The Theory of the Chinese Lunar Calendar
The Chinese calendar combines the lunar and solar systems together. The Year and Day cycles use the solar system. However, there are two different Month cycles in the Chinese calendar. One uses the lunar system and the other uses the solar system. In the lunar system of Month, the new moon day is the first day of a lunar month. The length of a lunar month is the length of time between two new moon days. The name of a lunar Month is taken from the solar system. The Chinese solar months are not like the months of a modern calendar. The Chinese calendar divides the year into 24 solar segments according to the sun positions on the tropical zodiac (Similar to western astrology). Each segment's name was given for ancient Chinese farmers' use. To understand the whole picture view the following chart.
|Start of Spring||315||1 - Tiger||Aquarius|
|Excited Insects||345||2 - Rabbit|
|Clear and Bright||15||3 - Dragon|
|Start of Summer||45||4 - Snake|
|Grain in Ear||75||5 - Horse|
|Slight Heat||105||6 - Sheep|
|Start of Autumn||135||7 - Monkey|
|White Dew||165||8 - Chicken|
|Cold Dew||195||9 - Dog|
|Start of Winter||225||10 - Pig|
|Heavy Snow||255||11 - Rat|
|Little Cold||285||12 - Cow|
The solar months are defined by the sun longitudes. The first month, Tiger month, begins from the Start of Spring segment or when the sun enters the 315th degree on the tropical zodiac. The second month, Rabbit month, begins from the Excited Insects segment or when the sun enters 345th degree. The beginning of a solar month is called the Segment Point. In the middle of a solar month is called the Center Point. For example, the segments of Rain Water and Vernal Equinox are Center Points. The astrology names of Pisces and Aries apply to these Center Points.
The lunar month name is derived from the Solar Center Point. For example, If a lunar month contains the Rain Water Center Point, then it is the first month of the lunar calendar, as known as the Tiger month.
If a lunar month does not contain any Solar Center Point, that month is known as a Leap Month. The name of this leap month is the same as previous lunar month. The reason to assign leap months is that we want the moon cycle to harmonize with the sun cycle. Because one year has about 365.2425 days and one month has about 29.53 days, one year has about 12.3685 months. 12.3685 is about 12 and 7/19. If we put seven extra months in 19 years, sun and moon should be back to the same sky position. "Seven Leap Months in 19 years" is easy for people to remember. However, 12.3685 is almost equal to 12 and 144/391. That means "144 Leap months in 391 years" is a more accurate way to assign Leap months. So far, no one has lived long enough to observe the entire cycle.
In the Chinese Lunar Calendar, the new moon day is the first day of a lunar month and the length of a lunar month is the length between two new moon days. In the Chinese Fortune-Telling (Astrology) Calendar, the first day of a month is the day on a Solar Segment Point and the length of a month is the length between two Solar Segment Points. Therefore there is no Leap Month in the Chinese Fortune-Telling System.
Without this knowledge, above-mentioned, most people will be confused about the solar months and lunar months. They may think all Chinese Fortune-Telling system use lunar months. Actually, the Fortune-Telling system called Eight Characters only uses the solar month, not the lunar month. The other popular system called Dipper uses solar month and lunar month together.
The counting system of Day is the Stem-Branch 60-day cycle system. No one knows who invented the Stem-Branch for Day counting system, but legend has it that characters of Day Stem-Branch were found on Oracle bones. The Animal names of Stem-Branch were applied into the Month system around 206 B.C. (between the Chin and Han dynasties). The Stem-Branch was applied into the Year system around 164 B.C..
Almost every Chinese dynasty had its own calendar. One reason was that the new emperor needed to announce the new rules including the new calendar to the public. The other reason was that the astronomer's officers had to make some adjustments on the calendar in order to match the sun and moon in the sky.
The first day of a year has been changed many times in Chinese calendars. The current Chinese calendar uses the first day of the first month of Tiger month as the first day of a year, which was initially adopted by the Shiah dynasty (2183-1752 B.C.). Today, some people consider the Winter Solstice as the first day of a year in the Chinese Fortune-Telling System, because that makes more sense from the astronomy view.
The Chinese Lunar Calendar system is not perfect, because the length of solar month is not always greater than the length of a lunar month. As a result, a lunar month might contain two solar Center Points. Those months are found in the winter of 1548, 1680, 1700, 1719, 2053, 2072 and so on. This imperfection causes the trouble in the assignments of the Chinese Lunar Leap Month. That's why there is no simple formula for Chinese Lunar Calendar conversion.
Because this imperfection, we need to add a new rule to adjust the Chinese Calendar system.