First, the multiple relations in mathematics.

B. Mathematical geometry embodied in music sound.

Digital elements in music.

D, there are no mathematical elements in music.

Music is the externalization of mind and emotion in sound, and mathematics is the product of highly abstract and logical thinking about objective things. So, does "sentimental" music have anything to do with "cold" math? Our answer is yes, and we can even say that music and mathematics are mutually infiltrated. Confucius said that the six arts are "ritual, music, shooting, imperial, calligraphy and number", in which "music" refers to music and "number" refers to mathematics. That is, Confucius put music and mathematics together.

China lyre (that is, guqin) takes chord length 1, 7/8, 5/6, 4/5, 3/4, 2/3, 3/5, 1/2, 2/5, 1/3. Cha Fuxi, a famous guqin artist in China, pointed out a long time ago that to learn guqin well, you must have certain mathematical literacy. 173 1 year, Euler, a great mathematician, wrote a monograph, A Novel Study of Music Theory Based on the Principle of Exact Resonance.

Later, some experts thought that this book was "too musical" for mathematicians and "too mathematical" for musicians. Mathematician Uhard Euler also wrote a paper on the relationship between harmony and integers, which shows that mathematicians pay attention to and study music.

1970, Liu Dehai, a famous Chinese pipa player, decided to use the "optimization method" to find the point that can produce the best timbre on each string of the pipa. Soon, Professor Hua helped him solve this problem with mathematical methods, and the pop-up sound was particularly pleasant at the chord length of112. 1At the National Pipa Concert in May, 1980, after listening to the performance of "The Best Point", dozens of performers all thought that there might be a profound internal connection between mathematics and music.

With the development of the times, people find that sound is a kind of wave that can cause hearing due to the vibration of objects, and it also contains sine functions, and each sound is composed of pure tones (pure tones are single tones). Having two basic characteristics of tone and loudness). The mathematical model of pure tone is y = asinω t.

Just like the music we usually hear, it is not just a sound, but a combination of many sounds, which is called polyphony. Generally, the function of the sound we hear is like this. The abstract beauty of mathematics and the artistic beauty of music have stood the test of years and infiltrated each other. Nowadays, with the technology of mathematical analysis and computer display, the eyes can also distinguish melody, and there is still a lack of more suitable mathematical tools to explore the deeper mystery of musical beauty, which requires the cooperation and efforts of musicians and mathematicians in the future.