First,? Three-point profit and loss method? Du You's Tong Dian in the Tang Dynasty said: There is yin from the front, but there are five tones. ? It can be seen that before the Shang Dynasty, there was already a five-tone title. What is the pentatonic? According to legend, the Six Pagodas of Lv Wang in the Zhou Dynasty said: There are five sounds in the twelve laws: public, commercial, diplomatic, just and proper. ? The origin of these five tones has a long history and is not clear. But Guanzi in the Spring and Autumn Period and the Warring States Period? The articles of local staff are very lively and interesting. It says:? Anyone who listens to it is as horrible as a negative feeling; Anyone who listens to feathers is like a?vagho?a； in the wild; Anyone who listens to the palace is like a cow singing, and anyone who listens to businessmen is like a lost sheep; Anyone who listens to a trumpet sounds like a pheasant climbing a tree. ?
It is also introduced that any one of palace, quotient, angle, sign and feather is used as the main tone, which is multiplied by 4/3 and 2/3 of its corresponding length in turn to get five tones in turn, which can form a pentatonic scale; The tonic is the symbol of this pentatonic scale. For example, let the chord length of the sound be 9? 9=8 1, so the chord length is 8 1? 4/3= 108; Is the upper chord length 108? 2/3=72; Is the chord length of feathers 72? 4/3=96; Is the chord length of the horn 96? 2/3=64。 Arrange the above five sounds according to their chord length as follows: sign, feather, official, quotient and angle, that is, a scale has five sounds.
This law is famous at home and abroad? Three-point profit and loss method? . Because chord length is inversely proportional to flexibility, the frequency ratio between them is three to two (that is, the difference is five degrees) or its multiple. Therefore, the pentatonic scale obtained by the three-point gain-loss method is actually composed of many tones with a difference of five degrees. So the three-point profit and loss method is also called? Five-degree generation method? . The five-degree law is simple, easy to calculate and harmonious, which occupies a very important position in the history of China law.
The music in the Spring and Autumn Period was based on this music system in general, and it was very moving to play. No wonder Confucius listened to the performance of Guan Ju, a famous article in The Book of Songs, and said excitedly, It is magnificent and full of ears! ? Its wonderful degree can be imagined. I don't know how many kinds of legal systems have appeared in thousands of years, but the charm of the five-degree law has been preserved, which shows that its vitality is very strong.
Second,? Twelve laws? Due to the development of musical instruments and the requirements of music practice, as well as the increasingly frequent exchanges between North and South ethnic groups in China, more and more voices and more complicated birth laws, the legal system will inevitably develop. First of all, in addition to the original five tones, two semitones of sign change and palace change are added to form a seven-tone scale. In order to meet the needs of tone sandhi, some semitones are added, so that there are twelve tones between an average (an octave), which becomes the so-called twelve laws.
By the third century BC, the Twelve Laws stood out from the three-point profit and loss law and stepped onto the stage of China's legal history. What is the name of the Twelve Laws? Huangzhong, Dachang, Taiqun, Jiazhong, Gu Xi, Zhonglu, Yan Bin, Lin Zhong, Yize, Lu Nan, Wushe and Zhong Ying. ?
The above twelve laws are also called six laws and six laws. As the name implies, Huang Zhong, Jia Zhong, Lin Zhong and Ying Zhong are undoubtedly bells; As for the words "Dachang", "Zhonglu" and "Deyu", according to the wording of "Guoyu", Lu is the same, and both are in charge, which means bamboo tube. It can be inferred that the mainland, China and Lu Nan originated from some bamboo wind instruments. There are also a few obscure and ancient names, such as Taiqun, Gu Xi, Yan Bin, Yize and Wushe. According to experts' opinions, it may have been transliterated from the southern minorities at that time and introduced into the Central Plains. The sound of a savage's tongue? And become.
The progress of law undoubtedly promoted the development of music in turn. During the Spring and Autumn Period and the Warring States Period, many famous musicians appeared in China, such as Shi Juan, Shi Zhi, Shi Kuang and Shi Xiang. Yu Boya, a great star, can play the style of aiming at mountains and rivers. With the rapid development of law, the problem of formulating the standards of music law is inevitably put on the agenda. Mencius said:? Shi Kuang's cleverness cannot be balanced by six tones. ? This can be seen.
Third, ancient China? By the law? It has always been questioned whether China adopted the pipe law or the string law in ancient times. How people look forward to the excavation of underground remains, let the facts judge.
1972, a group of drums dating back to 150 BC were first excavated from Mawangdui Han Tomb in Changsha, Hunan, China. These are twelve bamboo tubes that can emit different standard sounds, the shortest of which is 10.2 cm, and the longest is 17.65 cm, with a diameter of about 0.65 cm. The lower ends of the pipes are covered with books. Huang Zhong, Lu, Ying Zhong? Equidistant name. This provides new evidence for China's ancient theory of governing the country.
At the same time, in Europe, the reason why the sound frequency varies according to the chord length has always been based on the chord law. Their achievements are represented by Pythagoras (582-493 BC), an ancient Greek philosopher and mathematician in the 6th century BC. The law of five degrees of life he studied is called? Pythagoras' legal system? , dominated the European music scene for a long time, and the aftermath spread to later generations.
Strange to say, two different ancient civilizations have gone through a long process of development, but in the end they all got the five-degree rule. China's governance method and the western string governance method just reflect each other, and have the same effect.
It is worth mentioning that the law on the pipe is more difficult than the law on the string. In order to calculate the sound on the string, we only need to consider the actual length of the string, and in the pipeline, because of the vibration of the gas column in the pipeline, we must also consider the escape part of the gas column at the edge of the nozzle and make corrections. This is a very complicated job, so the management law in ancient China has experienced a gradual improvement process from simple to complex, from general to accurate. After Xun Xu discovered the nozzle correction number in Jin Dynasty, it was more standard to use the pipe as the regulator.
Four or three shortcomings of the twelve laws of profit and loss
Although the three-point law of profit and loss is an improvement compared with the past, it is still a fly in the ointment. In ancient times, the interval of major semitone was 1 14, and the interval of minor semitone was 90, with a difference of 24, commonly known as ancient semitone difference. When the rule is generated to 12 (i.e. rule 13) by three-point gain and loss method, the rule 13 should be restored to a clear Ling Huang (the interval value is 1200 minutes). However, the actual result of five degrees higher from the middle road is 522 (middle road) +702 (five degrees) = 1224, which is an ancient sound difference higher than that of the Qing Huang Zhong. It can be seen that such thirteen sounds can't really form a complete octave.
In order to meet the needs of official transition (also known as phase transition palace, that is, taking any law as the palace, choosing seven tones in turn to form a seven-tone scale) and tuning, and to meet the higher requirements of music art, this ancient sound difference must be eliminated as conveniently and reasonably as possible.
In order to solve this problem, musicians, musicians and pianists of later generations kept exploring and achieved great success after nearly two thousand years' efforts. In this long history, there are countless attempts to reform the legal system, so I won't introduce them here.
Verb (short for verb)? The law of twelve averages? Since then, music has developed very rapidly, especially in the Tang and Song Dynasties, when culture reached its peak. Yuefu, Tang poetry and Song ci were accompanied by music, and most of the literati needed a little knowledge of statutes, coupled with the assimilation of various ethnic groups, which led to the great integration of music culture. By the 16th century, the problem of the handover of palaces and palaces in various dynasties in China had been initially and completely solved.
The law of twelve averages is like a baby in a mother's womb, which is about to land. On the other hand, in Europe, under the impetus of the Renaissance (14-16th century), music circles began to study ancient Greek music. From the middle of16th century, instrumental music began to rise, and tone sandhi became more and more complicated. Although keyboard instruments (such as piano and organ) use the whole tone averaging law, it is more and more inconvenient, and the twelve-tone averaging law has become the goal pursued by music theorists. As the eastern and western civilizations advance along their own unique development routes, history will wait and see who can reach the victorious destination first.
/kloc-in the 6th century, during the Wanli period of the Ming Dynasty in China, Zhu Zaiyu, a great musician, wrote the book Lv Lu Jing Yi on the basis of summing up the experience of his predecessors, which was first expounded in the world? The law of twelve averages? . This is the inevitable result of the development of jurisprudence. As early as the Han Dynasty, China's pipa and other musical instruments had used some kind of average law in practice. Zhu Zaiyu is knowledgeable, sophisticated and proficient in mathematics. He considered that the theory of law should not only meet the needs of court rotation, but also have too many rules to facilitate the manufacture and performance of musical instruments (singing). Only by completely getting rid of the old-fashioned way and taking the road of the law of averages can he succeed.
His? Left-handed and right-handed? Theory, manufacturing? The twelve methods of the yellow bell are the beginning, and the bell should be the end, which is repeated and endless. Successfully solved the tonal modulation problem of scales, and even the creation of modern keyboard instruments depends on the acoustic theoretical basis provided by him.
After Zhu Zaiyu discovered the law of twelve averages, 52 years later, French music theorist Melson also developed the law of twelve averages, which echoed China's law of twelve averages. Whether the West created independently or was inspired and influenced by China has not been confirmed. Ironically, after Zhu Zaiyu respectfully presented his life's efforts to the emperor, these priceless treasures were regarded as a pile of waste paper, which was shelved and not implemented.
Emperor Qianlong of the Qing Dynasty also cursed it to death. It was not until it was introduced to Europe that it caused a sensation all over the world and won high praise from foreign Bole musicians, which made the European scientific community have to sit up and take notice of China people.
Today, the law of twelve averages has become popular in the world. European music basically adopts the law of twelve averages. However, when playing the grand piano and violin, they often tend to have the fifth degree, and they also retain the legacy of the ancient major scales. Due to the need of tone sandhi and the development of multi-voice in modern music in China, it is only a matter of time before the twelve-average law is adopted as the standard.
The law of twelve averages is an excellent cultural heritage of the Chinese nation. Taking the law of twelve averages as the standard, does the law of five degrees and its deduction not be excluded in practice? Pure law? what's up Flavor? . After the adoption of the law of twelve averages, it will not only damage the national style of our country, but also benefit the international music exchange.