Sexagenary cycle (Ganzhi 干支)
The sexagenary cycle (ganzhi 干支) is the wheel of sixty combinations pairing the ten heavenly stems with the twelve earthly branches. Its length of sixty is no arbitrary choice: it is the least common multiple of 10 and 12, that is 60. Stem and branch each advance one step every year, but since one counts by ten and the other by twelve, it takes sixty years for an exact combination to return. This wheel is what blends an animal with an element for any given year.
Why sixty and not one hundred twenty
You might think ten times twelve yields a hundred and twenty combinations. But stem and branch turn in phase, never freely: they advance only together. A yang stem meets only yang branches, a yin stem only yin branches. Half the pairings therefore never occur, leaving just sixty valid couples. The least common multiple of 10 and 12, exactly.
One life, one full turn
Sixty years is the span of a full turn. When you reach your sixtieth birthday, you return to the exact stem-branch combination of your birth: same animal, same element. The Chinese make this a threshold, a return to the starting point after a lifetime. Your year is never merely the Rat: it is, say, the Metal Rat of 1960, which will not come back until 2020.
Sources
- , Science and Civilization in China (1959)