Sexagenary cycle

Sexagenary cycle

The sexagenary cycle, also known as the Template:Tlit () 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.

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 Template:Tlit () combines the first heavenly stem with the first earthly branch. The second term Template:Tlit () combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with Template:Tlit (), after which it begins again at Template:Tlit. This termination at ten and twelve's least common multiple leaves half of the combinations—such as Template:Tlit ()—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 (descendants of the Dai people of Yunnan who migrated to Assam in the 13th century) 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 , . 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

Bone inscribed with a table of the sexagenary cycle, dated to the early 11th century BC

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 c. 1100 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 regnal 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.

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 Template:Tlit (, 52 of 60), corresponding to that year. 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: the year 1984 began the present cycle (a —Template:Tlit 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 Template:Tlit year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term [[Lichun|Template:Tlit]] (), 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.

The Korean (; ; ) and Japanese tradition ( Template:Tlit) of celebrating the 60th birthday (literally 'return of calendar') 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 Template:Tlit (the year of the Wood Rat), the first year of the Tibetan cycle is Template:Tlit (; year 4 on the Chinese cycle, year of the Fire Rabbit).

Heavenly Stems

No.	Heavenly Stem	Ahom Name	Chinese name				Japanese name		Korean name		Vietnamese name	Yin Yang	Wu Xing
			Mandarin (Pinyin)	Cantonese (Jyutping)	Middle Chinese (Baxter)	Old Chinese (Baxter–Sagart)	Onyomi	Kunyomi with corresponding kanji	Romanized	Hangul
1		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yang	wood
2		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yin
3		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yang	fire
4		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yin
5		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit (~ Template:Tlit)	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yang	earth
6		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yin
7		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yang	metal
8		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yin
9		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yang	water
10		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			yin

Earthly Branches

No.	Earthly Branch	Chinese name				Japanese name		Korean name		Vietnamese name	Vietnamese zodiac	Chinese zodiac	Corresponding hours
		Mandarin (Pinyin)	Cantonese (Jyutping)	Middle Chinese (Baxter)	Old Chinese (Baxter–Sagart)	Onyomi	Kunyomi	Romanized	Hangul
1		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit (	Template:Tlit			Rat ( )	Rat ()	23:00–01:00
2		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Water buffalo ( )	Ox ()	01:00–03:00
3		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Tiger ( 虎/ )	Tiger ()	03:00–05:00
4		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Cat ( )	Rabbit ()	05:00–07:00
5		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Dragon ( )	Dragon ()	07:00–09:00
6		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Snake ( )	Snake ()	09:00–11:00
7		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Horse ( )	Horse ()	11:00–13:00
8		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit () or Template:Tlit ()	Template:Tlit ()	Template:Tlit			Goat ( )	Goat ()	13:00–15:00
9		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Monkey ( )	Monkey ()	15:00–17:00
10		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Rooster ( )	Rooster ()	17:00–19:00
11		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Dog ( )	Dog ()	19:00–21:00
12		Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit	Template:Tlit ()	Template:Tlit ()	Template:Tlit			Pig ( / )	Pig ()	21:00–23:00

*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

24 cardinal directions

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 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 (Template:Zhi; Template:Tlit) 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 by 1.

As for example, the year 2697 BC (or −2696, using the astronomical year numbering), traditionally the first year of the reign of the legendary Yellow Emperor, was the first year (甲子; jiǎzǐ) 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.
3. 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.
4. The formula for years AD is (year – 3) mod 60 and for years BC is 60 − [(year + 2) mod 60].

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; rénchén), 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; gēngchén), as 60 − [(221+2) mod 60] = 17 (i.e., 60 minus the remainder of (221+2) divided by 60 is 17).

Examples

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. Show one of the Sexagenary Cycle tables (the following section), look for 44 in the first column (No) and obtain Fire Goat (丁未; dīngwèi).

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. Show one of the Sexagenary Cycle table (the following section), look for 52 in the first column (No) and obtain Wood Rabbit (乙卯; yǐmǎo).

Equivalent lookup method

Start from the AD year (1967), take directly the remainder mod 60, and look into column AD of the table "Sexagenary years" (just above).

1. 1967 = 60 × 32 + 47.
2. Remainder is therefore 47 and the AD column says 'Fire Goat' as it should be.

For a BC year: take the remainder of the year mod 60 and look into column BC. Applied to year 246 BC, this gives:

1. 246 = 60 × 4 + 6.
2. Remainder is therefore 6 and the BC column of table "Sexagenary years" (just above) gives 'Wood Rabbit'.

When doing these conversions, year 246 BC may be treated as −245 AD as in astronomical year numbering, but never as −246 AD, due to the lack of a year 0 in the Gregorian AD/BC system.

Recent cycles

Recent years (in the Gregorian calendar) and their corresponding years in the cycles

No.	Heavenly stem	Earthly branch	New Year Day
	(Element)	(Animal)	76th cycle	77th cycle	78th cycle	79th cycle
01	甲 Yang Wood	子 Rat	11 Feb 1804	08 Feb 1864	05 Feb 1924	02 Feb 1984
02	乙 Yin Wood	丑 Ox	31 Jan 1805	27 Jan 1865	24 Jan 1925	20 Feb 1985
03	丙 Yang Fire	寅 Tiger	18 Feb 1806	15 Feb 1866	13 Feb 1926	09 Feb 1986
04	丁 Yin Fire	卯 Rabbit	07 Feb 1807	05 Feb 1867	02 Feb 1927	30 Jan 1987
05	戊 Yang Earth	辰 Dragon	28 Jan 1808	25 Jan 1868	23 Jan 1928	18 Feb 1988
06	己 Yin Earth	巳 Snake	15 Feb 1809	11 Feb 1869	10 Feb 1929	06 Feb 1989
07	庚 Yang Metal	午 Horse	04 Feb 1810	01 Feb 1870	30 Jan 1930	27 Jan 1990
08	辛 Yin Metal	未 Goat	25 Jan 1811	20 Feb 1871	17 Feb 1931	15 Feb 1991
09	壬 Yang Water	申 Monkey	13 Feb 1812	09 Feb 1872	07 Feb 1932	04 Feb 1992
10	癸 Yin Water	酉 Rooster	01 Feb 1813	29 Jan 1873	26 Jan 1933	23 Jan 1993
11	甲 Yang Wood	戌 Dog	21 Jan 1814	17 Feb 1874	14 Feb 1934	11 Feb 1994
12	乙 Yin Wood	亥 Pig	09 Feb 1815	06 Feb 1875	04 Feb 1935	31 Jan 1995
13	丙 Yang Fire	子 Rat	29 Jan 1816	26 Jan 1876	24 Jan 1936	19 Feb 1996
14	丁 Yin Fire	丑 Ox	16 Feb 1817	13 Feb 1877	11 Feb 1937	07 Feb 1997
15	戊 Yang Earth	寅 Tiger	06 Feb 1818	02 Feb 1878	31 Jan 1938	28 Jan 1998
16	己 Yin Earth	卯 Rabbit	26 Jan 1819	23 Jan 1879	19 Feb 1939	16 Feb 1999
17	庚 Yang Metal	辰 Dragon	14 Feb 1820	10 Feb 1880	08 Feb 1940	05 Feb 2000
18	辛 Yin Metal	巳 Snake	03 Feb 1821	30 Jan 1881	27 Jan 1941	24 Jan 2001
19	壬 Yang Water	午 Horse	23 Jan 1822	18 Feb 1882	15 Feb 1942	12 Feb 2002
20	癸 Yin Water	未 Goat	11 Feb 1823	08 Feb 1883	05 Feb 1943	01 Feb 2003
21	甲 Yang Wood	申 Monkey	31 Jan 1824	28 Jan 1884	25 Jan 1944	22 Jan 2004
22	乙 Yin Wood	酉 Rooster	18 Feb 1825	15 Feb 1885	13 Feb 1945	09 Feb 2005
23	丙 Yang Fire	戌 Dog	07 Feb 1826	04 Feb 1886	02 Feb 1946	30 Jan 2006
24	丁 Yin Fire	亥 Pig	27 Jan 1827	24 Jan 1887	22 Jan 1947	18 Feb 2007
25	戊 Yang Earth	子 Rat	16 Feb 1828	12 Feb 1888	10 Feb 1948	07 Feb 2008
26	己 Yin Earth	丑 Ox	04 Feb 1829	31 Jan 1889	29 Jan 1949	26 Jan 2009
27	庚 Yang Metal	寅 Tiger	25 Jan 1830	21 Jan 1890	17 Feb 1950	14 Feb 2010
28	辛 Yin Metal	卯 Rabbit	13 Feb 1831	09 Feb 1891	06 Feb 1951	03 Feb 2011
29	壬 Yang Water	辰 Dragon	02 Feb 1832	30 Jan 1892	27 Jan 1952	23 Jan 2012
30	癸 Yin Water	巳 Snake	20 Feb 1833	17 Feb 1893	14 Feb 1953	10 Feb 2013
31	甲 Yang Wood	午 Horse	09 Feb 1834	06 Feb 1894	04 Feb 1954	31 Jan 2014
32	乙 Yin Wood	未 Goat	29 Jan 1835	26 Jan 1895	24 Jan 1955	19 Feb 2015
33	丙 Yang Fire	申 Monkey	17 Feb 1836	13 Feb 1896	12 Feb 1956	08 Feb 2016
34	丁 Yin Fire	酉 Rooster	06 Feb 1837	02 Feb 1897	31 Jan 1957	28 Jan 2017
35	戊 Yang Earth	戌 Dog	26 Jan 1838	22 Jan 1898	19 Feb 1958	16 Feb 2018
36	己 Yin Earth	亥 Pig	14 Feb 1839	10 Feb 1899	08 Feb 1959	05 Feb 2019
37	庚 Yang Metal	子 Rat	03 Feb 1840	31 Jan 1900	28 Jan 1960	25 Jan 2020
38	辛 Yin Metal	丑 Ox	23 Jan 1841	19 Feb 1901	15 Feb 1961	12 Feb 2021
39	壬 Yang Water	寅 Tiger	10 Feb 1842	08 Feb 1902	05 Feb 1962	01 Feb 2022
40	癸 Yin Water	卯 Rabbit	30 Jan 1843	29 Jan 1903	26 Jan 1963	22 Jan 2023
41	甲 Yang Wood	辰 Dragon	18 Feb 1844	16 Feb 1904	13 Feb 1964	10 Feb 2024
42	乙 Yin Wood	巳 Snake	07 Feb 1845	04 Feb 1905	02 Feb 1965	29 Jan 2025
43	丙 Yang Fire	午 Horse	27 Jan 1846	25 Jan 1906	22 Jan 1966	17 Feb 2026
44	丁 Yin Fire	未 Goat	16 Feb 1847	13 Feb 1907	09 Feb 1967	06 Feb 2027
45	戊 Yang Earth	申 Monkey	05 Feb 1848	02 Feb 1908	30 Jan 1968	26 Jan 2028
46	己 Yin Earth	酉 Rooster	24 Jan 1849	22 Jan 1909	17 Feb 1969	13 Feb 2029
47	庚 Yang Metal	戌 Dog	12 Feb 1850	10 Feb 1910	06 Feb 1970	03 Feb 2030
48	辛 Yin Metal	亥 Pig	01 Feb 1851	30 Jan 1911	27 Jan 1971	23 Jan 2031
49	壬 Yang Water	子 Rat	20 Feb 1852	18 Feb 1912	15 Feb 1972	11 Feb 2032
50	癸 Yin Water	丑 Ox	08 Feb 1853	06 Feb 1913	03 Feb 1973	31 Jan 2033
51	甲 Yang Wood	寅 Tiger	29 Jan 1854	26 Jan 1914	23 Jan 1974	19 Feb 2034
52	乙 Yin Wood	卯 Rabbit	17 Feb 1855	14 Feb 1915	11 Feb 1975	08 Feb 2035
53	丙 Yang Fire	辰 Dragon	07 Feb 1856	03 Feb 1916	31 Jan 1976	28 Jan 2036
54	丁 Yin Fire	巳 Snake	26 Jan 1857	23 Jan 1917	18 Feb 1977	15 Feb 2037
55	戊 Yang Earth	午 Horse	14 Feb 1858	11 Feb 1918	07 Feb 1978	04 Feb 2038
56	己 Yin Earth	未 Goat	03 Feb 1859	01 Feb 1919	28 Jan 1979	24 Jan 2039
57	庚 Yang Metal	申 Monkey	23 Jan 1860	20 Feb 1920	16 Feb 1980	12 Feb 2040
58	辛 Yin Metal	酉 Rooster	10 Feb 1861	08 Feb 1921	05 Feb 1981	01 Feb 2041
59	壬 Yang Water	戌 Dog	30 Jan 1862	28 Jan 1922	25 Jan 1982	22 Jan 2042
60	癸 Yin Water	亥 Pig	18 Feb 1863	16 Feb 1923	13 Feb 1983	10 Feb 2043

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, (: Template:Tlit, : Template:Tlit, etc.). 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 (Template:Zh). The Template:Tlit (()) is the month containing the winter solstice (i.e. the [[Dongzhi (solar term)|Template:Tlit]]) Template:Tlit. The Template:Tlit (()Template:Zh) is the month of the following Template:Tlit, which is [[Dahan (solar term)|Template:Tlit]] (), while the Template:Tlit (()) is that of the [[Yushui (solar term)|Template:Tlit]] () Template:Tlit, etc. Intercalary months have the same branch as the preceding month.

In the other system (Template:Zh) the "month" lasts for the period of two solar terms (two Template:Tlit). The Template:Tlit () is the period starting with [[Daxue (solar term)|Template:Tlit]] (), i.e. the solar term before the winter solstice. The Template:Tlit () starts with [[Xiaohan|Template:Tlit]] (), the term before Template:Tlit (), while the Template:Tlit () starts with [[Lichun|Template:Tlit]] (), the term before Template:Tlit (), 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 Template:Tlit, but earlier the first month was Template:Tlit (during the Zhou dynasty) or Template:Tlit (traditionally during the Shang dynasty) 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 Template:Tlit (; 1st) or Template:Tlit (Template:Zh; 6th) year. The first month of the Template:Tlit or Template:Tlit year is a Template:Tlit (; 3rd) month, the next one is a Template:Tlit (; 4th) month, etc., and the last month of the year is a Template:Tlit (, 14th) month. The next year will start with a Template:Tlit (; 15th) month, etc. following the cycle. The 5th year will end with a Template:Tlit (; 2nd) month. The following month, the start of a Template:Tlit or Template:Tlit year, will hence again be a Template:Tlit (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 months	Solar term	Template:Tlit (the Middle solar term)	Starts at	Ends at	Names in year of Template:Tlit or Template:Tlit (/)	Names in year of Template:Tlit or Template:Tlit (/)	Names in year of Template:Tlit or Template:Tlit (/)	Names in year of Template:Tlit or Template:Tlit (/)	Names in year of Template:Tlit or Template:Tlit (/)
Month of Template:Tlit ()	Lichun – Jingzhe	Yushui /	February 4	March 6	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Jingzhe – Qingming	Chunfen /	March 6	April 5	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Qingming – Lixia	Guyu /	April 5	May 6	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Lixia – Mangzhong	Xiaoman /	May 6	June 6	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Mangzhong – Xiaoshu	Xiazhi /	June 6	July 7	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Xiaoshu – Liqiu	Dashu /	July 7	August 8	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Liqiu – Bailu	Chushu /	August 8	September 8	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Bailu – Hanlu	Qiufen /	September 8	October 8	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Hanlu – Lidong	Shuangjiang /	October 8	November 7	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Lidong – Daxue	Xiaoxue /	November 7	December 7	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Daxue – Xiaohan	Dongzhi /	December 7	January 6	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /
Month of Template:Tlit ()	Xiaohan – Lichun	Dahan /	January 6	February 4	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /	Template:Tlit /

Sexagenary days

Table for sexagenary days

Day (stem)				Month (stem)				2-digit year mod 40 (stem)				Century (stem)					N	Century (branch)					2-digit year mod 16 (branch)							Month (branch)				Day (branch)
												Julian mod 2	Gregorian					Julian mod 4	Gregorian
00	10	20	30	Aug				Template:Encodefirst	02	21	23	00	Template:Encodefirst				00	00					Template:Encodefirst			07							Nov	00	12	24
01	11	21	31	Sep	Oct			Template:Encodefirst	06	25	27				21		01												14					01	13	25
02	12	22		Nov	Dec			Template:Encodefirst	10	29	31			19			02		Template:Encodefirst	19					05					Template:Encodefirst	Apr			02	14	26
03	13	23						Template:Encodefirst	14	33	35						03	03			22			03				Template:Encodefirst		Feb	Jun			03	15	27
04	14	24						Template:Encodefirst	18	37	39		17			Template:Encodefirst	04										10					Aug		04	16	28
05	15	25						01	03	Template:Encodefirst	22	01			22	15	05		15				01										Oct	05	17	29
06	16	26						05	07	Template:Encodefirst	26						06	02		18						Template:Encodefirst			15				Dec	06	18	30
07	17	27			Mar		Template:Encodefirst	09	11	Template:Encodefirst	30			Template:Encodefirst			07				21				06					Template:Encodefirst	Mar			07	19	31
08	18	28		Jan	Apr	May	Template:Encodefirst	13	15	Template:Encodefirst	34		18				08					Template:Encodefirst						13		Jan	May			08	20
09	19	29		Feb	Jun	Jul		17	19	Template:Encodefirst	38				23		09	01						Template:Encodefirst			11					Jul		09	21
Dates with yellow background indicate they are for this year.																	10		17				02											10	22
																	11				Template:Encodefirst	23				09						Sep		11	23

• N for the year: (5y + [y/4]) mod 10, y = 0–39 (stem); (5y + [y/4]) mod 12, y = 0–15 (branch)
• N for the Gregorian century: (4c + [c/4] + 2) mod 10 (stem); (8c + [c/4] + 2) mod 12 (branch), c ≥ 15
• N for the Julian century: 5c mod 10, c = 0–1 (stem); 9c mod 12, c = 0–3 (branch)

The table above allows one to find the stem & branch for any given date. For both the stem and the branch, find the N for the row for the century, year, month, and day, then add them together. If the sum for the stems' N is above 10, subtract 10 until the result is between 1 and 10. If the sum for the branches' N is above 12, subtract 12 until the result is between 1 and 12.

For any date before October 15, 1582, use the Julian century column to find the row for that century's N. For dates after October 15, 1582, use the Gregorian century column to find the century's N. When looking at dates in January and February of leap years, use the bold & italic Feb and Jan.

Examples

• Step-by-step example to determine the stem-branch for October 1, 1949.
  • Stem
    • (day stem N + month stem N + year stem N + century stem N) = number of stem. If over 10, subtract 10 until within 1 – 10.
      • Day 1: N = 1,
      • Month of October: N = 1,
      • Year 49: N = 7,
        • 49 isn't on the table, so we'll have to mod 49 by 40. This gives us year 9, which we can follow to find the N for that row.
      • Century 19: N = 2.
    • (1 + 1 + 7 + 2) = 11. This is more than 10, so we'll subtract 10 to bring it between 1 and 10.
      • 11 – 10 = 1,
      • Stem = 1, Template:Zh.
  • Branch
    • (day branch N + month branch N + year branch N + century branch N)= number of branch. If over 12, subtract 12 until within 1 – 12.
      • Day 1: N = 1,
      • Month of October: N = 5,
      • Year 49: N = 5,
        • Again, 49 is not in the table for year. Modding 49 by 16 gives us 1, which we can look up to find the N of that row.
      • Century 19: N = 2.
    • (1 + 5 + 5 + 2) = 13. Since 13 is more than 12, we'll subtract 12 to bring it between 1 and 12.
      • 13 – 12 = 1,
      • Branch = 1, Template:Zh.
  • Stem-branch = 1, 1 (Template:Zh, 1 in sexagenary cycle = 32 – 5 + 33 + 1 – 60).

More detailed examples

• Stem-branch for December 31, 1592
  • Stem = (day stem N + month stem N + year stem N + century stem N)
    • Day 31: N = 1; month of December: N = 2; year 92 (92 mod 40 = 12): N = 3; century 15: N = 5.
    • (1 + 2 + 3 + 5) = 11; 11 – 10 = 1.
    • Stem = 1, Template:Zh.
  • Branch = (day branch N + month branch N + year branch N + century branch N)
    • Day 31: N = 7; month of December: N = 6; year 92 (92 mod 16 = 12): N = 3; century 15: N = 5.
    • (7 + 6 + 3 + 5) = 21; 21 – 12 = 9.
    • Branch = 9, Template:Zh
  • Stem-branch = 1, 9 (Template:Zh, 21 in cycle = – 42 – 2 + 34 + 31 = 21)
• Stem-branch for August 4, 1338
  • Stem = 8, Template:Zh
    • Day 4: N = 4; month of August: N = 0; year 38: N = 9; century 13 (13 mod 2 = 1): N = 5.
    • (4 + 0 + 9 + 5) = 18; 18 – 10 = 8.
  • Branch = 12, Template:Zh
    • Day 4: N = 4; month of August: N = 4; year 38 (38 mod 16 = 6): N = 7; century 13 (13 mod 4 = 1): N = 9.
    • (4 + 4 + 7 + 9) = 24; 24 – 12 = 12
  • Stem-branch = 8, 12 (Template:Zh, 48 in cycle = 4 + 8 + 32 + 4)
• Stem-branch for May 25, 105 BC (−104).
  • Stem = 7, Template:Zh
    • Day 25: N = 5; month of May: N = 8; year −4 (−4 mod 40 = 36): N = 9; century −1 (−1 mod 2 = 1): N = 5.
    • (5 + 8 + 9 + 5) = 27; 27 – 10 = 17; 17 – 10 = 7.
  • Branch = 3, Template:Zh
    • Day 25: N = 1; month of May: N = 8; year −4 (−4 mod 16 = 12): N = 3; century −1 (−1 mod 4 = 3): N = 3.
    • (1 + 8 + 3 + 3) = 15; 15 – 12 = 3.
  • Stem-branch = 7, 3 (Template:Zh, 27 in cycle = – 6 + 8 + 0 + 25)
  • Alternately, instead of doing both century and year, one can exclude the century and simply use −104 as the year for both the stem and the branch to get the same result.

Algorithm for mental calculation

$SB=(y+c+m+day)mod60$

$S=SBmod10,B=SBmod12$

$y=(year(mod400)mod80(mod12)\times 5+\lfloor \frac{year(mod400)mod80}{4}\rfloor )mod60$

$c=\lfloor \frac{year}{400}\rfloor -\lfloor \frac{year}{100}\rfloor +10$ for Gregorian calendar and $c=8$ for Julian calendar.

$m=(month+1)mod2\times 30+\lfloor 0.6\times (month+1)-3\rfloor -i$
$i=5$ for Jan or Feb in a common year and $i=6$ in a leap year.

Month	Jan 13	Feb 14	Mar 03	Apr 04	May 05	Jun 06	Jul 07	Aug 08	Sep 09	Oct 10	Nov 11	Dec 12
m	00	31	−1	30	00	31	01	32	03	33	04	34
Leap year	−1	30	$m=\lfloor 30.6\times (month+1)-3\rfloor mod60-i$

• Stem-branch for February 22, 720 BC (−719).

y = 5 x (720–719) + [1/4] = 5

c = 8

m = 30 + [0.6 x 15 – 3] – 5 = 31

d = 22

SB = 5 + 8 + 31 + 22 – 60 = 6

S = B = 6, 己巳

• Stem-branch for November 1, 211 BC (−210).

y = 5 x (240–210) + [30/4] = 5 x 6 + 7 = 37

c = 8

m = 0 + [0.6 x 12 – 3] = 4

d = 1

SB = 37 + 8 + 4 + 1 = 50

S = 0, B = 2, 癸丑

• Stem-branch for February 18, 1912.

y = 5 x (1912–1920) + [-8/4] + 60 = 18

c = 4 – 19 + 10 = -5

m = 30 + [0.6 x 15 – 3] – 6 = 30

d = 18

SB = 18 – 5 + 30 + 18 – 60 = 1

S = B = 1, 甲子

• Stem-branch for October 1, 1949.

y = 5 x (1949–1920) + [29/4] = 5 x 5 + 7 = 32

c = -5

m = 30 + [0.6 x 11 -3] = 33

d = 1

SB = 32 – 5 + 33 + 1 – 60 = 1

S = B = 1, 甲子

Look up table for sexagenary days

Gregorian		17 24	15 22		20	18	23	16	21	19	Centuries
Julian			01					00
Dates	Mar Jan					Nov Dec	Sep Oct	Aug	Feb Jun Jul	Jan Apr May Feb	Years of the century
	01 11 21 31	02 12 22	03 13 23	04 14 24	05 15 25	06 16 26	07 17 27	08 18 28	09 19 29	10 20 30
天干	甲	乙	丙	丁	戊	己	庚	辛	壬	癸
Heavenly stems	A	B	C	D	E	F	G	H	I	J	00	02	21	23	40	42	61	63	80	82
	B	C	D	E	F	G	H	I	J	A	04	06	25	27	44	46	65	67	84	86
	C	D	E	F	G	H	I	J	A	B	08	10	29	31	48	50	69	71	88	90
	D	E	F	G	H	I	J	A	B	C	12	14	33	35	52	54	73	75	92	94
	E	F	G	H	I	J	A	B	C	D	16	18	37	39	56	58	77	79	96	98
	F	G	H	I	J	A	B	C	D	E	01	03	20	22	41	43	60	62	81	83
	G	H	I	J	A	B	C	D	E	F	05	07	24	26	45	47	64	66	85	87
	H	I	J	A	B	C	D	E	F	G	09	11	28	30	49	51	68	70	89	91
	I	J	A	B	C	D	E	F	G	H	13	15	32	34	53	55	72	74	93	95
	J	A	B	C	D	E	F	G	H	I	17	19	36	38	57	59	76	78	97	99
地支	子	丑	寅	卯	辰	巳	午	未	申	酉	戌	亥	干支纪日速查表
Earthly branches	A	B	C	D	E	F	G	H	I	J	K	L	00	07	16	23	32	39	48	55	64	71	80	87	96
	B	C	D	E	F	G	H	I	J	K	L	A		14		30		46		62		78		94
	C	D	E	F	G	H	I	J	K	L	A	B	05		21		37		53		69		85
	D	E	F	G	H	I	J	K	L	A	B	C	03	12	19	28	35	44	51	60	67	76	83	92	99
	E	F	G	H	I	J	K	L	A	B	C	D		10		26		42		58		74		90
	F	G	H	I	J	K	L	A	B	C	D	E	01		17		33		49		65		81		97
	G	H	I	J	K	L	A	B	C	D	E	F	08	15	24	31	40	47	56	63	72	79	88	95
	H	I	J	K	L	A	B	C	D	E	F	G	06		22		38		54		70		86
	I	J	K	L	A	B	C	D	E	F	G	H		13		29		45		61		77		93
	J	K	L	A	B	C	D	E	F	G	H	I	04	11	20	27	36	43	52	59	68	75	84	91
	K	L	A	B	C	D	E	F	G	H	I	J	02		18		34		50		66		82		98
	L	A	B	C	D	E	F	G	H	I	J	K		09		25		41		57		73		89
Dates	01 13 25	02 14 26	03 15 27	04 16 28	05 17 29	06 18 30	07 19 31	08 20	09 21	10 22	11 23	12 24	Years of the century
	Mar Jan	Dec	Oct	Aug	Feb Jun	Apr Feb		Nov	Sep		Jul	Jan May
Gregorian		15 18	21	24		17	20 23			16 19	22		Centuries
Julian		02			01			00			03

Sexagenary hours

Table for sexagenary hours (5-day cycle)

Stem of the day	Zǐ hour 23:00–1:00	Chǒu hour 1:00–3:00	Yín hour 3:00–5:00	Mǎo hour 5:00–7:00	Chén hour 7:00–9:00	Sì hour 9:00–11:00	Wǔ hour 11:00–13:00	Wèi hour 13:00–15:00	Shēn hour 15:00–17:00	Yǒu hour 17:00–19:00	Xū hour 19:00–21:00	Hài hour 21:00–23:00
Jia or Ji day ()	1	2	3	4	5	6	7	8	9	10	11	12
Yi or Geng day ()	13	14	15	16	17	18	19	20	21	22	23	24
Bing or Xin day ()	25	26	27	28	29	30	31	32	33	34	35	36
Ding or Ren day ()	37	38	39	40	41	42	43	44	45	46	47	48
Wu or Gui day ()	49	50	51	52	53	54	55	56	57	58	59	60

See also

• Doumu (斗母元君)
• Tai Sui (太歲)
• Chinese calendar
• Chinese era name
• Lunisolar calendar
• Japanese invasions of Korea (1592–1598), known in Korean as the "Imjin War", after the imjin (Yang Water Dragon) year 1592.
• Koshien Stadium (Japan), named after the kōshi (Yang Wood Rat) year 1924. One of the last examples of general usage of the cycle in Japan.
• Tet Offensive – Vietnamese name of the event, "Tết Mậu Thân Event", named after the Mậu Thân (Yang Earth Monkey) year 1968.
• Xinhai Revolution (China), named after the xinhai (Yin Metal Pig) year 1911
• Samvatsara

References

Sources

• 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. JSTOR 1158712. S2CID 143751434.
• Kalinowski, Marc (2007). "Time, space and orientation: figurative representations of the sexagenary cycle in ancient and medieval China". In Francesca Bray (ed.). 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 Steele, John (ed.). Calendars and Years II: Astronomy and time in the ancient and medieval world. Oxford: Oxbow. pp. 1–37. doi:10.7916/D8891CDX. ISBN 978-1-84217-987-1.
• Kapoor, Ramesh (2021), "Fixing the chronology in Tai-Ahom chronicles by using astronomical references", Journal of Astronomical History and Heritage, 24 (3): 665–687, doi:10.3724/SP.J.1440-2807.2021.03.07

• Phukan Baruah, B. N.N. (1964). Ahom lexicon. The government of Assam in the department of historical and antiquarian studies.

External links

• "Heavenly Stems and Earthly Branches". Hong Kong Observatory. Archived from the original on 2018-11-04. Retrieved 2018-11-04.
• Ganzhi.io An Open Source application and implementation of Gan & Zhi as well as Jeiqi