# الدورة الستينية

(تم التحويل من Sexagenary cycle)

الدورة الستينية sexagenary cycle، وتُعرف أيضاً بإسم الجذوع والفروع أو گان‌ژي ganzhi هي دورة من ستين مدة، تُستخدم لمعرفة الزمن في الصين وباقي 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.

الدورة الستينية
بالصينية
Stems-and-Branches
الصينية

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.

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## استعراض

تماثيل آلهة تاي سوي المسئولة عن السنوات المفردة في الدورة الستينية.

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.[3]

## عشرة جذوع سماوية

No. الجذع
السماوي
الاسم
الصيني
الاسم
الياباني
Korean
name
Vietnamese
name
Yin Yang Wu Xing
Mandarin
(Pinyin)
Cantonese
(Lau)
Onyomi Kunyomi with
corresponding kanji
Romanized Hangul
1 jiǎ gaap3 kō (こう) kinoe (木の兄) gap giáp yang wood
2 yuet3 otsu (おつ) kinoto (木の弟) eul ất yin
3 bǐng bing2 hei (へい) hinoe (火の兄) byeong bính yang fire
4 dīng ding1 tei (てい) hinoto (火の弟) jeong đinh yin
5 mo6 bo () tsuchinoe (土の兄) mu mậu yang earth
6 gei2 ki () tsuchinoto (土の弟) gi kỷ yin
7 gēng gang1 kō (こう) kanoe (金の兄) gyeong canh yang metal
8 xīn san1 shin (しん) kanoto (金の弟) shin tân yin
9 rén yam4 jin (じん) mizunoe (水の兄) im nhâm yang water
10 guǐ gwai3 ki () mizunoto (水の弟) gye quý yin

## إثناعشر فرعاً أرضياً

No. Earthly
Branch
الاسم
الصيني
الاسم
الياباني
Korean
name
Vietnamese
name
Vietnamese
zodiac
Chinese
zodiac
Corresponding
hours
Mandarin
(pinyin)
Cantonese
(Lau)
Onyomi Kunyomi Romanized Hangul
1 ji2 shi ne ja Rat (chuột;𤝞) Rat () 11 p.m. to 1 a.m.
2 chǒu chau2 chū ushi chuk sửu Water buffalo (trâu;𤛠) Ox () 1 to 3 a.m.
3 yín yan4 in tora in dần Tiger (hổ/cọp;虎/𧲫) Tiger () 3 to 5 a.m.
4 mǎo maau5 u myo mão/mẹo Cat (mèo;猫) Rabbit () 5 to 7 a.m.
5 chén san4 shin tatsu jin thìn Dragon (rồng;龍) Dragon () 7 to 9 a.m.
6 ji6 shi mi sa tỵ Snake (rắn;𧋻) Snake () 9 to 11 a.m.
7 ng5 go uma o ngọ Horse (ngựa;馭) Horse () 11 a.m. to 1 p.m.
8 wèi mei6 mi or bi hitsuji mi mùi Goat (dê;羝) Goat () 1 to 3 p.m.
9 shēn san1 shin saru shin thân Monkey (khỉ;𤠳) Monkey () 3 to 5 p.m.
10 yǒu jau5 tori yu dậu Rooster (gà;𪂮) Rooster () 5 to 7 p.m.
11 sut1 jutsu inu sul tuất Dog (chó;㹥) Dog () 7 to 9 p.m.
12 hài hoi6 gai i hae hợi Pig (lợn/heo;𤞼/㺧) 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.

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## السنوات الستينية

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## التحويل بين السنوات الدورية والسنوات الغربية

Relationship between sexagenary cycle and recent Common Era years

### أمثلة

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).

### طريقة مماثلة أقصر

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

• 1967 = 60 × 32 + 47. Remainder is therefore 47 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:

## الشهور الستينية

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 (; 1st) or (بالصينية: ; 6th) year. The first month of the jiǎ or 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 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 months Solar term Zhongqi (the Middle solar term) Starts at Ends at Names in year of Jia or Ji(/己年) Names in year of Yi or Geng (/庚年) Names in year of Bing or Xin (/辛年) Names in year of Ding or Ren (/壬年) Names in year of Wu or Gui (/癸年)
Month of Yin (寅月) LichunJingzhe Yushui 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)

JingzheQingming Chunfen 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) QingmingLixia Guyu 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) LixiaMangzhong Xiaoman 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) MangzhongXiaoshu Xiazhi 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) XiaoshuLiqiu Dashu 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) LiqiuBailu Chushu 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) BailuHanlu Qiufen 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) HanluLidong Shuangjiang 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) LidongDaxue Xiaoxue 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) DaxueXiaohan Dongzhi 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) XiaohanLichun Dahan 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

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.

### أمثلة

• Step-by-step example to determine the stem-branch for October 1, 1949.
• Stem
• (day stem N + month stem N + year stem N + century stem N) = number of stem. If over 10, subtract 10 until within 1 - 10.
• Day 1: N = 1,
• Month of October: N = 1,
• Year 49: N = 7 ,
• 49 isn't on the table, so we'll have to mod 49 by 40. This gives us year 9, which we can follow to find the N for that row.
• Century 19: N = 2.
• (1 + 1 + 7 + 2) = 11. This is more than 10, so we'll subtract 10 to bring it between 1 and 10.
• Branch
• (day branch N + month branch N + year branch N + century branch N)= number of branch. If over 12, subtract 12 until within 1 - 12.
• Day 1: N = 1,
• Month of October: N = 5,
• Year 49: N = 5,
• Again, 49 is not in the table for year. Modding 49 by 16 gives us 1, which we can look up to find the N of that row.
• Century 19: N = 2.
• (1 + 5 + 5 + 2) = 13. Since 13 is more than 12, we'll subtract 12 to bring it between 1 and 12.
• Stem-branch = 1, 1 (بالصينية: 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, بالصينية: .
• 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, بالصينية:
• Stem-branch = 1, 9 (بالصينية: 甲申, 21 in cycle = - 42 - 2 + 34 + 31 = 21)
• Stem-branch for August 4, 1338
• Stem = 8, بالصينية:
• 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, بالصينية:
• 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 (بالصينية: 辛亥, 48 in cycle = 4 + 8 + 32 + 4)
• Stem-branch for May 25, 105 BC (-104).
• Stem = 7, بالصينية:
• 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, بالصينية:
• 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 (بالصينية: 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.

### خوارزمية للحساب الذهني

${\displaystyle SB=(y+c+m+day){\bmod {6}}0}$
${\displaystyle S=SB{\bmod {1}}0,B=SB{\bmod {1}}2}$
${\displaystyle y=(year({\bmod {4}}00){\bmod {8}}0({\bmod {1}}2)\times 5+\left\lfloor {\frac {year({\bmod {4}}00){\bmod {8}}0}{4}}\right\rfloor ){\bmod {6}}0}$
${\displaystyle c=\left\lfloor {\frac {year}{400}}\right\rfloor -\left\lfloor {\frac {year}{100}}\right\rfloor +10}$  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, 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

## Sexagenary hours

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

23:00–1:00
Chǒu hour

1:00–3:00
Yín hour

3:00–5:00
Mǎo hour

5:00–7:00
Chén hour

7:00–9:00
Sì hour

9:00–11:00
Wǔ hour

11:00–13:00
Wèi hour

13:00–15:00
Shēn hour

15:00–17:00
Yǒu hour

17:00–19:00
Xū hour

19:00–21:00
Hài hour

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

## الهامش

### مراجع

1. ^ Nussbaum, Louis-Frédéric. (2005). "Jikkan-jūnishi" in Japan Encyclopedia, p. 420.
2. ^ Smith (2011), pp. 1, 28.
3. ^ For the Akan calendar, see Bartle (1978).

### المصادر

• 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.
• 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.
• Smith, Adam (2011). "The Chinese sexagenary cycle and the ritual origins of the calendar". In John Steele (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.