Mathematics and Musical Pitch

"I'll remember that punch Wan Yebai."

"You!"

"Learn to control yourself, be a dutiful daughter, and stop causing trouble for your father."

Si Ming laughed heartily, not one to tolerate such behavior, and continued singing his invincible song.

Chapter 573 Mathematics and Music

At noon, Si Ming and his group, who were on their way, passed through a small town and found a restaurant. They sat down by the window, ordered the waiter to bring them one of each of the restaurant's signature dishes, and casually tossed a piece of silver into their hands.

Such lavish behavior naturally attracted the attention of others, especially since this small town was located between the Western Martial World Southern Martial World, a no-man's-land where lawless people were everywhere. However, Si Ming did not have the habit of pretending to be weak to deceive others, or rather, he had no interest in showing off in front of non- Spirit Transformation artists, as that would only lower his status. So he released a little bit of fierce aura.

With his cultivation level, even the slightest bit of his aura was as fierce as a storm to others, as if a ferocious beast was roaring with its blood-red maw open in front of them, spitting on their faces. Those with ill intentions suddenly changed color, their hair stood on end, and they immediately put away their inappropriate thoughts. One by one, they put on the appearance of honest people, eating obediently, not looking to the side, and even lowering their voices by three points.

Si Ming ignored these guys and said to Yuezheng Yao, "Before the dishes arrive, continue explaining the Yellow Bell Responding to the Pitch Formula's from before."

The Yuezheng Lineage has two scriptures: the "Nine Shao Pitch-Setting Art" and the "Yellow Bell Responding to the Pitch Formula". The former is a martial arts manual, and the latter is a music manual. The Yuezheng Lineage created the "Nine Shao Pitch-Setting Art" by integrating martial arts knowledge on the basis of the "Yellow Bell Responding to the Pitch Formula". It can be said that the "Yellow Bell Responding to the Pitch Formula" is the original.

Learning only the "Nine Shao Pitch-Setting Art" is not impossible. It's like a mathematical formula; once you know it, you can use it without needing to understand why it works. It just works.

Only by learning the Yellow Bell Responding to the Pitch Formula " can one understand how this mathematical formula is derived; one is to know what it is, and the other is to know why it is so.

Originally, Yuezheng Yao was intrigued after hearing Si Ming sing the "Invincible Song" and wanted to test his mastery of the "Nine Shao Pitch-Setting Art." However, she was shocked to find that Si Ming's skill in it was no less than her own. Si Ming had only been learning it for less than half a year, yet he had already surpassed her, the once-in-a-century genius of the Yuezheng Lineage. Even if it was just to save face as his teacher, she had to show off her skills, so she took out the "Yellow Bell Responding to the Pitch Formula."

"... Based on the five musical notes generated by the method of dividing and subtracting, musical notes continue to be generated up to the twelfth note, namely Yellow Bell, Great Lü, Taicu, Intermediate Bell, Cleansing of the Old, Middle Lü, Drooping Guest, Forest Bell, Equalizing Rule, Southern Lü, Non-Exhaustion, Responding Bell. A note is generated every eight positions, which is called the method of generating notes every eight positions."

According to Si Ming, the "eight-note interval" method refers to the so-called octave interval. From a scientific point of view, since the human ear tends to treat two notes as the same note when hearing an octave harmony, there are two notes with the same note name in the notation of two notes with an interval difference of octave. To put it in a somewhat inaccurate way, it is like the eighth note returning to the first note: Do Re Mi Fa Sol La Ti Do.

Si Ming thought that Yuezheng Yao would talk about the structure of the human ear, intervals, and pitch levels next, but he forgot one thing: the foundation of the Sea Continent civilization is metaphysics, not science, or rather, metaphysics is the science here.

"The method of generation by skipping eight positions originates from the Book of Classic of Changes. If we arrange the Yellow Bell (Yellow Bell) in a circle starting from the Zi position of the twelve palaces, the position of the harmonious tone is always the eighth. For example, the harmonious tone of Yellow Bell is Forest Bell (Forest Bell). Counting from Yellow Bell and Dalu (Great Lü), it is exactly the eighth position; in turn, Forest Bell Taicu Taicu Cluster), Cleansing of the Old generates Southern Lü (Southern Lü generates Yingzhong (Cleansing of the Old Responding Bell), Responding Bell generates Drooping Guest (Various Bells), Drooping Guest generates Dalu (Great Lü), Equalizing Rule generates Equalizing Rule (Great Lü), Intermediate Bell), Jiazhong generates Non-Exhaustion (Intermediate Bell), Non-Exhaustion generates Middle Lü Lü), Middle Lü generates Yellow Bell), all of which are eight positions apart."

Yuezheng Yao dipped her finger in tea and drew a hexagram on the table. She then explained, "What is meant by 'loss upon reaching three'? For example, Yellow Bell Forest Bell, Forest Bell Great Cluster. Yellow Bell and Great Cluster are exactly three positions apart. This is described as 'Yi and Bing meet and move towards Xu, Xin and Ren meet and gather at Chen, Dou and Niu receive the Qi of Geng and Ding, and Jin Yang receives the spirit of Gui and Jia.' For instance, Yi and Bing are three positions apart, exactly flanking the Xun Palace. Xun is opposite the Qian Palace. Yi is eight positions apart and generates Qian, and Qian is eight positions apart and generates Bing. In Feng Shui terms, this means that the Xun dragon must follow the water Yi and Bing, flowing together and returning to the Xu tomb."

Si Ming was dumbfounded. "What is all this about? How did a perfectly good piece of music veer into feng shui?"

Yuezheng Yao said in a serious tone, "It's not that music is related to feng shui, but rather that music is related to the Classic of Changes, and feng shui is also related to the Classic of Changes. The twelve earthly branches correspond to the twelve musical pitches, so the two can be used interchangeably. In fact, feng shui itself is a way of interpreting the Classic of Changes. Later generations forced their way into associating it with the water and soil in reality, which led to the misunderstanding."

Si Ming stared at the picture, looking at it from left to right, from top to bottom, but still couldn't figure it out.

Seeing that she had finally stumped the other party, Yuezheng Yao revealed a satisfied expression. When she had discussed music and martial arts with Si Ming earlier, he had practically emptied her knowledge with his "one-to-many" speed, making her question her life and wonder if she had wasted the past twenty-odd years.

Now she finally feels like she's back in the human world, truly living in this world.

"The principles of musical scales have many other applications, such as the elimination of Jia (甲) in musical notation, the return of the Eight Trigrams to their origins, the determination of destiny through the Five Tones, and the positioning of Heaven and Earth..."

"Wait a minute, I think I understand now!"

Si Ming suddenly shouted, then reached out and erased the characters for the Earthly Branches and the twelve numbers, replacing them with Arabic numerals and twelve letters. "It's actually just solving twelve unknowns in octal, right?"

Then he picked up his chopsticks and quickly wrote a bunch of formulas on the table.

Seeing this, the shopkeeper felt a pang of heartache for his table, but he didn't dare to point it out. Even a novice in martial arts would understand what it meant to carve words on a table with chopsticks, especially considering how effortlessly the other person moved, making it seem easier than carving tofu. It was something that could only be done with profound Internal Cultivation.

Although Yuezheng Yao had received an elite Lineage education, and her math skills were consistently below average, she could roughly understand Si Ming's thinking. She quickly reminded him, "Pure numbers can't explain it. The Bagua diagram above is also useful; it's not just for decoration. There are corresponding transformation relationships between the hexagrams."

"I understand that, it's algebraic geometry."

Just as he finished speaking, Si Ming looked puzzled and said, "No, the Bagua diagram isn't an octagon in the conventional sense. Its size and shape are meaningless; what's important is the positional relationship between objects. 'Yellow Bell generates Forest Bell' means that the set of Yellow Bell corresponds to the set of Forest Bell, so it's topology? Let's try to calculate it using Euler's formula."

What the hell is topology? And what is Euler's formula?

Yuezheng Yao had no idea who was teaching whom, and could only watch helplessly as Si Ming kept exclaiming "I suddenly understand!"

"Is he always like this?" Wan Ziling asked hesitantly.

Yuezheng Yao shook her head and said, "I'm sorry, I've only known him for a little over a year, so I don't really know what he's like. Perhaps you could ask his childhood sweetheart."

"I'd better not bother them; it might scare them."

Whether Liu Qingqing manifests in human form or speaks in the form of blood droplets, it will cause a commotion.

Seeing that Si Ming was completely absorbed in writing and drawing on the table, oblivious to everyone else, the two had no choice but to change tables and let the restaurant serve the food first, ignoring him and paying for the table in return.

"It's truly unbelievable that he's the same Sick Young Master who founded the Heavenly Martial Alliance, and who even killed Li Ban, the sect leader of the Blood Abyss Sect, and defeated the Beast King Anye..."

When Wan Ziling resided in Liu Qingqing's body, her consciousness was hazy and she was unable to perceive the outside world. Only when Shang Yu was about to fulfill her wish could she sense the outside world. Therefore, when she woke up, the only thing she knew was that Si Ming easily defeated Li Ban, and that Li Ban had deliberately set up a trap to avoid Si Ming.

So when she learned about Si Ming's identity and his various "feats" from Liu Qingqing during her journey, she found it hard to believe. If she hadn't been on the same page as Liu Qingqing and known that she wasn't lying, she would have definitely thought it was a prank.

Moreover, after learning that Si Ming had saved the Evil-Slaying Sword School, she felt that her previous attitude was indeed disrespectful to her benefactor. However, she couldn't bring herself to apologize, since Si Ming's threat of "I'll beat your Laozi" was too infuriating and left no room for reconciliation.

Yuezheng Yao asked, "Do you think meeting them is not as good as hearing about them?"

Wan Ziling thought for a moment and said, "In terms of battle record, it should be said that seeing is believing... There is only one thing I can be sure of, and that is that a person's martial arts level has little to do with his personality."

When the waiter started serving the dishes, the two of them devoured them without any hesitation. After all, they were both martial artists and had large appetites, even though they were women. Although they could replenish their Primal Qi through martial arts training even if they ate less, there was no need to deprive themselves of food if they had the means.

After finishing the meal, Si Ming was still muttering to himself, so the two of them ordered a few more cold dishes and snacks and waited on the side without interrupting him. They even stood guard to prevent others from bothering him.

They believed that Si Ming had entered a profound and mysterious state of martial arts comprehension, a state that was rare and difficult to attain. Most martial artists might never experience it in their entire lives, and being interrupted would be a great regret, and they would definitely resent the person who interfered, since both of them had similar experiences.

A moment later, the two suddenly heard gongs and drums being played on the street below. The sound was particularly jarring. Startled, they quickly turned around and saw Si Ming's face light up with joy. He excitedly slammed his palm down, shattering the entire table into pieces.

"I understand now, it's algebraic topology! From the 'Yellow Bell Responding to the Pitch Formula' to the Nine Shao Pitch-Setting Art,' the essence is the application of algebraic topology in modern particle physics, from mathematics to physics, from theory to practice, from hypothesis to reality!"

Wan Ziling blinked and said to Yuezheng Yao, "I understand every single word he says, but I can't understand them when they're put together. Is it only by understanding these profound martial arts theories that one can reach his level of martial arts mastery?"