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 starting-point 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 starting-point of a lunisolar calendar was winter solstice day with new moon occurring at midnight (00h00m00s). Ancient Chinese named this ideal starting-point 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 Branch	Ganzhi		Stem and Branch	Ganzhi		Stem and Branch	Ganzhi		Stem and Branch	Ganzhi
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

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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

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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.

The first Zhang	Number of Lunar Month	The Big Remainder (New Moon, day)	The Small Remainder (time, x/940)	The Big Remainder (Winter Solstice, day)	The Small Remainder (time, x/32)
1st year	12	0	0	0	0
2nd year	12	54	348	5	8
3rd year	13	48	696	10	16
4th year	12	12	603	15	24
5th year	12	7	11	21	0
6th year	13	1	359	26	8
7th year	12	25	266	31	16
8th year	12	19	614	36	24
9th year	13	14	22	42	0
10th year	12	37	869	47	8
11th year	13	32	277	52	16
12th year	12	56	184	57	24
13th year	12	50	532	3	0
14th year	13	44	880	8	8
15th year	12	8	787	13	16
16th year	12	3	195	18	24
17th year	13	57	543	24	0
18th year	12	21	450	29	8
19th year	13	15	798	34	16

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.

Starting-point	The Big Remainder	The Small Remainder	The Big Remainder	The Small Remainder	Bu
1st Bu	00	0	00	0	Jia Zi
2nd Bu	39	0	39	0	Gui Mao
3rd Bu	18	0	18	0	Ren Wu
4th Bu	57	0	57	0	Xin You
5th Bu	36	0	36	0	Grng Zi
6th Bu	15	0	15	0	Ji Mao
7th Bu	54	0	54	0	Wu Wu
8th Bu	33	0	33	0	Ding You
9th Bu	12	0	12	0	Bing Zi
10th Bu	51	0	51	0	Yi Mao
11th Bu	30	0	30	0	Jia Wu
12th Bu	9	0	9	0	Gui You
13th Bu	48	0	48	0	Ren Zi
14th Bu	27	0	27	0	Xin Mao
15th Bu	6	0	6	0	Geng Wu
16th Bu	45	0	45	0	Ji You
17th Bu	24	0	24	0	Wu Zi
18th Bu	3	0	3	0	Ding Mao
19th Bu	42	0	42	0	Bing Wu
20th Bu	21	0	21	0	Yi You

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 starting-point 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 starting-point 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 big-cycle of Sifen calendar needs 4560 years.