Explain the "leap year" and "leap month" clearly in one breath

In the previous two issues, we have introduced in detail the causes of the solar, lunar, lunar calendars and other calendars, and in this issue we have focused on a knowledge point that is easy to confuse in the calendar: "leap years" and "leap months". (Some of the data and terminology in this article can be found in my previous articles))

In fact, there are only two "leap" characters involved in the calendar we say every day, namely the solar calendar "leap year" and the lunar calendar "leap month", but through the introduction of the previous issue, we found that there is actually a "leap year", which appears in the Islamic calendar. So how exactly do you differentiate between them?

The historical origin of the "leap year" of the solar calendar (the difference between 365 days and 366 days):

We know that the exact time for the earth to circle the sun is actually 5 hours, 48 minutes and 46 seconds more than the 1 year and 365 days of the solar calendar, so that every 4 years there will be 23 hours and 15 minutes and 4 seconds, which is about equal to 1 day, in order to keep the artificially prescribed solar year and the actual solar year consistent, so every 4 years to add 1 day in the solar calendar year, so that the year of the increase has 366 days, which is called "leap year". However, it has also been found that according to the method of "four years and one leap", after each 4 years of increase of 1 day, the actual increase is 44 minutes and 56 seconds, so that every 400 years, the solar calendar year will be 3 days longer than the total solar year, so people should continue to be consistent with the solar year, so in 400 years, 3 days should be removed, that is, 3 fewer leaps. But which month should this day of the leap year be placed? For historical reasons (see my earlier article for details), the Romans had only 28 days in February, so they put this day of leap years in February, so February of leap years is 29 days.

Solar calendar "leap year" calculation method:

The year is a multiple of 4, not a multiple of 100, and is an ordinary leap year; the year is a full hundred, and must be a multiple of 400 to be a leap year.

To sum it up, it is one sentence: "Four years a leap, a hundred years without a leap, four hundred years again." "In this way, every 400 years, what used to be 100 leap years can now be reduced by 3 times, for a total of 97 leap years. After remedying this method, the average length of the Gregorian calendar year is only 26 seconds away from the solar year, and every 3300 years, it is only one day, just reduce it by one leap year in 3300 years.

The historical origin of the "leap month" in the lunar calendar (the difference between 354 days and 384 days):

We know that the Moon takes about 11 days less to orbit the Earth 12 times than the Earth to orbit the Sun, so that every 3 years or so, the lunar calendar will be 1 month less than the Solar calendar. In order to balance the total length of the lunar calendar and the total duration of the solar calendar and facilitate people's daily use, people came up with a method of adding 1 "leap month", the purpose of which is to make the average number of days in the lunar calendar and the number of days in the solar calendar match. The years are divided into common and leap years, with a common year of 12 months and a leap year of 13 months. Now I understand why people often say, "This year is so long!" Sighed it.

The calculation method of "leap month" in the lunar calendar:

The average time it takes for the Moon to orbit the Earth is about 29.5 days, so the number of days in each month is uncertain, and the number of days each year is different. The current calendar stipulates that the New Year must be the first day of the lunar calendar, as long as the first day of each month is found, then the interval between the two first days can determine the size of the month. The average cycle of the synodic month is 29.5 days, and if this month starts from the new moon and starts with the new moon next month, less than 30 days, then it is counted as 29 days of the small month; if it exceeds 30 days, it is counted as the 30 days of the large month. In order to ensure that the first day of the lunar month (the first day of the first month) must be a new day, so that the arrangement of large and small months is not fixed, but need to be determined through strict observation and calculation, so it is common for the lunar calendar to be two consecutive months of large or small months.

Because the lunar calendar also has to maintain balance with the solar calendar, so every few years to add a leap month, the specific increase of the leap month is not fixed, need to consider from the season season and other aspects, the current use of 19 years 7 leap method: in the 19 years of the lunar calendar, stipulated 12 common years, every 1 flat year 12 months; there are 7 leap years, every 1 leap year 13 months, so that after adding 7 leap months in 19 solar years, the contradiction is eliminated only: 6939.6910-6939.6018 = 0.0892 (days), the error is only more than 2 hours and 9 minutes, put into the long river of history, this is already very accurate.

The specific lunar month in which the leap month will be added, the current calendar is based on the twenty-four solar terms. China's lunar calendar divides the twenty-four solar terms into twelve solar terms and twelve middle qi. Lunar months usually contain a solar term and a mid-term, and if a lunar month has only solar terms and no mid-term, the calendar adds an extra month to the month as a leap month. The date of the twenty-four solar terms in the lunar calendar is postponed month by month, so that in some lunar months, the middle qi falls at the end of the month, and the next month there is no middle gas. Generally, there is a month without a mid-breath every two years, which coincides with the year when a leap month is needed. Therefore, the lunar calendar stipulates that the month without neutral qi is called a leap month.

Twenty-four solar terms (the Earth orbits the Sun exactly 360 degrees)

In order to facilitate the use of the lunar calendar, many scholars have calculated in advance and released the well-known "perpetual calendar". The perpetual calendar is not really 10,000 years old, it is just a general term.

Origin of the "leap year" in the Islamic calendar (the difference between 354 and 355 days):

We know that the exact time it takes for the Moon to orbit the Earth is actually 8 hours, 48 minutes, and 33.6 seconds more than the 1 year, 354 days in the Islamic calendar, so that over time, if it is not adjusted, the gap between the islamic calendar and the exact time of the Moon around the Earth will become larger and larger. Therefore, in order to maintain balance, the Islamic calendar is also solved by setting up "leap years": 30 years as a cycle, the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th, 29th year of each cycle, a total of 11 years as leap years, plus 1 leap day at the end of December of each leap year, 355 days of leap years, and 19 years as a common year, 354 days of each year. Through 30 years of data statistics, we can calculate that the total length of the Islamic calendar and the moon's 30 years around the earth is basically the same, about 10361 days.

Through this issue, do you have a grasp of the knowledge of "leap year" and "leap month"? We welcome your valuable comments! Thank you!

For more information about the solar and lunar calendars, please click on the following links:

Finally, someone clearly explained the "solar calendar" year, month, and day at once

After reading it, you can thoroughly understand the knowledge points of "lunar calendar" and "lunar calendar"