Chinese sexagenary cycle

Chinese sexagenary cycle
Chinese 六十干支
Chinese 干支

The Chinese sexagenary cycle, also known as the Stems-and-Branches, is a cycle of sixty terms used for reckoning time.[1] It appears as a means of recording days in the first Chinese written texts, the Shang oracle bones of the late second millennium BC. Its use to record years began around the middle of the 3rd century BC.[2] The cycle and its variations have been an important part of the traditional calendrical systems in Chinese-influenced Asian states, particularly those of Japan, Korea, and Vietnam.

This traditional method of numbering days and years no longer has any significant role in modern Chinese time keeping or the official calendar. However, the sexagenary cycle is still used in names of many historical events, like Chinese Xinhai Revolution and Japanese Boshin War. It also continues to have a role in contemporary Chinese astrology and fortune telling.


Statues of Tai Sui deities responsible for individual years of the sexagenary cycle

Each term in the sexagenary cycle consists of two Chinese characters, the first being one of the ten Heavenly Stems of the Shang-era week and the second being one of the twelve Earthly Branches representing the years of Jupiter's duodecennial orbital cycle. The first term jiǎzǐ (甲子) combines the first heavenly stem with the first earthly branch. The second term yǐchǒu (乙丑) combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with guǐhài (癸亥), after which it begins again at jiǎzǐ. This termination at ten and twelve's least common multiple leaves half of the combinations—such as jiǎchǒu (甲丑)—unused; this is traditionally explained by reference to pairing the stems and branches according to their yin and yang properties.

This combination of two sub-cycles to generate a larger cycle and its use to record time have parallels in other calendrical systems, notably the Akan calendar.[3]


The sexagenary cycle is attested as a method of recording days from the earliest written records in China, records of divination on oracle bones, beginning ca. 1250 BC. Almost every oracle bone inscription includes a date in this format. This use of the cycle for days is attested throughout the Zhou dynasty and remained common into the Han period for all documentary purposes that required dates specified to the day.

Almost all the dates in the Spring and Autumn Annals, a chronological list of events from 722 to 481 BC, use this system in combination with reign years and months (lunations) to record dates. Eclipses recorded in the Annals demonstrate that continuity in the sexagenary day-count was unbroken from that period onwards. It is likely that this unbroken continuity went back still further to the first appearance of the sexagenary cycle during the Shang period.[4]

The use of the sexagenary cycle for recording years is much more recent. The earliest document showing this usage is a diagram among the silk manuscripts from Mawangdui tomb 3, sealed in 168 BC. An annotation marking the first year of the reign of Qin Shi Huang (秦始皇), 246 BC, is applied to the diagram next to the position of the 60-cycle term (51 of 60, 甲寅—jiǎ - yín) corresponding to that year.[5] Use of the cycle to record years became widespread for administrative time-keeping during the Western Han Dynasty (202 BC - 8 AD). The count of years has continued uninterrupted ever since:[6] the year 1984 began the present cycle (a 甲子—jiǎ-zǐ year), and 2044 will begin another. Note that in China the new year, when the sexagenary count increments, is not January 1, but rather the lunar new year of the traditional Chinese calendar. For example, the yi-chou 己丑 year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìchūn" (立春), which occurs near February 4.)

In Japan, according to Nihon shoki, the calendar was transmitted to Japan in 553. But it was not until the Suiko era that the calendar was used for politics. The year 604, when the Japanese officially adopted the Chinese calendar, was the first year of the cycle.[7]

The Japanese tradition of celebrating the 60th birthday (還暦 kanreki) (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years.[8]

The Tibetan calendar also counts years using a 60-year cycle based on 12 animals and 5 elements, but while the first year of the Chinese cycle is always the year of the Wood Rat, the first year of the Tibetan cycle is the year of the Fire Rabbit (丁卯—dīng-mǎo, year 4 on the Chinese cycle).[9]

Ten Heavenly Stems

Main article: Celestial stem
No. Heavenly
Yin Yang Wu Xing
Onyomi Kunyomi with
corresponding kanji
Romanized Hangul
1jiǎgaap3kō (こう)kinoe (木の兄)gapgiápyang wood
2yuet3otsu (おつ)kinoto (木の弟)eulấtyin
3bǐngbing2hei (へい)hinoe (火の兄)byeongbínhyang fire
4dīngding1tei (てい)hinoto (火の弟)jeongđinhyin
5mo6bo ()tsuchinoe (土の兄)mumậuyang earth
6gei2ki ()tsuchinoto (土の弟)gikỷyin
7gēnggang1kō (こう)kanoe (金の兄)gyeongcanhyang metal
8xīnsan1shin (しん)kanoto (金の弟)shintânyin
9rényam4jin (じん)mizunoe (水の兄)imnhâmyang water
10guǐgwai3ki ()mizunoto (水の弟)gyequýyin

Twelve Earthly Branches

Main article: Earthly Branches
No. Earthly
Onyomi Kunyomi Romanized Hangul
1ji2shinejaRat (chuột) Rat ()11 p.m. to 1 a.m.
2chǒuchau2chūushichuksửuWater buffalo (trâu) Ox ()1 to 3 a.m.
3yínyan4intoraindầnTiger (hổ/cọp) Tiger ()3 to 5 a.m.
4mǎomaau5umyomão/mẹoCat (mèo) Rabbit ()5 to 7 a.m.
5chénsan4shintatsujinthìnDragon (rồng) Dragon ()7 to 9 a.m.
6ji6shimisatỵSnake (rắn) Snake ()9 to 11 a.m.
7ng5goumaongọHorse (ngựa) Horse ()11 a.m. to 1 p.m.
8wèimei6mi or bihitsujimimùiGoat (dê) Goat ()1 to 3 p.m.
9shēnsan1shinsarushinthânMonkey (khỉ) Monkey ()3 to 5 p.m.
10yǒujau5toriyudậuRooster (gà) Rooster ()5 to 7 p.m.
11sut1jutsuinusultuấtDog (chó) Dog ()7 to 9 p.m.
12hàihoi6gaiihaehợiPig (lợn/heo) Pig ()9 to 11 p.m.

*The names of several animals can be translated into English in several different ways. The Vietnamese Earthly Branches use cat instead of Rabbit.

Sexagenary years

Conversion between cyclic years and Western years

Relationship between sexagenary cycle and recent Common Era years

As mentioned above, the cycle first started to be used for indicating years during the Han Dynasty, but of course it can be used to indicate earlier years retroactively. Since it repeats, by itself it cannot specify a year without some other information, but it is frequently used with the Chinese era name (年号; "niánhào") to specify a year.[10] Of course, the year starts with the new year of whoever is using the calendar. In China, the cyclic year normally changes on the Chinese Lunar New Year. In Japan until recently it was the Japanese lunar new year, which was sometimes different from the Chinese; now it is January 1. So when calculating the cyclic year of a date in the Gregorian year, you have to consider what your "new year" is. Hence, the following calculation deals with the Chinese dates after the Lunar New Year in that Gregorian year; to find the corresponding sexagenary year in the dates before the Lunar New Year would require the Gregorian year to be decreased by 1.

As for example, the year 2697 BC (or -2696, using the astronomical year count), traditionally the first year of the reign of the legendary Yellow Emperor, was the first year (甲子; jiǎ-zǐ) of a cycle. 2700 years later in 4 AD, the duration equivalent to 45 60-year cycles, was also the starting year of a 60-year cycle. Similarly 1980 years later, 1984 was the start of a new cycle.

Thus, to find out the Gregorian year's equivalent in the sexagenary cycle use the appropriate method below.

  1. For any year number greater than 4 AD, the equivalent sexagenary year can be found by subtracting 3 from the Gregorian year, dividing by 60 and taking the remainder. See example below.
  2. For any year before 1 AD, the equivalent sexagenary year can be found by adding 2 to the Gregorian year number (in BC), dividing it by 60, and subtracting the remainder from 60. See example below.
  3. 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.

The result will produce a number between 0 and 59, corresponding to the year order in the cycle; if the remainder is 0, it corresponds to the 60th year of a cycle. Thus, using the first method, the equivalent sexagenary year for 2012 AD is the 29th year (壬辰; rén-chén), as (2012-3) mod 60 = 29 (i.e., the remainder of (2012-3 divided by 60 is 29). Using the second, the equivalent sexagenary year for 221 BC is the 17th year (庚辰; gēng-chén), as 60- [(221+2) mod 60] = 17 (i.e., 60 minus the remainder of (221+2) divided by 60 is 17).


Step-by-step example to determine the sign for 1967:

  1. 1967 - 3 = 1964 ("subtracting 3 from the Gregorian year")
  2. 1964 ÷ 60 = 32 ("divide by 60 and discard any fraction")
  3. 1964 - (60 × 32) = 44 ("taking the remainder")
  4. Open the table 'Sexagenary Cycle' (the preceding section), look for 44 in the first column (No) and obtain Fire Goat (丁未; dīng-wèi).

Step-by-step example to determine the cyclic year of first year of the reign of Qin Shi Huang (246 BC):

  1. 246 + 2 = 248 ("adding 2 to the Gregorian year number (in BC)")
  2. 248 ÷ 60 = 4 ("divide by 60 and discard any fraction")
  3. 248 - (60 × 4) = 8 ("taking the remainder")
  4. 60 - 8 = 52 ("subtract the remainder from 60")
  5. Open the table 'Sexagenary Cycle' (the preceding section), look for 52 in the first column (No) and obtain Wood Rabbit (乙卯; yǐ-mǎo).

A shorter equivalent method

Start from the AD year, take directly the remainder mod 60, and look into column AD:

For a BC year: discard the minus sign, take the remainder of the year mod 60 and look into column BC:

When doing these conversions, year 246 BC cannot be treated as -246 AD due to the lack of a year 0 in the Gregorian AD/BC system.

The following tables show recent years (in the Gregorian calendar) and their corresponding years in the cycles:



Months in Sexagenary Cycle

The branches are used marginally to indicate months. Despite there being twelve branches and twelve months in a year, the earliest use of branches to indicate a twelve-fold division of a year was in the 2nd century BC. They were coordinated with the orientations of the Great Dipper, (建子月—jiànzǐyuè, 建丑月—jiànchǒuyuè, etc.).[11] There are two systems of placing these months, the lunar one and the solar one.

One system follows the ordinary Chinese lunar calendar and connects the names of the months directly to the central solar term (中氣; zhōngqì). The jiànzǐyuè ((建)子月) is the month containing the winter solstice (i.e. the 冬至— Dōngzhì) zhōngqì. The jiànchǒuyuè ((建)丑月) is the month of the following zhōngqì, which is Dàhán (大寒), while the jiànyínyuè ((建)寅月) is that of the Yǔshuǐ (雨水) zhōngqì, etc. Intercalary months have the same branch as the preceding month.

In the other system (節月; jiéyuè) the "month" lasts for the period of two solar terms (two 氣策—qìcì). The zǐyuè (子月) is the period starting with Dàxuě (大雪), i.e. the solar term before the winter solstice. The chǒuyuè (丑月) starts with Xiǎohán (小寒), the term before Dàhán (大寒), while the yínyuè (寅月) starts with Lìchūn (立春), the term before Yǔshuǐ (雨水), etc. Thus in the solar system a month starts anywhere from about 15 days before to 15 days after its lunar counterpart.

The branch names are not usual month names; the main use of the branches for months is astrological. However, the names are sometimes used to indicate historically which (lunar) month was the first month of the year in ancient times. For example, since the Han Dynasty, the first month has been jiànyínyuè, but earlier the first month was jiànzǐyuè (during the Zhou Dynasty) or jiànchǒuyuè (traditionally during the Shang Dynasty) as well.[12]

For astrological purposes stems are also necessary, and the months are named using the sexegenary cycle following a five-year cycle starting in a jiǎ (甲; 1st) or (己; 6th) year. The first month of the jiǎ or year is a bǐng-yín (丙寅; 3rd) month, the next one is a dīng-mǎo (丁卯; 4th) month, etc., and the last month of the year is a dīng-chǒu (丁丑, 14th) month. The next year will start with a wù-yín (戊寅; 15th) month, etc. following the cycle. The 5th year will end with a yǐ-chǒu (乙丑; 2nd) month. The following month, the start of a or jiǎ year, will hence again be a bǐng-yín (3rd) month again. The beginning and end of the (solar) months in the table below are the approximate dates of current solar terms; they vary slightly from year to year depending on the leap days of the Gregorian calendar.

Earthly Branches of the certain monthsSolar termZhongqi (the Middle solar term)Starts atEnds atNames in year of Jia or Ji(甲/己年)Names in year of Yi or Geng (乙/庚年)Names in year of Bing or Xin (丙/辛年)Names in year of Ding or Ren (丁/壬年)Names in year of Wu or Gui (戊/癸年)
Month of Yin (寅月) Lichun - JingzheYushuiFebruary 4March 6Bingyin / 丙寅月Wuyin / 戊寅月Gengyin / 庚寅月Renyin / 壬寅月Jiayin / 甲寅月

Month of Mao (卯月)

Jingzhe - Qingming ChunfenMarch 6April 5Dingmao / 丁卯月Jimao / 己卯月Xinmao / 辛卯月Guimao / 癸卯月Yimao / 乙卯月
Month of Chen (辰月)Qingming - LixiaGuyuApril 5May 6Wuchen / 戊辰月Gengchen / 庚辰月Renchen / 壬辰月Jiachen / 甲辰月Bingchen / 丙辰月
Month of Si (巳月)Lixia - MangzhongXiaomanMay 6June 6Jisi / 己巳月Xinsi / 辛巳月Guisi / 癸巳月Yisi / 乙巳月Dingsi / 丁巳月
Month of Wu (午月)Mangzhong - XiaoshuXiazhiJune 6July 7Gengwu / 庚午月Renwu / 壬午月Jiawu / 甲午月Bingwu / 丙午月Wuwu / 戊午月
Month of Wei (未月)Xiaoshu - LiqiuDashuJuly 7August 8Xinwei / 辛未月Guiwei / 癸未月Yiwei / 乙未月Dingwei / 丁未月Jiwei / 己未月
Month of Shen (申月)Liqiu - BailuChushuAugust 8September 8Renshen / 壬申月Jiashen / 甲申月Bingshen / 丙申月Wushen / 戊申月Gengshen / 庚申月
Month of You (酉月)Bailu - HanluQiufenSeptember 8October 8Guiyou / 癸酉月Yiyou / 乙酉月Dingyou / 丁酉月Jiyou / 己酉月Xinyou / 辛酉月
Month of Xu (戌月)Hanlu - LidongShuangjiangOctober 8November 7Jiaxu / 甲戌月Bingxu / 丙戌月Wuxu / 戊戌月Gengxu / 庚戌月Renxu / 壬戌月
Month of Hai (亥月)Lidong - DaxueXiaoxueNovember 7December 7Yihai / 乙亥月Dinghai / 丁亥月Jihai / 己亥月Xinhai / 辛亥月Guihai / 癸亥月
Month of Zi (子月)Daxue - XiaohanDongzhiDecember 7January 6Bingzi / 丙子月Wuzi / 戊子月Gengzi / 庚子月Renzi / 壬子月Jiazi / 甲子月
Month of Chou (丑月)Xiaohan - LichunDahanJanuary 6February 4Dingchou / 丁丑月Jichou / 己丑月Xinchou / 辛丑月Guichou / 癸丑月Yichou / 乙丑月

See also


  1. Nussbaum, Louis-Frédéric. (2005). "Jikkan-jūnishi" in Japan Encyclopedia, p. 420.
  2. Smith (2011), pp. 1, 28.
  3. For the Akan calendar, see Bartle (1978).
  4. Smith (2011), p. 24,26-27.
  5. Kalinowski (1998), pp. 135–148, and fig. 3; Smith (2011), p. 29.
  6. Smith (2011), p. 28.
  7. National Diet Library, "Calendar History; the Source" Archived January 6, 2013, at the Wayback Machine.; retrieved 2013-1-1.
  8. Encyclopedia of Shinto, "Kanreki"; retrieved 2013-1-1.
  9. Chattopadhyaya, Alaka. (1999). Atisa and Tibet: Life and Works of Dipamkara Srijnana in relation to the history and religion of Tibet, pp. 566-568.
  10. The Mathematics of the Chinese Calendar
  11. Smith (2011), p. 28, p. 29 fn2, ; Entry "建す” in the standard dictionary 広辞苑, 東京:岩波.
  12. Entry "三正” in the standard dictionary 広辞苑, 東京:岩波.


Bartle, P. F. W. (1978). "Forty days: the Akan calendar". Africa: Journal of the International African Institute. 48 (1): 80–84. doi:10.2307/1158712. 

Kalinowski, Marc (2007). "Time, space and orientation: figurative representations of the sexagenary cycle in ancient and medieval China". In Francesca Bray. Graphics and text in the production of technical knowledge in China : the warp and the weft. Leiden: Brill. pp. 137–168. ISBN 978-90-04-16063-7. 

Smith, Adam (2011). "The Chinese sexagenary cycle and the ritual origins of the calendar". In John Steele. Calendars and years II : astronomy and time in the ancient and medieval world (PDF). Oxford: Oxbow. pp. 1–37. ISBN 978-1-84217-987-1. 

This article is issued from Wikipedia - version of the 11/25/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.