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One day 500 years ago, the ancient Greek philosopher Pythagoras was out for a walk. He passed by a blacksmith shop and found that the sound of forging inside was louder than other blacksmith shops. Harmonious and pleasant. He walked into the shop, measured the size of the hammer and anvil, and discovered a rule. The harmony of the sound is related to a certain proportion of the volume of the sound source. Afterwards, he experimented on the strings and further discovered that as long as a vibrating string is divided in proportion, pleasant intervals can be produced: for example, 1:2 produces an octave, 2:3 produces a fifth, and 3:4 produces a pleasant musical interval. Four degrees and so on. In this way, Pythagoras discovered the connection between music and mathematics for the first time in the world. He then discovered that qualitative differences in sounds (such as length, height, severity, etc.) are determined by differences in the number of articulators. For thousands of years, studying the relationship between music and mathematics has been a popular topic in the West. From the Pythagoreans of ancient Greece to modern cosmologists and computer scientists, they have all been more or less influenced by the idea that "the entire universe is Influenced by the concept of "harmony and number", Kepler, Galileo, Euler, Fourier, Hardy and others all devoted themselves to studying the relationship between music and mathematics. Mathematical geometry and philosophy go hand in hand, penetrating into the entire spiritual life of Westerners and all artistic fields, becoming a major feature of Western art. St. Augustine even left a famous saying: "Numbers can also transform the world into music that communicates with our hearts." Modern composers Bartok, Schoenberg, Cage and others have all conducted bold experiments on the combination of music and mathematics. The Greek composer Xenakis (1933~) created "algorithmic music", replacing musical thinking with mathematical methods. The creative process is also a calculation process. The names of the works are similar to mathematical formulas, such as "S+/10-1.080262" for 10 pieces It was written for musical instruments and was calculated on February 8, 1962. Maccahel developed Stockhausen's idea of ??"graphic music" (music of reading and seeing) and made "geometric music" by rotating geometric figures.

Mathematics is a science that studies the quantitative relationships between spatial forms in the real world. It has long been transformed from a science of counting into a science of formal symbol systems. The use of symbols makes mathematics highly abstract. Music is the art of studying sound forms and controlling them in the real world. It also uses symbology and is the most abstract of all arts. Mathematics gives people the impression of being monotonous, boring, and indifferent, while music is rich, interesting, and full of emotions and fantasy. On the surface, music and mathematics are "insulated" and have nothing to do with each other, but this is not the case. The famous German philosopher and mathematician Leibniz once said: "Music, in terms of its foundation, is mathematical; in terms of its appearance, it is intuitive." And Einstein said it even more interestingly : "Our world can be composed of musical notes or mathematical formulas." Mathematics is the arrangement and combination of numbers as basic symbols. It is the quantitative abstraction of things, and through various formulas, it reveals the characteristics of the objective world. Internal laws: Music is an arrangement and combination of notes as basic symbols. It is an abstraction of natural sounds, and it organizes and arranges them through the grammar that connects these symbols. It summarizes various activities in our subjective world. It is precisely in Abstraction connects music and mathematics. They both reflect and grasp the infinite through the finite.

Mathematics and music are located at the two extremes of the human spirit. All a person’s creative spiritual activities unfold within the scope of these two opposite points, and what humans create in the fields of science and art Everything is distributed between these two. Music and mathematics are beautiful flowers blooming in the realm of abstraction. With these two flowers, we can grasp the spiritual wealth created by human civilization. The Greek philosopher and mathematician Pythagoras, known as the ancestor of number theory, believed: "The reason music is sacred and sublime is because it reflects the relationship between numbers as the essence of the universe." Wherever there are numbers in the world, there are beautiful. Mathematics, like music and other arts, can arouse people's aesthetic feeling and aesthetic taste. In the creative activities of mathematicians, aesthetic factors such as emotion, will, belief, and hope are also involved. The concepts, axioms, theorems, formulas, and rules created by mathematicians are like all art forms such as poetry, music, painting, sculpture, drama, Like movies, it can make people emotionally intoxicated and enjoy the beauty from it.