Dragon and Rooster compatibility
Dragon (Chen, 辰) and Rooster (You, 酉): a six harmony (Liu He, 六合).
These are fixed relations among the twelve branches of the Chinese calendar, set out in the classic San Ming Tong Hui (三命通会), written in 1578, quoted below. They describe the signs, not two people: no classic gives a method for matching two people by their signs, so there is no score here.
What the book says
Six harmony (Liu He, 六合)
The six harmonies pair each yang sign with a yin one. Dragon and Rooster are one of the six pairs. The book’s explanation is in numbers: each sign has a place in the count of yin and yang, and a pair adds up to three or nine.
A harmony is a joining: yin and yang in accord, so that their qi joins of itself.
夫合者，和也，乃阴阳相和，其气自合。
Rat, Tiger, Dragon, Horse, Monkey and Dog are the six yang; Ox, Rabbit, Snake, Goat, Rooster and Pig the six yin. So one yin and one yang in accord are called a harmony.
子寅辰午申戌六者为阳，丑卯已未酉亥六者为阴，是以一阴一阳和而谓之合。
The Dragon is the fifth yang and the Rooster the fourth yin: five and four make nine.
辰为五阳，酉为四阴，五四得九数
Rat and Ox, Horse and Goat each make three, and three gives birth to all things. The rest all make nine, the highest of the yang numbers.
子丑午未各得三者，三生万物，余皆得九者，乃阳数极也。
San Ming Tong Hui, volume 2: On the six harmonies of the branches (论支元六合) · source text
The book also quotes an older work, the Tian Yuan Bian Hua Shu (天元变化书), which gives the pair a line each way round:
Dragon joining Rooster: the blessing is weak. Rooster joining Dragon: great profit.
辰合酉福弱，酉合辰大利
San Ming Tong Hui, volume 2: On the six harmonies of the branches (论支元六合) · source text
On what a harmony brings to a chart:
Wherever a six harmony or a three harmony enters a chart, it means a person of fine looks and settled spirit, who loves life and hates killing, straight of heart, easy to deal with, bright and quick to understand.
凡六合三合入命，主人形容姿美，神气安定，好生恶死，心地平直，周旋方便，聪慧疏通。
Broadly: a harmony with good stars is good, and a harmony with bad ones is bad.
大率合吉神则吉，合凶神则凶。
San Ming Tong Hui, volume 2: On the three harmonies of the branches (论支元三合) · source text
Their elements
The Dragon is Earth and the Rooster is Metal: Earth feeds Metal.
How much it counts
A sign is one character of the eight in a BaZi chart, the year’s branch. The book reads these relations between the pillars of one chart, and tells the reader to look at the whole chart’s elements first:
Clash and break, three harmony and six harmony: where a chart has them, ask next how its five elements get on. Misfortune may give rise to blessing, and blessing to misfortune.
相冲相破，三合六合，命中有之，即求五行相得何如。或祸中生福，福中生祸
San Ming Tong Hui, volume 3: On the symbolic stars as a whole (总论诸神煞) · source text
Birth years, and 2027
- Dragon: 1928, 1940, 1952, 1964, 1976, 1988, 2000, 2012, 2024. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Dragon has no clash with the year.
- Rooster: 1933, 1945, 1957, 1969, 1981, 1993, 2005, 2017. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Rooster has no clash with the year.
A sign’s year is usually counted from Chinese New Year, between late January and mid-February; BaZi counts it from the Start of Spring, about 4 February. Born in January or early February? You may be the sign before: the sign pages check your date.
Two real people?
Each person’s chart has eight characters, and the same relations run between all of them, not only the two signs. The two-chart page sets both charts side by side, branch by branch, and gives what each chart says about marriage on its own. No score there either.
Dragon with the other signs: Rat · Ox · Tiger · Rabbit · Dragon · Snake · Horse · Goat · Monkey · Dog · Pig.
Rooster with the other signs: Rat · Ox · Tiger · Rabbit · Snake · Horse · Goat · Monkey · Rooster · Dog · Pig.