What did the pipe section record? Five tones and seven tones.

Guan Zhong's "Guan Di Zi Yuan Pian" in the Spring and Autumn Period recorded the "three-point gain and loss method", which is a theory to obtain pentatonic scale, heptatonic scale and twelve laws by mathematical methods.

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.

Extended data

The basic principle of "three-point profit and loss method" is:

1, based on an absolutely uniform diameter sound tube-gong (1);

2. Then, divide the sounding pipe into three sections, discard one section and leave two sections, that is, "two-thirds lose one", and the sound produced by the remaining two-thirds length of the sounding pipe is the pure fifth tone of Gong (5);

3. Divide the collection and management into three parts, plus one part, that is, four-thirds of the collection and management length, which is "three points benefit one", so it is a pure four-degree bass-business (2);

4. Two-thirds of the commercial management is reserved, and "three points lose one", so it is concluded that the pure five-degree three treasures of commercial management are feathers (6);

5. "Three-thirds of the feather tube is beneficial to one", that is, four-thirds of the length of the feather tube is an angle tube, and the angle tube emits the pure four-degree bass of the feather angle (3).