The twelve-average law, also known as the "twelve-step interval law", is a universal law system in the world in which a group of tones (octaves) are divided into twelve semitones, and the wavelength ratio between two adjacent laws is completely equal. The law of twelve averages was discovered by Zhu Zaikun of Ming Dynasty in China.
The law of twelve averages refers to dividing the octave into twelve equal parts according to the wavelength proportion, and each equal part is called a semitone (second degree). A sophomore is two equal parts, called a whole sound. There are some amazing coincidences in dividing an octave into 12 equal parts. This is because the wavelength ratio of two notes in their pure fifth interval, that is, the power of 7/ 12, is very close to 2/3, about 0.6667.
Because wavelength is directly proportional to chord length, the wavelength relationship can be transformed into chord length relationship. Therefore, even in the16th century, when western physics just started and mechanical waves were not discovered, it was a great and amazing thing for Zhu Zai _ of Ming Dynasty in China to discover this approximate law with his superb mathematical calculation ability.
The law of twelve averages is widely used in symphony orchestras and keyboard instruments, and the piano is also tuned according to the law of twelve averages.