Why does the lunar calendar sometimes have 13 months?

I found this from Baidu. I don't know if it will help you.

The calendar year of the lunar calendar is based on the tropic year, but a tropic year is more than 12 months and less than 13 months. When ancient astronomers compiled the lunar calendar, in order to make any day in a month contain the meaning of the moon phase, that is, the first day is moonless night and the fifteenth day is full moon, with the moon as the main factor, taking into account the seasons. There are seven leap years and each leap year has thirteen months.

Why adopt the method of "seven leaps in nineteen years"? The average lunar month is 29.5306 days, and there are 12.368 lunar months in a tropical year. The progressive scores of the fractional part of 0.368 are 1/2, 1/3, 3/8, 4/1,7/68. Because 19 tropical year = 6939. 18 days, and 19 lunar year (after seven leap months) * * has 235 moons, which is equal to 6939.438+00 days, so the two are almost the same.

In addition, "the seventh leap in nineteen years" is only a general statement. In fact, astronomers in the Spring and Autumn Period pioneered the method of seven jumps in nineteen years. Zu Chongzhi Daming Calendar adopts 20 groups of 65438+7 leap years in 2009 1 group1leap 4 years, accounting for 39 1 leap 144 years, which makes the average calendar year of the lunar calendar closer to the tropic year. In addition, there were 123 leap and 102 1 376 leap in 334, and the difference between them was even smaller. However, since the Qing Dynasty, China has completely adopted astronomical phenomena to determine the calendar year and calendar month, so that the average calendar year of the lunar calendar is exactly the same as the tropic year.

There are seven leap months in nineteen years, and the placement method is very particular. The setting of the lunar leap month is completely artificial from ancient times to the present, and the setting of leap months in past dynasties is different. Before the Qin Dynasty, the leap month was placed at the end of a year and was called "March". The leap month in the early Han dynasty was placed after September, which was called "post-September". In the first year of Emperor Wu of the Han Dynasty, leap months were inserted in every month of the year. Later, it was stipulated that "the month without neutral gas was the leap month of the previous month", which is still in use today.

Why are there no gas in some months? The average interval between solar terms and solar terms or neutral gas and neutral gas is 30.4368 days (that is, the 365.2422 days in the tropic year are divided into 12 equal parts), while the average interval in a lunar month is 29.5306 days, so the date of solar terms or neutral gas in the lunar month is postponed month by month. At a certain time, the neutral gas is not in the middle of the month, but moves to the end of the month, and the next neutral gas moves to the beginning of the next month.

As mentioned earlier, when the ancients compiled the lunar calendar, they took twelve China Qi as the symbol of twelve months, that is, the rain was the symbol of the first month, the vernal equinox was the symbol of February, and Grain Rain was the symbol of March ... The month without China Qi was regarded as a leap month, which made the calendar name correspond to China Qi one by one, thus maintaining the original symbol of China Qi.

From the seventh leap of 19, the tropic year of 19 has 228 solar terms and 228 neutral qi, while the lunar calendar 19 has 235 new months. Obviously, there are seven months without solar terms and seven months without neutral atmosphere, so it is logical to designate the months without neutral atmosphere as leap months.

The size of the lunar month is very irregular, sometimes two, three, four big months or two three small months are connected together, and the length of the calendar year varies greatly. The distribution dates of solar terms and gas in the lunar calendar are very unstable and vary greatly. In this way, the lunar calendar seems very complicated. In fact, the lunar calendar still has a certain cyclical law: because the number of days in the 19 tropic year is almost equal to that in the 19 lunar year, every 19 lunar year is almost the same. Every nineteen years, the Gregorian calendar days on the first day of each month in the same month of the lunar calendar are generally the same or one or two days apart. Every nineteen years, solar terms and neutral dates generally repeat, with individual differences of one or two days. The months separated by 19 leap month are repeated or differ by one month.