Sexagenary cycle

The sexagenary cycle, also known as the Stems-and-Branches or ganzhi, is a cycle of sixty terms, each corresponding to one year, thus a total of sixty years for one cycle, historically used for reckoning time in China and the rest of the East Asian cultural sphere.[1] It appears as a means of recording days in the first Chinese written texts, the Shang oracle bones of the late second millennium BC. Its use to record years began around the middle of the 3rd century BC.[2] The cycle and its variations have been an important part of the traditional calendrical systems in Chinese-influenced Asian states and territories, particularly those of Japan, Korea, and Vietnam, with the old Chinese system still in use in Taiwan, and to a lesser extent, in Mainland China.[3]

Sexagenary cycle
Chinese六十干支
Stems-and-Branches
Chinese干支

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, and the Korean Imjin War. It also continues to have a role in contemporary Chinese astrology and fortune telling. There are some parallels in this with current 60-year cycle of the Tamil calendar.

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

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

This combination of two sub-cycles to generate a larger cycle and its use to record time have parallels in other calendrical systems, notably the Akan calendar.[4]

History

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

Almost all the dates in the Spring and Autumn Annals, a chronological list of events from 722 to 481 BC, use this system in combination with 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.[5]

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 (秦始皇), 246 BC, is noted on the diagram next to the position of the 60-cycle term yǐ-mǎo (乙卯, 52 of 60), corresponding to that year.[6] [7] 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:[8] the year 1984 began the present cycle (a 甲子—jiǎ-zǐ year), and 2044 will begin another. Note that in China the new year, when the sexagenary count increments, is not January 1, but rather the lunar new year of the traditional Chinese calendar. For example, the ji-chou 己丑 year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìchūn" (立春), which occurs near February 4.)

In Japan, according to Nihon shoki, the calendar was transmitted to Japan in 553. But it was not until the Suiko era that the calendar was used for politics. The year 604, when the Japanese officially adopted the Chinese calendar, was the first year of the cycle.[9]

The Korean (환갑; 還甲 hwangap) and Japanese tradition (還暦 kanreki) of celebrating the 60th birthday (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years.[10]

The Tibetan calendar also counts years using a 60-year cycle based on 12 animals and 5 elements, but while the first year of the Chinese cycle is always the year of the Wood Rat, the first year of the Tibetan cycle is the year of the Fire Rabbit (丁卯—dīng-mǎo, year 4 on the Chinese cycle).[11]

Ten Heavenly Stems
No. Heavenly
Stem		 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甲jiǎgaap3kæp*[k]ˤr[a]pkō (こう)kinoe (木の兄)gap갑giápyang wood
2乙yǐjyut3ʔit*qrətotsu (おつ)kinoto (木の弟)eul을ấtyin
3丙bǐngbing2pjængX*praŋʔhei (へい)hinoe (火の兄)byeong병bínhyang fire
4丁dīngding1teng*tˤeŋtei (てい)hinoto (火の弟)jeong정đinhyin
5戊wùmou6muwH*m(r)uʔ-s (~ *m(r)uʔ)bo (ぼ)tsuchinoe (土の兄)mu무mậuyang earth
6己jǐgei2kiX*k(r)əʔki (き)tsuchinoto (土の弟)gi기kỷyin
7庚gēnggang1kæng*kˤraŋkō (こう)kanoe (金の兄)gyeong경canhyang metal
8辛xīnsan1sin*si[n]shin (しん)kanoto (金の弟)sin신tânyin
9壬rénjam4nyim*n[ə]mjin (じん)mizunoe (水の兄)im임nhâmyang water
10癸guǐgwai3kjwijX*kʷijʔki (き)mizunoto (水の弟)gye계quýyin

Twelve Earthly Branches
Main article: 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子zǐzi2tsiX*[ts]əʔshi (し)ne (ね)ja자týRat (chuột 𤝞) Rat (鼠)11 p.m. to 1 a.m.
2丑chǒucau2trhjuwX*[n̥]ruʔchū (ちゅう)ushi (うし)chuk축sửuWater buffalo (trâu 𤛠) Ox (牛)1 to 3 a.m.
3寅yínjan4yij*[ɢ] (r)ərin (いん)tora (とら)in인dầnTiger (hổ 虎/cọp 𧲫) Tiger (虎)3 to 5 a.m.
4卯mǎomaau5mæwX*mˤruʔbō (ぼう)u (う)myo묘mão/mẹoCat (mèo 猫) Rabbit (兔)5 to 7 a.m.
5辰chénsan4dzyin*[d]ərshin (しん)tatsu (たつ)jin진thìnDragon (rồng 龍) Dragon (龍)7 to 9 a.m.
6巳sìzi6ziX*s-[ɢ]əʔshi (し)mi (み)sa사tỵSnake (rắn 𧋻) Snake (蛇)9 to 11 a.m.
7午wǔng5nguX*[m].qʰˤaʔgo (ご)uma (うま)o오ngọHorse (ngựa 馭) Horse (馬)11 a.m. to 1 p.m.
8未wèimei6mjɨjH*m[ə]t-smi (み) or bi (び)hitsuji (ひつじ)mi미mùiGoat (dê 羝) Goat (羊)1 to 3 p.m.
9申shēnsan1syin*l̥i[n]shin (しん)saru (さる)sin신thânMonkey (khỉ 𤠳) Monkey (猴)3 to 5 p.m.
10酉yǒujau5yuwX*N-ruʔyū (ゆう)tori (とり)yu유dậuRooster (gà 𪂮) Rooster (雞)5 to 7 p.m.
11戌xūseot1swit*s.mi[t]jutsu (じゅつ)inu (いぬ)sul술tuấtDog (chó 㹥) Dog (狗)7 to 9 p.m.
12亥hàihoi6hojX*[g]ˤəʔgai (がい)i (い)hae해hợiPig (lợn 𤞼/heo 㺧) Pig (豬)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
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 (年号; "niánhào") to specify a year.[12] 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 count), traditionally the first year of the reign of the legendary Yellow Emperor, was the first year (甲子; jiǎ-zǐ) of a cycle. 2700 years later in 4 AD, the duration equivalent to 45 60-year cycles, was also the starting year of a 60-year cycle. Similarly 1980 years later, 1984 was the start of a new cycle.

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

  1. For any year number greater than 4 AD, the equivalent sexagenary year can be found by subtracting 3 from the Gregorian year, dividing by 60 and taking the remainder. See example below.
  2. For any year before 1 AD, the equivalent sexagenary year can be found by adding 2 to the Gregorian year number (in BC), dividing it by 60, and subtracting the remainder from 60.
  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 or + 57) 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; rén-chén), as (2012-3) mod 60 = 29 (i.e., the remainder of (2012-3) divided by 60 is 29). Using the second, the equivalent sexagenary year for 221 BC is the 17th year (庚辰; gēng-chén), as 60- [(221+2) mod 60] = 17 (i.e., 60 minus the remainder of (221+2) divided by 60 is 17).

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; dīng-wèi).

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

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

A shorter equivalent method

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

  • 1967 - 3 (because of Gregorian Year) = 1964 = 60 × 32 + 44.

Formula: (year-3) mod 60

Remainder is therefore 44 and the AD column of the table "Sexagenary years" (just above) gives 'Fire Goat'

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

  • 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 Great Dipper, (建子月: jiànzǐyuè, 建丑月: jiànchǒuyuè, etc.).[13][14] There are two systems of placing these months, the lunar one and the solar one.

One system follows the ordinary Chinese lunar calendar and connects the names of the months directly to the central solar term (中氣; zhōngqì). The jiànzǐyuè ((建)子月) is the month containing the winter solstice (i.e. the 冬至 Dōngzhì) zhōngqì. The jiànchǒuyuè ((建)丑月) is the month of the following zhōngqì, which is Dàhán (大寒), while the jiànyínyuè ((建)寅月) is that of the Yǔshuǐ (雨水) zhōngqì, etc. Intercalary months have the same branch as the preceding month. [15] In the other system (節月; jiéyuè) the "month" lasts for the period of two solar terms (two 氣策 qìcì). The zǐyuè (子月) is the period starting with Dàxuě (大雪), i.e. the solar term before the winter solstice. The chǒuyuè (丑月) starts with Xiǎohán (小寒), the term before Dàhán (大寒), while the yínyuè (寅月) starts with Lìchūn (立春), the term before Yǔshuǐ (雨水), etc. Thus in the solar system a month starts anywhere from about 15 days before to 15 days after its lunar counterpart.

The branch names are not usual month names; the main use of the branches for months is astrological. However, the names are sometimes used to indicate historically which (lunar) month was the first month of the year in ancient times. For example, since the Han dynasty, the first month has been jiànyínyuè, but earlier the first month was jiànzǐyuè (during the Zhou dynasty) or jiànchǒuyuè (traditionally during the Shang dynasty) as well.[16]

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

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

Month of Mao (卯月)

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

Sexagenary days
Table for sexagenary days
Day
(stem)		Month
(stem)		2-digit year
mod 40
(stem)		Century
(stem)		NCentury
(branch)		2-digit year
mod 16
(branch)		Month
(branch)		Day
(branch)
Julian
mod 2
GregorianJulian
mod 4		Gregorian
00102030Aug00022123001600000007Nov001224
01112131SepOct04062527210114011325
021222NovDec081029311902161905FebApr021426
031323121433350303220312FebJun031527
0414241618373917240410Aug041628
05152501032022012215051501Oct051729
061626050724260602180815Dec061830
071727MarJan0911283020072106JanMar071931
081828JanAprMayFeb1315323418082413JanMay0820
091929FebJunJul171936382309010411Jul0921
Dates with the pale yellow background indicate they are for this year. 1017021022
11202309Sep1123
  • 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, 甲.
    • 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, 子.
    • Stem-branch = 1, 1 (甲子, 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, 甲.
    • 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, 申
    • Stem-branch = 1, 9 (甲申, 21 in cycle = - 42 - 2 + 34 + 31 = 21)
  • Stem-branch for August 4, 1338
    • Stem = 8, 辛
      • 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, 亥
      • 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 (辛亥, 48 in cycle = 4 + 8 + 32 + 4)
  • Stem-branch for May 25, 105 BC (-104).
    • Stem = 7, 庚
      • 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, 寅
      • 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 (庚寅, 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

for Gregorian calendar and for Julian calendar.

for Jan or Feb in a common year and 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 0031-1300031013203330434
Leap year -130
  • 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
Gregorian17
24		15
22
20		18


23
16


21
19

Centuries
Julian0100
DatesMar
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 stemsABCDEFGHIJ00022123404261638082
BCDEFGHIJA04062527444665678486
CDEFGHIJAB08102931485069718890
DEFGHIJABC12143335525473759294
EFGHIJABCD16183739565877799698
FGHIJABCDE01032022414360628183
GHIJABCDEF05072426454764668587
HIJABCDEFG09112830495168708991
IJABCDEFGH13153234535572749395
JABCDEFGHI17193638575976789799
地支子丑寅卯辰巳午未申酉戌亥干支纪日速查表
Earthly branchesABCDEFGHIJKL00071623323948556471808796
BCDEFGHIJKLA143046627894
CDEFGHIJKLAB052137536985
DEFGHIJKLABC03121928354451606776839299
EFGHIJKLABCD102642587490
FGHIJKLABCDE01173349658197
GHIJKLABCDEF081524314047566372798895
HIJKLABCDEFG062238547086
IJKLABCDEFGH132945617793
JKLABCDEFGHI041120273643525968758491
KLABCDEFGHIJ02183450668298
LABCDEFGHIJK092541577389
Dates01
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
Gregorian15
18



21

24		17



20
23		16
19



22		Centuries
Julian02010003

Sexagenary hours
Table for sexagenary hours (5-day cycle)
Stem of the dayZǐ hour
子时
23:00–1:00		Chǒu hour
丑时
1:00–3:00		Yín hour
寅时
3:00–5:00		Mǎo hour
卯时
5:00–7:00		Chén hour
辰时
7:00–9:00		Sì hour
巳时
9:00–11:00		Wǔ hour
午时
11:00–13:00		Wèi hour
未时
13:00–15:00		Shēn hour
申时
15:00–17:00		Yǒu hour
酉时
17:00–19:00		Xū hour
戌时
19:00–21:00		Hài hour
亥时
21:00–23:00
Jia or Ji day
(甲/己)		 1 甲子2乙丑3 丙寅4 丁卯5 戊辰6 己巳7 庚午8 辛未9 壬申10 癸酉11 甲戌12 乙亥
Yi or Geng day
(乙/庚)		 13 丙子14 丁丑15 戊寅16 己卯17 庚辰18 辛巳19 壬午20 癸未21 甲申22 乙酉23 丙戌24 丁亥
Bing or Xin day
(丙/辛)		 25 戊子26 己丑27 庚寅28 辛卯29 壬辰30 癸巳31 甲午32 乙未33 丙申34 丁酉35 戊戌36 己亥
Ding or Ren day
(丁/壬)		 37 庚子38 辛丑39 壬寅40 癸卯41 甲辰42 乙巳43 丙午44 丁未45 戊申46 己酉47 庚戌48 辛亥
Wu or Gui day
(戊/癸)		 49 壬子50 癸丑51 甲寅52 乙卯53 丙辰54 丁巳55 戊午56 己未57 庚申58 辛酉59 壬戌60 癸亥
gollark: GTech™ orbital facilities.
gollark: Only if they use certain authentication modules.
gollark: https://httpd.apache.org/security/vulnerabilities_22.html
gollark: Oh, no, I was incorrect, hmm.
gollark: It seems like all which can be done to the http://pn webserver is a few denial of service attacks.

See also

References

Citations
  1. Nussbaum, Louis-Frédéric (2005). "Jikkan-jūnishi". Japan Encyclopedia. Translated by Roth, Käthe. p. 420.
  2. Smith 2011, pp. 1, 28.
  3. For example, the annual Lunar New Year's Eve Chunwan gala has continued to announce the sexagenary term of the upcoming year (庚子, gengzi for 2020).
  4. For the Akan calendar, see (Bartle 1978).
  5. Smith 2011, pp. 24, 26-27.
  6. Kalinowski 2007, p. 145, fig. 3.
  7. Smith 2011, p. 29.
  8. Smith 2011, p. 28.
  9. "Calendar History; the Source". National Diet Library. Archived from the original on January 6, 2013. Retrieved January 1, 2013.
  10. "Kanreki". Encyclopedia of Shinto. Retrieved January 1, 2013.
  11. Chattopadhyaya, Alaka (1999). Atisa and Tibet: Life and Works of Dipamkara Srijnana in relation to the history and religion of Tibet. pp. 566–568.
  12. Aslaksen, Helmer (July 17, 2010). "Mathematics of the Chinese calendar". www.math.nus.edu.sg/aslaksen. Department of Maths, National University of Singapore. Archived from the original (PDF) on April 24, 2006. Retrieved December 12, 2011.
  13. Smith 2011, pp. 28, 29 fn2.
  14. 建す. Kōjien. Tokyo: Iwanami Shoten.
  15. "Records part 6" 本紀第六 肅宗 代宗. Xīn Tángshū 新唐書 [New Book of Tang]. 二年……，九月壬寅，大赦，去「乾元大圣光天文武孝感」号，去「上元」号，称元年，以十一月为岁首，月以斗所建辰为名。赐文武官阶、勋、爵，版授侍老官，先授者叙进之。停四京号。
    　　元年建子月癸巳，曹州刺史常休明及史朝义将薛崿战，败之。己亥，朝圣皇天帝于西内。丙午，卫伯玉及史朝义战于永宁，败之。己酉，朝献于太清宫。庚戌，朝享于太庙及元献皇后庙。建丑月辛亥，有事于南郊。己未，来瑱及史朝义战于汝州，败之。乙亥，侯希逸及朝义将李怀仙战于范阳，败之。宝应元年建寅月甲申，追册靖德太子琮为皇帝，妃窦氏为皇后。乙酉，葬王公妃主遇害者。丙戌，盗发敬陵、惠陵。甲辰，李光弼克许州。吐蕃请和。戊申，史朝义陷营州。建卯月辛亥，大赦。赐文武官阶、爵。五品以上清望及郎官、御史荐流人有行业情可矜者。停贡鹰、鹞、狗、豹。以京兆府为上都，河南府为东都，凤翔府为西都，江陵府为南都，太原府为北都。壬子，羌、浑、奴剌寇梁州。癸丑，河东军乱，杀其节度使邓景山，都知兵马使辛云京自称节度使。乙丑，河中军乱，杀李国贞及其节度使荔非元礼。戊辰，淮西节度使王仲升及史朝义将谢钦让战于申州，败绩。庚午，敦子仪知朔方、河中、北庭、潞仪泽沁节度行营，兴平、定国军兵马副元帅。壬申，鄜州刺史成公意及党项战，败之。建辰月壬午，大赦，官吏听纳赃免罪，左降官及流人罚镇效力者还之。甲午，奴剌寇梁州。戊申，萧华罢。户部侍郎元载同中书门下平章事。建巳月庚戌，史朝义寇泽州，刺史李抱玉败之。壬子，楚州献定国宝玉十有三。甲寅，圣皇天帝崩。乙丑，皇太子监国。大赦，改元年为宝应元年，复以正月为岁首，建巳月为四月。丙寅，闲厩使李辅国、飞龙厩副使程元振迁皇后于别殿，杀越王系、兗王亻闲。是夜，皇帝崩于长生殿，年五十二。查《壽星萬年曆》，
    唐肅宗之元年
    冬至所在月（761.12）：初一壬午大雪，十三癸巳，十七冬至，十九己亥，廿五丙午，廿八己酉，廿九庚戌
    大寒所在月（762.02）：初一辛亥，初三小寒，初九己未，十八大寒，廿五乙亥
    雨水所在月（762.03）：初一辛巳，初三立春，初四甲申，初五乙酉，初六丙戌，十八雨水，廿四甲辰，廿八戊申
    春分所在月（762.3）：初一辛亥，初四驚蜇，初二壬子，初三癸丑，十五乙丑，十八戊辰，十九春分，二十庚午，廿一壬申，
    穀雨所在月（762.4）：初一庚辰，初三壬午，初五清明，十五甲午，二十穀雨，廿九戊申
    小滿所在月（762.5）：初一庚戌，初三壬子，初五甲寅立夏，初五乙丑，十六丙寅。
    大寒所在月初一辛亥，已稱建丑月，初三才小寒
    春分所在月初一辛亥，已稱建卯月，初四才驚蜇
    穀雨所在月初三壬午，已稱建辰月，初五才清明
    小滿所在月初一庚戌、初三壬子，已稱建巳月，初五才立夏
    由此可見，唐代地支紀月自朔日始，非自節氣始。
  16. 三正, Kōjien, Toyko: Iwanami Shoten

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.CS1 maint: ref=harv (link)
  • 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.CS1 maint: ref=harv (link)
  • 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. ISBN 978-1-84217-987-1.CS1 maint: ref=harv (link)
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