The three-point profit-loss method is a biological law used by China in ancient times when he invented and formulated temperament. According to the pipe length or chord length of a certain standard tone, a certain length ratio must be followed when calculating the pipe length or chord length of other series of melodies. The three-point profit and loss method provides a criterion for the ratio of length to length.

The three-point profit and loss method is to calculate the proportion of the length of each legal pipe by mathematical method. In ancient China, twelve pipes with different lengths were used for tuning, and the pitch was also different.

Three-point gain and loss is to define the sound produced by clarinet as vowel, and then shorten clarinet by one third (loss by one) or increase it by one third (gain by one) to get the fifth sound above vowel and the fourth sound below vowel respectively, which can benefit first and then lose. By changing the length of the pipe, we can find different pitches and control short pitches, and vice versa.

Extended data

The three-point profit and loss method was first seen in "Pipe? Therefore, it is necessary to start with this book and find out the invention age and characters of this law. About pipes? In the past, there were two views about the author of Yuan Di Pian: one thought that the author was Guan Zhong, the prime minister of Qi Huangong in the Spring and Autumn Period; First, according to the writing atmosphere at that time, I think that books should be created collectively, not individually.

Judging from a story recorded in Lv's Spring and Autumn Annals about Guan Zhong's escape from life by singing, Guan Zhong is an accomplished musician with the musical quality of inventing the law of three-point profit and loss.

Secondly, the excavation of the bone flute in Wuyang, Henan Province shows that there were examples of using pentatonic scale, hexatonic scale and heptatonic scale in music practice as early as the Spring and Autumn Period. It can be seen that the principle of three-point profit and loss method has long been applied in music practice before the Spring and Autumn Period. ?

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