The writing of music scores is the most obvious place where mathematics shows its influence in music. In music scores, we can find the time signature (4:4, 3:4 or 1:4, etc.), each The beat of a measure, whole note, half note, quarter note, eighth note, etc. To compose music, make it suitable for the number of beats per syllable. This is similar to the process of finding a common denominator - in a fixed beat, Notes of different lengths must fit together into a specific beat. However, when the composer created the music, he was able to organically integrate them with the strict structure of the score beautifully and effortlessly. For a complete work Analyzing, we will see that each syllable has a prescribed number of beats, and notes of various appropriate lengths are used.

In addition to the obvious connection between mathematics and musical notation, music is also related to proportion and exponent. Curves, periodic functions, and computer science are related. The followers of Pythagoras (585-400 BC) were the first to use proportions to combine music and mathematics. They discovered that there is a connection between the coordination of musical sounds and the knowledge of integers. There is a close relationship between plucked strings and the sound produced depends on the length of the string. They also found that the consonance is given by a taut string whose length is an integer ratio to the length of the original string. In fact, when plucked Every harmonious combination of strings can be expressed as an integer ratio. The entire scale can be produced by increasing the length of the string to an integer ratio. For example, starting with a string that produces the note C, then 16/15 of C Give B, 6/5 of the length of C gives A, 4/3 of C gives G, 3/2 of C gives F, 8/5 of C gives E, 16/9 of C gives D , 1/2 of C gives the bass C.

You may be surprised, why does the grand piano have its unique shape? In fact, the shapes and structures of many musical instruments are related to different mathematical concepts. Exponents Function is one of them. For example, y=2x. Musical instruments, whether string or wind instruments, reflect the shape of exponential curves in their structure.

The study of the nature of music began in the 19th century It reached its pinnacle in the works of the French mathematician Fourier. He proved that all musical sounds, whether instrumental or vocal, can be described by mathematical expressions. They are the sum of some simple sinusoidal periodic functions. Each sound has three Three qualities: pitch, volume and timbre, which are distinguished from other musical sounds.

Fourier's discovery allows people to describe and distinguish the three qualities of sound through diagrams. Tone and Curve It is related to the frequency, the volume is related to the amplitude of the curve, and the timbre is related to the shape of the periodic function.

Few people are proficient in both mathematics and music, which makes computers used in synthetic music and musical instrument design. It is difficult to succeed. The discovery of mathematics: periodic function is the essence of modern musical instrument design and computer sound design. Many musical instruments are manufactured by comparing the image of the sound they produce with the image of the ideal sound of these instruments and then improving it. Electronics The faithful reproduction of music is also closely related to periodic images. Musicians and mathematicians will continue to play equally important roles in the generation and reproduction of music.