roughly twelve years. It was therefore called the "year star" (suixing 歲星) and used for the calendar. Its path around the earth was divided into twelve segments or "paces" (shi'er ci 十二次), and it was so possible to name an individual year according to Jupiter's position on the background of the starry sky. Ancient histories of the Spring and Autumn period therefore say, for instance, "it was the year (when Jupiter was in) Leo" (sui zai chunhuo 歲在鶉火). With the help of such statements, historical event can be dated more exactly. In the history Guoyu the astronomer Ling Zhou Jiu 伶州鳩 says that the conquest of the Shang by King Wu of Zhou took place in the Jupiter year Dunhuo 鶉火 (1057 BCE). The Jupiter positions are also called the "twelve regions" (shi'er fenye 十二分野). Their designations are: xingji 星紀, xuanxiao 玄枵 (zhuanxu 顓頊), zouzi 諏訾 (shiwei 豕韋), jianglou 降婁, daliang 大梁, shichen 實沈, chunshou 鶉首, chunhuo 鶉火, chunwei 鶉尾, shouxing 壽星, dahuo 大火 and zhemu 析木.
Except the twelve segments for the Jupiter years, Chinese astronomers divided the celestial globe into twelve "double-hour" segments that were named according to the twelve Terrestrial Branches. The direction of the sequence was opposite to that of the Jupiter segments that follow the direction from west to east. It was believed that there was a counter-Jupiter or "Grand Jupiter" (taisui 太歲), a kind of imaginary celestial body according to whose movements the double-hours were counted. Similar to Jupiter, the counter-Jupiter revolved once around the earth every twelve years, but in the opposite direction, yet in a fix relation to the Jupiter, so that the position of the imaginary counter-Jupiter can always be known once that of the real planet is analyzed.
The twelve stations of the counter-Jupiter were also given individual names, additionally to the twelve Branches namely: Kundun 困敦 (zi), Chifenruo 赤奮若 (chou), Shetige 攝提格 (yin), Dan’e 單閼 (mao), Zhixu 執徐 (chen), Dahuangluo 大荒落 (si), Dunzang 敦牂 (wu), Xieqia 協洽 (wei), Tuntan 涒灘 (shen), Zuo’e 作噩 (you), Yanmao 閹茂 (xu) and Dayuanxian 大淵獻 (hai). Like these alternative names for the twelve Branches, the ten Celestial Stems have also alternative designations: Efeng 閼逢 (jia), Zhanmeng 旃蒙 (yi), Rouzhao 柔兆 (bing), Qiangyu 強圉 (ding), Zhuyong 著雍 (wu), Tuwei 屠維 (ji), Shangzhang 上章 (geng), Chongguang 重光 (xin), Xuanyi 玄黓 (ren) and Zhaoyang 昭陽 (gui). Of both cycles, these alternative names can be used instead of the cyclical combination of the sexagenary cycle, like for Efeng shetige 閼逢攝提格 instead of jiayin 甲寅. These names are occasionally mentioned in very elegant literature. In some books these designations are slightly differently written.
It might be that the twelve stations of the Jupiter are derived from the four symbols of the cardinal directions (sigong 四宮 "four palaces" or sixiang 四象 "four appearances", i.e. the Black Tortoise 玄武 for the North, the White Tiger 白虎 for the West, the Vermillion Bird 朱雀 for the South and the Green Dragon 青龍 for the East) that are divided into three sub-regions. Unfortunately this geometrical division is not congruent with area of the right ascension of the Jupiter. In the chapter on music and astronomy (Lüli zhi 律曆志) in the official dynastic history Hanshu 漢書 the twelve stations of the Jupiter correspond with the twenty-four solar terms (ershishi jieqi), the jieqi marking the beginning of the station, and the zhongqi term being located within the Jupiter station.
From the late Ming period on, under the influence of European astronomny brought to China by the Jesuits, the designation of the twelve Jupiter stations were also used to designate the twelve zodiacal signs (shi'er gong 十二宮) of the solar ecliptic, yet the corresponding areas are not exactly congruent. Capricornus (mojie gong 魔羯宮), for instance, corresponds to the Xingji area (xingji gong 星紀宮), but the beginning (entering point) of this area is identical to the Dongzhi term 冬至.
The "Jupiter year" is in fact only 11.86 solar years long, and therefore laps to the solar year. Its use (called suixing jinian 歲星紀年 "recording years by the Jupiter year") was in practice abolished with the introduction of the Sifen Calendar 四分曆 in the Later Han period.

Sources:
Chen Jiujin 陳久金 (1980). "Suixing jinian 歲星紀年", in: Zhongguo da baike quanshu 中國大百科全書, Tianwenxue 天文學, Beijing/Shanghai: Zhongguo da baike quanshu chubanshe, p. 339.
Wang Jianmin 王健民 (1980). "Shi'er ci 十二次", in: Zhongguo da baike quanshu 中國大百科全書, Tianwenxue 天文學, Beijing/Shanghai: Zhongguo da baike quanshu chubanshe, p. 318.

History of the Chinese Calendar and Astronomy

China developed a calendar on its own already during times immemorial. The oldest written traces of the calendar can be found in the oracle bone inscriptions of the Shang period. The calendar is already developed to full maturity during the Warring States period. The amount of literature on astronomical matters is vast, and only third to the large treasure of writings on agriculture and medicine. Astronomy was from the beginning connected to both mathematics and astrology. The latter ranges between philosophy and mathematics, and can therefore be called a kind of pseudo-science. A lot of data are preserved in ancient writings about solar eclipses (rishi 日食), lunar eclipses (yueshi 月食), lunar occultations (yue yanxing 月掩星), sunspots (taiyang heizi 太阳黑子, a modern term), meteors (liuxing 流星), comets (huixing 彗星) and novae (xinxing 新星).
In comparison to the Western calendar, there are a lot of idiosyncratic features that have to be explained in order to understand the Chinese way of calculating and recording time. The difficulty of astronomy made it necessary that the ancient kings employed a "Grand Scribe" (taishi 太史) who was astronomer, astrologer, and then also a historian. Among the treatises of most official dynastic histories a chapter on astronomy is to be found (Lizhi 曆志 or Lüli zhi 律曆志). The duty of the astronomer and his bureau was to calculate the beginning of the year, the twelve months, intercalary months, the twenty-four solar terms, the occurrence of lunar and solar eclipses, and the movement and positions of the five planets. This set of data is called the "calendric standard" (lifa 曆法). Chinese astronomy was predominantly occupied with the calculation of the data for the calendar, and among these, particularly the movement of the moon and the sun, because these two celestial bodies were both significant for the Chinese luni-solar calendar.
Another important field of Chinese astronomy was the observation of celestial phenomena. The respective treatises in the official dynastic histories are called Tianwen zhi 天文志 "On the patterns of Heaven". The most important instrument for their observation was the armillary sphere (hunyi 渾儀). While the ancient Greeks focused on the ecliptic of the sun (huangdao 黄道 "yellow path"), the Chinese astronomers were interested into the celestial equator (chidao 赤道). This was divided into 360 degrees (du 度). During the Yuan period the Shoushi Calendar 授時曆 was introduced which can be seen as the most perfect development of the Chinese calendar before the Jesuits brought Western astronomical science to China.
According to mythology the oldest Chinese astronomer was Xi He 羲和, an official of the mythological emperor Yao 堯. As a cultural hero Xi He created the calendar and handed it over to mankind. In the chapter Yaodian 堯典 of the Confucian Classic Shangshu 尚書 "Book of Documents" it is also said that Zhong He 羲仲 lived in the Yanggu Valley 暘谷 of Mt. Yuyi 嵎夷, where he brought sacrifices to the sun and brought agriculture in accord with the seasons. This spot is believed to have been located near modern Juxian 莒縣, Shandong, where in the 1960s Neolithic pottery was found on which a symbol of the sun was engraved. This is interpreted as an ancient "character" for 旦 "dawn", the rising sun. Three other persons were sent to the other cardinal directions: Xi Shu 羲叔 to Nanjiao 南交 in the South, He Zhong 和仲 to Meigu 昧谷 in the West, and He Shu 和叔 to Youdu 幽都 in the North. These persons determined the seasons by the observation of different stars that appear on the southern sky at dusk (huanghun 黃昏). It is also said which activities the peasants undergo during these periods of the year:
日中，星鳥，以殷仲春 'The day,' (said he), 'is of the medium length, and the star is in Niao - you may thus exactly determine mid-spring."
日永，星火，以正仲夏 'The day,' (said he), 'is at its longest, and the star is in Huo - you may thus exactly determine mid-summer.
宵中，星虛，以殷仲秋 'The night' (said he), 'is of the medium length, and the star is in Xu - you may thus exactly determine mid-autumn.
日短，星昴，以正仲冬 'The day,' (said he), 'is at its shortest, and the star is in Mao - you may thus exactly determine mid-winter. (Transl. Legge)
The names mentioned for the four seasons in this text are Zhongchun 仲春 "mid-spring", Zhongxia 仲夏, Zhongqiu 仲秋 and Zhongdong 仲冬. In later times these names were used to designate the middle month of the four seasons (middle month of Spring, etc.).
The chapter Yaodian continues to explain that the year is 366 days long, with four seaons (siji 四季), and that intercalary months (runyue 閏月) are used to bring the lunar calendar back into accord with the solar calendar. The oldest known calendar is the so-called Xia xiaozheng 夏小正 "Small Correctness of the Xia" (zheng being the correct beginning of the year). It was supposedly created during the Xia period and has been handed down as a chapter of the book Da Dai Liji 大戴禮記. In this calendar all months are characterized by a certain marks, except the second, eleventh and twelfth month. The calendar does not only note which starry constellation is to be observed at dusk in the southern sky (the hunzhong xing 昏中星 "evening star"), but also which constellations is to be seen at dawn in this place (the danzhong xing 旦中星 "morning star"). It also notes down in which direction the handle of the Northern Dipper (Beidou 北斗, Ursa Maior) shows.
Another trace of Xia period astronomy is the fact that among the posthumous names of last kings of the Xia dynasty like Kong Jia 孔甲, Yin Jia 胤甲 or Lü Gui 履癸 include signs of the ten Celestial Stems. These must therefore have already been used as "numbers" during that time. The oracle bone inscriptions from the Shang period show that the tem Celestial Stems and twelve Terrestrial Branches were used to designate days in the sexagenary cycle. A long list of these designations is to be found in an oracle bone from the reign of King Wu Yi XXX.
The months were designated with common numbers, except the first which is called zhengyue. The length of the months differed. Large months (dayue 大月) had a length of 30 days, small months (xiaoyue 小月) of 29 days. The intercalary month that was used to bring the solar calendar (365 days) into accord with the lunar year (360 days) was put at the end of the year, and not, like in later times, in midst. A lot of eclipses and novae are mentioned in the oracle bone inscriptions. Lunar phases (yuexiang 月相) play an important role in the bronze vessel inscriptions or in the texts of the Shangshu and the Yizhoushu 逸周書. Many texts begin with the indication of a date, like wei shiyue you yiyue dinghai 唯十月又一月丁亥 "In the eleventh month, on the day with the cyclical combination dinghai [the king was in the xyz Palace and did this and that]". The word shuo 朔 for the new moon is not mentioned in this type of text, but all other phases of the moon, namely chuji 初吉 (first day after the newmoon to the 7th or 8th day), ji shengba 既生霸(or ji shengpo 既生魄, from the 8th or 9th day to the 14th or 15th day of the month), ji wang 既望 "full moon" (from the 15th or 16th day to the 22nd or 23rd day of the month), and ji siba 既死霸 (or ji sipo 既死魄, from the 23rd day of the month to the next newmoon). Astronomical phenomena are also mentioned in the Classic Shijing 詩經 "Book of Songs".
Astronomical knowledge of the Eastern Zhou period is reflected in the chapter Yueling 月令 "Proceedings of government in the different months" in the Classic Liji 禮記. This text operates with the twenty-eight starry constellations (ershiba xiu 二十八宿) as an instrument to measure time. The text explains which constellations is positioned in the southern sky at dawn in the beginning of each month, and in which position the sun sets, for instance, Mengchun zhi yue, ri zai ying Shi, hun 孟春之月，日在營室，昏參中，旦尾中。其日甲乙。 "In the first month of spring the sun is in Shi, the star culminating at dusk being Shen, and that culminating at dawn Wei. Its days are jia and yi" (transl. Legge). The histories Chunqiu 春秋 and Zuozhuan 左傳 include rich information on the calendar. They mention 37 solar eclipses, 32 of which can in fact be identified with historical eclipses. The year 687 BCE (7th year of Duke Zhuang of Lu 魯莊公, summer, 4th month, day xinmao) records: ye, hengxing bu jian, yezhong, xingyun ru yu 夜，恆星不見，夜中，星隕如雨 "at night, the regular stars were not visible. At midnight, there was a fall of stars like rain." (transl. Legge). This is the oldest record of a meteorite shower in the constellation Lyra. The year 613 (autumn, 7th month) records: You xing bei ru yu Beidou 有星孛入于北斗 "there was a comet, which entered the Northern Bushel". This might be the earliest mentioning of Halley's Comet.
Around the year 600 astronomers began to make use of gnomons to measure the length of days and the turning points in the year, the winter and the summer solstice. The winter solstice was called Rinanzhi 日南至 "southern arrival of the sun", and not, as later, Dongzhi 冬至 "arrival of the winter". This was the beginning point of the year, and the first month was called Chun wang zhengyue 春王正月 "Spring, correcting month of the King". The winter solstice is mentioned two times in the Zuozhuan, with a distance of 133 years, and in-between 48 intercalary months (with only one record missing). This exactly corresponds to a relation of seven intercalary months in 19 years. In order to correlate the lunar year with the solar year the calendar consisted of 365¼ days, and therefore had the name of Sifen li 四分曆 "Quarter Calendar". The six old calendars (gu liu li 古六曆: the Calendar of the Yellow Emperor 黃帝曆, the Calendar of Zhuan Xu 顓頊曆, the Xia Calendar 夏曆, the Yin Calendar 殷曆 of the Shang dynasty, the royal Zhou Calendar 周曆 and the ducal Calendar of Lu 魯曆) before the calendar reform under Emperor Wu of the Han dynasty were "quarter calendars". These calendars did in fact not differ in the calculation method, but had their names from mythological emperors, dynasties, or (in the case of Lu) that of the territory where it was used.
In the various regional states of the Warring States period there were astronomers, some of whom are known by name. In the state of Qi the astronomer Gan Gong 甘公 or Gan De 甘德 had written the book Tianwen xinzhang 天文星占, and in the state of Wei, master Shi Shen 石申 had authored the book Tianwen 天文. Both books dealt largely with astrology, but also included important information about the movement of planets and the constellations. These are preserved in the text Shishi xingjing 石氏星經 that is now known under the name Gan-Shi xingjing 甘石星經.
It was common for historiographers to name a year according to the year in which a ruler was master of his state. The problem of the Warring States period was that except the king of Zhou, each one of the regional rulers (zhuhou 諸侯) claimed to be a more or less independent ruler, and used his own calendar. In order to circumvent this confusion, it was therefore necessary to create a designation for years that was independent from worldly rulers. The result was the introduction of the Jupiter calendar (suixing jinian fa 岁星纪年法) that provided the opportunity to call years with the name of a certain position in which the planet Jupiter was located on the path of its "revolution around the earth".
The many "masters and philosophers" of the age began contemplating about the shape and the construction of the universe. The book Zhuangzi 莊子 (chapter Tianyun 天運) and the ballad Tianwen 天問 of the collection Chuci 楚辭 include many questions in this direction. The sky was seen as "large cover" with a round shape, while the earth was believed to be "square like a chessboard". The book Laozi 老子 (Daodejing 道德经) touches on the question of the creation of the universe, but only the Han period book Huainanzi 淮南子 (chapter Tianwen xun 天文训) gives a clear account of the conception that there was in the beginning a chaos (hundun 混沌) that then separated into the light and pure that ascended to the sky, and the heavy and muddy parts that constituted the earth. The sky represented the active energy (yangqi 阳气), the earth the inactive energy (yinqi 阴气). Both mixed together, produced the ten thousand creatures. The Huainanzi is also the first book in which astronomical knowledge is precicely laid down, and the mathematical relations of the musical pitch pipes, weights and measures are explained.
In the last part of the Warring States period the twenty-four solar terms became more important because they were directly related to agronomical activities, and so to the economic output and the financial revenue of the contending states. These, too, are described in the book Huainanzi. At that time the most important constituents of the calendar were the solar terms, connected with the solar year, and the new moon intervals, connected with the lunar year.
When the kingdom of Qin had conquered the various regional states and created the Qin empire, the Zhuan Xu calendar was introduced as the empire-wide valid calendar. In this calendar, the tenth month (roughly corresponding to the Western November and December) was the beginning of the year, and the intercalary months were added to the end of a year. The beginning of the calendar was inaugurated in the year with the cyclical combinations jiayin 甲寅, on the day jiayin 甲寅 of the first month (zhengyue 正月) and the solar term Lichun 立春, a day of a new moon, and when the five planets were seen in the east.
The Han dynasty adopted the Qin calendar in the beginning, but Emperor Wu initiated a reform of the calendar and in 104 ordered the astronomer Deng Ping 邓平 and Luoxia Hong 落下闳 to supervise the reform. The same year (the 7th of the reign period Yuanfeng 元封) was renamed the 1st of the reign-period Taichu 太初. The new calendar was therefore called the Taichu Calendar 太初曆. It is the oldest Chinese calendar whose data are recorded in total. The calculation method of this calendar was not as exact as that of the Sifen Calendar, especially concerning the congruence of the lunar and solar years (or tropical year), but it had some decisive advantages compared to the older calendars: The beginning of the year as fixed as the first month zhengyue 正月 (corresponding to Western January and February), and not the tenth month. This brought back a direct relation between the beginning of the year and the seasonal phenomena (the beginning of spring as the beginning of the year, like the month begins after a new moon). The intercalary month was flexibly positioned at the end of a month including a zhongqi term, and not at the end of the year. The orbital periods of the planets are stated very exactly, and the exact times of lunar and solar eclipses are given, and the eclipse year is calculated as 346.66 days.
The Taichu Calendar was in use of 188 years before it was replaced again by the Sifen Calendar in 85 CE. At that time the tropical year and the times of the new moon were not any more coherent with the calculated data. The scholar Jia Kui 贾逵 therefore advocated the use of a different method for calculation invented by Fu An 傅安, not based on days, but on the movement of the sun and moon along the ecliptic and the position of the 28 constellations. As a consequence, the beginning of the Dongzhi winter term 冬至 was moved from the position in the constellation Qianniu 牵牛 to the constellation Dou 斗. Jia Kui had probably observed the phenomenon of the precession (suicha 歲差) of the axis of the earth, which results in a precession of the equinoxes along the ecliptic. He had also become aware of the different velocities of the moon on its orbit, which is higher when the moon is closer to the earth. He therefore suggested the "method of the nine ways" (jiudaoshu 九道術) or nine segments of the orbit.
In the very late years of the Han period Liu Hong 劉洪 created the Qianxiang Calendar 乾象曆 in which he reduced the fractional number of the length of the tropical year to less than ¼ and calculated the solar year with a length of 365.2462 days. The Qianxiang calendar was the first calendar that was based on a correct calculation of the lunar month, with the consideration of the change of the moon's velocity, and so using a sidereal month instead of a synodic month.
The most famous astronomer is the Eastern Han period scholar Zhang Heng 張衡 who did not only invent the so-called Hou Feng's earthquake detector 后風地動儀, but also developed an armillary sphere that was moved by a waterclock (loushui zhuan huntian yi 漏水轉渾天儀) that was an advancement of Geng Shouchang's 耿壽昌 celestial globe (hunxiang 渾象). Somewhat earlier than Zhang Heng, Xi Meng 郗萌, wrote a text called Xuanyeshuo 宣夜说, in which he explained that the sky cannot be like a hard-shelled egg, but must be boundless and filled with air, on which the celestial bodies float. Zhang Heng later said that the sky is round like a pill and the earth like the yolk of an egg.
In 1973 an important document of Han period astronomy was discovered in the tomb no. 3 of the Mawangdui site in Changsha, Hunan. Written on a silk cloth, an illustrated text of 8,000 characters speaks about divination methods of the Five Planets (Wuxingzhan 五星占). It records the position of the planets in a time frame of 70 years, and in 29 illustrations the shapes of comets and their tails are described. The treatise on the Five Agents (Wuxing zhi 五行志) in the history Hanshu provides a detailed description of a lunar eclipse in 89 BCE, and sunspots seen in the year 28 BCE. This is the earliest mentioning of this astronomical phenomenon. The Chinese were always interested in extraordinary phenomena in the sky because these were interpreted as auspicious or inauspicious phenomena influencing the course of political life. Because of this context between astrology and astronomy Chinese sources are therefore extremely rich in reporting appearances and abnormalities in the sky.
During the Three Empires period Yang Wei 楊偉 became aware that the intersection of the ecliptic with the moon's orbit plane (huangbai jiaodian 黄白交点) had moved. In his Jingchu calendar 景初曆 from 237 CE he described this phenomenon and explained that the beginning point of an eclipse was not any more to be found on the point of intersection, but could be found on any point of the eclipse area (shixian 食限). He developed a better method to calculate XXX 日月食食分和初亏方位角. His collegue Chen Zhuo 陈卓 compiled a synopsis of the data on stars that had been compiled in earlier times, those of Master Shi 石氏, Master Gan 甘氏 and Wu Xian 巫咸. This synopsis describes 283 constellations (xingguan 星官 "star offices") with exact data of 1,464 individual stars. It remained in use until the late Ming period, when Western knowledge supported Chinese astronomers. Ge Heng 葛衡 invented an astronomical device, the astrolabe (huntianxiang 浑天象.
In the statelet of Later Qin Jiang 姜岌 developed a new method to calculate the position of the sun with the help of lunar eclipses. The results were laid down in his Sanji jiazi yuanli 三纪甲子元历 Calendar from 384. He was the first scholar who guessed that the red colour of dusk and dawn was the cause of the sunrays having to cross a larger amout of air. Zhao Fei 赵{非+欠}, who lived in the state of Northern Liang, made progess in the question of intercalary years and explained that in a period of 19 years there must be 7 intercalary months, or, in other relations, 221 intercalary months in a timespan of 600 years. He published the Yuanshi Calendar 元始历 in 412.

Sources: