Why does the lunar calendar have a leap month?
The purpose of setting a leap month in the lunar calendar is to reconcile the contradiction between the tropical year and the lunar year.What is the contradiction between the tropical year and the lunar year? Remember this: the total length of a tropical year is 365.2422 days, and the length of a synodic month is 29.5306 days.
Twelve synodic months make up a lunar year, which is 29.5306 × 12 = 354.3546 days, which is shorter than the tropical year by about 10.88 days, nearly 11 days, and each month is short by 0.91 days, nearly 1 day.
Accordingly, if the Spring Festival in a lunar year is in the winter with heavy snow, the next year's Spring Festival will be 11 days earlier in the season, and the 16th lunar year will appear in the summer with scorching sun.
If thirteen synodic months make up a lunar year, its length is 29.5306 × 13 = 383.8978 days, which is more than the tropical year by over 18 days.
If we make a calendar according to the above rules, there would be strange phenomena such as mismatch between the seasons and the calendar, and confusion in the sequence of time — this is the contradiction.
To overcome this defect, our ancestors found the method of "leap month" based on astronomical observations, ensuring that the first month of the lunar year is spring, the fourth to sixth months are summer, the seventh to ninth months are autumn, and the tenth to twelfth months are winter, while also ensuring that the beginning of the lunar year is at the end of winter and the beginning of spring.
The lunar calendar uses the length of a synodic month (29.5306 days) as the basis for the month, so a large month has 30 days and a small month has 29 days. To ensure that the first day of each month (the first day of the month) must be a new moon, the arrangement of large and small months is not fixed and requires strict observation and calculation. Therefore, it is common for two consecutive months to be large or small months, and even rare cases such as three and four months being small months and nine, ten, eleven, and twelve months being large months in 1990.
How often should a leap month be added? The best way is to find the least common multiple of the number of days in a tropical year and the number of days in a synodic month: we hope that the number of days in m tropical years is equal to the number of days in n synodic months, meaning that the equation should be:
m × 365.2422 = n × 29.5306
In this equation, we cannot directly find m and n, but we can find their ratio:
The approximate values of these fractions are:
In these fractions, the numerator represents the number of tropical years, and the denominator represents the number of synodic months. For example, the sixth fraction indicates that 7 leap months must be added in 19 tropical years.
The result of adding 7 leap months in 19 tropical years is:
19 tropical years = 19 × 365.2422 = 6939.6118 (days)
One synodic month has 29.5306 days, 235 synodic months = 235 × 29.5306 = 6939.6910 (days)
After adding 7 leap months in 19 tropical years, the difference is only 6939.6910 - 6939.6018 = 0.0892 (days) — approximately 2 hours and 9 minutes, which is already quite accurate.
Therefore, the lunar calendar adopts the method of adding 7 leap months in 19 years, known as the "19-year 7-leap-month method," effectively coordinating the tropical year and the lunar year, ensuring that the Lunar New Year (Spring Festival) always remains at the end of winter and the beginning of spring. The ancients called 235 synodic months "the leap cycle."
The method of setting a leap month allows the average length of the lunar year to approach the tropical year, and the lunar month has distinct characteristics of the moon phase, thus achieving the advantages of both the solar and lunar calendars.
The current method of setting a leap month is that if there are only 12 months between two winter solstices, no leap month is set; if there are 13 months, a leap month is set. The leap month starts from the "Winter Solstice." When the first month without a "mid-season" appears, that month is the leap month, and its name is prefixed with the character "leap" before the previous month's name.
Which month is the leap month in the lunar calendar?
It depends on the twenty-four solar terms in a year.In the Chinese lunar calendar, the twenty-four solar terms are divided into twelve terms and twelve mid-terms.
The lunar calendar is based on the moon's cycle (lunar calendar), and the total of twelve lunar months is about 354 days. It is combined with the solar calendar (solar calendar), which is based on the cycle formed by the Earth's revolution around the Sun, resulting in the four seasons. The lunar calendar is shorter than the solar calendar by about 11 days, so every 19 years, 7 leap months are added to compensate for the error. The determination of which month becomes a leap month is based on the twenty-four solar terms. Normally, each lunar month contains one term and one mid-term, such as Awakening of Insects / Autumn Equinox. If a lunar month contains only a term but no mid-term, the calendar adds an extra month as a leap month. For example, in 2006, the seventh lunar month happened to be a month containing a term but no mid-term, so a leap seventh month was added to adjust the error.
The dates of the twenty-four solar terms in the lunar calendar are gradually delayed each month, so some lunar months have mid-terms falling at the end of the month, and the next month has no mid-term.
Generally, there is a month without a mid-term every two years or so, which coincides with the need to add a leap month. Therefore, the lunar calendar stipulates that the month without a mid-term is the leap month.
Destiny, or fate and luck, refers to a pattern composed of fixed and variable elements. Fate and luck are two different concepts. Do you know your destiny? Click on the following excellent calculations to predict your destiny.
