Sexagenary cycle

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Template:Short description Template:Redirect Template:Infobox Chinese

The sexagenary cycle, also known as the ganzhi or stems-and-branches is a cycle of sixty terms, each corresponding to one year, thus a total of sixty years for one cycle, historically used for recording time in China and the rest of the East Asian cultural sphere and Southeast Asia.[1][2] It appears 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.Template:Sfn 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.[3] 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.[4][5]

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.

Overview

Template:Sexagenary cycle

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 (Template:Lang) combines the first heavenly stem with the first earthly branch. The second term yǐchǒu (Template:Lang) combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with guǐhài (Template:Lang), 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 (Template:Lang)—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.[6]

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 Template:Circa.[7] 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.Template:Sfn

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 (Template:Lang), 246 BC, is noted on the diagram next to the position of the 60-cycle term yǐmǎo (Template:Lang, 52 of 60), corresponding to that year.Template:SfnTemplate:Sfn 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:Template:Sfn the year 1984 began the present cycle (a Template:Lang—jiǎzǐ 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 jichou Template:Lang year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìchūn" (Template:Lang), 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.[8]

The Korean (Template:Lang hwangap) and Japanese tradition (Template:Lang kanreki) of celebrating the 60th birthday (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years.[9]

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 year of the Wood Rat), the first year of the Tibetan cycle is dīngmǎo (Template:Lang; year 4 on the Chinese cycle, year of the Fire Rabbit).[10]

Heavenly Stems

Template:Main

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:Lang kap jiǎ gaap3 kæp *[k]ˤr[a]p kō (Template:Lang) kinoe (Template:Lang) gap Template:Lang Template:Lang yang wood
2 Template:Lang dap yǐ jyut3 ʔit *qrət otsu (Template:Lang) kinoto (Template:Lang) eul Template:Lang Template:Lang yin
3 Template:Lang rai bǐng bing2 pjængX *praŋʔ hei (Template:Lang) hinoe (Template:Lang) byeong Template:Lang Template:Lang yang fire
4 Template:Lang Mueang dīng ding1 teng *tˤeŋ tei (Template:Lang) hinoto (Template:Lang) jeong Template:Lang Template:Lang yin
5 Template:Lang plaek wù mou6 muwH *m(r)uʔ-s (~ *m(r)uʔ) bo (Template:Lang) tsuchinoe (Template:Lang) mu Template:Lang Template:Lang yang earth
6 Template:Lang kat jǐ gei2 kiX *k(r)əʔ ki (Template:Lang) tsuchinoto (Template:Lang) gi Template:Lang Template:Lang yin
7 Template:Lang khut gēng gang1 kæng *kˤraŋ kō (Template:Lang) kanoe (Template:Lang) gyeong Template:Lang Template:Lang yang metal
8 Template:Lang rung xīn san1 sin *si[n] shin (Template:Lang) kanoto (Template:Lang) sin Template:Lang Template:Lang yin
9 Template:Lang tao rén jam4 nyim *n[ə]m jin (Template:Lang) mizunoe (Template:Lang) im Template:Lang Template:Lang yang water
10 Template:Lang ka guǐ gwai3 kjwijX *kʷijʔ ki (Template:Lang) mizunoto (Template:Lang) gye Template:Lang Template:Lang yin

Earthly Branches

Template:Main

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:Lang zǐ zi2 tsiX *[ts]əʔ shi (Template:Lang) ne (Template:Lang ja Template:Lang Template:Lang Rat (Template:Lang Template:Lang) Rat (Template:Lang) 11 p.m. to 1 a.m.
2 Template:Lang chǒu cau2 trhjuwX *[n̥]ruʔ chū (Template:Lang) ushi (Template:Lang) chuk Template:Lang Template:Lang Water buffalo (Template:Lang Template:Lang) Ox (Template:Lang) 1 to 3 a.m.
3 Template:Lang yín jan4 yij *[ɢ](r)ər in (Template:Lang) tora (Template:Lang) in Template:Lang Template:Lang Tiger (Template:Lang Template:Vi-nom/Template:Lang Template:Lang) Tiger (Template:Lang) 3 to 5 a.m.
4 Template:Lang mǎo maau5 mæwX *mˤruʔ bō (Template:Lang) u (Template:Lang) myo Template:Lang Template:Lang Cat (Template:Lang Template:Lang) Rabbit (Template:Lang) 5 to 7 a.m.
5 Template:Lang chén san4 dzyin *[d]ər shin (Template:Lang) tatsu (Template:Lang) jin Template:Lang Template:Lang Dragon (Template:Lang Template:Lang) Dragon (Template:Lang) 7 to 9 a.m.
6 Template:Lang sì zi6 ziX *s-[ɢ]əʔ shi (Template:Lang) mi (Template:Lang) sa Template:Lang Template:Lang Snake (Template:Lang Template:Lang) Snake (Template:Lang) 9 to 11 a.m.
7 Template:Lang wǔ ng5 nguX *[m].qʰˤaʔ go (Template:Lang) uma (Template:Lang) o Template:Lang Template:Lang Horse (Template:Lang Template:Lang) Horse (Template:Lang) 11 a.m. to 1 p.m.
8 Template:Lang wèi mei6 mjɨjH *m[ə]t-s mi (Template:Lang) or bi (Template:Lang) hitsuji (Template:Lang) mi Template:Lang Template:Lang Goat (Template:Lang Template:Lang) Goat (Template:Lang) 1 to 3 p.m.
9 Template:Lang shēn san1 syin *l̥i[n] shin (Template:Lang) saru (Template:Lang) sin Template:Lang Template:Lang Monkey (Template:Lang Template:Lang) Monkey (Template:Lang) 3 to 5 p.m.
10 Template:Lang yǒu jau5 yuwX *N-ruʔ yū (Template:Lang) tori (Template:Lang) yu Template:Lang Template:Lang Rooster (Template:Lang Template:Lang) Rooster (Template:Lang) 5 to 7 p.m.
11 Template:Lang xū seot1 swit *s.mi[t] jutsu (Template:Lang) inu (Template:Lang) sul Template:Lang Template:Lang Dog (Template:Lang Template:Lang) Dog (Template:Lang) 7 to 9 p.m.
12 Template:Lang hài hoi6 hojX *[g]ˤəʔ gai (Template:Lang) i (Template:Lang) hae Template:Lang Template:Lang Pig (Template:Lang Template:Lang/Template:Lang Template:Lang) Pig (Template:Lang) 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

No. Stem-Branch Mandarin Chinese Pinyin Korean Japanese Vietnamese Associations AD BC Current Cycle
1 甲子 jiǎzǐ gapja 갑자 Template:Unbulleted list Giáp Tý Yang Wood Rat 4 57 1984
2 乙丑 yǐchǒu eulchuk 을축 Template:Unbulleted list Ất Sửu Yin Wood Ox 5 56 1985
3 丙寅 bǐngyín byeongin 병인 Template:Unbulleted list Bính Dần Yang Fire Tiger 6 55 1986
4 丁卯 dīngmǎo jeongmyo 정묘 Template:Unbulleted list Đinh Mão Yin Fire Rabbit 7 54 1987
5 戊辰 wùchén mujin 무진 Template:Unbulleted list Mậu Thìn Yang Earth Dragon 8 53 1988
6 己巳 jǐsì gisa 기사 Template:Unbulleted list Kỷ Tỵ Yin Earth Snake 9 52 1989
7 庚午 gēngwǔ gyeongo 경오 Template:Unbulleted list Canh Ngọ Yang Metal Horse 10 51 1990
8 辛未 xīnwèi sinmi 신미 Template:Unbulleted list Tân Mùi Yin Metal Goat 11 50 1991
9 壬申 rénshēn imsin 임신 Template:Unbulleted list Nhâm Thân Yang Water Monkey 12 49 1992
10 癸酉 guǐyǒu gyeyu 계유 Template:Unbulleted list Quý Dậu Yin Water Rooster 13 48 1993
11 甲戌 jiǎxū gapsul 갑술 Template:Unbulleted list Giáp Tuất Yang Wood Dog 14 47 1994
12 乙亥 yǐhài eulhae 을해 Template:Unbulleted list Ât Hợi Yin Wood Pig 15 46 1995
13 丙子 bǐngzǐ byeongja 병자 Template:Unbulleted list Bính Tý Yang Fire Rat 16 45 1996
14 丁丑 dīngchǒu jeongchuk 정축 Template:Unbulleted list Đinh Sửu Yin Fire Ox 17 44 1997
15 戊寅 wùyín muin 무인 Template:Unbulleted list Mậu Dần Yang Earth Tiger 18 43 1998
16 己卯 jǐmǎo gimyo 기묘 Template:Unbulleted list Kỷ Mão Yin Earth Rabbit 19 42 1999
17 庚辰 gēngchén gyeongjin 경진 Template:Unbulleted list Canh Thìn Yang Metal Dragon 20 41 2000
18 辛巳 xīnsì sinsa 신사 Template:Unbulleted list Tân Tỵ Yin Metal Snake 21 40 2001
19 壬午 rénwǔ imo 임오 Template:Unbulleted list Nhâm Ngọ Yang Water Horse 22 39 2002
20 癸未 guǐwèi gyemi 계미 Template:Unbulleted list Quý Mùi Yin Water Goat 23 38 2003
21 甲申 jiǎshēn gapsin 갑신 Template:Unbulleted list Giáp Thân Yang Wood Monkey 24 37 2004
22 乙酉 yǐyǒu euryu 을유 Template:Unbulleted list Ất Dậu Yin Wood Rooster 25 36 2005
23 丙戌 bǐngxū byeongsul 병술 Template:Unbulleted list Bính Tuất Yang Fire Dog 26 35 2006
24 丁亥 dīnghài jeonghae 정해 Template:Unbulleted list Đinh Hợi Yin Fire Pig 27 34 2007
25 戊子 wùzǐ muja 무자 Template:Unbulleted list Mậu Tý Yang Earth Rat 28 33 2008
26 己丑 jǐchǒu gichuk 기축 Template:Unbulleted list Kỷ Sửu Yin Earth Ox 29 32 2009
27 庚寅 gēngyín gyeongin 경인 Template:Unbulleted list Canh Dần Yang Metal Tiger 30 31 2010
28 辛卯 xīnmǎo sinmyo 신묘 Template:Unbulleted list Tân Mão Yin Metal Rabbit 31 30 2011
29 壬辰 rénchén imjin 임진 Template:Unbulleted list Nhâm Thìn Yang Water Dragon 32 29 2012
30 癸巳 guǐsì gyesa 계사 Template:Unbulleted list Quý Tỵ Yin Water Snake 33 28 2013
31 甲午 jiǎwǔ gabo 갑오 Template:Unbulleted list Giáp Ngọ Yang Wood Horse 34 27 2014
32 乙未 yǐwèi eulmi 을미 Template:Unbulleted list Ất Mùi Yin Wood Goat 35 26 2015
33 丙申 bǐngshēn byeongsin 병신 Template:Unbulleted list Bính Thân Yang Fire Monkey 36 25 2016
34 丁酉 dīngyǒu jeongyu 정유 Template:Unbulleted list Đinh Dậu Yin Fire Rooster 37 24 2017
35 戊戌 wùxū musul 무술 Template:Unbulleted list Mậu Tuất Yang Earth Dog 38 23 2018
36 己亥 jǐhài gihae 기해 Template:Unbulleted list Kỷ Hợi Yin Earth Pig 39 22 2019
37 庚子 gēngzǐ gyeongja 경자 Template:Unbulleted list Canh Tý Yang Metal Rat 40 21 2020
38 辛丑 xīnchǒu sinchuk 신축 Template:Unbulleted list Tân Sửu Yin Metal Ox 41 20 2021
39 壬寅 rényín imin 임인 Template:Unbulleted list Nhâm Dần Yang Water Tiger 42 19 2022
40 癸卯 guǐmǎo gyemyo 계묘 Template:Unbulleted list Quý Mão Yin Water Rabbit 43 18 2023
41 甲辰 jiǎchén gapjin 갑진 Template:Unbulleted list Giáp Thìn Yang Wood Dragon 44 17 2024
42 乙巳 yǐsì eulsa 을사 Template:Unbulleted list Ất Tỵ Yin Wood Snake 45 16 2025
43 丙午 bǐngwǔ byeongo 병오 Template:Unbulleted list Bính Ngọ Yang Fire Horse 46 15 2026
44 丁未 dīngwèi jeongmi 정미 Template:Unbulleted list Đinh Mùi Yin Fire Goat 47 14 2027
45 戊申 wùshēn musin 무신 Template:Unbulleted list Mậu Thân Yang Earth Monkey 48 13 2028
46 己酉 jǐyǒu giyu 기유 Template:Unbulleted list Kỷ Dậu Yin Earth Rooster 49 12 2029
47 庚戌 gēngxū gyeongsul 경술 Template:Unbulleted list Canh Tuất Yang Metal Dog 50 11 2030
48 辛亥 xīnhài sinhae 신해 Template:Unbulleted list Tân Hợi Yin Metal Pig 51 10 2031
49 壬子 rénzǐ imja 임자 Template:Unbulleted list Nhâm Tý Yang Water Rat 52 9 2032
50 癸丑 guǐchǒu gyechuk 계축 Template:Unbulleted list Quý Sửu Yin Water Ox 53 8 2033
51 甲寅 jiǎyín gabin 갑인 Template:Unbulleted list Giáp Dần Yang Wood Tiger 54 7 2034
52 乙卯 yǐmǎo eulmyo 을묘 Template:Unbulleted list Ất Mão Yin Wood Rabbit 55 6 2035
53 丙辰 bǐngchén byeongjin 병진 Template:Unbulleted list Bính Thìn Yang Fire Dragon 56 5 2036
54 丁巳 dīngsì jeongsa 정사 Template:Unbulleted list Đinh Tỵ Yin Fire Snake 57 4 2037
55 戊午 wùwǔ muo 무오 Template:Unbulleted list Mậu Ngọ Yang Earth Horse 58 3 2038
56 己未 jǐwèi gimi 기미 Template:Unbulleted list Kỷ Mùi Yin Earth Goat 59 2 2039
57 庚申 gēngshēn gyeongsin 경신 Template:Unbulleted list Canh Thân Yang Metal Monkey 60 1 2040
58 辛酉 xīnyǒu sinyu 신유 Template:Unbulleted list Tân Dậu Yin Metal Rooster 1 60 2041
59 壬戌 rénxū imsul 임술 Template:Unbulleted list Nhâm Tuất Yang Water Dog 2 59 2042
60 癸亥 guǐhài gyehae 계해 Template:Unbulleted list Quý Hợi Yin Water Pig 3 58 2043
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.[11] 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 Template:Nowrap

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; 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 Template:Math and for years BC is Template:Math.

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).

A shorter equivalent 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: 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" (just above) 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.

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

1804–1923

1924–2043

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:Lang: jiànzǐyuè, Template:Lang: jiànchǒuyuè, etc.).Template:Sfn[12] 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; zhōngqì). The jiànzǐyuè ((Template:Lang)Template:Lang) is the month containing the winter solstice (i.e. the Template:Lang Dōngzhì) zhōngqì. The jiànchǒuyuè ((Template:Lang)Template:Zh) is the month of the following zhōngqì, which is Dàhán (Template:Lang), while the jiànyínyuè ((Template:Lang)Template:Lang) is that of the Yǔshuǐ (Template:Lang) zhōngqì, etc. Intercalary months have the same branch as the preceding month.[13] In the other system (Template:Lang; jiéyuè) the "month" lasts for the period of two solar terms (two Template:Lang qìcì). The zǐyuè (Template:Lang) is the period starting with Dàxuě (Template:Lang), i.e. the solar term before the winter solstice. The chǒuyuè (Template:Lang) starts with Xiǎohán (Template:Lang), the term before Dàhán (Template:Lang), while the yínyuè (Template:Lang) starts with Lìchūn (Template:Lang), the term before Yǔshuǐ (Template:Lang), 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.[14]

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 (Template:Lang; 1st) or jǐ (Template:Zh; 6th) year. The first month of the jiǎ or jǐ year is a bǐngyín (Template:Lang; 3rd) month, the next one is a dīngmǎo (Template:Lang; 4th) month, etc., and the last month of the year is a dīngchǒu (Template:Lang, 14th) month. The next year will start with a wùyín (Template:Lang; 15th) month, etc. following the cycle. The 5th year will end with a yǐchǒu (Template:Lang; 2nd) month. The following month, the start of a jǐ or jiǎ year, will hence again be a bǐngyín (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 Zhongqi (the Middle solar term) Starts at Ends at Names in year of Jia or Ji(Template:Lang/Template:Lang) Names in year of Yi or Geng (Template:Lang/Template:Lang) Names in year of Bing or Xin (Template:Lang/Template:Lang) Names in year of Ding or Ren (Template:Lang/Template:Lang) Names in year of Wu or Gui (Template:Lang/Template:Lang)
Month of Yin (Template:Lang) Lichun – Jingzhe Yushui / 雨水 February 4 March 6 Bingyin / Template:Lang Wuyin / Template:Lang Gengyin / Template:Lang Renyin / Template:Lang Jiayin / Template:Lang

Month of Mao (Template:Lang)

Jingzhe – Qingming Chunfen / 春分 March 6 April 5 Dingmao / Template:Lang Jimao / Template:Lang Xinmao / Template:Lang Guimao / Template:Lang Yimao / Template:Lang
Month of Chen (Template:Lang) Qingming – Lixia Guyu / 谷雨 April 5 May 6 Wuchen / Template:Lang Gengchen / Template:Lang Renchen / Template:Lang Jiachen / Template:Lang Bingchen / Template:Lang
Month of Si (Template:Lang) Lixia – Mangzhong Xiaoman / 小满 May 6 June 6 Jisi / Template:Lang Xinsi / Template:Lang Guisi / Template:Lang Yisi / Template:Lang Dingsi / Template:Lang
Month of Wu (Template:Lang) Mangzhong – Xiaoshu Xiazhi / 夏至 June 6 July 7 Gengwu / Template:Lang Renwu / Template:Lang Jiawu / Template:Lang Bingwu / Template:Lang Wuwu / Template:Lang
Month of Wei (Template:Lang) Xiaoshu – Liqiu Dashu / 大暑 July 7 August 8 Xinwei / Template:Lang Guiwei / Template:Lang Yiwei / Template:Lang Dingwei / Template:Lang Jiwei / Template:Lang
Month of Shen (Template:Lang) Liqiu – Bailu Chushu / 处暑 August 8 September 8 Renshen / Template:Lang Jiashen / Template:Lang Bingshen / Template:Lang Wushen / Template:Lang Gengshen / Template:Lang
Month of You (Template:Lang) Bailu – Hanlu Qiufen / 秋分 September 8 October 8 Guiyou / Template:Lang Yiyou / Template:Lang Dingyou / Template:Lang Jiyou / Template:Lang Xinyou / Template:Lang
Month of Xu (Template:Lang) Hanlu – Lidong Shuangjiang / 霜降 October 8 November 7 Jiaxu / Template:Lang Bingxu / Template:Lang Wuxu / Template:Lang Gengxu / Template:Lang Renxu / Template:Lang
Month of Hai (Template:Lang) Lidong – Daxue Xiaoxue / 小雪 November 7 December 7 Yihai / Template:Lang Dinghai / Template:Lang Jihai / Template:Lang Xinhai / Template:Lang Guihai / Template:Lang
Month of Zi (Template:Lang) Daxue – Xiaohan Dongzhi / 冬至 December 7 January 6 Bingzi / Template:Lang Wuzi / Template:Lang Gengzi / Template:Lang Renzi / Template:Lang Jiazi / Template:Lang
Month of Chou (Template:Lang) Xiaohan – Lichun Dahan / 大寒 January 6 February 4 Dingchou / Template:Lang Jichou / Template:Lang Xinchou / Template:Lang Guichou / Template:Lang Yichou / Template:Lang

Sexagenary days

Table for sexagenary days
Day
(stem)		 Month
(stem)		 2-digit year
mod 40
(stem)		 Century
(stem)		 rowspan="2" Template:Yes 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:Tooltip 02 Template:Maybe21 23 00 Template:Tooltip Template:Yes 00 Template:Tooltip 07 Nov 00 12 24
01 11 21 31 Sep Oct Template:Tooltip 06 25 27 21 Template:Yes 14 01 13 25
02 12 22 Nov Dec Template:Tooltip 10 29 31 19 Template:Yes Template:Tooltip 19 Template:Maybe05 Template:Tooltip Apr 02 14 26
03 13 23 Template:Tooltip 14 33 35 Template:Yes 03 22 03 Template:Tooltip Feb Jun 03 15 27
04 14 24 Template:Tooltip 18 37 39 17 Template:Tooltip Template:Yes 10 Aug 04 16 28
05 15 25 01 03 Template:Tooltip 22 01 22 15 Template:Yes 15 01 Oct 05 17 29
06 16 26 05 07 Template:Tooltip 26 Template:Yes 02 18 Template:Tooltip 15 Dec 06 18 30
07 17 27 Mar Template:Tooltip 09 11 Template:Tooltip 30 Template:MaybeTemplate:Tooltip Template:Yes 21 06 Template:Tooltip Mar 07 19 31
08 18 28 Jan Apr May Template:Tooltip 13 15 Template:Tooltip 34 18 Template:Yes Template:Tooltip 13 Jan May 08 20
09 19 29 Feb Jun Jul 17 19 Template:Tooltip 38 23 Template:Yes 01 Template:Tooltip 11 Jul 09 21
Dates with yellow background indicate they are for this year. Template:Yes 17 02 10 22
Template:Yes Template:MaybeTemplate:Tooltip 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.
    • 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.
    • Stem-branch = 1, 1 (Template:Zh, 1 in sexagenary cycle = 32 – 5 + 33 + 1 – 60).

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  • 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)×5+⌊year(mod400)mod804⌋)mod60
c=⌊year400⌋−⌊year100⌋+10 for Gregorian calendar and c=8 for Julian calendar.
m=(month+1)mod2×30+⌊0.6×(month+1)−3⌋−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=⌊30.6×(month+1)−3⌋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

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

See also

References

Citations

Template:Reflist

Sources

Template:Refbegin

Template:Refend

Template:- Template:Chronology

Template:Authority control

  1. ↑ Template:Cite encyclopedia
  2. ↑ For non-mathematical readers, a simple explanation for the number "60" in the 60-year cycle of the Lunar calendar can be found in Template:Citation.
  3. ↑ For example, the annual CCTV New Year's Gala gala has continued to announce the sexagenary term of the upcoming year (庚子, gengzi for 2020).
  4. ↑ "...the Ahom reckoned time by means of a sexagenary cycle"Template:Harvcol
  5. ↑ "..migration from Mong Mao in Yunnan into Mungdunshunkhām..."Template:Harvcol
  6. ↑ For the Akan calendar, see Template:Harv.
  7. ↑ Template:Cite book
  8. ↑ Template:Cite web
  9. ↑ Template:Cite encyclopedia
  10. ↑ Template:Cite book
  11. ↑ Template:Cite web
  12. ↑ Template:Cite dictionary
  13. ↑ Template:Cite book
  14. ↑ Template:Citation
  15. ↑ Template:Cite book
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