The sexagenary cycle, liùshí huājiǎ (六十花甲), also known as the () or stems-and-branches, is a cycle of sixty terms used to designate successive years, historically used within Traditional Chinese Acupuncture, Herbology, Sociology and Psychology and publicly for recording of time in China and the rest of the East Asian cultural sphere, as well as in Southeast Asia.For non-mathematical readers, a simple explanation for the number "60" in the 60-year cycle of the Lunar calendar can be found in .
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.For example, the annual CCTV New Year's Gala has continued to announce the sexagenary term of the upcoming year (, for 2020).
This traditional method of numbering days and years no longer has any significant role in modern Chinese time-keeping or the official calendar. However, the sexagenary cycle is used in the names of many historical events, such as the Chinese Xinhai Revolution, the Japanese Boshin War, the Korean Imjin War and the Vietnamese Famine of , . It also continues to have a role in contemporary Chinese astrology and fortune telling. There are some parallels in this with Tamil calendar.
This combination of two sub-cycles to generate a larger cycle and its use to record time have parallels in other calendrical systems, notably the Akan calendar.For the Akan calendar, see .
History
The sexagenary cycle is attested as a method of recording days from the earliest written records in China, records of divination on oracle bones, beginning . Almost every oracle bone inscription includes a date in this format. This use of the cycle for days is attested throughout the Zhou dynasty and remained common into the Han period for all documentary purposes that required dates specified to the day.
Almost all the dates in the Spring and Autumn Annals, a chronological list of events from 722 to 481 BC, use this system in combination with regnal years and months (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 (), 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
No.Heavenly StemAhom Name Chinese nameJapanese nameKorean nameVietnamese nameYin YangWu XingMandarin(Pinyin)Cantonese(Jyutping)Middle Chinese(Baxter)Old Chinese(Baxter–Sagart)OnyomiKunyomi withcorresponding kanjiRomanizedHangul1 () ()yangwood2 () ()yin3 () ()yangfire4 () ()yin5 (~ ) () ()yangearth6 () ()yin7 () ()yangmetal8 () ()yin9 () ()yangwater10 () ()yin
Earthly Branches
No.Earthly BranchChinese nameJapanese nameKorean nameVietnamesenameVietnamesezodiacChinesezodiacCorrespondinghoursMandarin(Pinyin)Cantonese(Jyutping)Middle Chinese(Baxter)Old Chinese(Baxter–Sagart)OnyomiKunyomiRomanizedHangul1 () (Rat ( )Rat () 23:00–01:002 () ()Water buffalo ( )Ox () 01:00–03:003 () ()Tiger ( / )Tiger () 03:00–05:004 () ()Cat ( )Rabbit () 05:00–07:005 () ()Dragon ( )Dragon () 07:00–09:006 () ()Snake ( )Snake () 09:00–11:007 () ()Horse ( )Horse () 11:00–13:008 () or () ()Goat ( )Goat () 13:00–15:009 () ()Monkey ( )Monkey () 15:00–17:0010 () ()Rooster ( )Rooster () 17:00–19:0011 () ()Dog ( )Dog () 19:00–21:0012 () ()Pig ( / )Pig () 21:00–23:00 *The names of several animals can be translated into English in several different ways. The Vietnamese Earthly Branches use cat instead of Rabbit.
Sexagenary years No.Stem-BranchMandarin Chinese PinyinJapaneseKoreanVietnameseAssociationsBCADCurrent Cycle1 Yang Wood Rat57419842 Yin Wood Ox56519853 Yang Fire Tiger55619864 Yin Fire Rabbit54719875 Yang Earth Dragon53819886 Yin Earth Snake52919897 Yang Metal Horse511019908 Yin Metal Goat501119919 Yang Water Monkey4912199210 Yin Water Rooster4813199311 Yang Wood Dog4714199412 Yin Wood Pig4615199513 Yang Fire Rat4516199614 Yin Fire Ox4417199715 Yang Earth Tiger4318199816 Yin Earth Rabbit4219199917 Yang Metal Dragon4120200018 Yin Metal Snake4021200119 Yang Water Horse3922200220 Yin Water Goat3823200321 Yang Wood Monkey3724200422 Yin Wood Rooster3625200523 Yang Fire Dog3526200624 Yin Fire Pig3427200725 Yang Earth Rat3328200826 Yin Earth Ox3229200927 Yang Metal Tiger3130201028 Yin Metal Rabbit3031201129 Yang Water Dragon2932201230 Yin Water Snake2833201331 Yang Wood Horse2734201432 Yin Wood Goat2635201533 Yang Fire Monkey2536201634 Yin Fire Rooster2437201735 Yang Earth Dog2338201836 Yin Earth Pig2239201937 Yang Metal Rat2140202038 Yin Metal Ox2041202139 Yang Water Tiger1942202240 Yin Water Rabbit1843202341 Yang Wood Dragon1744202442 Yin Wood Snake1645202543 Yang Fire Horse1546202644 Yin Fire Goat1447202745 Yang Earth Monkey1348202846 Yin Earth Rooster1249202947 Yang Metal Dog1150203048 Yin Metal Pig1051203149 Yang Water Rat952203250 Yin Water Ox853203351 Yang Wood Tiger754203452 Yin Wood Rabbit655203553 Yang Fire Dragon556203654 Yin Fire Snake457203755 Yang Earth Horse358203856 Yin Earth Goat259203957 Yang Metal Monkey160204058 Yin Metal Rooster601204159 Yang Water Dog592204260 Yin Water Pig5832043
Traditional Chinese Medicine and Stems and Branches
Conversion between cyclic years and Western years
As mentioned above, the cycle first started to be used for indicating years during the Han dynasty, but it also can be used to indicate earlier years retroactively. Since it repeats, by itself it cannot specify a year without some other information, but it is frequently used with the Chinese era name (; ) to specify a year. The year starts with the new year of whoever is using the calendar. In China, the cyclic year normally changes on the Chinese Lunar New Year. In Japan until recently it was the Japanese lunar new year, which was sometimes different from the Chinese; now it is January 1. So when calculating the cyclic year of a date in the Gregorian year, one has to consider what their "new year" is. Hence, the following calculation deals with the Chinese dates after the Lunar New Year in that Gregorian year; to find the corresponding sexagenary year in the dates before the Lunar New Year would require the Gregorian year to be decreased
As for example, the year 2697 BC (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'.