The ancient Chinese believed that a ruler received his right to rule from heaven. If his administration was just, then the heavens would be free from unusual events; but if it was defective then this would be indicated by unpredicted events in the sky such as comets, novae, etc. After a change of ruler a new calendar was drawn up to make it public that there was a new ruler with new celestial influences.
Astronomy details on scapulae used for divination during the Shang Dynasty (1600-1046 BC) show that by 1400 BC the Chinese had achieved a calendar with mean lunar months of 29½ days by having alternating months of 29 and 30 days. Most years contained twelve months but extra, intercalary, months were added when appropriate. The nineteen-year Metonic cycle was discovered around the sixth century BC.
Throughout its history the Chinese calendar went through many changes that were all largely due to further discoveries associated with the various phenomena involved. During the Eastern Han Dynasty (AD 25-220), Jia Kui (30-101) discovered the inconsistent motion of the Moon; and during the Northern Qi Dynasty (550-577), Zhang Zixin (fl.520-60) found that solar motion was irregular.
Precession causes a difference of about twenty minutes between the measured lengths of the tropical year (i.e. w.r.t. the Sun) and the sidereal year (i.e. w.r.t. the stars). The first mention of the precession of the equinoxes in China is in c.320 during Eastern Jìn Dynasty (317-420) by Yu Xi (fl.c.307-338) with a measurement of about one degree in fifty years; but precession was first included in calendar calculations by Zu Chongzhi (429-501) during the Liu Song (420-479) and Southern Qi (420-479) dynasties.
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