The most significant and outstanding counting system in the Chinese Calendar is the Heavenly Stem and Earthly Branch. There are 10 Stems and 12 Branches. The Stem and the Branch are used together. The Stem is used in front of (on top of) the Branch. The Chinese call them Heavenly Stem and Earthly Branch and use a specific sequence as a counting system for the calendar.
10 Stems and 12 Branches are combined into a cycle of 60 counting systems which begin fromWooden Rat and end with Water Pig. 1999 is the year of the Brown Rabbit which is the 16th of the Stem-Branch system. Year 2000 is the White (Golden) Dragon.
Nobody knows who invented the Stem-Branch counting system. This means that the Chinese knew about Stem-Branch before the invention of Chinese characters. Today we can see the Stem-Branch symbols in the ancient Chinese oracle bones. At the beginning, Stem-Branch was for counting the DAY only. Later, the Yin-Yang Five-Element scholars applied Stem-Branch into a MONTH, YEAR and HOUR system. The Five-Element scholars also applied Stem-Branch to the Five Elements which are the foundation of Chinese Fortune-Telling systems.
When Yin-Yang applies to the numbers, the odd numbers (1,3,5...) are in the Yin group and the even numbers (2,4,6...) are in the Ying group. Yang implies male and Yin implies female. From the sequence order of Stem-Branch, we know the Rat, Tiger, Dragon, Horse, Monkey, and Dog are Yang or male and Cow, Rabbit, Snake, Sheep, Chicken (Hen) and Pig are Yin or female. Therefore. there is no Ox, Bull, Goat or Rooster in this animal list.
Also in the counting system, a Yang Stem must match a Yang Branch and a Yin Stem must match a Yin Branch. That's why the Wooden Rat means Male Wooden Rat. There is no female Wooden Rat in the calendar.