Beyond the animal it carries, a branch enters three fixed sets of relations that the almanac and the fate-calculation tradition use constantly. Mao belongs to the trio Hai, Mao and Wei, one of the four groups of three branches spaced four apart which are read as combining into Wood. It clashes with You, the branch six places away, and it forms one of the six harmonies with Xu. 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 Mao names a period of two hours as well as a year and a month; they mark the twelve directions of the compass, Mao standing at east; 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.
Mao is one of the four cardinal branches, standing due east with Zi at north, Wu at south and You at west, and these four are treated in the fate-calculation tradition as the strongest expressions of their phases, since each falls at the middle month of a season, the month containing an equinox or a solstice, rather than at a seasonal transition.
Sources Chinese Mathematical Astrology: Reaching Out to the StarsHo Peng Yoke with The Chinese Sexagenary Cycle and the Ritual Origins of the CalendarAdam Smith