5: Would you please teach me the quick method to calculate the Gan Zhi (heavenly Stems and Earthly Branches) of the day and shichen?

Both Zi Wu Liu Zhu (Midnight Noon Flow Ebb) and Ling Gui Ba Fa (Eight Methods of Miraculous Turtle) need Gan Zhi of the day and shichen (2-hour time period)” to decide the point. Would you please teach me the quick method to calculate the Gan Zhi (heavenly Stems and Earthly Branches) of the day and shichen?

Reviewing the journals of the Chinese medicine in various regions in the past decades, one can find several dozens of articles on the topic “Quick Calculating Methods on Gan Zhi (Heavenly Stems and Earthly Branches”. Those methods usually need to refer to certain tables or charts, or convert between several formulas, or memorize songs of the Gan Zhi of the January firsts. Not only the memorizations are difficult, the calculations are not fast anyhow. Besides, if the person does not bring the pamphlet of the ten thousand year calendar with him, then he will not be able to calculate. In calculating the Gan Zhi of shichen, one needs to know the Gan Zhi of the day first. Once the Gan Zhi of the day is calculated, the Gan Zhi of the shichen is quite simple. I taught the theory of Yi Jing and Ba Zi (Eight Characters) before, and apply them to predict the constitutions and general health weakness of a person. I have been using the following formulas to calculate the Gan Zhi of a day and shichen. I believe it is a quick method.

Formula A: 〔5(x-1)+((x-1)/4)r+15+y〕/10＝....the remainder is the Gan of the day
Formula B: 〔5(x-1)+((x-1)/4)r+15+y〕/12＝.....the remainder is the Zhi of the day

Explanation: “Y” is the total of days from January first of the year. “X” is the last two digits of the year. If the year is after year 2000, then use the last three digits instead (ex. 100, 101….). “r” is the integer (leave the remainder out). Although I list two formulas above, in fact, there is only one to remember; because one divisor is 10 and the other 12.

The 10 possible remainder from formula A:

1 2 3 4 5 6 7 8 9 0
Jia Yi Bing Ding Wu Ji Gen Xin Ren Gui

The 12 possible remainder from formula B:

1 2 3 4 5 6 7 8 9 10 11 0
Zi Chou Yin Mou Chen Si Wu Wei Shen You Xu Hai

Example:

1). Gan and Zhi of March 1st, 2005

Gan of the day:
[5(105-1)+((105-1)/4)r+15+(31+28+1)]/10= (520+26+15+60=621)/10=62…1
(the remainder is 1, refers to Jia)

Zhi of the day:
[5(105-1)+((105-1)/4)r+15+(31+28+1)]/12=520+26+15+60=621/12=51…. 9
(the remainder is 9, refers to Shen)Hence, the Gan and Zhi of March 1st, 2005 is Jia and Shen.

2). Gan and Zhi of May 1st, 2010

Gan of the day:
5×(110-1)+(110/4)r+15+(31+28+31+30+1)=545+27+15+121=708/10=70….. 8
(the remainder is 8, equals to Xin)

Zhi of the day:
5×(110-1)+(110/4)r+15+(31+28+31+30+1)=545+27+15+121=708/12=59….0
(the remainder is 0, equals to Hai) The Gan and Zhi of May 1st, 2005 is Xin and Hai.

As how to calculate the Gan and Zhi of the time (shichen), once the Gan and Zhi of the day are known, they are simple to calculate. There are twelve shichen in a day. There will be sixty shichen in five days, which equals to the sixty Jia Zhi. Hence, the sixty shichen restart and circulate in every five days. If the Zi shi (11:00pm-1:00am) of the Jia day is Jia Zi, then the Hai shi of the Wu day is Qui Hai and the Zi shi of the Ji day will be Jia Zi again. As long as one knows the Heavenly Stem (Tien Gan) of the day, it is not difficult to calculate the Gan Zhi of the shichen on that day. The below is the two songs of the starting Shichen of the day. They help memorization. One song takes Zi shi as the starting and is called “Wu Zi Jien Yuan Fa” (Five Zi establishing the start). The other takes Yin shi as starting and is called “Wu Hu Jien Yuan Fa” (Five Tiger establishing the start). The first method is more popular. It is as follow.

The song of Wu Zi Jien Yuan Fa
Jia Ji start from Jia Zi
Yi Gen start from Bing Zi
Bing Xin start from Wu Zi
Ding Ren start from Gen Zi
Wu Gui start from Ren Zi

That means:

On the days of Jia and Ji: the heavenly stem (Gan) of the Zi shi is Jia
On the days of Yi and Gen: the heavenly stem (Gan) of the Zi shi is Bing
On the days of Bing and Xin: the heavenly stem (Gan) of the Zi shi is Wu
On the days of Ding and Ren: the heavenly stem (Gan) of the Zi shi is Gen
On the days of Wu and Gui,: the heavenly stem (Gan) of the Zhi shi is Ren

The Gan Zhi of the rest shichen can be determined by following the sequence. For example, the Gan Zhi of the Zi shi on Yi day is Bing Zi, so the Gan Zhi of Chou shi is Ding Chou, and the Gan Zhi of Yin shi is Wu Yin…… Another example, the Gan Zhi of Zi shi on Xin day is Wu zi, and so the Gan Zhi of Chou shi is Ji Chou, and Gan Zhi of Yin shi is Gen Yin, Gan Zhi of Mao shi is Xin Mao; Gan Zhi of Chen shi is Ren Chen….. The rest follows the pattern.