What is the application of the golden section, 0.618, in music?

Almost all of the world’s most famous buildings contain the “golden ratio”. Whether it is famous ancient buildings such as the pyramids of ancient Egypt, the Parthenon of ancient Greece, the Hoover Pyramid of ancient Egypt, the Taj Mahal of India, the Forbidden City of China, Notre Dame de Paris in France, or many outstanding modern and modern buildings all over the world. Their styles are different, but in terms of composition and layout design, they all use the rule of the golden section intentionally or unintentionally, giving people an overall harmony and pleasing beauty.

For example, the ratio of the height and width of the facade of Notre Dame Cathedral in Paris, France is 8:5, as is the length-to-width ratio of each window.

:::::Gold Partition is also found in beautiful music and poetry. It is said that in the 6th century BC, the ancient Greek mathematician and philosopher Pythagoras (580-500 BC) passed by a blacksmith shop one day and was attracted by the crisp and sweet sound of forging inside. He stopped and listened carefully. , intuitively determined that this voice had a "secret". He walked into his shop, carefully measured the sizes of the anvil and hammer, and found that the ratio between them was close to 1:0.618. After returning home, he took a wooden stick and asked his students to carve on the wooden stick. A mark that is positioned so that the distance between the two ends of the stick is unequal and yet looks satisfactory. After many experiments, a very consistent result was obtained, that is, dividing the stick AB at point C, the ratio of the entire section AB to the long section CB is equal to the ratio of the long section CB to the short section CA. Pythagoras then discovered that, Placing a shorter section on top of a longer section also creates the same proportions. This story shows that the earliest invention of the "golden section" seems to be related to sound. Later, musicians consciously used this proportion to "beautify" their works. Typical examples include the 7 pairs of interludes in Bach's "Goya" in D minor and the refrains in Woznesensky's poem "Goya".