Calendrical Jia Zi
(Si Fen Calendar)
The chapter "Calendrical Jia Zi" of SHI JI (The Book of Historian) is a record of the earliest and systematic calendrical calculation. This systematic Chinese calendar was probably first put into practice in 427 B.C.E. And the real startingpoint of this calendar is the winter solstice of 428 B.C.E. The above picture shows the simulated phenomenon at the winter solstice of 428 B.C.E. This chapter also shows us how ancient Chinese linked Ganzhi (sixty combinations of Celestial/Heavenly Stem and Terrestrial/Earthly Branch) and calendrical calculation and kept track of time passage together.
The first of sixty Ganzhi is Jiazi. Ancient Chinese believed that the ideal startingpoint of a lunisolar calendar was winter solstice day with new moon occurring at midnight (00h00m00s). Ancient Chinese named this ideal startingpoint of a calendar is "Jiazi year Jiazi month Jiazi day Jiazi hour".
The following tables let us better understand the information that was mentioned in the chapter Calendrical Jiazi.
Stem
and
BranchGanzhi Stem
and
BranchGanzhi Stem
and
BranchGanzhi Stem
and
BranchGanzhi 00 Jia Zi 15 Ji Mao 30 Jia Wu 45 Ji You 01 Yi Chou 16 Geng Chen 31 Yi Wei 46 Geng Xu 02 Bing Yin 17 Xin Si 32 Bing Shen 47 Xin Hai 03 Ding Mao 18 Ren Wu 33 Ding You 48 Ren Zi 04 Wu Chen 19 Gui Wei 34 Wu Xu 49 Gui Chou 05 Ji Si 20 Jia Shen 35 Ji Hai 50 Jia Yin 06 Geng Wu 21 Yi You 36 Geng Zi 51 Yi Mao 07 Xin Wei 22 Bing Xu 37 Xin Chou 52 Bing Chen 08 Ren Shen 23 Ding Hai 38 Ren Yin 53 Ding Si 09 Gui You 24 Wu Zi 39 Gui Mao 54 Wu Wu 10 Jia Xu 25 Ji Chou 40 Jia Chen 55 Ji Wei 11 Yi Hai 26 Geng Yin 41 Yi Si 56 Geng Shen 12 Bing Zi 27 Xin Mao 42 Bing Wu 57 Xin You 13 Ding Chou 28 Ren Chen 43 Ding Wei 58 Ren Xu 14 Wu Yin 29 Gui Si 44 Xu Shen 59 Gui Hai
The following tables were compiled from the chapter Calendrical Jiazi of SHI JI.
In the first year, the year name is "Yan Feng, She Ti Ge" (Jia Yin). The month name is "Bi Ju" and the day name is Jiazi. The new moon with winter solstice occurs at midnight. North

Lunar Month 
Remainder (Lunar month) 
Remainder (x/940) 
Remainder (Solar Month) 
Remainder (x/32) 


















































































































West

Lunar Month 
Remainder (Lunar month) 
Remainder (x/940) 
Remainder (Solar Month) 
Remainder (x/32) 


















































































































South

Lunar Month 
Remainder (Lunar month) 
Remainder (x/940) 
Remainder (Solar Month) 
Remainder (x/32) 


















































































































East

Lunar Month 
Remainder (Lunar month) 
Remainder (x/940) 
Remainder (Solar Month) 
Remainder (x/32) 


















































































































The chapter "Calendrical Jiazi" gives us all information of the first Bu ( ) of Sifen Calendar, totally four Zhang. If we replace all numbers in the two columns of "The Big Remainder" listed in the First Zhang table with Ganzhi (please refer to the above Ganzhi table), we will clearly see the content of the First Zhang table's as follows.

Lunar Month 
Remainder (New Moon, day) 
Remainder (time, x/940) 
Remainder (Winter Solstice, day) 
Remainder (time, x/32) 


















































































































The first row of this table indicates that the first new moon with winter solstice occurs at Jia Zi day Jia Zi hour in Zi month. And, there is 12 lunar months before the next winter solstice.
The second row indicates that the second winter solstice occurs at Ji Si day Ding Mao hour, and the new moon occurs at Wu Wu day Bing Chen hour in Zi month, and so on.Here is the rules for this calendar.
1 day = 12 Shi (Chinese "hour", 1 Shi = 2 hours)
Each of 24 Jieqi = 15 ^{7}/_{32} days
1 solar year = 365¼ days
1 lunar month (Lunar Synodical Period) = 29 ^{499}/_{940} days
1 Zhang = 19 solar years (containing 7 leap lunar months)
1 Bu = 4 Zhang (76 solar years)
20 Bu = 1 Ji (1520 solar years)
3 Ji = 1 Yuan (4560 solar years)If we compile all twenty Bu tables according to above rules, we will find that the first row of the first Zhang of each Bu indicates the new moon and the winter solstice occurs at Zi Shi (Chinese hour) of the same day. So, ancient Chinese used the corresponding Ganzhi (stem and branch) of the day as the name of Bu.

Remainder 
Remainder 
Remainder 
Remainder 














































































































































The maker of this calendar chose 427 B.C.E., Jia Yin year, to put this workable calendar into practice, because the winter solstice day of 428 B.C.E. nearly fulfilled the criterion for establishing the ideal startingpoint of a calendar; the new moon with winter solstice occurred at the same Chinese "hour" and in the same day (Ji You day) in Zi month of 428 B.C.E.The Ganzhi of the winter solstice day in 428 B.C.E. is Ji You, therefore 427 B.C.E. (Jia Yin year) was the first year of 16th Bu, Ji You Bu. According to the aforementioned rules, the year was taken as 365¼ days and a lunar month was taken as 29 ^{499}/_{940} days, the creator supposed that the winter solsctice day in 1568 B.C.E. was the presumptive startingpoint of this calendar.
According to the aforementioned rules, after 20 Bu the Ganzhi of the day having new moon and winter solstice is Jiazi (20 Bu = 1 Ji =1520 solar years), but the Ganzhi of the year is not Jiazi. After 3 Ji the Ganzhi of year, month, day, and Shi (Chinese hour) are Jiazi (3 Ji = 1 Yuan = 4560 solar years). One bigcycle of Sifen calendar needs 4560 years.