Mathematics is everywhere. Professor Sheng laughed.

Sheng Yunxi glared at him with doting eyes.

The old man began to show off again.

"Art and mathematics are intertwined."

During the time that Yi Cheng was doing the question, the professor began to explain to everyone.

"In addition to being a world-renowned painter, Leonardo da Vinci was also a mathematician, and the golden section law is reflected everywhere in the smile of the Mona Lisa.

0.618 is the perfect ratio recognized in the painter's mind. That's why the composition is so beautiful when you use mathematics. ”

"The fastest line is a very beautiful curve, and when we draw it, it's like a girl's beautiful turning little white dress."

"We can use the two-dimensional Gaussian function to construct beautiful mountains."

Professor Sheng's eyes sparkled when he said this.

This may be a common problem among mathematicians who came out of Princeton University.

I think John Nash was also regarded as a freak back then, even though he had a very serious mental illness, but John Nash's wife was unwilling to let him leave Princeton University.

Why?

Because as Mrs. Yuan said, any place, any university, John would be regarded as a freak, as an alternative existence, and discriminated against.

Only in a freaky place like Princeton would people think of him as a genius.

Maybe this is like gathering like things, right?

Now Professor Sheng looks at Yi Cheng's eyes, and he also has a similar feeling of sympathy.

"In the same way, the essence of music is mathematics." Professor Sheng continued.

"Dad, I don't agree with that." Sheng Yunxi interrupted him with a smile.

"Haha, it's excessive, it's exaggerated, I'll put it another way, the principles of music can be explained and deduced mathematically." Professor Sheng laughed, "You didn't say anything wrong this time, right?" ”

Sheng Yunxi smiled, did not speak, and motioned for him to continue.

The old man finally had a time when he could play, so let him enjoy it.

Anyway, these theories are callousing to her and her mother's ears at home.

"For example, why does music use twelve equal temperaments?

That is, why should a note within an octave be divided into 12 equal parts, not 10 equal parts, or 13 equal parts?

Why choose a specific number of tones from the 12 chromatic scales to form a major scale, or a pentatonic scale?

Why is the pure harmony of fifths and the increase of fifths dissonant? ”

The professor asked with a smile.

More acutely: Why is the minor third harmonic and the second dissonant, even though they are equal intervals according to the twelfth equal law?

Again: to what extent is the criterion of harmony based on customary conventions, and to what extent is it based on physical considerations?

According to the Pythagoras school, the frequencies of the harmonic intervals have simple integer ratios.

But in the 12 chromatic scales of the 12 equal temperaments, the frequency ratio of any two tones is irrational.

How can this be explained? ”

Everyone looked at each other.

What the hell is this old man talking about?

I didn't understand math before.

Now I can't even understand the music.

"Dad, do you think others can understand this?" Sheng Yunxi glanced at him dissatisfied.

"Haha, I'm sorry, I'm sorry, I'm sorry." Professor Sheng apologized to everyone.

He ignores the level of object-orientation.

"To put it more simply, there are several very important characteristics of music:

Pitch, timbre, timbre, intensity.

Pitch makes up the melody of music, such as dolemifaso;

Time is the cornerstone of the beat and speed of the music, such as 44 beats, 43 beats, how many notes in a beat, if it is fast, it will give people a sense of intensity, and if it is slow, it will give people a sense of soothing.

Even without pitch, rhythm is enough to be at the heart of the music.

For example, when we listen to a drum kit, it's basically not a pitch change, it's a rhythm change.

The pitch expresses the mood of the music;

Timbre is a different interpretation of the color of the music, for example, the same piece, played on the violin and played on the piano, we hear completely different effects. ”

Hearing the professor's explanation, everyone finally had a basic understanding of music.

"We can deduce from the basic mathematical method of mathematics that any timbre can be described with absolute precision and precision from the point of view of sound waves by the method of a complete Fourier series. Therefore, as long as it is an instrument or timbre that exists in this world, it can eventually be synthesized and imitated by the method of Fourier series of mathematical methods. This is entirely achievable, at least in theory. ”

Professor Sheng spent more than ten minutes talking about it again.

This time he succeeded.

No one understood.

It's also strange to talk about humans, talking about music, talking about painting, talking about physics, and it feels easy to understand.

But when I go back to the math, I look confused.

Forget it.

The people who eat melons think, aren't we just here to eat a melon?

Why be so masochistic and listen to someone else's math class here?

The point is, you think you understand, but you don't understand anything.

Give you a candy and another slap in the face.

That's the most shocking thing.

……

Professor Sheng smiled at the corner of his mouth, and he was not ready to continue, he began to look back and look intently at Yi Cheng's mathematical derivation.

"Did you study music before, young man?"

He asked, somewhat confused.

"No, but I have some knowledge of music math."

Yi Cheng was telling the truth, when he acquired the math skill of lv4, all kinds of messy math knowledge was stuffed into his brain.

Among them are the 12 equal temperaments and harmonious intervals that the professor just mentioned...... Fourier series and so on.

When it comes to creating music with inspiration, Yi Cheng said that unless he is given a goddess of music, he will not dare to think of it.

But when it comes to writing music in mathematics, he still has a little bit of confidence.

"But, young man, there will be an infinite number of solutions to your solution." Professor Sheng reminded.

"And the further you go, the more solutions you have."

"Okay, I know." Yi Cheng said impatiently.

What is the most feared thing about doing questions?

I am most afraid of being disturbed by others.

As soon as I bothered, the train of thought was broken.

Professor Sheng closed his mouth strangely.

Young man, he is very strong-blooded.

"It is precisely because there are infinite solutions that there will be a steady stream of new songs coming out, and human creation, isn't it just to pick one of the infinite solutions that already exist?"

Yi Cheng was talking to himself as he wrote.

"Oh? Oh hehe......" Professor Sheng smiled very happily, he liked this young man more and more.

While everyone was watching Yi Cheng compose music with mathematics.

A shadow slipped into the barbecue table.

It was a bamboo pole girl with ankle-length hair.

In addition to his mediocre figure, his appearance is amazing.

Gong Sinan identified their location through her aunt's bag.

She sat down in seat number 6 and began to feast.

"It's really boring, doing such a simple math problem, where is there joy in eating?"

The goddess descends to the dreamland