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One of the two methods that they used to make this calendar was to add an extra month of 29 or 30 days, which they termed the 13th month, to the end of a regular 12-month year. There is also evidence that suggests that the Chinese developed the Metonic cycle (see above Complex cycles) -- i.e., 19 years with a total of 235 months--a century ahead of Meton's first calculation (no later than the Spring and Autumn period, 770-476 BC). During this cycle of 19 years there were seven intercalations of months. The other method, which was abandoned soon after the Shang started to adopt it, was to insert an extra month between any two months of a regular year. Possibly, a lack of astronomical and arithmetical knowledge allowed them to do this. By the 3rd century BC, the first method of intercalation was gradually falling into disfavour, while the establishment of the meteorological cycle, the erh-shih-ssu chieh-ch'i (Pinyin ershisi jieqi), during this period officially revised the second method. This meteorological cycle contained 24 points, each beginning one of the periods named consecutively the Spring Begins, the Rain Water, the Excited Insects, the Vernal Equinox, the Clear and Bright, the Grain Rains, the Summer Begins, the Grain Fills, the Grain in Ear, the Summer Solstice, the Slight Heat, the Great Heat, the Autumn Begins, the Limit of Heat, the White Dew, the Autumn Equinox, the Cold Dew, the Hoar Frost Descends, the Winter Begins, the Little Snow, the Heavy Snow, the Winter Solstice, the Little Cold, and the Severe Cold. The establishment of this cycle required a fair amount of astronomical understanding of the Earth as a celestial body, and without elaborate equipment it is impossible to collect the necessary information. Modern scholars acknowledge the superiority of pre-Sung Chinese astronomy (at least until about the 13th century AD) over that of other, contemporary nations. The 24 points within the meteorological cycle coincide with points 15º apart on the ecliptic (the plane of the Earth's yearly journey around the Sun or, if it is thought that the Sun turns around the Earth, the apparent journey of the Sun against the stars). It takes about 15.2 days for the Sun to travel from one of these points to another (because the ecliptic is a complete circle of 360º), and the Sun needs 365 1/4 days to finish its journey in this cycle. Supposedly, each of the 12 months of the year contains two points, but, because a lunar month has only 29 1/2 days and the two points share about 30.4 days, there is always the chance that a lunar month will fail to contain both points, though the distance between any two given points is only 15º. If such an occasion occurs, the intercalation of an extra month takes place. For instance, one may find a year with two "Julys" or with two "Augusts" in the Chinese calendar. In fact, the exact length of the month in the Chinese calendar is either 30 days or 29 days--a phenomenon which reflects its lunar origin. Also, the meteorological cycle means essentially a solar year. The Chinese thus consider their calendar as yin-yang li, or a "lunar-solar calendar."
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