Sexagenary cycle

The sexagenary cycle, also known as the gānzhī or stems-and-branches, is a cycle of sixty terms used to designate successive years, historically used for recording time in China and the rest of the East Asian cultural sphere, as well as in Southeast Asia.
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 combines the first heavenly stem with the first earthly branch. The second term yǐchǒu combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with guǐhài, 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 —unused; this is traditionally explained by reference to pairing the stems and branches according to their yin and yang properties.
It appeared as a means of recording days in the first Chinese written texts, the oracle bones of the late second millennium BC Shang dynasty. Its use to record years began around the middle of the 3rd century BC. The cycle and its variations have been an important part of the traditional calendrical systems in Chinese-influenced Asian states and territories, particularly those of Japan, Korea, and Vietnam, with the old Chinese system still in use in Taiwan, and in Mainland China. In India, the Ahom people also used the sexagenary cycle known as Lak-Ni.
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 used in the names of many historical events, such as the Chinese Xinhai Revolution, the Japanese Boshin War, the Korean Imjin War and the Vietnamese Famine of Ất Dậu, Tết Mậu Thân. It also continues to have a role in contemporary Chinese astrology and fortune telling. There are some parallels in this with Tamil calendar.
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.

History

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. 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 regnal years and months 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.
The use of the sexagenary cycle for recording years is much more recent. The earliest discovered documents showing this usage are among the silk manuscripts recovered from Mawangdui tomb 3, sealed in 168 BC. In one of these documents, a sexagenary grid diagram is annotated in three places to mark notable events. For example, the first year of the reign of Qin Shi Huang, 246 BC, is noted on the diagram next to the position of the 60-cycle term yǐmǎo, corresponding to that year. Use of the cycle to record years became widespread for administrative time-keeping during the Western Han dynasty. The count of years has continued uninterrupted ever since: the year 1984 began the present cycle, 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 jichou 己丑 year began on January 26, 2009.
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.
The Korean and Japanese tradition of celebrating the 60th birthday reflects the influence of the sexagenary cycle as a count of years.
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 jiǎzǐ, the first year of the Tibetan cycle is dīngmǎo.

Heavenly Stems

Earthly Branches

*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

As mentioned above, the cycle first started to be used for indicating years during the Han dynasty, but it also 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 to specify a year. 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, one has to consider what their "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
As for example, the year 2697 BC, traditionally the first year of the reign of the legendary Yellow Emperor, was the first year 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.

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.
For any year before 1 AD, the equivalent sexagenary year can be found by adding 2 to the Gregorian year number, dividing it by 60, and subtracting the remainder from 60.
1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.
The formula for years AD is and for years BC is.

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, as mod 60 = 29. Using the second, the equivalent sexagenary year for 221 BC is the 17th year, as 60- = 17.

Examples

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

1967 – 3 = 1964
1964 ÷ 60 = 32
1964 – = 44
Show one of the Sexagenary Cycle tables, look for 44 in the first column and obtain Fire Goat.

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

246 + 2 = 248
248 ÷ 60 = 4
248 – = 8
60 – 8 = 52
Show one of the Sexagenary Cycle table, look for 52 in the first column and obtain Wood Rabbit.
Shorter equivalent method

Start from the AD year, take directly the remainder mod 60, and look into column AD of the table "Sexagenary years".

1967 = 60 × 32 + 47.

Remainder is therefore 47 and the AD column says 'Fire Goat' as it should be.
For a BC year: discard the minus sign, take the remainder of the year mod 60 and look into column BC. Applied to year -246, this gives:

246 = 60 × 4 + 6. Remainder is therefore 6 and the BC column of table "Sexagenary years" gives 'Wood Rabbit'.

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.

Recent cycles

Sexagenary months

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 Big Dipper,. 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. The jiànzǐyuè is the month containing the winter solstice zhōngqì. The jiànchǒuyuè ) is the month of the following zhōngqì, which is Dàhán, while the jiànyínyuè is that of the Yǔshuǐ zhōngqì, etc. Intercalary months have the same branch as the preceding month.
In the other system the "month" lasts for the period of two solar terms. The zǐyuè is the period starting with Dàxuě, i.e. the solar term before the winter solstice. The chǒuyuè starts with Xiǎohán, the term before Dàhán, while the yínyuè starts with Lìchūn, the term before Yǔshuǐ, 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 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 or jiànchǒuyuè as well.
For astrological purposes stems are also necessary, and the months are named using the sexagenary cycle following a five-year cycle starting in a jiǎ or jǐ year. The first month of the jiǎ or jǐ year is a bǐngyín month, the next one is a dīngmǎo month, etc., and the last month of the year is a dīngchǒu month. The next year will start with a wùyín month, etc. following the cycle. The 5th year will end with a yǐchǒu month. The following month, the start of a jǐ or jiǎ year, will hence again be a bǐngyín month again. The beginning and end of the 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 months	Solar term	Zhongqi	Starts at	Ends at	Names in year of Jia or Ji	Names in year of Yi or Geng	Names in year of Bing or Xin	Names in year of Ding or Ren	Names in year of Wu or Gui
Month of Yin	Lichun – Jingzhe	Yushui / 雨水	February 4	March 6	Bingyin / 丙寅月	Wuyin / 戊寅月	Gengyin / 庚寅月	Renyin / 壬寅月	Jiayin / 甲寅月
Month of Mao	Jingzhe – Qingming	Chunfen / 春分	March 6	April 5	Dingmao / 丁卯月	Jimao / 己卯月	Xinmao / 辛卯月	Guimao / 癸卯月	Yimao / 乙卯月
Month of Chen	Qingming – Lixia	Guyu / 谷雨	April 5	May 6	Wuchen / 戊辰月	Gengchen / 庚辰月	Renchen / 壬辰月	Jiachen / 甲辰月	Bingchen / 丙辰月
Month of Si	Lixia – Mangzhong	Xiaoman / 小满	May 6	June 6	Jisi / 己巳月	Xinsi / 辛巳月	Guisi / 癸巳月	Yisi / 乙巳月	Dingsi / 丁巳月
Month of Wu	Mangzhong – Xiaoshu	Xiazhi / 夏至	June 6	July 7	Gengwu / 庚午月	Renwu / 壬午月	Jiawu / 甲午月	Bingwu / 丙午月	Wuwu / 戊午月
Month of Wei	Xiaoshu – Liqiu	Dashu / 大暑	July 7	August 8	Xinwei / 辛未月	Guiwei / 癸未月	Yiwei / 乙未月	Dingwei / 丁未月	Jiwei / 己未月
Month of Shen	Liqiu – Bailu	Chushu / 处暑	August 8	September 8	Renshen / 壬申月	Jiashen / 甲申月	Bingshen / 丙申月	Wushen / 戊申月	Gengshen / 庚申月
Month of You	Bailu – Hanlu	Qiufen / 秋分	September 8	October 8	Guiyou / 癸酉月	Yiyou / 乙酉月	Dingyou / 丁酉月	Jiyou / 己酉月	Xinyou / 辛酉月
Month of Xu	Hanlu – Lidong	Shuangjiang / 霜降	October 8	November 7	Jiaxu / 甲戌月	Bingxu / 丙戌月	Wuxu / 戊戌月	Gengxu / 庚戌月	Renxu / 壬戌月
Month of Hai	Lidong – Daxue	Xiaoxue / 小雪	November 7	December 7	Yihai / 乙亥月	Dinghai / 丁亥月	Jihai / 己亥月	Xinhai / 辛亥月	Guihai / 癸亥月
Month of Zi	Daxue – Xiaohan	Dongzhi / 冬至	December 7	January 6	Bingzi / 丙子月	Wuzi / 戊子月	Gengzi / 庚子月	Renzi / 壬子月	Jiazi / 甲子月
Month of Chou	Xiaohan – Lichun	Dahan / 大寒	January 6	February 4	Dingchou / 丁丑月	Jichou / 己丑月	Xinchou / 辛丑月	Guichou / 癸丑月	Yichou / 乙丑月