The writing of music score is the place where mathematics shows the most obvious influence in music. In music, we can find time symbols (4:4, 3:4 or 1:4, etc. ), the beat of each bar, whole notes, half notes, quarter notes, eighth notes, etc. Writing music should be adapted to the beat of each syllable per minute, which is similar to the process of finding the common denominator-merging into one. Notes of different lengths must be combined into a specific beat. But composers can combine them with the strict structure of music score beautifully and effortlessly when creating music. When analyzing a complete work, we will see that each syllable has a specified number of beats and uses various notes of appropriate length.

Besides mathematics and music score, music is also related to proportion, exponential curve, periodic function and computer science. The followers of Pythagoras (585-400 BC) first combined music and mathematics in proportion. They found that there is a close relationship between the harmony of music and known integers. The sound produced by plucking a string depends on the length of the string. 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, the harmonious combination of each plucked string can be expressed by integer ratio. By increasing the length of the string to an integer multiple, all scales can be produced. For example, starting from the string with the sound of C, then B is given by 16/ 15 of C. 4/3 of C gives G, 3/2 of C gives F, 8/5 of C gives E, C 16/9 gives D, and C1/.

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 research on the nature of music sound reached its peak in the works of French mathematician Fourier in the19th century. 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 the characteristics that distinguish it from other musical sounds.

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 use computers in music synthesis and musical instrument design. Mathematical discovery: Periodic function is the essence of modern musical instrument design and computer sound design. Many musical instruments are made by comparing the image of their voices with that of ideal voices and then improving them. The faithful reproduction of electronic music is also closely related to periodic images. Musicians and mathematicians will continue to play equally important roles in the production and reproduction of music.