The writing of music score is the place where mathematics shows the most obvious influence in music. In the score, we can find the time signature (4:4, 3:4 or 1:4, etc. ), the beat of each bar, whole notes, half notes, quarter notes, eighth notes and so on. Writing music should be suitable for the beat of each syllable per minute, which is similar to the process of finding the common denominator-in a fixed beat, notes of different lengths must be made into a specific beat. However, when composing music, composers can combine them with the strict structure of music score perfectly and effortlessly. Analyzing a complete work, we can see that each syllable has a specified number of beats, and all kinds of notes with appropriate length are used.

Music is not only related to mathematics, but also to proportion, exponential curve, periodic function and computer science. The followers of Pythagoras (585-400 BC) were the first people to combine music and mathematics in proportion. They found that there is a close relationship between the harmony of music and known integers, and the sound produced by plucking the strings depends on the length of the strings. They also found that harmony is produced by taut strings, the length of which is an integer multiple of the length of the original string. In fact, every harmonious combination of plucked strings can be expressed by an integer ratio. By increasing the length of the string to an integer multiple, all scales can be produced. For example, starting from a string with a C sound, then 16/ 15 of C gives B, 6/5 of C gives A, 4/3 of C gives G, 3/2 of C gives F, 8/5 of C gives E, and 16/9 of C gives D and 650 of C.

You may be surprised why the platform piano has its unique shape. In fact, the shapes and structures of many musical instruments are related to different mathematical concepts. Exponential function is one of them. For example, y=2x. Musical instruments, whether strings or wind music, all show the shape of exponential curve in structure.

The study of the essence of music reached its peak in the works of French mathematician Fourier in the 9th century/KLOC-0. He proved that all musical sounds, whether instrumental or vocal, can be described by mathematical expressions, which are the sum of some simple sinusoidal periodic functions. Every sound has three characteristics: tone, volume and timbre, which are different from other music.

The discovery of Fourier enables people to describe and distinguish the three qualities of sound through charts. Tone is related to the frequency of the curve, volume is related to the amplitude of the curve, and timbre is related to the shape of the periodic function.

Few people are familiar with both mathematics and music, which makes it difficult to synthesize music and design musical instruments with computers. Mathematical discovery: Periodic function is the essence of modern musical instrument design and computer sound design. Many musical instruments are made by comparing the sound image with the ideal sound image and then improving it. The faithful reproduction of electronic music is also closely related to periodic images. Musicians and mathematicians will continue to play an equally important role in the production and regeneration of music.