Tai Chu Calendar

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Tai Chu Calendar
(Si Fen Calendar)

The chapter "Calendar Jia Zi" of Shi Ji, The Book of Historian, keeps a record of the earliest and systematic calendrical calculation that we have seen on Chinese historical literatures. It is probable that this calendar was put into first practice in 427 B.C.E., not 104 B.C.E., and the supposed beginning point of this calendar was the winter solstice of 1568 B.C.E. The following tables are compiled referring to this chapter.

The first year, yearly name is "Yan Feng, She Ti Ge", Jia Yin. The monthly name is "Bi Ju". The day comes Jia Zi. The new moon occur at midnight with winter solstice. North.

The first Zhang	Number of Lunar Month	The Big Remainder	The Small Remainder	The Big Remainder	The Small Remainder
	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	The Small Remainder	The Big Remainder	The Small Remainder
	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	The Small Remainder	The Big Remainder	The Small Remainder
	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	The Small Remainder	The Big Remainder	The Small Remainder
	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

Chinese calendar is lunisolar calendar. Ancient Chinese thought that the ideal beginning moment of a lunisolar calendar was the day the winter solstice with new moon occurring at midnight (00h00m00s). It means that the ideal beginning moment for a calendar is "Jia Zi year Jia Zi month Jia Zi day Jia Zi hour", and is the day the winter solstice with new moon occurring at midnight.

The chapter "Calendar Jia Zi" give us useful data about the first Bu, totally four Zhang. If we number 60 "stem and branch" combinations in order from 0 to 59, we will see the content of the above tables. The content of the first Zhang of the first Bu is as follow.

The first Zhang	Number of Lunar Month	The Big Remainder (Mean Moon)	The Small Remainder (x/940)	The Big Remainder (Mean Sun)	The Small Remainder (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

On the first row of the above table, we see that the last new moon and winter solstice to the first year occurs at Jia Zi day Jia Zi hour in Zi month.
And, the second row shows us that the last new moon to the second year occurs at Wu Wu day Bing Chen hour and the winter solstice occurs at Ji Si day Ding Mao hour in Zi month of the last (1st) year, and so on.

Here is the rules for this calendar.
Each of 24 Jie Qi = 15 ⁷/₃₂ days
1 solar year = 365¼ days
1 lunar month = 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 information, we will find the last new moon with winter solstice to the first year of each Bu occuring at the same day and same hour but the day not named Jia Zi. So, Chinese use the corresponding "stem and branch" combination as the name of Bu's.

	The Big Remainder	The Small Remainder	The Big Remainder	The Small Remainder
1st Bu	0	0	0	0
2nd Bu	39	0	39	0
3rd Bu	18	0	18	0
4th Bu	57	0	57	0
5th Bu	36	0	36	0
6th Bu	15	0	15	0
7th Bu	54	0	54	0
8th Bu	33	0	33	0
9th Bu	12	0	12	0
10th Bu	51	0	51	0
11th Bu	30	0	30	0
12th Bu	9	0	9	0
13th Bu	48	0	48	0
14th Bu	27	0	27	0
15th Bu	6	0	6	0
16th Bu	45	0	45	0
17th Bu	24	0	24	0
18th Bu	3	0	3	0
19th Bu	42	0	42	0
20th Bu	21	0	21	0

Some people misapprehend that the term "Tai Chu" which mentioned in the beginning of the chapter "Calendar Jia Zi" meant Tai Chu calendar, and this calendar was firstly put into practice and established in 104 B.C.E., because of the name of era was named Tai Chu in 104 B.C.E. But, the yearly "stem and branch" of 104B.C.E. was Ding Chou, and referring to this chapter the first year of this calendar was Jia Yin.

The creator of this calendar chose 427 B.C.E. as the 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 beginning day of a calendar. In Zi month of Jia Yin year (428 B.C.E.), new moon with winter solstice occurred at the same "hour" and in the same day "Ji You day". Referring to the above table, 427 B.C.E. was the first year of 16th Bu, Ji You Bu. The 60 "stem and branch" cycle has been used for keeping track of days since ancient times. The creator, of course, was unable to change the yearly "stem and branch" of 427B.C.E., Jia Yin, to Jia Zi.

Because of the year was taken as 365¼ days and a lunar month was taken as 29 ⁴⁹⁹/₉₄₀ days, the creator supposed that Jia Yin year (1568 B.C.E.) Jia Zi month Jia Zi day Jia Zi hour was the supposted beginining point of Tai Chu / Si Fen Calendar not Jia Zi year Jia Zi month Jia Zi day Jia Zi hour.

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