Sexagenary cycle

The sexagenary cycle, also known as the () 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.

thumb|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 () combines the first heavenly stem with the first earthly branch. The second term () combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with (), after which it begins again at . This termination at ten and twelve's least common multiple leaves half of the combinations—such as ()—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 , Tet Offensive|. 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

thumb|right|upright|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 . 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 (, 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 — 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 year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term Lichun| (), 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 ( ) 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 (the year of the Wood Rat), the first year of the Tibetan cycle is (; year 4 on the Chinese cycle, year of the Fire Rabbit).

Heavenly Stems

{| class="wikitable"

!rowspan=2|No.

!rowspan=2|Heavenly Stem

! rowspan="2" |Ahom Name

! colspan="4" |Chinese name

!colspan=2|Japanese name

!colspan=2|Korean name

!rowspan=2|Vietnamese name

!rowspan=2|Yin Yang

!rowspan=2|Wu Xing

!Mandarin (Pinyin)

!Cantonese (Jyutping)

!Middle Chinese (Baxter)

!Old Chinese (Baxter–Sagart)

!Onyomi

!Kunyomi with corresponding kanji

!Romanized

!Hangul

|- align="center"

|1||

||||||||||| ()|| ()||||||||yang

|rowspan=2 |wood

|- align="center"

|2||

||||||||||| ()|| ()||||||||yin

|- align="center"

|3||

||||||||||| ()|| ()||||||||yang

|rowspan=2 |fire

|- align="center"

|4||

| |||||||||| ()|| ()||||||||yin

|- align="center"

|5||

||||||||| (~ )|| ()|| ()||||||||yang

|rowspan=2 |earth

|- align="center"

|6||

||||||||||| ()|| ()||||||||yin

|- align="center"

|7||

||||||||||| ()|| ()||||||||yang

| rowspan=2 |metal

|- align="center"

|8||

||||||||||| ()|| ()||||||||yin

|- align="center"

|9||

||||||||||| ()|| ()||||||||yang

| rowspan=2 |water

|- align="center"

|10||

||||||||||| ()|| ()||||||||yin

Earthly Branches

{| class="wikitable"

!rowspan=2|No.

!rowspan=2|Earthly Branch

!colspan=4|Chinese name

!colspan=2|Japanese name

!colspan=2|Korean name

!rowspan=2|Vietnamese name

!rowspan=2|Vietnamese zodiac

!rowspan=2|Chinese zodiac

!rowspan=2|Corresponding hours

!Mandarin (Pinyin)

!Cantonese (Jyutping)

!Middle Chinese (Baxter)

!Old Chinese (Baxter–Sagart)

!Onyomi

!Kunyomi

!Romanized

!Hangul

|- align="center"

|1|||||||||||| ()|| (||||||||Rat ( )

|Rat ()|| 23:00–01:00

|- align="center"

|2|||||||||||| ()|| ()||||||||Water buffalo ( )

|Ox ()|| 01:00–03:00

|- align="center"

|3|||||||||||| ()|| ()||||||||Tiger ( / )

|Tiger ()|| 03:00–05:00

|- align="center"

|4|||||||||||| ()|| ()||||||||Cat ( )

|Rabbit ()|| 05:00–07:00

|- align="center"

|5|||||||||||| ()|| ()||||||||Dragon ( )

|Dragon ()|| 07:00–09:00

|- align="center"

|6|||||||||||| ()|| ()||||||||Snake ( )

|Snake ()|| 09:00–11:00

|- align="center"

|7|||||||||||| ()|| ()||||||||Horse ( )

|Horse ()|| 11:00–13:00

|- align="center"

|8|||||||||||| () or ()|| ()||||||||Goat ( )

|Goat ()|| 13:00–15:00

|- align="center"

|9|||||||||||| ()|| ()||||||||Monkey ( )

|Monkey ()|| 15:00–17:00

|- align="center"

|10|||||||||||| ()|| ()||||||||Rooster ( )

|Rooster ()|| 17:00–19:00

|- align="center"

|11|||||||||||| ()|| ()||||||||Dog ( )

|Dog ()|| 19:00–21:00

|- align="center"

|12|||||||||||| ()|| ()||||||||Pig ( / )

|Pig ()|| 21:00–23:00

<nowiki>*</nowiki>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

{|class="wikitable collapsible"

!No.||Stem-Branch||Mandarin Chinese Pinyin||Japanese||Korean||Vietnamese||Associations||BC||AD||Current Cycle

|- align="center"

|1|||||||| ||||Yang Wood Rat||57||4||1984

|- align="center"

|2|||||||| ||||Yin Wood Ox||56||5||1985

|- align="center"

|3|||||||| ||||Yang Fire Tiger||55||6||1986

|- align="center"

|4|||||||| ||||Yin Fire Rabbit||54||7||1987

|- align="center"

|5|||||||| ||||Yang Earth Dragon||53||8||1988

|- align="center"

|6|||||||| ||||Yin Earth Snake||52||9||1989

|- align="center"

|7|||||||| ||||Yang Metal Horse||51||10||1990

|- align="center"

|8|||||||| ||||Yin Metal Goat||50||11||1991

|- align="center"

|9|||||||| ||||Yang Water Monkey||49||12||1992

|- align="center"

|10|||||||| ||||Yin Water Rooster||48||13||1993

|- align="center"

|11|||||||| ||||Yang Wood Dog||47||14||1994

|- align="center"

|12|||||||| ||||Yin Wood Pig||46||15||1995

|- align="center"

|13|||||||| ||||Yang Fire Rat||45||16||1996

|- align="center"

|14|||||||| ||||Yin Fire Ox||44||17||1997

|- align="center"

|15|||||||| ||||Yang Earth Tiger||43||18||1998

|- align="center"

|16|||||||| ||||Yin Earth Rabbit||42||19||1999

|- align="center"

|17|||||||| ||||Yang Metal Dragon||41||20||2000

|- align="center"

|18|||||||| ||||Yin Metal Snake||40||21||2001

|- align="center"

|19|||||||| ||||Yang Water Horse||39||22||2002

|- align="center"

|20|||||||| ||||Yin Water Goat||38||23||2003

|- align="center"

|21|||||||| ||||Yang Wood Monkey||37||24||2004

|- align="center"

|22|||||||| ||||Yin Wood Rooster||36||25||2005

|- align="center"

|23|||||||| ||||Yang Fire Dog||35||26||2006

|- align="center"

|24|||||||| ||||Yin Fire Pig||34||27||2007

|- align="center"

|25|||||||| ||||Yang Earth Rat||33||28||2008

|- align="center"

|26|||||||| ||||Yin Earth Ox||32||29||2009

|- align="center"

|27|||||||| ||||Yang Metal Tiger||31||30||2010

|- align="center"

|28|||||||| ||||Yin Metal Rabbit||30||31||2011

|- align="center"

|29|||||||| ||||Yang Water Dragon||29||32||2012

|- align="center"

|30|||||||| ||||Yin Water Snake||28||33||2013

|- align="center"

|31|||||||| ||||Yang Wood Horse||27||34||2014

|- align="center"

|32|||||||| ||||Yin Wood Goat||26||35||2015

|- align="center"

|33|||||||| ||||Yang Fire Monkey||25||36||2016

|- align="center"

|34|||||||| ||||Yin Fire Rooster||24||37||2017

|- align="center"

|35|||||||| ||||Yang Earth Dog||23||38||2018

|- align="center"

|36|||||||| ||||Yin Earth Pig||22||39||2019

|- align="center"

|37|||||||| ||||Yang Metal Rat||21||40||2020

|- align="center"

|38|||||||| ||||Yin Metal Ox||20||41||2021

|- align="center"

|39|||||||| ||||Yang Water Tiger||19||42||2022

|- align="center"

|40|||||||| ||||Yin Water Rabbit||18||43||2023

|- align="center"

|41|||||||| ||||Yang Wood Dragon||17||44||2024

|- align="center"

|42|||||||| ||||Yin Wood Snake||16||45||2025

|- align="center" style="background: cadetblue; color: white"

|43|||||||| ||||Yang Fire Horse||15||46||2026

|- align="center"

|44|||||||| ||||Yin Fire Goat||14||47||2027

|- align="center"

|45|||||||| ||||Yang Earth Monkey||13||48||2028

|- align="center"

|46|||||||| ||||Yin Earth Rooster||12||49||2029

|- align="center"

|47|||||||| ||||Yang Metal Dog||11||50||2030

|- align="center"

|48|||||||| ||||Yin Metal Pig||10||51||2031

|- align="center"

|49|||||||| ||||Yang Water Rat||9||52||2032

|- align="center"

|50|||||||| ||||Yin Water Ox||8||53||2033

|- align="center"

|51|||||||| ||||Yang Wood Tiger||7||54||2034

|- align="center"

|52|||||||| ||||Yin Wood Rabbit||6||55||2035

|- align="center"

|53|||||||| ||||Yang Fire Dragon||5||56||2036

|- align="center"

|54|||||||| ||||Yin Fire Snake||4||57||2037

|- align="center"

|55|||||||| ||||Yang Earth Horse||3||58||2038

|- align="center"

|56|||||||| ||||Yin Earth Goat||2||59||2039

|- align="center"

|57|||||||| ||||Yang Metal Monkey||1||60||2040

|- align="center"

|58|||||||| ||||Yin Metal Rooster||60||1||2041

|- align="center"

|59|||||||| ||||Yang Water Dog||59||2||2042

|- align="center"

|60|||||||| ||||Yin Water Pig||58||3||2043

100px|thumb|right|24 [[cardinal directions]]

Conversion between cyclic years and Western years

thumb|250px|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 (; ) 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 (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.

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 (in BC), 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 (壬辰; rénchén), as (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 (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:

1967 – 3 = 1964 ("subtracting 3 from the Gregorian year")
= 32 ("divide by 60 and discard any fraction")
1964 – (60 × 32) = 44 ("taking the remainder")
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):

246 + 2 = 248 ("adding 2 to the Gregorian year number (in BC)")
= 4 ("divide by 60 and discard any fraction")
248 – (60 × 4) = 8 ("taking the remainder")
60 – 8 = 52 ("subtract the remainder from 60")
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).

1967 = 60 × 32 + 47.
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:

246 = 60 × 4 + 6.
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

{| class="wikitable collapsible collapsed" style="min-width: 40ch"

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

!rowspan=2| No.

! Heavenly stem !! Earthly branch !!colspan=4| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 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 ||style="border-bottom-width:medium"| 癸 Yin Water ||style="border-bottom-width:medium"| 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, (: , : , 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 (). The (()) is the month containing the winter solstice (i.e. the Dongzhi (solar term)|) . The (()) is the month of the following , which is Dahan (solar term)| (), while the (()) is that of the Yushui (solar term)| () , 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 (two ). The () is the period starting with Daxue (solar term)| (), i.e. the solar term before the winter solstice. The () starts with Xiaohan| (), the term before (), while the () starts with Lichun| (), the term before (), 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 , but earlier the first month was (during the Zhou dynasty) or (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 (; 1st) or (; 6th) year. The first month of the or year is a (; 3rd) month, the next one is a (; 4th) month, etc., and the last month of the year is a (, 14th) month. The next year will start with a (; 15th) month, etc. following the cycle. The 5th year will end with a (; 2nd) month. The following month, the start of a or year, will hence again be a (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.

{| class=wikitable

!Earthly Branches of the certain months||Solar term|| (the Middle solar term)||Starts at||Ends at||Names in year of or (/)||Names in year of or (/)||Names in year of or (/)||Names in year of or (/)||Names in year of or (/)

||Month of () ||Lichun – Jingzhe||Yushui / ||February 4||March 6|| / || / || / || / || /

|Month of ()

||Jingzhe – Qingming ||Chunfen / ||March 6||April 5|| / || / || / || / || /

|Month of ()||Qingming – Lixia||Guyu / ||April 5||May 6|| / || / || / || / || /

|Month of ()||Lixia – Mangzhong||Xiaoman / ||May 6||June 6|| / || / || / || / || /

|Month of ()||Mangzhong – Xiaoshu||Xiazhi / ||June 6||July 7|| / || / || / || / || /

|Month of ()||Xiaoshu – Liqiu||Dashu / ||July 7||August 8|| / || / || / || / || /

|Month of ()||Liqiu – Bailu||Chushu / ||August 8||September 8|| / || / || / || / || /

|Month of ()||Bailu – Hanlu||Qiufen / ||September 8||October 8|| / || / || / || / || /

|Month of ()||Hanlu – Lidong||Shuangjiang / ||October 8||November 7|| / || / || / || / || /

|Month of ()||Lidong – Daxue||Xiaoxue / ||November 7||December 7|| / || / || / || / || /

|Month of ()||Daxue – Xiaohan||Dongzhi / ||December 7||January 6|| / || / || / || / || /

|Month of ()||Xiaohan – Lichun||Dahan / ||January 6||February 4|| / || / || / || / || /

Sexagenary days

{| class="wikitable collapsible"

|+ Table for sexagenary days

!Julian mod 2 !! colspan="4" | Gregorian!!Julian mod 4!! colspan="4" | Gregorian

| 00 || 10 || 20 || 30 || Aug || colspan="3" | || || 02 || 21 || 23 || style="text-align:center| 00 || || colspan="3" | || || 00 || colspan="4"| || || colspan="2"| || 07 ||colspan="3"| ||colspan="3" | || Nov || 00 || 12 || 24

| 01 || 11 || 21 || 31 || Sep || Oct || colspan="2" | || || 06 || 25 || 27 || || colspan="2" | || 21 || || || || colspan="4"| ||colspan="6"| || 14 || colspan="4" | || 01 || 13 || 25

| 02 || 12 || 22 || || Nov || Dec || colspan="2" | || || 10 || 29 || 31 || || || 19 || colspan="2" | || || || || 19 || colspan="2" | ||colspan="2"| || 05 ||colspan="4"| || || Apr || colspan="2" | || 02 || 14 || 26

| 03 || 13 || 23 || || colspan="4"| || || 14 || 33 || 35 || || colspan="4" | || || 03 || colspan="2" | || 22 || || || 03 ||colspan="3"| || || || Feb || Jun || colspan="2" | || 03 || 15 || 27

| 04 || 14 || 24 || || colspan="4"| || || 18 || 37 || 39 || || 17 ||colspan="2" | || || || || colspan="4"| ||colspan="4"| || 10 ||colspan="2"| || colspan="2" | || Aug || || 04 || 16 || 28

| 05 || 15 || 25 || || colspan="4"| || 01 || 03 || || 22 || style="text-align:center| 01 || colspan="2" | || 22 || 15 || || || 15 || colspan="3"| || 01 ||colspan="6"| || colspan="3" | || Oct || 05 || 17 || 29

| 06 || 16 || 26 || || colspan="4"| || 05 || 07 || || 26 || || colspan="4"| || || 02 || ||18 || colspan="2" | || colspan="3"| || ||colspan="2"| || 15 || colspan="3" | || Dec || 06 || 18 || 30

| 07 || 17 || 27 || || || Mar || || || 09 || 11 || || 30 || || || || colspan="2" | || || || colspan="2" | || 21 || ||colspan="2"| || 06 ||colspan="4"| || || Mar || colspan="2" | || 07 || 19 || 31

| 08 || 18 || 28 || || Jan || Apr || May || || 13 || 15 || || 34 || || 18 || colspan="3" | || || || colspan="3" | || ||colspan="5"| || 13 || || Jan || May || colspan="2" | || 08 || 20

|rowspan="4"|

| 09 || 19 || 29 || || Feb || Jun || Jul || || 17 || 19 || || 38 || || colspan="2" | || 23 || || || 01 || colspan="4"| || || ||colspan="2"| || 11 ||colspan="2"| || colspan="2" | || Jul || || 09 || 21

|rowspan="2" colspan="17"| Dates with yellow background indicate they are for this year.

| || ||17 || colspan="3" | || 02 ||colspan="6"| || colspan="4"| || 10 || 22

| || || colspan="2" | || || 23 ||colspan="3"| || 09 ||colspan="3"| || colspan="2" | || 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, .
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, .
Stem-branch = 1, 1 (, 1 in sexagenary cycle = 32 – 5 + 33 + 1 – 60).

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, .
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,
Stem-branch = 1, 9 (, 21 in cycle = – 42 – 2 + 34 + 31 = 21)
Stem-branch for August 4, 1338
Stem = 8,
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,
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 (, 48 in cycle = 4 + 8 + 32 + 4)
Stem-branch for May 25, 105 BC (−104).
Stem = 7,
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,
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 (, 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

:<math>SB = (y + c + m + day) \bmod 60</math>

:<math>S = SB \bmod 10, B = SB \bmod 12</math>

:<math>y = (year(\bmod 400) \bmod 80 (\bmod 12) \times 5 + \left\lfloor\frac{year(\bmod 400) \bmod 80}{4}\right\rfloor) \bmod 60</math>

:<math>c = \left\lfloor\frac{year}{400}\right\rfloor - \left\lfloor\frac{year}{100}\right\rfloor + 10 </math> for Gregorian calendar and <math>c = 8 </math> for Julian calendar.

:<math>m =(month + 1)\bmod 2\times 30+\left\lfloor{0.6\times (month + 1) - 3}\right\rfloor - i </math> <math>i = 5</math> for Jan or Feb in a common year and <math>i = 6 </math> in a leap year.

{| class="wikitable" style="text-align:center"

! 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||colspan="10"|<math>m =\left\lfloor{30.6 \times (month + 1)} -

3 \right\rfloor \bmod 60 - i </math>

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

{| class="wikitable" style="text-align:center"

|+Look up table for sexagenary days

|Gregorian || || 17 24 || 15 22 || || 20 || 18 || 23 || 16 || 21 || 19 ||rowspan=2 colspan=10| Centuries

| Julian || || || 01 || || || || || 00 || ||

|rowspan=2|Dates || Mar Jan || || || || || Nov Dec || Sep Oct || Aug || Feb Jun Jul || Jan Apr May Feb || rowspan=3 colspan=10| 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

|rowspan=10|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 ||colspan=13| 干支纪日速查表

|rowspan=12|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 ||

|rowspan=2|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 ||rowspan=2 colspan=13|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 || ||rowspan=2 colspan=13| Centuries

| Julian || || 02 || || || 01 || || || 00 || || || 03 ||

Sexagenary hours

{| class="wikitable"

|+ 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

References

Citations

Sources

External links

Ganzhi.io An Open Source application and implementation of Gan & Zhi as well as Jeiqi

Sexagenary cycle

History

Heavenly Stems

Earthly Branches

Sexagenary years

Conversion between cyclic years and Western years

Examples

Equivalent lookup method

Recent cycles

Sexagenary months

Sexagenary days

Examples

<span class="anchor" id="Sexagenary hours"></span>Sexagenary hours

See also

References

Citations

Sources

External links