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 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


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

The first Zhang
Number of
Lunar Month
The Big
Remainder
(Lunar month)
The Small
Remainder
(x/940)
The Big
Remainder
(Solar Month)
The Small
Remainder
(x/32)
 
12
0
0
0
0
 
12
54
348
5
8
 
13
48
696
10
16
 
12
12
603
15
24
 
12
7
11
21
0
 
13
1
359
26
8
 
12
25
266
31
16
 
12
19
614
36
24
 
13
14
22
42
0
 
12
37
869
47
8
 
13
32
277
52
16
 
12
56
184
57
24
 
12
50
532
3
0
 
13
44
880
8
8
 
12
8
787
13
16
 
12
3
195
18
24
 
13
57
543
24
0
 
12
21
450
29
8
 
13
15
798
34
16

West

The second Zhang
Number of
Lunar Month
The Big
Remainder
(Lunar month)
The Small
Remainder
(x/940)
The Big
Remainder
(Solar Month)
The Small
Remainder
(x/32)
 
12
39
705
39
24
 
12
34
113
45
0
 
13
28
461
50
8
 
12
52
368
55
16
 
12
46
716
0
24
 
13
41
124
6
0
 
12
5
31
11
8
 
12
59
379
16
16
 
13
53
727
21
24
 
12
17
634
27
0
 
13
12
42
32
8
 
12
35
889
37
16
 
12
30
297
42
24
 
13
24
645
48
0
 
12
48
552
53
8
 
12
42
900
58
16
 
13
37
308
3
24
 
12
1
215
9
0
 
13
55
563
14
8

South

The third Zhang
Number of
Lunar Month
The Big
Remainder
(Lunar month)
The Small
Remainder
(x/940)
The Big
Remainder
(Solar Month)
The Small
Remainder
(x/32)
 
12
19
470
19
16
 
12
13
818
24
24
 
13
8
226
30
0
 
12
32
133
35
8
 
12
26
481
40
16
 
13
20
829
45
24
 
12
44
736
51
0
 
12
39
144
56
8
 
13
33
492
1
16
 
12
57
399
6
24
 
13
51
747
12
0
 
12
15
654
17
8
 
12
10
62
22
16
 
13
4
410
27
24
 
12
28
317
33
0
 
12
22
665
38
8
 
13
17
73
43
16
 
12
40
920
48
24
 
13
35
328
54
0

East

The fourth Zhang
Number of
Lunar Month
The Big
Remainder
(Lunar month)
The Small
Remainder
(x/940)
The Big
Remainder
(Solar Month)
The Small
Remainder
(x/32)
 
12
59
235
59
8
 
12
53
583
4
16
 
13
47
931
9
24
 
12
11
838
15
0
 
12
6
246
20
8
 
13
0
594
25
16
 
12
24
501
30
24
 
12
18
849
36
0
 
13
13
257
41
8
 
12
37
164
46
16
 
13
31
512
51
24
 
12
55
419
57
0
 
12
49
767
2
8
 
13
44
175
7
16
 
12
8
82
12
24
 
12
2
430
18
0
 
13
56
778
23
8
 
12
20
685
28
16
 
13
15
93
33
24



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
2nd year
12
54 
348
8
3rd year
13
48 
696
10 
16
4th year 
12
12 
603
15 
24
5th year
12
11
21 
0
6th year
13
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
0
14th year
13
44 
880
8
8
15th year
12
787
13 
16
16th year
12
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.



 

 

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