The basis of the promotion steps in the quarterly calendar and the technical description of Chapter A of the calendar.

The lunar calendar actually consists of three parts: the lunar calendar, the solar calendar and the leap. Leap is used to ensure that the lunar calendar and the solar calendar basically correspond. For example, a tropical year is 365.25 days, a new moon is 29.53 days, and 65438+ February only gets 354.37 days, which is about 10 days less than the tropical year, and three years are worse than January, so leap months are added.

Basic data of calendar: the actual years are 365 and 1/4 days, and the New Year is 29 and 499/940 days. Among them, 940 is called (Shuodan) Japanese law.

All calendars are measured, and how to set leap is calculated according to their data.

The calendar starts from a certain era, assuming that the sun and the moon meet at that moment, which happens to be midnight on Jiazi Day, and the sun is in winter to day, which is called "November Jiazi's winter to day night", that is, November Jiazi, midnight, Shuodan and winter to day are equal.

Starting from the calendar year, the integer part of a day is the remainder of 60 Jiazi, which is called (Shuodan) Dayu, and the remainder corresponds to the serial number of Jiazi table, which is the main branch of a day. The decimal part is converted into a fraction with the day as the denominator, and the numerator is called the remainder. At that time, all the big and small surpluses were zero, so it was called "no big surplus, no small surplus".

To ask for the size of any year, month and day, first ask for the date of winter solstice in that year, which is called "the day is the new moon"

For example, it took 12 months from the first year of the Gregorian calendar year to the first month of the second year. 354 and 348/940 days. 54 is a big surplus and 348 is a small surplus. Similarly, the second year is 696/940 days away from 708, so "Dayu 48, Xiaoyu 696". But in the third year, because of the leap, the actual distance from the Great Era has passed 37 months, so "Dayu 12, Xiaoyu 603" (37 * (29+499/940) =1092 and 603/940).

But in order to find the surplus in any year, we must first know where to start. Take the leap surplus method as an example:

The 29th and 499/940 of the first lunar month, that is, 27759/940, are the same as the previous year, that is, 27759/4 in 235, which is exactly 19. At this time, the winter solstice and Shuodan appeared at the same time (Shuodan winter solstice). That is, 6939.75 days is a leap period, that is, 19 years, that is, there are 7 leaps in total, which was called chapter in ancient times. In this way, taking July of 19 as a leap, we know that there is a leap every July/19, and the year of 1 month is a leap. That is, to find the surplus of any year, first find the leap number. If the distance is 50 years, leap is 350/65438+September, and leap is 18 times. So the calendar is June1August, in which 18250+62/940 days, so "Dayu 10, Xiaoyu 62".

The number of days in the whole chapter is still 0.75, and it's not midnight yet. If you want to get the winter solstice at midnight, you need to read 4 chapters. Every year is 76 years, 27,759 days, which was called a day in ancient times.

If the number of days is full, you still can't tell 60 jiazi. The least common multiple of the remaining 39 and 60 is 780, which is 20 times of 60, and every 20 years is 1520 years. 1520 years later, Jiazi will be recovered every day, and the winter solstice will be held at midnight. Up to now, the calendar is almost complete, but the trunk and branches of the calendar year are different from those of the era. 1520 is divided by 60 jiazi, and the rest is 20, thus eliminating the Three Dynasties (each called Heaven and Earth Man). Then take 4560 as one yuan, and the calendar is ready here.

(The number of years of the Zhangbi era starts from 1. For example, the first year of a calendar year is the first year of Chapter 1, and 50 years from the calendar year is 13 years of Chapter 3. )

Any year is just a new moon. To find the size of the new moon in any January of that year, we just need to add new strategies. For example, in the third chapter, the son of 13 is in August, which is calculated before, Daying 10, Xiaoying 62. For 10 and 62/940 days, add 7*27759/940 days to get 128 and 178/940, then the remainder is 36 and the remainder is 735.

However, if there is a leap year in that year, we must first know what month the leap year is. For example, the remaining days in the following year are 357/ 19 months (that is, 15/ 19 months), and any month ≥ 12/ 19 months should be set as leap. Because this year's July/65438+September is full of 1 month, leap is only expressed by the molecule 15), so we know that there is leap this year. If the leap is before August, you need to add 1 month; if the leap is after June, you don't need to add 1 month.

Where there are 7 leap months in 228 months, there are 7/228 leap months every month. The day of the year is 1 5/1September, and the leap in August is 7*7/228, which is 229/228, that is,1full moon, and the leap is in July. Then it will take 8 months from that day to the end of August, so first find that the balance of that day is 4 and the balance is 4 10. Add 8*27759/940 to get 240 and 642/940, that is, in August of that year, the surplus was 0 and the surplus was 642.

1. Find the first year: from the last yuan, take 4,560 yuan as a big cycle, and the daily surplus of the main branch is the same in this cycle, so find the surplus of 4,560 yuan.

2. Seek the current year: from the head of state, take 76 years as a short cycle, and the surplus is the same every day in this cycle. Therefore, finding the remainder of 76 is transformed into solving the problem in one year, finding the main branch and adding the first branch.

3. Seek leap profit: if leap is 7 in 19, leap is 7/ 19 every year, and before leap is 1. The remainder of the leap is numerator 7, and the leap is set to 12 years.

Monthly leap: use 19 to leap July 7, 235, and then leap July /235 every month. The remainder of the leap is numerator 7, and the leap is set at the time of the moon 228.

4. integration date: that is, the number of years (that is, the year has been converted into one year) multiplied by the number of days in a year 365 and 1/4.

5. Find the remainder: that is, the integer day is the remainder of 60, the integer part is the remainder, and the decimal part is the remainder. Number, with numerator as remainder).

Dayu: From the first time, it was Dayu who earned more than 60 yuan a day.

Xiaoyu: The accumulated day is converted into a false fraction with 940 as the denominator, and the numerator takes the remainder of 940, which is Xiaoyu.

6. Seek dry expenditure: increase the surplus with the first dry expenditure, or seek the surplus from the accumulated days in the first year.

Calendar stepping can basically be written in the form of congruence. If the year you want is year, then:

When calculating, the first year and year of entry start from 0, and when it is expressed, it starts from 1, so the results are added with 1 respectively (it is not substituted into the formula for calculation, but only used as an expression).

The calendar of four seasons in the pre-Qin period has its own era, namely:

Zhou Li, Shangdingyuansi: The Short Distance Era:-1624.

Li Yin, Shangyuan Jiayin: Short-distance Calendar:-1567

Lu Li, Shang Yuan Geng Zi: Short-term epoch:-184 1.

Still ugly: short-distance calendar:-1076

Zhuan Xu calendar, Shang Mao: short-distance calendar:-1506.

Huangdi calendar, Shang: short-distance calendar:-1350.

When calculating, you only need to use the nearest epoch, which is 605 yuan away from it. Among them, Zhuan Xu Liyuan is beginning of spring, on the first day of the first month.