Zi

Zi is the first of the twelve Earthly Branches (dizhi), the cyclical signs that combine with the ten Heavenly Stems to form the sexagenary cycle of sixty. Its zodiac animal is the Rat, its element is Water, its direction is due north, and its double-hour runs from 11 pm to 1 am, the hour of midnight, when one day turns to the next. As the first branch, Zi opens the cycle of the twelve, and the year, month, day, and hour it names carry the Rat's associations in the almanac. The branches order the twelve-year animal cycle, the twelve months, and the twelve double-hours of the day. These are the conventions of the Chinese calendrical and cosmological tradition; the twelve branches, paired with the ten stems, recombine only after sixty steps, giving the great cycle its length.

Zi is the first of the twelve Earthly Branches (Dizhi), attested alongside the Heavenly Stems on Shang-dynasty oracle bones, and it corresponds to the Rat in the twelve-animal cycle used to name years, and, in the traditional Chinese double-hour system, to the two hours around midnight, 11 pm to 1 am, when the day is reckoned to turn over. Through the theory of hidden stems, by which each branch is said to harbour one or more of the ten Heavenly Stems within it and so carry its own elemental association, Zi's primary hidden stem is Gui, giving it the Water phase; it is also assigned the north as a fixed direction. Zi pairs with the ten stems within the sixty-term sexagenary cycle, so a Zi year always falls with a Yang-polarity stem, Jia, Bing, Wu, Geng or Ren, never with a Yin one.

Beyond the animal it carries, a branch enters three fixed sets of relations that the almanac and the fate-calculation tradition use constantly. Zi belongs to the trio Shen, Zi and Chen, one of the four groups of three branches spaced four apart which are read as combining into Water. It clashes with Wu, the branch six places away, and it forms one of the six harmonies with Chou. These relations are properties of position in the twelve, not of the animal.

The branches also do more work than the year cycle they are best known for. They divide the day into twelve double hours, so Zi names a period of two hours as well as a year and a month; they mark the twelve directions of the compass, Zi standing at north; and they carry the twelve stations against which the movement of Jupiter was tracked, which is one proposed origin for the twelve-year cycle itself.

The stem-and-branch day count is the longest continuously running day count known. Numbering days by ganzhi begins in the Shang inscriptions and has run without acknowledged interruption since, through every dynastic change and every calendar reform, because the cycle of sixty is independent of any astronomical quantity and therefore needs no correction. Chinese historical dates from the classical period onward can be checked against it.

Zi holds the midnight double hour, when one day gives way to the next, and it is the branch on which the sexagenary day count turns. In the twelve-month assignment used since the Han, the branches begin at Yin rather than at Zi, so Zi names the eleventh month, the one containing the winter solstice, and its position at the head of the branch list and in the middle of winter are two different orderings that a reader has to keep apart.

Sources Chinese Mathematical Astrology: Reaching Out to the StarsHo Peng Yoke with The Chinese Sexagenary Cycle and the Ritual Origins of the CalendarAdam Smith