Chinese Sexagenary Cycle
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Chinese Sexagenary Cycle
Sexagenary cycle
Chinese?
Stems-and-Branches
Chinese

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]

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 ji?z? () combines the first heavenly stem with the first earthly branch. The second term y?ch?u () combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with gu?hài (), 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 ()--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 (), 246 BC, is noted on the diagram next to the position of the 60-cycle term y?-m?o (, 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 --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 year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìch?n" (), 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 (; hwangap) and Japanese tradition ( 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 (--d?ng-m?o, 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 ? ji? gaap3 kæp *[k]?r[a]p k? () kinoe () gap ? giáp yang wood
2 ? y? jyut3 ?it *qr?t otsu () kinoto () eul ? ?t yin
3 ? b?ng bing2 pjængX *pra hei () hinoe () byeong ? bính yang fire
4 ? d?ng ding1 teng *t?e? tei () hinoto () jeong ? ?inh yin
5 ? mou6 muwH *m(r)u?-s (~ *m(r)u?) bo (?) tsuchinoe () mu ? m?u yang earth
6 ? j? gei2 kiX *k(r) ki (?) tsuchinoto () gi ? k? yin
7 ? g?ng gang1 kæng *k?ra? k? () kanoe () gyeong ? canh yang metal
8 ? x?n san1 sin *si[n] shin () kanoto () sin ? tân yin
9 ? rén jam4 nyim *n[?]m jin () mizunoe () im ? nhâm yang water
10 ? gu? gwai3 kjwijX *k?ij? ki (?) mizunoto () gye ? quý yin

## Twelve 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 ? z? zi2 tsiX *[ts] shi (?) ne (?) ja ? Rat (chu?t ?) Rat (?) 11 p.m. to 1 a.m.
2 ? ch?u cau2 trhjuwX *[n?]ru? ch? () ushi () chuk ? s?u Water buffalo (trâu ?) Ox (?) 1 to 3 a.m.
3 ? yín jan4 yij *[?] (r)?r in () tora () in ? d?n Tiger (h? ?/c?p ?) Tiger (?) 3 to 5 a.m.
4 ? m?o maau5 mæwX *m?ru? b? () u (?) myo ? mão/m?o Cat (mèo ?) Rabbit (?) 5 to 7 a.m.
5 ? chén san4 dzyin *[d]?r shin () tatsu () jin ? thìn Dragon (r?ng ?) Dragon (?) 7 to 9 a.m.
6 ? zi6 ziX *s-[?] shi (?) mi (?) sa ? t? Snake (r?n ?) Snake (?) 9 to 11 a.m.
7 ? w? ng5 nguX *[m].qa? go (?) uma () o ? ng? Horse (ng?a ?) Horse (?) 11 a.m. to 1 p.m.
8 ? wèi mei6 mj?jH *m[?]t-s mi (?) or bi (?) hitsuji () mi ? mùi Goat ( ?) Goat (?) 1 to 3 p.m.
9 ? sh?n san1 syin *l?i[n] shin () saru () sin ? thân Monkey (kh? ?) Monkey (?) 3 to 5 p.m.
10 ? y?u jau5 yuwX *N-ru? y? () tori () yu ? d?u Rooster ( ?) Rooster (?) 5 to 7 p.m.
11 ? x? seot1 swit *s.mi[t] jutsu () inu () sul ? tu?t Dog (chó ?) Dog (?) 7 to 9 p.m.
12 ? hài hoi6 hojX *[g] gai () i (?) hae ? 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.

## 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 (; "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 (; 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 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 (; 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 (; g?ng-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 (; d?ng-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 (; y?-m?o).

### 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:

## 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, (: jiànz?yuè, : jiànch?uyuè, 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 (; zh?ngqì). The jiànz?yuè ((?)) is the month containing the winter solstice (i.e. the D?ngzhì) zh?ngqì. The jiànch?uyuè ((?)) is the month of the following zh?ngqì, which is Dàhán (), while the jiànyínyuè ((?)) is that of the Y?shu? () zh?ngqì, etc. Intercalary months have the same branch as the preceding month. [15] In the other system (; jiéyuè) the "month" lasts for the period of two solar terms (two qìcì). The z?yuè () is the period starting with Dàxu? (), i.e. the solar term before the winter solstice. The ch?uyuè () starts with Xi?ohán (), the term before Dàhán (), while the yínyuè () starts with Lìch?n (), the term before Y?shu? (), 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 jiànz?yuè (during the Zhou dynasty) or jiànch?uyuè (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 ji? (?; 1st) or j? (?; 6th) year. The first month of the ji? or j? year is a b?ng-yín (; 3rd) month, the next one is a d?ng-m?o (; 4th) month, etc., and the last month of the year is a d?ng-ch?u (, 14th) month. The next year will start with a wù-yín (; 15th) month, etc. following the cycle. The 5th year will end with a y?-ch?u (; 2nd) month. The following month, the start of a j? or ji? year, will hence again be a b?ng-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 months Solar term Zhongqi (the Middle solar term) Starts at Ends at Names in year of Jia or Ji(?/) Names in year of Yi or Geng (?/) Names in year of Bing or Xin (?/) Names in year of Ding or Ren (?/) Names in year of Wu or Gui (?/)
Month of Yin () Lichun - Jingzhe Yushui February 4 March 6 Bingyin / Wuyin / Gengyin / Renyin / Jiayin /

Month of Mao ()

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

## Sexagenary days

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

• Step-by-step example to determine the stem-branch for October 1, 1949.
• Stem
• (day stem N + month stem N + year stem N + century stem N) = number of stem. If over 10, subtract 10 until within 1 - 10.
• Day 1: N = 1,
• Month of October: N = 1,
• Year 49: N = 7,
• 49 isn't on the table, so we'll have to mod 49 by 40. This gives us year 9, which we can follow to find the N for that row.
• Century 19: N = 2.
• (1 + 1 + 7 + 2) = 11. This is more than 10, so we'll subtract 10 to bring it between 1 and 10.
• 11 - 10 = 1,
• Stem = 1, ?.
• Branch
• (day branch N + month branch N + year branch N + century branch N)= number of branch. If over 12, subtract 12 until within 1 - 12.
• Day 1: N = 1,
• Month of October: N = 5,
• Year 49: N = 5,
• Again, 49 is not in the table for year. Modding 49 by 16 gives us 1, which we can look up to find the N of that row.
• Century 19: N = 2.
• (1 + 5 + 5 + 2) = 13. Since 13 is more than 12, we'll subtract 12 to bring it between 1 and 12.
• 13 - 12 = 1,
• Branch = 1, ?.
• Stem-branch = 1, 1 (, 1 in sexagenary cycle = 32 - 5 + 33 + 1 - 60).
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, ?.
• Branch = (day branch N + month branch N + year branch N + century branch N)
• Day 31: N = 7; month of December: N = 6; year 92 (92 mod 16 = 12): N = 3; century 15: N = 5.
• (7 + 6 + 3 + 5) = 21; 21 - 12 = 9.
• Branch = 9, ?
• Stem-branch = 1, 9 (, 21 in cycle = - 42 - 2 + 34 + 31 = 21)
• Stem-branch for August 4, 1338
• Stem = 8, ?
• Day 4: N = 4; month of August: N = 0; year 38: N = 9; century 13 (13 mod 2 = 1): N = 5.
• (4 + 0 + 9 + 5) = 18; 18 - 10 = 8.
• Branch = 12, ?
• Day 4: N = 4; month of August: N = 4; year 38 (38 mod 16 = 6): N = 7; century 13 (13 mod 4 = 1): N = 9.
• (4 + 4 + 7 + 9) = 24; 24 - 12 = 12
• Stem-branch = 8, 12 (, 48 in cycle = 4 + 8 + 32 + 4)
• Stem-branch for May 25, 105 BC (-104).
• Stem = 7, ?
• Day 25: N = 5; month of May: N = 8; year -4 (-4 mod 40 = 36): N = 9; century -1 (-1 mod 2 = 1): N = 5.
• (5 + 8 + 9 + 5) = 27; 27 - 10 = 17; 17 - 10 = 7.
• Branch = 3, ?
• Day 25: N = 1; month of May: N = 8; year -4 (-4 mod 16 = 12): N = 3; century -1 (-1 mod 4 = 3): N = 3.
• (1 + 8 + 3 + 3) = 15; 15 - 12 = 3.
• Stem-branch = 7, 3 (, 27 in cycle = - 6 + 8 + 0 + 25)
• Alternately, instead of doing both century and year, one can exclude the century and simply use -104 as the year for both the stem and the branch to get the same result.

Algorithm for mental calculation

${\displaystyle SB=(y+c+m+day){\bmod {6}}0}$
${\displaystyle S=SB{\bmod {1}}0,B=SB{\bmod {1}}2}$
${\displaystyle y=(year({\bmod {4}}00){\bmod {8}}0({\bmod {1}}2)\times 5+\left\lfloor {\frac {year({\bmod {4}}00){\bmod {8}}0}{4}}\right\rfloor ){\bmod {6}}0}$
${\displaystyle c=\left\lfloor {\frac {year}{400}}\right\rfloor -\left\lfloor {\frac {year}{100}}\right\rfloor +10}$ for Gregorian calendar and ${\displaystyle c=8}$ for Julian calendar.
${\displaystyle m=(month+1){\bmod {2}}\times 30+\left\lfloor {0.6\times (month+1)-3}\right\rfloor -i}$
${\displaystyle i=5}$ for Jan or Feb in a common year and ${\displaystyle i=6}$ in a leap year.
 Month m Leap year Jan13 Feb14 Mar03 Apr04 May05 Jun06 Jul07 Aug08 Sep09 Oct10 Nov11 Dec12 00 31 -1 30 00 31 01 32 03 33 04 34 -1 30 ${\displaystyle m=\left\lfloor {30.6\times (month+1)}-3\right\rfloor {\bmod {6}}0-i}$
• 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,
• 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,
• 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,
• 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,
 Gregorian 1724 1522 20 18 23 16 21 19 Centuries Julian 01 00 Dates MarJan NovDec SepOct Aug FebJunJul JanAprMayFeb Years of the century 01112131 021222 031323 041424 051525 061626 071727 081828 091929 102030 ? ? ? ? ? ? ? ? ? ? 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 ? ? ? ? ? ? ? ? ? ? ? ? ? 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 011325 021426 031527 041628 051729 061830 071931 0820 0921 1022 1123 1224 Years of the century MarJan Dec Oct Aug FebJun AprFeb Nov Sep Jul JanMay Gregorian 1518 21 24 17 2023 1619 22 Centuries Julian 02 01 00 03

## Sexagenary hours

Table for sexagenary hours (5-day cycle)
Stem of the day Z? hour

23:00-1:00
Ch?u hour

1:00-3:00
Yín hour

3:00-5:00
M?o hour

5:00-7:00
Chén hour

7:00-9:00
Sì hour

9:00-11:00
W? hour

11:00-13:00
Wèi hour

13:00-15:00
Sh?n hour

15:00-17:00
Y?u hour

17:00-19:00
X? hour

19:00-21:00
Hài hour

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

## References

### Citations

1. ^ Nussbaum, Louis-Frédéric (2005). "Jikkan-j?nishi". Japan Encyclopedia. Translated by Roth, Käthe. p. 420. ISBN 9780674017535.
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 (, 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 2013.
10. ^ "Kanreki". Encyclopedia of Shinto. Retrieved 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. ISBN 9788120809284.
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 2011.
13. ^ Smith 2011, pp. 28, 29 fn2.
14. ^ . K?jien. Tokyo: Iwanami Shoten.
15. ^ "Records part 6" ? . X?n Tángsh? [New Book of Tang]. ......,?,,,,,?,,,
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16. ^ , K?jien, 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)