The basic elements of China's ancient calendar —— the sun, the atmosphere and the new moon —— China adopted the sub-calendar at the latest from Shang Dynasty. From Jiazi to Guihai, the daily names of 60 branches are recycled in turn. "Qi" is the solar calendar in the ancient calendar of China. The time from the winter solstice to the next winter solstice is one year (tropic year). A year is divided into twenty-four "qi", which is called twenty-four solar terms. Divide the time equally, which is called flat gas. According to the distance traveled by the sun in one year, it is called constant gas. From the solstice of winter, there is air every once in a while, such as cold, rain, vernal equinox and so on. , called gas; The other 12 species, such as: slight cold, beginning of spring, fright, etc. , are called solar terms. The new moon is the lunar part of China's ancient calendar. The moment when the longitude of the ecliptic of the sun and the moon is the same is called the new moon. The speed of the moon's rotation around the earth is uneven, and the period of its speed change is called perihelion. The speed of the sun's apparent motion is also uneven every year. Its change cycle has always been considered as the tropic of cancer until the end of the Ming Dynasty (see year). Because the movement of the sun and the moon is uneven, the time between two consecutive new moons is also unequal. But after long-term observation and statistics, we can get a relatively stable average, which is called the new moon. ? Bark? Falcon blowing is called Pingshuo. Correct the imbalance between daily and monthly exercise in Pingshuo and get a real new moon, which is called Dingshuo (see Wang Shuo). According to the changes of Qi and Shuo, the ancient civil calendar in China can be divided into three periods: the Spring and Autumn Period and the Warring States Period to the early Tang Dynasty, which is the period of using Pingqi and Pingshuo. From the beginning of the Tang Dynasty to the end of the Ming Dynasty, it was a time to make use of peace and settle the new moon. After the Qing dynasty, it was a period of setting the new moon with a steady breath.

Key points of calendar calculation In order to calculate the annual calendar spectrum, we must first set a starting point for calculation, which is called epoch. Most ancient calendars in China take the following ideal times as their epochs: a certain year 1 1 midnight on the first day of the month, which happens to be the new moon and the winter solstice, and it is also the time when the moon passes near (that is, the point where the moon runs fastest), and so on. Because the data of various calendars are different, they push the ideal time differently. However, such an ideal moment is usually far from the calendar year. This era is called Shangyuan (see Shangyuan products? /A & gt； )。

Let A be the tropic year, B the lunar month and C the recent month, all in "day". It is also set to the cumulative number of years from Shangyuan to the expected year. Then A is the total time from Shangyuan to the winter solstice of a year. Because the trunk and branch calendar takes 60 days as a week, a is divided by 60, and the remainder r is the total time from the winter solstice to the midnight of the previous year. The number of days in this time is called Dayu, and the odd part of a day is called Xiaoyu. Usually, the calendar stipulates that Dayu is born outside Jiazi, that is, Jiazi Day is 0, Ugly Day is 1, and so on. Therefore, according to Dayu's figures, we can know the names of the branches and branches from winter to sun. In some calendars, the date of Jiazi should be 1, the ugly date should be 2, and so on. There are also a few calendars, such as the epoch calendar in the Northern Song Dynasty, which choose Keith Day as Shangyuan instead of Jiazi Day. If fortune is told, the rest are counted as Keith 0, Wu Geng 1, and so on. Light rain is a time from midnight to winter solstice, which can be converted into a time according to the twelve-hour system or the hundred-hour system (see missing time). From the time a /24 of R accumulation, we can get the dry days and minute days of each gas from winter to the future.

Mathematically, the above algorithm of R is expressed as an expression: a ≡r (mod60). This formula is called linear congruence formula. Similarly, other linear congruences can be listed: a ≡r (modb), a ≡r (modc), where r is the time interval between winter solstice and 1 1 moon. R is the time interval between the winter solstice and a perigee on the moon. R-r is the time from 1 1 month to midnight on Jiazi Day. Like the winter solstice, its integer part represents the dry day and the branch day after Jiazi, and the zero part is the time from midnight to Pingshuo.

Let this time be t, and generally give a solar motion table and a moon motion table in the calendar. According to the solar motion table, according to the position of Pingshuo in 1 1 month in the twenty-four atmosphere (or, after 1 1 month heavy snow, the time is; Or, if, 1 1 month, Pingshuo is before the heavy snow and after the light snow, at this time, the time from the light snow is), the correction number t caused by the uneven movement of the sun can be calculated by interpolation method; From the lunar motion table, according to the position of 1 1 moon in a perigee month cycle (that is, r), the correction number t caused by uneven lunar motion can be interpolated and calculated. Therefore, 1 1 month will be t = t+t+t. 1, the second day of Pingshuo; T<0, the new moon is scheduled for the day before Pingshuo; 0<T< 1, the new moon and the new moon are on the same day. The monthly average after 1 1 month is obtained by (r -r) accumulating the value of B. When the total reaches 60, it can be discarded and the remainder can be taken. The method of correcting the new moon is the same as the above method.

Tycho system and Kepler's ellipse area method were adopted after Qing Dynasty. The calculation of the new moon has also been changed to the European geometric method.

Twelve months is a civil calendar year. There is a difference between it and a tropical year, R =α- 12b, which is about 10 ~ 1 1 day. In less than three years, the difference accumulated for more than one month. At this time, a leap month will be added in this calendar year to avoid being out of touch with the tropical year. From the beginning of the calendar of the Han Dynasty, it was stipulated that the month without breath was a leap month, which also meant that every breath should be in a fixed month, such as 1 1 month's winter solstice, 1 February's severe cold,1month's rainy weather and so on. In different calendars, the names of months can be different (see Sanzheng), but a certain gas must be in a certain month. This principle is the same in all calendars after taichu calendar Law. This makes the composition of lunar calendar and solar calendar more closely combined. Generally speaking, such as r > (b -R), it is stipulated that there will be a leap this year. R/12 is the difference between two phases that are longer than the full moon. Add this number to r, and when the cumulative sum is greater than b, it is the time when the gas exceeds the moon. At this time, the excess month is designated as leap month.

In ancient China, some calendars used close distance to get elements, instead of the previous special moment, that is, taking the winter solstice time of one year and the known values of r, r and r (set as a and a pa) as the era. For example, Shoushi Calendar takes the winter solstice as its epoch. It is called a Qi Ying, a Leaping Camp and a Transformation Camp. At this point, the primary congruence group is changed to:

a y +a ≡r (mod60)，

a y +a ≡r (modb)，

a y +a ≡r (modc).

The above is the most basic content of calendars all over the world, that is, arranging calendar days according to the calculated folk calendar spectrum. However, the contents of China's ancient calendars are more abundant and extensive. Including the movement and position calculation of the sun, the moon and the five stars; The determination of stars and time is weak and denier; The forecast of solar eclipse and so on. To some extent, the ancient calendar in China is a kind of work of compiling astronomical almanac. It includes many important contents of ancient astronomy in China. Its development is a main line in the history of astronomy in China.

Tibetan calendar refers to the calendar of Tibetans in China. In front of Jokhang Temple in Lhasa, Xizang Autonomous Region, there is a monument to the Tang-Fan Alliance in Changqing. The inscription is in Tibetan, and there is a comparison between Tibetan calendar and Tang calendar in the inscription. The inscription said: "In the seventh year of Dafantai, the first year of Tang Changqing was the Year of the Silver and Iron Ox, and the tenth day of Meng Dongyue." Meng Dongyue is the first month of winter. The Tibetan calendar year is coordinated by five elements, ten branches and twelve branches. The combination of ten dry elements and five elements, the wood is one yang and one yin, the fire is three yang and one ding yin, the soil is five yang and one yin, the gold is Geng yang and A Xin yin, and the water is nonyang and decyl yin. The chronology of branches and branches distinguishes yin and yang with five elements, and there is no name of ten branches and branches. What's the point? 9 bite the string? d？ Iron is gold) is hatred and ugliness, consistent with the first year of Tang Changqing.

In the 26th year of Emperor Kangxi of Qing Dynasty (A.D. 1687), Tibetan Sanjay Gyatso wrote a book "White Glazed Glazed Glass", which contained a chronology. The year when this book was written was zero, and it was pushed back to 660. He said, "The basic code of the time wheel was introduced into Tibet, so it is the beginning of the 60th anniversary." According to 1687 MINUS 660 years, it is 1027. At that time, Ding Mao was the Yin-fire rabbit in the Tibetan calendar, and it is said that the Tibetan calendar began in the year of Yin-fire rabbit.

The fourteenth section of Volume II of Four Medical Codes, a masterpiece of Tibetan medicine, discusses the living habits of each season, and also introduces the Tibetan calendar. He said, "A year is divided into six seasons and twelve months." He also said, "One hundred and twenty seconds is a Camachomo, sixty Camachomos are a fork, thirty forks are a compliment, thirty forks are a day and night, and thirty forks are a month."