Calendar-Making in Ancient China

An important aspect of the Chinese calendar is the sexagenary cycle (gan zhi), which is 60 years long. This is a combination of the 10 heavenly stems (tian gan), and the 12 earthly branches (di zhi). The following is a table showing the sexagenary:
 

To explain how this cycle works, let us denote both the stems and the branches by their numbers. We denote 1 by (1,1) or (甲,子), 2 by (2,2) or (乙,丑) and so on up to (10,10) or (癸,酉). But now we have run out of stems, so we denote 11 by (1, 11) or (甲,戌) and 12 by (2, 12) or (乙,亥). Now we have run out of branches, too, so 13 becomes (3, 1) or (丙,子). We continue in this way through 6 cycles of stems and 5 cycles of branches up to 60, which is (10, 12) or (癸,亥). The next number is then (1,1) or (甲,子), which starts a new sexagenary cycle.

Great importance was attached to the celestial observation in making a new calendar during ancient China. The gnomon (a column for measuring the sun's meridian altitude) and sundial were the timekeeping instruments with the sun as the object for observation. Although simple structures, the two instruments could serve many purposes, and were said to be China' oldest astronomic instruments.

By the middle of the Spring and Autumn Period (770-446BC), to use the gnomon for making a calendar had become an important calendar-making method, through which the conclusion of a tropical year being 365.25 days long was reached.