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Ancient Chinese people had the skill to calculate the history of five thousands years and record the chronological sequence of events. They invented a measurement by two sets of signs in a certain sequence - Heavenly Stems and Earthly Branches. As early as about 2700BC, the ancestor of Chinese nation, Yellow Emperor (Huangdi), sent Da Rao Shi to create a calendar system. Da Rao Shi explored the rule of changes between sky and earth, as well as that of the four seasons. Then he created ten heavenly stems and twelve earthly branches to make combinations representing a sexagenary cycle. A year can be represented by the composition of two characters, one from the heavenly set, and one from the other. That is believed to be the start of the stem-branch calendar. Thus came a way of counting time which has been passed down through thousands of years.

The Heavenly Stems

乙   丙    戊  己  辛 
jiǎ bǐng dīng gēng xīn rén guǐ
Jia Yi Bing Ding Wu Ji Geng Xin Ren Gui

Earthly Branches can be used to count time of years, months and hours. When counting years, people use them with the 12 Chinese zodiacs and strictly one Earthly Branch corresponds to one fixed zodiac. For example, our ancestors have divided a day and night into twelve sections and named each as a 'shi chen', which is equal to today's two hours and has a fixed Earthly Branch name. From 11 pm at night to 1 am is decided to be the first one - 'zi shi', then the second two hours 'chou shi', on the analogy of this.

The Earthly Branches and Corresponding Chinese Zodiac Animal Signs  

chǒu yín maǒ chén weì  shēn yǒu haì
Zi Chou Yin Mao Chen Si Wu Wei Shen You Xu Hai
Rat Ox Tiger Rabbit Dragon Snake Horse Sheep Monkey Rooster Dog Pig

Take the year of 2005 for example, 2005 can be described as 'Yi You', a combination of the second sign in Heavenly Stems and the tenth one in the Earthly Branches. Then the next year 2006 will be 'Bing Xu' - the third sign and the eleventh one's association. 

The Four Pillar of Life (also the Eight Characters of Birth Time or 'ba zi' in Chinese) was very popular and mostly used in fortune-telling. In four pairs of year, month, day, and hour of a person's birth, each pair includes one Heavenly Stems and one Earthly Branchs. There are compatibility and incompatibility relations among the stems and branches. The expression of one's birth time in this way has always been vital especially when it is used for fortune foretelling.
  To know the Compatibility Charts of Chinese Zodiac Animal Signs

The Five Compatibilities of Heavenly Stems – Jia and Ji, Yi and Geng, Bing and Xin, Ding and Ren, Wu and Gui
Explanation: Wood is the corresponding element in Wu Xing to Jia, so is Earth to Ji. Wood grows in earth, so they are compatible combination. The rest can be explained in the same manner. 

The Six Combinations of Earthly Branches – Zi and Chou combined into Earth, Yin and Hai combined into Wood, Mao and Xu combined into Fire, Si and Shen combined into Water, Wu and Wei combined into the sun and moon

The Three Combinations of the Early Branches – Shen, Xi, Chen combine and form Water, Hai, Mao, Wei combine and form Wood, Yin, Wu, Xu combine and form Fire, Si, You, Chou combine and form Metal, Chen, Xu, Chou, Wei combine and forms Earth.

The following content is to introduction the braches in opposition, listing from strong to week power of harms. 

Six Clashes of the Earthly Branches – Zi vs Wu, Yin vs Shen, Mao vs You, Chen vs Xu, Si vs Hai, Chou vs Wei

Earthly Branches punishment:
Special - Yin vs Si, Si vs Shen, Shen vs Yin
Ungrateful – Chou vs Xu, Xu vs Wei, Wei vs Chou
Rudeness – Zi vs Mao
Self Punishment – Chen vs Chen, Wu vs Wu, You vs You, Hai vs Hai
Earthly Branches Harm – Zi vs Wei, Chou vs Wu, Yin vs Si, Mao vs Chen, Shen vs Hai, You vs Hai