Around 400 AD, China Southern Dynasty mathematician He Chengtian put forward the earliest recorded twelve-average law series in the world history: 900 849 802 758 715 677 638 601570 536 509.5 479 450 (original: ... Huang Zhong is nine inches long, Tai Cong is eight inches long and two centimeters long, Lin Zhong.
Galileo Vincenzo, the father of Italian physicist galileo galilei, tried to solve the problem of 12 average rate, but he used the magnification of 18: 17 instead of 2 quarts ({\ sqrt [{/kloc-).
1605, Simon steffen, a Dutch mathematician, put forward in an unfinished manuscript "Van de Spiegheling der singconst" that 1/2 Kai 12 power ({\ sqrt [{12}] {/kloc-0. Simon steffen's frequency ratio, one rate per tone, is different and incorrect.
In the 12th year of Wanli (1584), Zhu Zaiyu, a musician of Ming Dynasty in China, put forward the "new secret ratio" for the first time (see Lv Lu's Jingyi and Lu Yuequan's Book), and calculated that the octave was divided into 12 power ({\ sqrt [{ 12}}) at the ratio of 2. In order to verify the created theory of the twelve-average law and calculate the required length and inner diameter of the law tube, Zhu Zaiyu specially selected superior bamboo and spun the inner diameter according to the required data, creating the world's earliest 36 twelve-average law tubes, namely 12 new density multiplier tube, 12 constant law tube and 12 half law tube. Choose the best bamboo to make, including Jinmen bamboo, Spotted bamboo or Purple bamboo, but the best bamboo is Biguan bamboo produced in the south of the Yangtze River. Bamboo tubes are made of natural materials and need not be painted. If there is no suitable inner diameter, it needs to be processed, and the processed bamboo tube needs to be painted; Guqin should use black paint, avoid red paint, which is too tacky.
/kloc-At the end of 0/6, Chinese and foreign traffic was in the ascendant. Starting from 1580, the Guangdong Bureau of the Ming Dynasty held a trade fair in Guangzhou for several weeks every two years. At that time, merchants and missionaries from East and West exchanged goods and ideas. When Zhu Zaiyu published The Twelve Equal Laws, Matteo Ricci, an Italian Jesuit missionary, came to China, and Zhu Zaiyu's The Twelve Equal Laws was likely to spread to the west through missionaries at this time. In fact, Matteo Ricci mentioned Zhu Zaiyu's new calendar theory in his personal diary. Matteo Ricci himself was proficient in astronomy and mathematics. He probably knew that Zhu Zaiyu worked out the ratio between the vernal equinox and the summer solstice with 2 quarts of 12 power ({\sqrt[{ 12}]{2}}). Coincidentally, Matteo Ricci was also a friend of Peremarine Mei Sen, a senior French scientist, and they shared the same academic interests. In the process of their communication, Matteo Ricci will certainly gain the power of Mei Sen12 ({\ sqrt [{12}] {2}} = 65438+. 1638, Mei Sen published an Introduction to Harmony, in which the number 1.059463 first appeared in the western world. Before this, no one in the west knew this figure. Therefore, the invention right of the twelve-average law prevailing in the world music scene today belongs to Zhu Zaiyu. /kloc-Hermann von helmholtz, a German physicist in the 10th and 9th centuries, wrote in his book Sense of Sound: "There was a prince named Jae Ga in China who promoted public opinion and created seven tones. The method of dividing octaves into twelve semitones was also invented by this talented and clever country. "
1890, Victor Charles Mahilon, curator of the Royal Museum of Music in Brussels, copied a set of musical instruments based on Zhu Zaiyu's Twelve Average Musical Instruments. After the test, he wrote: "We know nothing about the diameter of musical instruments, and China people know much more than we do. We copied a set of laws according to Wang Zi's data in the first place, and the test results showed the accuracy of his theory. "