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Sexagenary cycle

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"Xinwei" redirects here. For the town in China, see Xinwei, Meizhou .
Sexagenary cycle
Chinese 六十干支
stems-and-branches
Chinese 干支

The sexagenary cycle , also known as the stems-and-branches or ganzhi ( Chinese : 干支 ), 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 Shang oracle bones of the late second millennium BC. Its use to record years began around the middle of the 3rd century BC. [3] 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 . [4] In India, the Dai-Ahom (descendants of Dai ethnic minority of Yunnan who migrated to Assam in 13th century) also used the sexagenary cycle known as Lak-Ni. [5] [6]

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 ?t D?u , T?t M?u Than . It also continues to have a role in contemporary Chinese astrology and fortune telling . There are some parallels in this with the current 60-year cycle of the Hindu calendar .

Overview [ edit ]

Sexagenary cycle
1
Wood Rat 		2
Wood Ox  [ ja ] 		3
Fire Tiger  [ ja ] 		4
Fire Rabbit  [ ja ] 		5
Earth Dragon 		6
Earth Snake  [ ja ]
7
Metal Horse  [ ja ] 		8
Metal Goat  [ ja ] 		9
Water Monkey  [ ja ] 		10
Water Rooster  [ ja ] 		11
Wood Dog  [ ja ] 		12
Wood Pig  [ ja ]
13
Fire Rat  [ ja ] 		14
Fire Ox  [ ja ] 		15
Earth Tiger  [ ja ] 		16
Earth Rabbit  [ ja ] 		17
Metal Dragon  [ ja ] 		18
Metal Snake  [ ja ]
19
Water Horse  [ ja ] 		20
Water Goat  [ ja ] 		21
Wood Monkey  [ ja ] 		22
Wood Rooster  [ ja ] 		23
Fire Dog  [ ja ] 		24
Fire Pig  [ ja ]
25
Earth Rat  [ ja ] 		26
Earth Ox  [ ja ] 		27
Metal Tiger  [ ja ] 		28
Metal Rabbit  [ ja ] 		29
Water Dragon  [ ja ] 		30
Water Snake  [ ja ]
31
Wood Horse  [ ja ] 		32
Wood Goat  [ ja ] 		33
Fire Monkey  [ ja ] 		34
Fire Rooster  [ ja ] 		35
Earth Dog  [ ja ] 		36
Earth Pig  [ ja ]
37
Metal Rat  [ ja ] 		38
Metal Ox  [ ja ] 		39
Water Tiger  [ ja ] 		40
Water Rabbit  [ ja ] 		41
Wood Dragon  [ ja ] 		42
Wood Snake  [ ja ]
43
Fire Horse 		44
Fire Goat  [ ja ] 		45
Earth Monkey  [ ja ] 		46
Earth Rooster  [ ja ] 		47
Metal Dog  [ ja ] 		48
Metal Pig  [ ja ]
49
Water Rat  [ ja ] 		50
Water Ox  [ ja ] 		51
Wood Tiger  [ ja ] 		52
Wood Rabbit  [ ja ] 		53
Fire Dragon  [ ja ] 		54
Fire Snake  [ ja ]
55
Earth Horse  [ ja ] 		56
Earth Goat  [ ja ] 		57
Metal Monkey 		58
Metal Rooster 		59
Water Dog  [ ja ] 		60
Water Pig  [ ja ]
Heavenly Stems ? Earthly Branches
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 ji?z? ( 甲子 ) combines the first heavenly stem with the first earthly branch. The second term y?ch?u ( 乙丑 ) combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with gu?hai ( 癸亥 ), after which it begins again at ji?z? . This termination at ten and twelve's least common multiple leaves half of the combinations?such as ji?ch?u ( 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 . [7]

History [ edit ]

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

The sexagenary cycle is attested as a method of recording days from the earliest written records in China, records of divination on oracle bones , beginning c.  1100 BC . [8] 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. [9]

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 y?-m?o ( 乙卯 , 52 of 60), corresponding to that year. [10] [11] 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: [12] the year 1984 began the present cycle (a 甲子 ? ji?-z? 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 "Lich?n" ( 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. [13]

The Korean ( 還甲; 還甲 hwangap ) and Japanese tradition ( 還? kanreki ) of celebrating the 60th birthday (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years. [14]

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 ? d?ng-m?o , year 4 on the Chinese cycle). [15]

Ten Heavenly Stems [ edit ]

Main article: Celestial 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 ji? gaap 3 kæp *[k]?r[a]p k? ( こう ) kinoe ( 木の兄 ) gap 甲 giap yang wood
2 乙 y? jyut 3 ?it *qr?t otsu ( おつ ) kinoto ( 木の弟 ) eul 을 ?t yin
3 丙 b?ng bing 2 pjæng X *praŋ? hei ( へい ) hinoe ( 火の兄 ) byeong 病 binh yang fire
4 丁 d?ng ding 1 teng *t?eŋ tei ( てい ) hinoto ( 火の弟 ) jeong 情 đinh yin
5 戊 wu mou 6 muw H *m(r)u?-s (~ *m(r)u?) bo ( ぼ ) tsuchinoe ( 土の兄 ) mu 무 m?u yang earth
6 己 j? gei 2 ki X *k(r)?? ki ( き ) tsuchinoto ( 土の弟 ) gi 基 k? yin
7 庚 g?ng gang 1 kæng *k?raŋ k? ( こう ) kanoe ( 金の兄 ) gyeong 警 canh yang metal
8 辛 x?n san 1 sin *si[n] shin ( しん ) kanoto ( 金の弟 ) sin 新 tan yin
9 壬 ren jam 4 nyim *n[?]m jin ( じん ) mizunoe ( 水の兄 ) im 임 nham yang water
10 癸 gu? gwai 3 kjwij X *k?ij? ki ( き ) mizunoto ( 水の弟 ) gye 界 quy yin

Twelve Earthly Branches [ edit ]

Main article: Terrestrial 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 z? zi 2 tsi X *[ts]?? shi ( し ) ne ( ね) ja 者 ty Rat ( chu?t ?? ) Rat ( 鼠 ) 11 p.m. to 1 a.m.
2 丑 ch?u cau 2 trhjuw X *[n?]ru? ch? ( ちゅう ) ushi ( うし ) chuk 軸 s?u Water buffalo ( trau ?? ) Ox ( 牛 ) 1 to 3 a.m.
3 寅 yin jan 4 yij *[?] (r)?r in ( いん ) tora ( とら ) in 人 d?n Tiger ( h? 虎 / c?p ?? ) Tiger ( 虎 ) 3 to 5 a.m.
4 卯 m?o maau 5 mæw X *m?ru? b? ( ぼう ) u ( う ) myo 墓 mao/m?o Cat ( meo 猫 ) Rabbit ( ? ) 5 to 7 a.m.
5 辰 chen san 4 dzyin *[d]?r shin ( しん ) tatsu ( たつ ) jin 陳 thin Dragon ( r?ng 龍 ) Dragon ( 龍 ) 7 to 9 a.m.
6 巳 si zi 6 zi X *s-[?]?? shi ( し ) mi ( み ) sa 社 t? Snake ( r?n ?? ) Snake ( 蛇 ) 9 to 11 a.m.
7 午 w? ng 5 ngu X *[m].q??a? go ( ご ) uma ( うま ) o 오 ng? Horse ( ng?a 馭 ) Horse ( 馬 ) 11 a.m. to 1 p.m.
8 未 wei mei 6 mj?j H *m[?]t-s mi ( み ) or bi ( び ) hitsuji ( ひつじ ) mi 美 mui Goat ( de ? ) Goat ( 羊 ) 1 to 3 p.m.
9 申 sh?n san 1 syin *l?i[n] shin ( しん ) saru ( さる ) sin 新 than Monkey ( kh? ?? ) Monkey ( ? ) 3 to 5 p.m.
10 酉 y?u jau 5 yuw X *N-ru? y? ( ゆう ) tori ( とり ) yu 有 d?u Rooster ( ga ?? ) Rooster ( ? ) 5 to 7 p.m.
11 戌 x? seot 1 swit *s.mi[t] jutsu ( じゅつ ) inu ( いぬ ) sul 술 tu?t Dog ( cho ? ) Dog ( 狗 ) 7 to 9 p.m.
12 亥 hai hoi 6 hoj X *[g]??? gai ( がい ) i ( い ) hae 해 h?i Pig ( l?n ?? / heo ? ) Pig ( ? ) 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 [ edit ]

No. Stem-Branch Mandarin Chinese Pinyin Korean Japanese Vietnamese Associations AD BC Current Cycle
1 甲子 ji?-z? gapja 甲子
  • k?shi
  • kasshi
  • kinoe-ne
Giap Ty Yang Wood Rat 4 57 1984
2 乙丑 y?-ch?u eulchuk 乙丑
  • itch?
  • kinoto-ushi
?t S?u Yin Wood Ox 5 56 1985
3 丙寅 b?ng-yin byeongin 病인
  • heiin
  • hinoe-tora
Binh D?n Yang Fire Tiger 6 55 1986
4 丁卯 d?ng-m?o jeongmyo 丁卯
  • teib?
  • hinoto-u
đinh Mao Yin Fire Rabbit 7 54 1987
5 戊辰 wu-chen mujin 無盡
  • boshin
  • tsuchinoe-tatsu
M?u Thin Yang Earth Dragon 8 53 1988
6 己巳 j?-si gisa 記事
  • kishi
  • tsuchinoto-mi
K? T? Yin Earth Snake 9 52 1989
7 庚午 g?ng-w? gyeongo 경오
  • k?go
  • kanoe-uma
Canh Ng? Yang Metal Horse 10 51 1990
8 辛未 x?n-wei sinmi 辛未
  • shinbi
  • kanoto-hitsuji
Tan Mui Yin Metal Goat 11 50 1991
9 壬申 ren-sh?n imsin 妊娠
  • jinshin
  • mizunoe-saru
Nham Than Yang Water Monkey 12 49 1992
10 癸酉 gu?-y?u gyeyu 戒喩
  • kiy?
  • mizunoto-tori
Quy D?u Yin Water Rooster 13 48 1993
11 甲戌 ji?-x? gapsul 甲戌
  • k?jutsu
  • kinoe-inu
Giap Tu?t Yang Wood Dog 14 47 1994
12 乙亥 y?-hai eulhae 乙亥
  • itsugai
  • kinoto-i
At H?i Yin Wood Pig 15 46 1995
13 丙子 b?ng-z? byeongja 病者
  • heishi
  • hinoe-ne
Binh Ty Yang Fire Rat 16 45 1996
14 丁丑 d?ng-ch?u jeongchuk 丁丑
  • teich?
  • hinoto-ushi
đinh S?u Yin Fire Ox 17 44 1997
15 戊寅 wu-yin muin 無人
  • boin
  • tsuchinoe-tora
M?u D?n Yang Earth Tiger 18 43 1998
16 己卯 j?-m?o gimyo 己卯
  • kib?
  • tsuchinoto-u
K? Mao Yin Earth Rabbit 19 42 1999
17 庚辰 g?ng-chen gyeongjin 競進
  • k?shin
  • kanoe-tatsu
Canh Thin Yang Metal Dragon 20 41 2000
18 辛巳 x?n-si sinsa 神社
  • shinshi
  • kanoto-mi
Tan T? Yin Metal Snake 21 40 2001
19 壬午 ren-w? imo 壬午
  • jingo
  • mizunoe-uma
Nham Ng? Yang Water Horse 22 39 2002
20 癸未 gu?-wei gyemi 癸未
  • kibi
  • mizunoto-hitsuji
Quy Mui Yin Water Goat 23 38 2003
21 甲申 ji?-sh?n gapsin 甲申
  • k?shin
  • kinoe-saru
Giap Than Yang Wood Monkey 24 37 2004
22 乙酉 y?-y?u euryu 乙酉
  • itsuy?
  • kinoto-tori
?t D?u Yin Wood Rooster 25 36 2005
23 丙戌 b?ng-x? byeongsul 丙戌
  • heijutsu
  • hinoe-inu
Binh Tu?t Yang Fire Dog 26 35 2006
24 丁亥 d?ng-hai jeonghae 定해
  • teigai
  • hinoto-i
đinh H?i Yin Fire Pig 27 34 2007
25 戊子 wu-z? muja 巫子
  • boshi
  • tsuchinoe-ne
M?u Ty Yang Earth Rat 28 33 2008
26 己丑 j?-ch?u gichuk 己丑
  • kich?
  • tsuchinoto-ushi
K? S?u Yin Earth Ox 29 32 2009
27 庚寅 g?ng-yin gyeongin 京仁
  • k?in
  • kanoe-tora
Canh D?n Yang Metal Tiger 30 31 2010
28 辛卯 x?n-m?o sinmyo 辛卯
  • shinb?
  • kanoto-u
Tan Mao Yin Metal Rabbit 31 30 2011
29 壬辰 ren-chen imjin 臨津
  • jinshin
  • mizunoe-tatsu
Nham Thin Yang Water Dragon 32 29 2012
30 癸巳 gu?-si gyesa 繫辭
  • kishi
  • mizunoto-mi
Quy T? Yin Water Snake 33 28 2013
31 甲午 ji?-w? gabo 甲午
  • k?go
  • kinoe-uma
Giap Ng? Yang Wood Horse 34 27 2014
32 乙未 y?-wei eulmi 乙未
  • itsubi
  • kinoto-hitsuji
?t Mui Yin Wood Goat 35 26 2015
33 丙申 b?ng-sh?n byeongsin 病身
  • heishin
  • hinoe-saru
Binh Than Yang Fire Monkey 36 25 2016
34 丁酉 d?ng-y?u jeongyu 精油
  • teiy?
  • hinoto-tori
đinh D?u Yin Fire Rooster 37 24 2017
35 戊戌 wu-x? musul 武術
  • bojutsu
  • tsuchinoe-inu
M?u Tu?t Yang Earth Dog 38 23 2018
36 己亥 j?-hai gihae 期해
  • kigai
  • tsuchinoto-i
K? H?i Yin Earth Pig 39 22 2019
37 庚子 g?ng-z? gyeongja 경자
  • k?shi
  • kanoe-ne
Canh Ty Yang Metal Rat 40 21 2020
38 辛丑 x?n-ch?u sinchuk 新築
  • shinch?
  • kanoto-ushi
Tan S?u Yin Metal Ox 41 20 2021
39 壬寅 ren-yin imin 壬人
  • jin'in
  • mizunoe-tora
Nham D?n Yang Water Tiger 42 19 2022
40 癸卯 gu?-m?o gyemyo 癸卯
  • kib?
  • mizunoto-u
Quy Mao Yin Water Rabbit 43 18 2023
41 甲辰 ji?-chen gapjin 甲辰
  • k?shin
  • kinoe-tatsu
Giap Thin Yang Wood Dragon 44 17 2024
42 乙巳 y?-si eulsa 乙巳
  • itsushi
  • kinoto-mi
?t T? Yin Wood Snake 45 16 2025
43 丙午 b?ng-w? byeongo 丙午
Binh Ng? Yang Fire Horse 46 15 2026
44 丁未 d?ng-wei jeongmi 정미
  • teibi
  • hinoto-hitsuji
đinh Mui Yin Fire Goat 47 14 2027
45 戊申 wu-sh?n musin 무신
  • boshin
  • tsuchinoe-saru
M?u Than Yang Earth Monkey 48 13 2028
46 己酉 j?-y?u giyu 己酉
  • kiy?
  • tsuchinoto-tori
K? D?u Yin Earth Rooster 49 12 2029
47 庚戌 g?ng-x? gyeongsul 庚戌
  • k?jutsu
  • kanoe-inu
Canh Tu?t Yang Metal Dog 50 11 2030
48 辛亥 x?n-hai sinhae 신해
  • shingai
  • kanoto-i
Tan H?i Yin Metal Pig 51 10 2031
49 壬子 ren-z? imja 임자
  • jinshi
  • mizunoe-ne
Nham Ty Yang Water Rat 52 9 2032
50 癸丑 gu?-ch?u gyechuk 癸丑
  • kich?
  • mizunoto-ushi
Quy S?u Yin Water Ox 53 8 2033
51 甲寅 ji?-yin gabin 甲寅
  • k?in
  • kinoe-tora
Giap D?n Yang Wood Tiger 54 7 2034
52 乙卯 y?-m?o eulmyo 乙卯
  • itsub?
  • kinoto-u
?t Mao Yin Wood Rabbit 55 6 2035
53 丙辰 b?ng-chen byeongjin 丙辰
  • heishin
  • hinoe-tatsu
Binh Thin Yang Fire Dragon 56 5 2036
54 丁巳 d?ng-si jeongsa 情事
  • teishi
  • hinoto-mi
đinh T? Yin Fire Snake 57 4 2037
55 戊午 wu-w? muo 戊午
  • bogo
  • tsuchinoe-uma
M?u Ng? Yang Earth Horse 58 3 2038
56 己未 j?-wei gimi 幾微
  • kibi
  • tsuchinoto-hitsuji
K? Mui Yin Earth Goat 59 2 2039
57 庚申 g?ng-sh?n gyeongsin 更新
  • k?shin
  • kanoe-saru
Canh Than Yang Metal Monkey 60 1 2040
58 辛酉 x?n-y?u sinyu 辛酉
  • shin'y?
  • kanoto-tori
Tan D?u Yin Metal Rooster 1 60 2041
59 壬戌 ren-x? imsul 壬戌
  • jinjutsu
  • mizunoe-inu
Nham Tu?t Yang Water Dog 2 59 2042
60 癸亥 gu?-hai gyehae 癸亥
  • kigai
  • mizunoto-i
Quy H?i Yin Water Pig 3 58 2043
24 cardinal directions

Conversion between cyclic years and Western years [ edit ]

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?; "nianhao") to specify a year. [16] 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; ji?-z? ) of a cycle. 2700 years later in 4 AD, the duration equivalent to 45 60-year cycles, was also the starting year of a 60-year cycle. Similarly 1980 years later, 1984 was the start of a new cycle.

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

  1. For any year number greater than 4 AD, the equivalent sexagenary year can be found by subtracting 3 from the Gregorian year, dividing by 60 and taking the remainder . See example below.
  2. For any year before 1 AD, the equivalent sexagenary year can be found by adding 2 to the Gregorian year number (in BC), dividing it by 60, and subtracting the remainder from 60.
  3. 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.
  4. The formula for years AD is (year ? 3) mod 60 and for years BC is (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; ren-chen ), 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; g?ng-chen ), as 60- [(221+2) mod 60] = 17 (i.e., 60 minus the remainder of (221+2) divided by 60 is 17).

Examples [ edit ]

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; d?ng-wei ).

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; y?-m?o ).

A shorter equivalent method [ edit ]

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 [ edit ]

1924?2043 [ edit ]

Sexagenary months [ edit ]

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 : jianz?yue , 建丑月 : jianch?uyue , etc.). [17] [18] 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 ; zh?ngqi ). The jianz?yue (( 建 ) 子月 ) is the month containing the winter solstice (i.e. the 冬至 D?ngzhi ) zh?ngqi . The jianch?uyue (( 建 ) 丑月 ) is the month of the following zh?ngqi , which is Dahan ( 大寒 ), while the jianyinyue (( 建 ) 寅月 ) is that of the Y?shu? ( 雨水 ) zh?ngqi , etc. Intercalary months have the same branch as the preceding month. [19] In the other system ( 節月 ; jieyue ) the "month" lasts for the period of two solar terms (two 氣策 qici ). The z?yue ( 子月 ) is the period starting with Daxu? ( 大雪 ), i.e. the solar term before the winter solstice. The ch?uyue ( 丑月 ) starts with Xi?ohan ( 小寒 ), the term before Dahan ( 大寒 ), while the yinyue ( 寅月 ) starts with Lich?n ( 立春 ), the term before Y?shu? ( 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 jianyinyue , but earlier the first month was jianz?yue (during the Zhou dynasty ) or jianch?uyue (traditionally during the Shang dynasty ) as well. [20]

For astrological purposes stems are also necessary, and the months are named using the sexagenary cycle following a five-year cycle starting in a ji? ( 甲 ; 1st) or j? ( 己 ; 6th) year. The first month of the ji? or j? year is a b?ng-yin ( 丙寅 ; 3rd) month, the next one is a d?ng-m?o ( 丁卯 ; 4th) month, etc., and the last month of the year is a d?ng-ch?u ( 丁丑 , 14th) month. The next year will start with a wu-yin ( 戊寅 ; 15th) month, etc. following the cycle. The 5th year will end with a y?-ch?u ( 乙丑 ; 2nd) month. The following month, the start of a j? or ji? year, will hence again be a b?ng-yin (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( 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 ? Jingzhe Yushui / 雨水 February 4 March 6 Bingyin / 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 ? Qingming Chunfen / 春分 March 6 April 5 Dingmao / 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 ? Lixia Guyu / 谷雨 April 5 May 6 Wuchen / 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 ? Mangzhong Xiaoman / 小? May 6 June 6 Jisi / 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 ? Xiaoshu Xiazhi / 夏至 June 6 July 7 Gengwu / 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 ? Liqiu Dashu / 大暑 July 7 August 8 Xinwei / 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 ? Bailu Chushu / ?暑 August 8 September 8 Renshen / 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 ? Hanlu Qiufen / 秋分 September 8 October 8 Guiyou / 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 ? Lidong Shuangjiang / 霜降 October 8 November 7 Jiaxu / 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 ? Daxue Xiaoxue / 小雪 November 7 December 7 Yihai / 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 ? Xiaohan Dongzhi / 冬至 December 7 January 6 Bingzi / 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 ? Lichun Dahan / 大寒 January 6 February 4 Dingchou / 丁丑月 Jichou / 己丑月 Xinchou / 辛丑月 Guichou / 癸丑月 Yichou / 乙丑月

Sexagenary days [ edit ]

Table for sexagenary days
Day
(stem) 		Month
(stem) 		2-digit year
mod 40
(stem) 		Century
(stem) 		N Century
(branch) 		2-digit year
mod 16
(branch) 		Month
(branch) 		Day
(branch)
Julian
mod 2
Gregorian Julian
mod 4 		Gregorian
00 10 20 30 Aug 00 02 21 23 00 16 00 00 00 07 Nov 00 12 24
01 11 21 31 Sep Oct 04 06 25 27 21 01 14 01 13 25
02 12 22 Nov Dec 08 10 29 31 19 02 16 19 05 Feb Apr 02 14 26
03 13 23 12 14 33 35 03 03 22 03 12 Feb Jun 03 15 27
04 14 24 16 18 37 39 17 24 04 10 Aug 04 16 28
05 15 25 01 03 20 22 01 22 15 05 15 01 Oct 05 17 29
06 16 26 05 07 24 26 06 02 18 08 15 Dec 06 18 30
07 17 27 Mar Jan 09 11 28 30 20 07 21 06 Jan Mar 07 19 31
08 18 28 Jan Apr May Feb 13 15 32 34 18 08 24 13 Jan May 08 20
09 19 29 Feb Jun Jul 17 19 36 38 23 09 01 04 11 Jul 09 21
Dates with the pale yellow background indicate they are for this year. 10 17 02 10 22
11 20 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 [ edit ]

  • 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 00 31 ?1 30 00 31 01 32 03 33 04 34
Leap year ?1 30
  • Stem-branch for February 22, 720 BC (?719).
y = 5 x (720?719) + [1/4] = 5
c = 8
m = 30 + [0.6 x 15 ? 3] ? 5 = 31
d = 22
SB = 5 + 8 + 31 + 22 ? 60 = 6
S = B = 6, 己巳
  • Stem-branch for November 1, 211 BC (?210).
y = 5 x (240?210) + [30/4] = 5 x 6 + 7 = 37
c = 8
m = 0 + [0.6 x 12 ? 3] = 4
d = 1
SB = 37 + 8 + 4 + 1 = 50
S = 0, B = 2, 癸丑
  • Stem-branch for February 18, 1912.
y = 5 x (1912?1920) + [-8/4] + 60 = 18
c = 4 ? 19 + 10 = -5
m = 30 + [0.6 x 15 ? 3] ? 6 = 30
d = 18
SB = 18 ? 5 + 30 + 18 ? 60 = 1
S = B = 1, 甲子
  • Stem-branch for October 1, 1949.
y = 5 x (1949?1920) + [29/4] = 5 x 5 + 7 = 32
c = -5
m = 30 + [0.6 x 11 -3] = 33
d = 1
SB = 32 ? 5 + 33 + 1 ? 60 = 1
S = B = 1, 甲子
Look up table for sexagenary days
Gregorian 17
24 		15
22
20 		18


23
16


21
19

Centuries
Julian 01 00
Dates Mar
Jan


Nov
Dec


Sep
Oct


Aug



Feb
Jun
Jul

Jan
Apr
May
Feb 		Years of the century
01
11
21
31 		02
12
22

03
13
23

04
14
24

05
15
25

06
16
26

07
17
27

08
18
28

09
19
29

10
20
30

天干 甲 乙 丙 丁 戊 己 庚 辛 壬 癸
Heavenly stems A B C D E F G H I J 0 0 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?日速?表
Earthly branches A B C D E F G H I J K L 0 0 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 [ edit ]

Table for sexagenary hours (5-day cycle)
Stem of the day Z? hour
子?
23:00?1:00 		Ch?u hour
丑?
1:00?3:00 		Yin hour
寅?
3:00?5:00 		M?o hour
卯?
5:00?7:00 		Chen hour
辰?
7:00?9:00 		Si hour
巳?
9:00?11:00 		W? hour
午?
11:00?13:00 		Wei hour
未?
13:00?15:00 		Sh?n hour
申?
15:00?17:00 		Y?u hour
酉?
17:00?19:00 		X? hour
戌?
19:00?21:00 		Hai hour
亥?
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

See also [ edit ]

References [ edit ]

Citations [ edit ]

  1. ^ Nussbaum, Louis-Frederic (2005). "Jikkan-j?nishi" . Japan Encyclopedia . Translated by Roth, Kathe. p. 420. ISBN   9780674017535 .
  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 Vu-Quoc-Loc; Vu-Quoc-Hung; Vu-Le-Thao-Uyen (2024), The triennial H??ng exam: Deducing laureates’ birth years , Internet Archive , retrieved 2024-05-12 .
  3. ^ Smith 2011 , pp. 1, 28.
  4. ^ 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).
  5. ^ "...the Ahom reckoned time by means of a sexa- genary cycle"( Kapoor 2021 :666)
  6. ^ "..migration from Mong Mao in Yunnan into Mungdunshunkh?m..."( Kapoor 2021 :666)
  7. ^ For the Akan calendar, see ( Bartle 1978 ).
  8. ^ Selin, Helaine (2012-12-06). Mathematics Across Cultures: The History of Non-Western Mathematics . Springer Science & Business Media. p. 390. ISBN   978-94-011-4301-1 .
  9. ^ Smith 2011 , pp. 24, 26?27.
  10. ^ Kalinowski 2007 , p. 145, fig. 3.
  11. ^ Smith 2011 , p. 29.
  12. ^ Smith 2011 , p. 28.
  13. ^ "Calendar History; the Source" . National Diet Library. Archived from the original on January 6, 2013 . Retrieved January 1, 2013 .
  14. ^ "Kanreki" . Encyclopedia of Shinto . Retrieved January 1, 2013 .
  15. ^ Chattopadhyaya, Alaka (1999). Atisa and Tibet: Life and Works of Dipamkara Srijnana in relation to the history and religion of Tibet . Motilal Banarsidass Publ. pp. 566?568. ISBN   9788120809284 .
  16. ^ 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 .
  17. ^ Smith 2011 , pp. 28, 29 fn2.
  18. ^ 建す . K?jien . Tokyo: Iwanami Shoten .
  19. ^ "Records part 6" 本紀第六 肅宗 代宗 . X?n Tangsh? 新唐書 [ New Book of Tang ]. 二年……，九月壬寅，大赦，去「乾元大?光天文武孝感」?，去「上元」?，?元年，以十一月??首，月以斗所建辰?名。?文武官?、?、爵，版授侍老官，先授者??之。停四京?。
    　　元年建子月癸巳，曹州刺史常休明及史朝??薛??，?之。己亥，朝?皇天帝于西?。丙午，?伯玉及史朝??于永?，?之。己酉，朝?于太??。庚戌，朝享于太?及元?皇后?。建丑月辛亥，有事于南郊。己未，??及史朝??于汝州，?之。乙亥，侯希逸及朝??李?仙?于范?，?之。??元年建寅月甲申，追?靖德太子琮?皇帝，妃?氏?皇后。乙酉，葬王公妃主遇害者。丙戌，??敬陵、惠陵。甲辰，李光弼克?州。吐蕃?和。戊申，史朝?陷?州。建卯月辛亥，大赦。?文武官?、爵。五品以上?望及?官、御史?流人有行?情可矜者。停??、?、狗、豹。以京兆府?上都，河南府??都，?翔府?西都，江陵府?南都，太原府?北都。壬子，羌、?、奴剌寇梁州。癸丑，河???，?其?度使?景山，都知兵?使辛云京自??度使。乙丑，河中??，?李??及其?度使?非元?。戊辰，淮西?度使王仲升及史朝??????于申州，??。庚午，敦子?知朔方、河中、北庭、潞??沁?度行?，?平、定??兵?副元?。壬申，?州刺史成公意及???，?之。建辰月壬午，大赦，官吏???免罪，左降官及流人??效力者?之。甲午，奴剌寇梁州。戊申，???。?部侍?元?同中??下平章事。建巳月庚戌，史朝?寇?州，刺史李抱玉?之。壬子，楚州?定??玉十有三。甲寅，?皇天帝崩。乙丑，皇太子??。大赦，改元年???元年，?以正月??首，建巳月?四月。丙寅，??使李??、???副使程元振?皇后于?殿，?越王系、?王??。是夜，皇帝崩于?生殿，年五十二。?《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，?五丙午，?八己酉，?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，?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，?四甲辰，?八戊申
    春分所在月（762.3）：初一辛亥，初四驚?，初二壬子，初三癸丑，十五乙丑，十八戊辰，十九春分，二十庚午，?一壬申，
    穀雨所在月（762.4）：初一庚辰，初三壬午，初五?明，十五甲午，二十穀雨，?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?
    穀雨所在月初三壬午，已稱建辰月，初五才?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。
  20. ^ 三正 , K?jien , Tokyo: Iwanami Shoten
  21. ^ Conflicting Memories: Tibetan History under Mao Retold . BRILL. 2020-09-07. p. 640. ISBN   978-90-04-43324-3 .

Sources [ edit ]

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

External links [ edit ]

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