Music contains many mathematical elements (ABC).
A. Multiple relationships in mathematics.
B. Mathematical geometry reflected in music sound.
C. Digital elements in music.
D. There are no mathematical elements in music.
Music is the externalization of soul and emotion in sound, and mathematics is the product of highly abstract and logical thinking of objective things. So, is there a relationship between "sentimental" music and "cold" mathematics? Our answer is yes, we can even say that music and mathematics are interpenetrated. The six arts mentioned by Confucius are "ritual, music, archery, charioteering, calligraphy, and mathematics", among which "music" refers to music and "mathematics" refers to mathematics. That is to say, Confucius already juxtaposed music and mathematics.
The string length of our country's lyre (i.e. Guqin) is 1, 7/8, 5/6, 4/5, 3/4, 2/3, 3/5, 1/2, 2/5 , 1/3, 1/4, 1/5, 1/6, 1/8 are the so-called 13 emblem positions, including the purity of 1 degree to 22 degrees, which is very natural and is an ideal string instrument. Zha Fuxi, the famous guqin player in my country, has long pointed out that to learn guqin well, one must have certain literacy in mathematics. In 1731, the great mathematician Euler wrote a monograph "Novel Research in the Theory of Music Based on the Exact Principle of Resonance".
Some experts in later generations believed that this book was "too musical" for mathematicians and "too mathematical" for musicians. The mathematician Unhard Uller also wrote The paper "On the Relationship between Harmony and Integers" shows mathematicians' concern and research on music.
In 1970, the famous Chinese pipa player Liu Dehai decided to use the "optimization method" to find the point on each string of the pipa that can produce the best timbre. Soon, Professor Hua Luogeng used mathematical methods to help him solve this problem. , at 1/12 of the string length, the sound that pops up is particularly beautiful and pleasant. At the National Pipa Concert in May 1980, dozens of performers listened to the "Best Point" performance and believed that there might be a profound internal connection between mathematics and music.
With the development of the times, people have discovered that sound is a wave that can cause hearing due to the vibration of an object. The sound also contains a sine function, and each sound is composed of a pure tone (a pure tone is a single tone. It has the two basic characteristics of pitch and loudness) synthesized. The mathematical model of pure tone is y=Asinωt.
The musical sound we usually hear is not just one sound, but a combination of many sounds, called compound sounds. Generally, the function of the sound we hear is like this. The abstract beauty of mathematics and the artistic beauty of music have withstood the test of time and penetrated each other. Nowadays, with mathematical analysis and computer display technology, the eyes can also distinguish the rhythm. However, there is still a lack of more suitable mathematical tools to explore the deeper mysteries of musical beauty, and it still needs the future cooperation and efforts of musicians and mathematicians.