Chinese calendar combines solar yearly cycle, lunar monthly cycle, and Stem-Branch daily cycle. The cycles of the Sun and the Moon never have a matching point. Ancient Chinese must adjust the calendar every one hundred years. It's very often that every Chinese emperor published a new calendar for the new nation.
Many historical books were burned during the first emperor of China in the Chin Dynasty (221 B.C.). There is no solid evidence of the first Chinese Lunar Calendar. But the Chinese calendar has a Stem-Branch counting system, which is a cycle of 60. The first king of China is the Yellow King . According to the historical document, Yellow King used the day of Winter Solstice as the first day of the year in the Rat month. The first Stem-Branch is Wooden Rat. Chinese trace back the Yellow King should found the nation in 2697 B.C.
We have about 365 days a year. A new moon to another new moon takes about 29.5 days. 12 lunar months takes 29.5 X 12 = 354 days. The cycle of Moon is off the cycle of Sun 11 days a year. After three years, the cycle of the Moon has an extra 33 days. The lunar calendar needs to add an extra lunar month to match up the cycle of the Sun. The history of the Chinese Lunar Calendar focused on how to add that lunar leap month into the calendar.
Dynasty (2205 B.C.) used the Tiger month as
the first month of the year
Chou Dynasty (1122 B.C.) used the Rat (Winter Solstice) month as the first month of the year
Yin Dynasty (1401 B.C.) used the Cow month as the first month of the year
Chin Dynasty (221 B.C.) used the Pig month as the first month of the year
Han (104 B.C.) Dynasty used the Tiger month as the first month of the year
8-22 (A.D.) used the Cow month as the first month of the year for a short period
In order to find out the good solution for the Lunar Leap month, ancient Chinese astronomers had been looking for the common cycle of Sun and Moon. They studied the length of lunar and solar months, the length of a day and year, the number of lunar months in a year and so on, then made many changes in the calendar system. For example, in the Yin Dynasty (1401 B.C.), the Chinese calendar determined a Leap Month by a lunar month without a Sector Point instead of a Center Point. The major changes in the Chinese calendar reform history were the definition of the beginning time of a lunar month and a solar month.
Before 619 A.D., the Chinese used Mean Moon times and Mean Sun times to determine the Leap Months over one thousand years long.
After 619, during the Tang Dynasty, the Chinese used True Moon times and Mean Sun times to assign the Leap Months for about another one thousand years. That means the new moon time is much easier to observe than the sun longitude position in the sky.
the Ching Dynasty, the Chinese used
True Moon times and True Sun times to find the Leap Month locations. That's because the Ching Dynasty imported modern astronomical instruments and had the ability to observe precise the Sun and Moon positions in the sky during years.
The Mean Moon time is the length of a lunar month is the average length of lunar months a year.
The True Moon time is the length of a lunar month is the length between two new moons.
The Mean Sun time is the length of a solar month is the average length of solar months in a year.
The True Moon time is the length of a lunar month is the length between two solar Sector Points.
After the Ching Dynasty, China government began to use the Gregorian Calendar instead of the lunar month for daily activities.
Many ancient Chinese astronomers in different dynasties kept trying to calculate back and searching for the beginning of the Chinese calendar cycle. The theoretic day of the starting point of Chinese Calendar is that the day must be
They all failed to get a satisfying answer.