What is the fifth greatest invention in ancient China?

China's "Fifth Great Invention" —— Ancient jurisprudence

Among China's outstanding scientific and technological achievements in ancient times, besides the four well-known inventions of gunpowder, papermaking, compass and printing, there is also a little-known ancient Chinese law. For more than 2,000 years, the achievements of China ancients in law have been at the leading level in the world.

The so-called "law" is the basic unit that constitutes the legal system. When every law is highly precisely defined and forms a system, it becomes a "legal system". "Fa" is a systematic and comprehensive study of music production. Specifically, temperament is a subject that studies the relationship between tones of music system by using mathematical methods according to the principle of "acoustics", and it is an interdisciplinary subject that music acoustics, mathematics and musicology penetrate each other. In the research and application of pitch system, temperament is almost everywhere.

China is a country that attaches great importance to music tradition. In Shangshu, there is a record that "the sun and the moon are the same, and the statutes are the same". In ancient China, it was a top priority for a country's monarch to make a calendar to observe astronomical phenomena and unify pitch standards and weights and measures. Starting from Historical Records, there is a chapter 16 in the 24-year history, which specifically describes the legal achievements of the relevant era and the calculation of pitch standards. The source of China's written legal practice can be traced back to at least 1 1 century BC, such as "The King of Wu attacked Zhou and listened to the sound by blowing" in Historical Records. In the following three thousand years, China's legal theory and practice developed continuously, and new breakthroughs emerged one after another.

As early as the Spring and Autumn Period, the law of "three-point profit and loss" was recorded in Guan Zi Yuan Di in the 6th century BC. "three-point profit and loss" is both a legal method and a legal method. According to the three-point gain and loss method, starting from the length of a string (or tube) recognized as pitch, it is divided into three equal parts, and then one point is removed (loss one) or one point is added (gain one) to determine the length of another law. In mathematics, it is to multiply the chord length of pitch by two-thirds or three-quarters. And so on, until the sound on the string (or tube) is slightly higher or lower than the pitch, and the calculation of the twelve laws in a scale is completed. The rule that the pitch changes with the length of the string (or tube) is that the length difference (or frequency difference) between two adjacent laws of the twelve laws calculated by the three-point gain-loss method is not exactly the same.

After the calculation of each law in a scale is completed by the three-point gain-loss method, the notes that are eight octaves higher (or lower) than the notes can only be twice (or twice lower) than the pitch, not just twice. Assuming that the relative frequency of the pitch do is 1, the relative frequency of the high octave do sound calculated by the three-point gain-loss method is not exactly 2, such as 2.003. This is an extra difference of 0.003. On the long road of legal history, in order to eliminate this difference and make it accurately return to the second, people have sought various methods and spent nearly two thousand years.

Jing Fang in Han Dynasty (BC 1 century), Qian Lezhi in Liu Song Dynasty (5th century AD) and Liang Chong (6th century AD) in Southern and Northern Dynasties. , all want to eliminate or narrow this difference by increasing the number of laws on a scale. Fang Jing increased the number of laws in a scale to 56 (named 60) and the sum of money and music to 360 by the method of three-point gain and loss. However, their approach can only narrow the differences, but not eliminate them. Because it is meaningless to increase the number of rules in music practice, Cai increased the number of rules to only eighteen in Song Dynasty (A.D. 1 1 century).

He Chengtian made bold innovations in the Southern and Northern Dynasties. He divided the difference into parts with the length of 12, and then added it to the rule after pitch. In this way, pitch and high octave only multiply in length. This method distributes the difference according to the length rather than the frequency, so it also has some defects. However, this method opens the way for the final completion of the law of twelve averages.

Twelve-step law: a law system that divides a group of tones (octaves) into twelve semitones, which is commonly used in the world at present. The ratio of vibration numbers between two adjacent laws is completely equal, also known as the "twelve-step law". According to Yang's textual research, according to historical records, the average law was applied in Chinese music practice in the second century BC, but the average law theory appeared in 1584 when Zhu Zaiyu's New Law Theory came out. Practice and theory appeared successively, time difference 1685.

In the middle of Ming Dynasty, Prince Zhu Zaiyu invented the method of calculating square root by abacus, and obtained the geometric series of testimonies. Specifically, the pitch is calculated by the length of the pronunciation body. Suppose that the rhythm of the yellow bell is 1 foot, the chord length of the lower octave is 2 feet, and then multiplied by the second frequency common ratio is 1.05943094. This method solved the eternal problem of the twelve laws for the first time, and his "new secret law" (that is, the twelve average laws) became one of the most important discoveries in the history of human science.

This legal system includes the standard pitch of musical sounds, as well as the relevant rules and laws of musical sounds. There are 88 black and white keys on the piano keyboard, which are made according to the principle of the law of twelve equal parts. Zhu Zaiyu's theory of "Twelve Equal Laws" has made great contributions to the world music theory. It was not until more than a hundred years later that the German musician Wilkmeister put forward the same theory. /kloc-At the end of 0/9, the Belgian audiologist Ma Rong experimented with this method invented by Zhu Zaiyu, and the conclusion was exactly the same as that of Zhu Zaiyu.

It is another great invention and creation of ancient jurisprudence in China to take the yellow bell flute with fixed pitch as the length benchmark. This method is strikingly similar to today, thousands of years later, when the wavelength of light wave is used as the length benchmark in the world.

In recent years, a simple musical instrument of this period-Tao Xun has been unearthed. As early as in Shun Shu, there was such a sentence: "In February, I went hunting in the east. As for Daizong and Chai. Looking at the mountains and rivers, after facing the east, the association is against Japan, with the same method and the same amount. " After inheriting the throne, Shun traveled all over the country, offering sacrifices to gods in Dai Temple under Mount Tai. In order to appease the people, cultivate one's morality in time, and unify the calendar with the sun and the moon in the four seasons, he ordered the unification of temperament and weights and measures. Lu's "Spring and Autumn Annals" recorded the method of Guan: "In the past, the Yellow Emperor ordered Ling Lun to be the method, and Ling Lun was from the west of the summer, which was the yin of Ruan, taking bamboo in the Chuxi Valley, and breaking two sections to gain deep knowledge. It is three inches long and nine minutes long. Listening to the sound of the phoenix and other twelve methods, its male voice is six. " The meaning of this passage is that in ancient times, the Yellow Emperor sent his musician Ling Lun to the shady side of Kunlun Mountain to look for bamboo with uniform wall thickness. As a musical instrument, the basic melody was a stable and beautiful bird song. When the sound made by the flute is consistent with the call of the bird, the pitch is defined as Huang Zhonglu, the sound is a public sound, the song of the male bird is Fa, and the song of the female bird is Lu. Although this passage is somewhat mythical, it also contains some scientific contents: although it is not necessary to go to Kunlun Mountain to get bamboo, the bamboo growing on the shady and sunny sides of the northwest is dense and uniform, which is suitable for legal management. Although the bird's method is not necessarily a phoenix, according to Mr. Yang, a musician, he once heard a bird make a steady G tone in guanxian, Sichuan. (44) This shows that the law of birdsong can be used completely. As for the golden tongue, there are still many controversies, which may be incorrect. According to the research of musicians in past dynasties, most people think that the pipe length should be nine inches. (45) This shows that this passage in Lv Chunqiu has certain practical significance. It shows that more than 2000 years ago, scientists in China had a profound understanding of temperament and realized that the length of musical instruments was closely related to audio.

The sound made by the music tube is due to the vibration of the air column in the tube. When the vibration frequency increases, you will feel the pitch increase. The lower the frequency, the lower the pitch. Frequency is inversely proportional to the wavelength of sound waves. Theoretically, the fundamental wavelength of the air column in a closed tube is equal to four times the length of the tube, so if the diameter of the tube

The speed of sound is constant at a certain temperature, so it can be concluded that the sound is low when the pipeline is long and the frequency is small. Doubling the frequency will increase the pitch by an octave. Therefore, if the diameter and length of the pipeline are determined, the absolute pitch of the pipeline can be determined. Therefore, if you want to make a musical instrument with a certain frequency, you must determine the scientific size. On the other hand, if the frequency of the tuning tube is fixed, its length can be obtained. Therefore, it is completely in line with scientific principles that China used Huang Zhong's law to correct scales in ancient times.

However, in ancient times, limited by scientific and technological conditions, it was impossible to measure and record audio with instruments and equipment, and it was only by the ears of experienced musicians and musicians. When people realize that the length and inner diameter of the yellow bell flute that can emit accurate pitch are certain, they fix the length and diameter of the flute by the method of fatigue and correct it with weights and measures. As Hanshu said: "The degree is divided into minutes, inches, rulers, rulers and quotations, so the length of the degree also starts from the length of the yellow bell. The millet in the middle is the width of a millet and the length of 90%. One is a little, ten is an inch, ten is a ruler, ten is enough, and ten is five times. " "Quantity, we, together, get up, fight, welcome also, so quantity also, this starts from Huang Zhong. To some extent, there are 200 people in the valley, and they are based on the level of the well. Two are combined, ten are promoted, ten are fights, ten are welcome, and five are good. " "Power, baht, second, gold, monarch, and stone also make things flat and know the weight, which begins with Huang Zhongzhi's weight. One can hold 1200 millet and weigh 12 baht, so two is two. Twenty-four baht is two, sixteen ounces is gold, thirty pounds is jun, and four ounces is stone. " This passage has a far-reaching influence on later generations. Anyone who studies weights and measures in Qin and Han Dynasties first explains and demonstrates it. Among them, many people have misunderstandings about Huang Zhongsheng's weights and measures; Often the simple argument is whether Ling Huang originated from scales or scales originated from Ling Huang. (46) In fact, its real meaning should be to define the length of one foot at that time with the yellow bell instrument, which means that the yellow bell instrument is the standard length of nine inches. Divide the instrument into nine points and add another point to make it one foot long. Although the length of the yellow bell tube has to be reproduced with the help of worn-out millet, its function is essentially the same as the definition of one meter given today-the length of light traveling in a vacuum 1/299792458 seconds. It is worth noting that ancient scientists not only used various methods to determine the three weights and measures, but also considered unifying the three weights and measures to the yellow bell instrument, which means that a yellow bell instrument can be used as the standard of the three weights and measures. Although under certain conditions, the stability and accuracy of this length defined by the constant sound velocity are not equal to those defined by the wavelength of light waves in modern metrology, it was an achievement worthy of a great book in ancient China thousands of years ago, that is, using sound to determine the length and using legal pipes to correct the weights and measures.