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The Theory of Chinese Lunar Calendar

How does the Chinese Lunar Calendar work?

Many people wonder how the Chinese Lunar Calendar works. Is there any mathematical or astronomical formula to convert the Gregorian calendar to the Chinese lunar calendar? The following explanation of the theory of the Chinese Lunar Calendar can answer these questions.

The Chinese calendar combines the lunar and solar systems. 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 節氣 according to the sun's 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.

The first month of the year is Tiger month. The first day of Tiger Month is the Start of Spring, which is around February 4 each year.

立春 Start of Spring 315 1 - 虎 Tiger Aquarius
雨水 The Rains 330 Pisces
驚蟄 Excited Insects 345 2 - 兔 Rabbit
春分 Vernal Equinox 0 Aries
清明 Clear and Bright 15 3 - 龍 Dragon
穀雨 Grain Rains 30 Taurus
立夏 Start of Summer 45 4 - 蛇 Snake
小滿 Grain Fills 60 Gemini
芒種 Grain in Ear 75 5 - 馬 Horse
夏至 Summer solstice 90 Cancer
小暑 Slight Heat 105 6 - 羊 Goat
大暑 Great Heat 120 Leo
立秋 Start of Autumn 135 7 - 猴 Monkey
處暑 Still Hot 150 Virgo
白露 White Dew 165 8 - 雞 Rooster
秋分 Autumnal Equinox 180 Libra
寒露 Cold Dew 195 9 - 狗 Dog
霜降 Frost Descends 210 Scorpio
立冬 Start of Winter 225 10 - 豬 Pig
小雪 Light Snow 240 Sagittarius
大雪 Heavy Snow 25511 - 鼠 Rat
冬至 Winter Solstice 270 Capricorn
小寒 Little Cold 285 12 - 牛 Ox
大寒 Severe Cold 300 Aquarius

The solar months are defined by the sun's longitudes. The first month, Tiger Month, begins at 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 the 345th degree. The beginning of a solar month is called the 節氣 Segment Point. The middle point of a solar month is called the 中氣 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 name of the lunar month 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, also known as the Tiger month.

How does the Chinese Lunar Leap Month work?

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 the 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, the 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.

Anyway, the principles of the Chinese Calendar use the following four rules which the ancient Chinese made them thousand of years ago.

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 systems use lunar months. Actually, the Fortune-Telling system called 八字 Eight Characters only uses the solar month, not the lunar month. The other popular system called 紫微斗數 Dipper uses solar month and lunar month together.

Stem-Branch is the Chinese calendar counting system

The counting system of Day is the 干支 Stem-Branch 60-day cycle system. No one knows who invented the Stem-Branch for the 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 秦 Chin and 漢 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 夏 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.

Leap Month Problems in the Chinese Lunar Calendar

The Chinese Lunar Calendar system is not perfect, because the length of a 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 trouble in the assignments of the Chinese Lunar Leap Month. That's why there is no simple formula for Chinese Lunar Calendar conversion.

Because of this imperfection, we need to add a new rule to adjust the Chinese Calendar system.

Chinese Calendar 2023

By Master Allen Tsai on February 4, 2023

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