What is the basis of the leap month in the lunar calendar?

Leap moon refers to a phenomenon in the lunar calendar. The lunar calendar arranges the big moon and the small moon, that is, the moon, according to the full and short moon. The length of a moon is 29.5306 days, which is the cycle of the moon's profit and loss. According to the lunar calendar, there are 30 days for the big moon and 29 days for the small moon, and a year is 12 months * * 354 days. The lunar month has no seasonal significance, so just after 17, the date of the lunar calendar will be reversed with the seasons. For example, one year's New Year is spent in the snow, and after 17, the vermicelli will be shaken to celebrate the New Year. The use of such a calendar naturally cannot meet the needs of agricultural production, so the lunar calendar in China has been in parallel with the 24 solar terms since the Qin and Han Dynasties, and the 24 solar terms are used to guide agricultural production.

Twenty-four solar terms can be divided into two groups: "solar terms" and "middle qi": the ancients regarded every 300 meridian from slight cold as a solar term; From the winter solstice, every 300 meridian is a neutral gas, and there are 12 solar terms and 12 neutral gas in a year. 12 solar terms divide a year into 12 months, and each month has a solar term and a neutral atmosphere. Solar term is the starting point of solar term month; Zhongqi is the midpoint of the festival. The traditional calendar in China does not adopt the method of day-to-day and month-to-month sequence and long-term arrangement of big month, small month, normal year and leap year, but emphasizes the calculation from year to month. The state sets up special institutions to calculate calendars.

(1) Set the date order according to the moon phase. It calculates the date and time of the conjunction of the sun and the moon one by one, and the first day of each month is the date of the conjunction; Determine the size of last month according to the number of days included in the second conjunction. If the interval between this new moon and the next one is 30 days, then this month is the big moon; If it is only once every 29 days, it is an abortion.

(2) Set the month order with neutral gas. First of all, the calendar month and leap month are distinguished by whether the calendar month is neutral or not. We know that there are 12 neutral gases in a tropical year, but it contains 365.2422 ÷ 29.5306 = 2.3682 satellites. After several calendar months of rotation, there must be a calendar month without neutral gas. "Han Shu Li Biao" contains: "The new moon cannot be seized, which is called leap moon". This month without neutrality is a leap month. When the previous calendar day is a few months, it is a leap month. For example, the leap month of 1984 appears after October of the old calendar, so it is called "leap October". Leap months are calculated, not fixed in the monthly order of the year. In addition to 1 1 month,1February and the first lunar month, leap month is possible, and it is the seventh leap month in the nineteenth year.

To sum up, leap year is a phenomenon in the solar calendar, which is fixed in February, 29 days longer than the normal year; Leaping moon is a phenomenon in the lunar calendar. This is a leap month. That year, there were 13 months in the lunar calendar, and that year was called leap month year. Leap Moon is 384 years old.

First, calculate the formula of annual trunk and branches.

From the palm of your hand, you can count the annual stems and branches, and the flowers in Zhi Zi begin.

Yangzhi began on the 10th and lasted for four years.

Every other position is reversed for ten years, and the end of the year is 503.

Sixty numbers are added and subtracted one by one, and thousands of years are counted in the palm of your hand.

Calculation method: "Palm counts one year of dry branches and Zhi Zi flower roots." This method is to arrange the branches on the palm of your hand and calculate the annual branches on the palm of your hand. First locate the ground branch on the palm of your hand (Figure 1), and then start with the ground branch position as Jiazi, which can be set to 1864, 1924, or 1984, all of which are Jiazi years. "Yangzhi is the beginning of ten days, and Tiangan is the end of four years." Zi, Yin, Chen, Wu, Shen and Xu in the earthly branches are all Yang branches, and they are also the beginning of every ten days. Everything is A, that is, Jia Zi, Jia Xu, Shen Jia, Wu Jia, Chen Jia and Jia Yin. The mantissa of the Gregorian calendar in these years is 4. "Every other place for ten years, 503 at the end of the year." There are ten days to dry twelve earthly branches, heavenly stems and earthly branches combination. Every time the heavenly stems circulate, the earth branch is always with the next two branches (Xun Kong). The first branch left is the beginning of the later period. We start from the sub-position of the earthly branch and push back every other one, that is, from the sub-position to the tenth anniversary of JOE, and then from the tenth anniversary of JOE to Shenwei-the mantissa is four every year, and the annual interval is ten years. After the beginning of the tenth day is determined, the mantissa of the year is 4 as the starting point, and the mantissa of the calendar year is 5, 6, 8, 9, 0, 1, 2, 3 from the next branch, and then it is the beginning of the later period. According to this method, if the year of Jiazi is set to 1984, we can know that 1994 is JOE, 2004 is Shen Jia, and 20 14 is Wu Jia. After determining the number of Gregorian calendar years starting every ten days, we can push forward the trunk and branches of any year as needed. Although it is meaningful, it can push the trunks and branches of thousands of years forward.

Second, the formula for calculating months and hours.

Do it the day before the fifth day, and the order of months is from one to five.

The number of dry days per year matches the monthly appearance, and the number of people per day is the same.

Throughout the ages, from the beginning of a year to the beginning of a day, it can be divided into five situations according to the method of combining heaven and earth, that is, both parties have the same method of fixing the month (time) in a year (day). We also use this method, mainly to go to work the day before, that is, both Party A and Party G mainly focus on Party B-"the annual work is separated from silver moon", and the monthly work of a certain year is calculated. First, look at the combination of annual stem and trunk branch, then find out the ordinal number of trunk branch according to the method of "before the combination of five heavenly stems", set this trunk branch to zero, and determine the heavenly stems in silver moon according to the ordinal number. For example, 1998 is Wuyin, the reform movement of 1898, and the reform movement of 1898 is the same as the reform movement of 1898, which belongs to the same silver moon method. The ordinal number of five ends with five, starting from five, and after five days of self, Geng, Xin, man and ghost, it can be calculated that 1998 silver moon's heavenly stems are A, and other months' heavenly stems are easy to calculate. The calculation method of this sentence is basically the same as that of silver moon's annual dry combination, except that after the daily dry combination is determined, the dry combination is calculated from the last dry combination itself and checked by ordinal number, which is the dry combination of the day. Such as auspicious day, auspicious day and Jiazi are the same type, with Jiazi as the main type, and Jiazi's ordinal number is "1". When matched with itself, Tiangan on that day is Jiazi. Similarly, the heavenly stems in bedsore are mainly five because of the combination of five and bedsore, and the ordinal number is five, from five to non-healing, and bedsore is non-healing.

Second, the size formula of the lunar month divination

Make up two hexagrams a year, and it will be safe in early July and February.

Bian Xiao divination, meet leap moon thirteen Yin ocean.

Leap between adjacent buildings, and set the year and month according to the festival.

Calculation method: In order to know the arrangement order of lunar months and whether there is a leap month in a certain year, this formula is compiled. Under normal circumstances, the lunar calendar is twelve months a year. We can make up the first divination from January to June, the last divination from July to December, two divinations for several years, the first divination in January and the first divination in July. "Yin and Yang are small strings of divination, and when it meets the 13th day of leap month", we use Yin as the symbol of the big month, Yang as the symbol of the small month, and Yin and Yang as the symbol of the year in order of size. If there is a leap month, there is one more month, and a year is thirteen months. "In leap years, adjacent buildings are separated, and the year and month are counted according to the festival". When there is a leap month in a year, it is represented by yin and yang according to the size of the leap month, and it is marked on the left side of the middle of the leap month before and after the leap month. Just like divination, you can tell at a glance whether a leap month is a big one or a small one. At the same time, I remind you that the year and day of the lunar calendar are not determined by the month in which the perpetual calendar is compiled, but by the solar terms. For example, 1998, according to the above method, two hexagrams of well and ridge can be compiled. May this year is a small moon, and the symbol of the first half is ":". : 。 . In the second half of the year, the monthly divination symbol is "= = = =", while in the first half of the year, between five hexagrams and six hexagrams, there is happiness and yang. It can be seen that this year's Runmei is 29 days.

Fourth, calculate the daily expenditure formula.

The daily branch can be calculated by the solar calendar and the lunar calendar.

(1) formula for calculating the daily branch of the lunar calendar:

The hexagrams of the big moon and the small moon are remembered in mind, which is helping to take root.

Rush in the same place after the big trunk, and retreat for one day after the small trunk.

On the first day of 13 and 25th, the same branch counts as a branch.

Calculation method: "The big and small moon hexagrams are remembered in the heart, which is the fundamental reason." The big moon in the lunar calendar is 30 days and the small moon is 29 days, which is fixed. In order to calculate the number of the lunar calendar, we must first compile the estimated year with two hexagrams according to the formula of the lunar calendar, so as to calculate the thousand fortunes in a day. In addition, you should also remember the branches and branches on the first day of the first lunar month, because this is the basis of daily calculation in a year. "After the big trunk, I rushed in the same place, and after the small trunk, I retired for one day." The heavenly stems and earthly branches of the lunar calendar is combined, and the sky is dry for 2.5 times. According to this law, the first day of a month is the main branch. If this month is a miscarriage, it should be in the case of the same branch, and the main branch should be reduced by one, which is the first day of the next month after the miscarriage. For example, on the first day of this month, the main branch is your own, this month is a big month, and on the first day of next month, the main branch is your own. If this month is a miscarriage, then the first day of next month should be decided after a person retires, that is, Wushen Day. "On the first day, 13 and 25th, the same branch counts as one." After determining the first day of a month, these two sentences divide the month into three stages, that is, from the first day to the twelfth day, from the thirteenth day to the twenty-fourth day. The first, thirteenth and twenty-fifth days of junior high school are also regular in terms of cadres and branch offices. On the first day of knowing the trunk, you only need to push the trunk once every other day, but the branches remain the same. Similarly, 13 knows the main branch, and 25 knows the main branch. If the first day is Jiazi, thirteen is Bingzi and twenty-five is Wuzi. If you master this method, you can quickly know what day it is according to which section it belongs to.

(2) Calculation formula of daily trunk and branch in Gregorian calendar:

New Year's Day is the root, and the size of February is in mind.

The little moon stays where it is, and the big moon adds a day.

Shen leaps every year, and the same branch rushes back to one day.

On February 28th of the remaining year, the same branch was closed for one day.

On13rd and 25th of the first month of each month, each branch is counted as a branch.

Calculation method: "New Year's Day is the root, and February is the heart." To calculate the branches of the Gregorian calendar every day, we must first remember the branches of New Year's Day. At the same time, you should also know the number of days in January and February. In the Gregorian calendar, the big month is 3 1 day and the small month is 30 days. Its size and month are fixed, but February has 29 days and 28 days. So pay special attention to which year February is 29 days and that year February is 28 days. "The abortion is in the same place, and the big month adds one day." The first month of the solar calendar is 30 days. According to the formula of the lunar calendar, we know that the first day of this month is the same as the first day of next month. The big month in the Gregorian calendar is 365,438+0 days. On the basis of the collision between abortion and dry land, one digit is added to each branch, which is the branch on the first day of next month after the big month. "Shen Niannian leaps, and the same branch will retreat for one day." Through research, it is found that the year when the earthly branches are Shen, Zi and Chen is a leap year in the Gregorian calendar, and February is 29 days. When calculating the main branch of March 1 day, we can calculate it according to the daily main branch method after the lunar new year, that is, on the basis of doing the same thing in situ, the main branch is reduced by one, which is the main branch of March 3. "On February 28th, the rest of the year, I did the same thing for two more days." Except for the land, Shenzichen has 29 days in February and 28 days in other years. After the main branch was known in February 1 day, the main branch was reduced by two places in March 1 day according to the same branch rule. "On the 13th and 25th of the first month, each branch counts as one." The first day of each month represents the 1 day of each month. Its deduction method is the same as the last two sentences of the lunar calendar.

5. Example: Calculate the main branch of 1998 at the beginning of June of the lunar calendar at noon of 10.

1. First of all, according to the eight diagrams formula of the Lunar New Year, arrange the Lunar New Year of 1998 with two hexagrams, and mark the leap month. At the same time, remember the first day of the first month and the first day of the New Year.

4. Calculate the main branch of 1998. According to the formula for calculating the annual trunk, we set the position of the ground branch as Jiazi in the palm of our hand, that is, 1984, and press our thumb on the position of the ground branch. According to the principle of "pushing back every other position for ten years", the thumb is pushed forward from 1994, that is, 1994 is JOE, 1995 is yihai, 1996 is Bingzi, and 1997 is Ding Chou.

3. Calculate the main branch of the lunar calendar in June. 1998 After determining the main branch of Wuyin, according to the "fixed moon main branch tactics", the combination of Wuyin main branch and Guigan main branch is E, and the ordinal number of E is 5, so the thumb is fixed at E position. "Dry silver moon every year", starting from the fifth place, the thumb is counted in turn, which is1the first month of 998, that is, the first month is Jiayin, and then the first month is dry, and the last month is dry according to A, Ji, C, D and E.

4. Calculate the trunk and branches in June of 1 0 (Gregorian calendar1August).

(1) Calculate the daily branch of the lunar calendar. As mentioned earlier, in 1998, the hexagrams of the big moon and the small moon were wells and ridges. Because the leap month in May is 29 days, it is a sun, located in the fifth and sixth questions of "well", and the hexagram shape is = 丨 = 丨 =.

Because we want to calculate that the trunk and branch of 1998 are from the sea on the first day of the first lunar month, we must first locate the trunk and branch on the palm of our hand with our thumb, and then calculate the trunk and branch of 1 day month by month according to the stipulation that "the big trunk and branch are in one place, and the small trunk and branch are back one day" in the calculation of the daily trunk and branch of the lunar calendar. The first month is big, the trunk is the same as the branches, and the thumb jumps to the fourth position. At the beginning of February, the trunk was the second one on 1; The trunk and branches are reduced by 1 respectively, and the thumb is reduced by 1 after jumping to sea level. At the beginning of March, the trunk and branch of JOE were 1; March is small, and the trunk and branches decrease 1 respectively. The thumb jumped behind Chen Zhi with 1, and it was 1 in early April. April is big, the stems are the same branch, and the thumb jumps to a single stem. In early May, it is 1. May is a small moon, the trunk and branches decrease by 1 respectively, the thumb jumps to the branches and then retreats by 1, and the leap in early May is 1. The leap in May is small, and the trips of the same branch are reduced by 1 respectively. After the thumb jumps to apply for a branch, step back one place. At the beginning of June, the first branch was Xin Wei. After knowing the main branch of 1 in early June, the main branch of 10 in early June is Chen Geng.

(2) Calculate August 1 of Gregorian calendar.

1998 The main branch is Wuyin, and the annual branch does not belong to Shen, so 1998 is 28 days in February. According to the calculation formula of the Gregorian calendar, it is calculated month by month according to the rule of "the branches of the small moon are offset in the same place, the previous sentence of the big moon is added with one day, and the branches of the remaining year are offset by two days on February 28th". 1998 applied for the post of Wu Shen, and the thumb was fixed at the application position. June 1 is the big moon, one day is added to the same branch of the trunk, the thumb jumps from the application position to the shade position, 1 is added to the socket, February 1 is the socket, February 28th is the trunk drying for two days, and the thumb jumps to the unitary position for two branches, and March 1 is the Ding Wei. 3 is big, the same branch is rushing and the thumb jumps to ugly 1 day. April 1, the main branch is wuyin; April is a small dry rush, and the thumb jumps to the application position. 1 May, with Wu Shen as the main branch; May is a big day, the trunk is added with the same branch 1 day, and the thumb jumps to the unitary position. July 1, the trunk is unitary; In July, it was a big day, and the trunk rushed 1 day, and the thumb jumped into 1 position and arrived in Chen Chen. In August, trunks and branches are in Chen Geng.

5. It is estimated that the first day of June in the lunar calendar is 10 (August in the solar calendar, 1), and the main branch of that day is Chen Geng. We know from "Punctuality Tactics of Ganzhi" that Gangeng was consistent with self-nature that day, and according to "Five Combinations of Tiangan", the ordinal number of self-nature was 2, and the thumb was set in the position of Tiangan self-nature. "Days of drying itself", from the second to the third, we can know that one day in Chen Geng is the third. Thumb pushed from C to noon, dry day, dry at noon.

By calculating the year, month, day and hour on the palm of your hand, you can know that the noon branch of 10 (1 in August of Gregorian calendar) at the beginning of June of 998 is at noon on Chen Geng Day, which is the last month of Wuyin.

Six, several issues that need attention.

On the basis of understanding Feng Qiao's method of calculating the year, month, day and time in the palm of his hand, this paper combines the clever memorization of the formula with the positioning calculation of the palm, and often compares it with the perpetual calendar to make it skilled and easy to use.

When using this method again, we should first make a table and take it with us to calculate the annual expenditure.

This form is as follows:

Year serial number This year's big and small month hexagrams (leap) beginning of spring month, the first day of the first month, the main branch of New Year's Day.

1988: 丨丨:: 丨: On the eighth day of the first month, Gengzi arrived in Shanghai.

1999 丨丨:: 丨: On the 19th of the twelfth lunar month, when the sea was fixed, Jiazi lost power.

When calculating the main branch of the day, we must pay attention to the size of the month and distinguish the main branch from the main branch.

How to skillfully hold the year, month, day and time in your hand (appendix)

First of all, calculate the formula of New Year's Day cadres year by year.

If we want to postpone New Year's Day next year, the prophet will make a difference this year.

Shen's branch year is a leap year, and six branches have been added.

Add five more people in the remaining years, and you will know when you retire.

Calculation method: "If we want to postpone New Year's Day next year, the prophet will do something this year." To calculate the trunk and branches of New Year's Day next year, we must first know the trunk and branches of New Year's Day this year and position them on the palm of your hand with your thumb. "Shengan year is a leap year, plus six branches." Every year when Shenlai comes, it is a leap year, February 29th. To calculate the new year's day next year, as long as the thumb jumps from this year's new year's day to the competitive new year's day, and then the sky is dry and six, it is the new year's day next year. "I will add five more people for the rest of this year, and I will know when I retire." Except for the year of Shen, February in other years is 28 days. The thumb is fixed on the palm of your hand to determine the position of the New Year's Day branch this year. When calculating the new year's day branch next year, jump your thumb on the conflicting branch and retreat one place, and add five days to the trunk, which is the trunk branch next year.

Second, calculate the formula of the first day of the first month year by year.

If we want to push the coming year to January, the prophet will do something this year.

Returns the number of small months throughout the year, and the leap month decimal is 567.

Small six cadres every three days, the first sentence of five plus one.

Every seven branches are separated by three days, and each branch must be the same.

Calculation method: "If we want to push the next year to January, the prophet will do something this year." To calculate the dry branch on the first day of the first month of next year, we must first know the dry branch on the first day of the first month of this year. "The number of small months is returned throughout the year, and the decimal number of leap months is 567." Perennial refers to a year without leap months. To calculate the first day of the first lunar month, two hexagrams should be compiled year by year according to the formula of the lunar calendar, so as to determine the number of small months in a certain year. If there is no leap month this year, ask for the first day of the first month of the next year. According to research, every leap month year has five, six and seven small months. "Small six cadres are separated by three days, and one is added to each of the first five sentences." In leap month year, when the number of small months is six, one branch is the same at the beginning of the first month of the following year, one branch is the same at the beginning of last year, and the branches are separated by three places. If the number of abortions is five, the first day of the first month of the following year shall prevail. "Every seven branches are every three days, and it is the same to return one." If the number of small months in a leap month is 7, the first day of the first month of the next year will be calculated after the first day of the first month of the current year is determined. As long as the branches are separated by three places, the branches will be reduced by one place, and the branches will be on the first day of the first month of the following year.

Third, the method of calculating the first day of each month in Gregorian calendar with divinatory symbols

Calculating the branches and branches of the first day of each month in the solar calendar with divinatory symbols is mainly based on the fact that the size of the solar calendar and the month are inconvenient to fix, and a divinatory symbol suitable for any year is compiled. Then, according to the cycle law of large and small branches, the branch on the first day of each month is calculated. In the Gregorian calendar, the months of the year have fixed divination images. In the first half of the year, it was the divination of Wei Ji, and in the second half, it was the divination image as shown in Figure 3. In the process of calculation, we should pay special attention to February, because there are 28 days and 29 days, so the words leap year and non-leap year are marked in wiki divination to attract attention in calculation. When calculating, we should determine the trunk and branch on the first day of the following month based on the formula for calculating trunk and branch in Gregorian calendar, and then calculate the trunk and branch on the required date according to the principle of "first month 13: 25, one branch is separated from the other". Figure 3.

June 1+ 1 65438+ February = 1+ 1.

May = one day for one day 1 1 month for one day+1.

April1+110 =1+00.

March = leap day, in-situ dry+1 September, in-situ dry+1.

On February 29th of leap year, it is not the same branch in one day-August = the same branch in one day+1.

On February 28th of a non-leap year, one day's work is the same as another day+1.

65438+ 10 month = New Year's Day, main branch, July = one day, same branch.

Fourth, the method of calculating the first day of the lunar month with hexagrams.

The number of months in the lunar calendar is fixed, that is, the big month is 30 days and the small month is 29 days. However, due to the irregular arrangement of large and small months, it is necessary to compile monthly divination in the first half of this year according to the formula of the lunar calendar. Then, according to the two numbers, referring to the calculation formula of the daily branch and branch in the lunar calendar, after knowing the branch and branch on the first day of the first month, according to the law of "big branch and branch in one place, small branch and branch back one day", the branch and branch on the first day of each lunar month are calculated by numbers. Through research, it is found that there are four types of lunar calendar, and the calculation method of the first day of each month is as follows:

(1) Two miscarriages run together (2) Two big miscarriages.

-Do the same stroke next month.-1 = Do it next month.

-The first day of this month = the first day of this month.

(3) adjacent to each other (4) adjacent to each other.

-Same offset next month = Same offset next month-1

= the first day of this month-the first day of this month

△ Example: Calculate the first branch of every month in 200 1.

1. According to the formula of the lunar calendar, the year of 200 1 is compiled as the last month's divination. In the first half of the year, it was the "Gen" divination, and in the second half, it was the "Ji" divination.

4.200 1 the first day of the first month, the main branch is Dinghai.

3. When calculating, compare the adjacent two months of 1, February, March and April with the four arrangement types, and then calculate according to the same type.

4. According to the divinatory symbols, it is calculated month by month.

June, "-"Gantongzhichong Ji You 65438+February "=" Gantongzhichong 1 New Temple.

In May, "-"tongkechong-1 bazaar11"-"tongkechong lunzi.

Leap April "-"trunks and branches rush to Xu Bing 65438+ October "=" trunks and branches-1 noon.

April, "——" Dry with the same branch —— 1 Chen Bing September, "——" Dry with the same branch and rush to the sunflower field.

March "-"The main branch will rush to the sea in August "=" The main branch will rush at the end of the year-1.

February "-"Dead branches rush in April "-"Dead branches rush-1 Jiayin

65438+ October "-"Ding Hai on the first day of the first month.

After divination, it is estimated that 65438+ the first day of February in the lunar calendar is Xin Si.