Who invented the twelve laws?

Twelve-tone archaic words are ancient tuning methods. That is, the method of dividing an octave into twelve different semitones by three-point profit and loss. The order of law from low to high is: Huang Zhong, Lu Da, Tai Cluster, Jia Zhong, Gu Xi, Zhonglu, Lin Zhong, Yize, Nanlu, Wushe and Ying Zhong. Twelve methods are divided into yin and yang, of which six odd methods are called yang methods and six even methods are called yin methods. In addition, the odd law is called "law" and the even law is called "law", so the twelve laws are also called "law" for short.

Three-point profit and loss method

In Sima Qian's Historical Records and Three Laws, he wrote: "... 998 1 thought it was a palace. One-third, fifty-four. One out of three points, 72 points is business. One third, forty-eight feathers. Three points are one, and sixty-four is an angle. 」

It means taking a bamboo tube for tuning, with a length of 8 1 unit, and setting it as the pitch of "Gong Yin". Then, we remove one-third of its length, that is, 8 1 times 2/3, and get 54 units, which is the so-called "sign sound". Increase the bamboo tube length of phonetic symbols by one third, that is, 54 times 4/3 to get 72 units, which is called "Shang Yin". Remove one third (loss of one third), 72 times 2/3 to get 48 units, which is called "feather sound". Add one-third (one-third profit) and 48 times 4/3 to get 64 units, which is the "horn sound". The five pitches of Gong, Shang, Jiao, Zheng and Yu are called China's pentatonic.