Chapter 238: The Law of Twelve Equals

So the old man is now playing the piano and writing all day long, plus the trouble of finding Su You.

The map of Yizhou Road has finally been made, and this is the first time that anyone has been able to see the complete water conservancy project in the Dujiangyan Irrigation Area.

Zhao Pan looked at the grand map and kept asking Su You what the various legends meant.

Su You was very impatient, because he was enthusiastically preparing to educate Old Man Zhao with a copper rod.

Not to beat him, but because not so long ago, the two had a musical disagreement.

Old man Zhao loves to play the piano, in fact, the doctors and ladies of the Song Dynasty basically know this, but Su You doesn't understand music.

This baby can't learn well, so Old Man Zhao scolded him for being stupid and stupid.

Then Su You told Old Man Zhao that for him, sound is sound waves, and music is a sound wave superimposed on multiple sounds.

There are two most common types of superposition: one is called harmonic superposition and the other is called beat superposition.

He also told the old man that each single tone is made up of multiple harmonics, and the superposition of multiple single tones forms a beat. Monophonies and beats from different instruments intertwine to form harmonies, and finally a series of harmonies make up the beautiful music.

Then the old and the young began to tear up their daily lives again.

Old man Zhao looked at Su You contemptuously, from "Chinese" to "Pipe • Ground Member", and from "Pipe" to "Lü's Spring and Autumn • Musical Rhythm", and also expounded the relevant content in "Huainanzi" in the middle, crushing and crushing, and finally summed up three words - you! No! Understand!

This thing is called the number of laws, which is the foundation of music, and for the ancient Chinese, it is to use mathematical methods to obtain five tones and twelve laws.

This method is called the "three-point profit and loss method". The basic principle is to use a sounding tube with an absolutely uniform diameter as the base, and the scale obtained from this base is - Gong;

Then, the sound tube is divided into three sections, and one of them is discarded to retain two sections, which is "three points lose one", and the sound produced by the remaining two-thirds of the length of the sound tube is the pure fifth treble of the "palace" - sign;

Divide the sign into three parts, plus one part, that is, four-thirds of the length of the sign, this is "three points benefit one", so the pure fourth bass of the sign is produced - quotient;

The business management retains two-thirds, and "three points lose one", so the pure fifth treble of the merchant is obtained-feather;

The "three-thirds of the feather", that is, the four-thirds length of the feather, is the horn tube, and the horn tube emits the pure fourth bass of the feather - the horn.

In this way, after having the basic tone "Gong", after two "three-point loss one" and two "three-point plus one", the five scales of Gong, Shang, Jiao, Zheng, and Yu are generated.

Gong Sheng Zheng, Zheng Sheng Shang, Shang Sheng Yu, Han Sheng Jiao, because it is "five or five phases", therefore, the musicians talk about the five scales, they do not say "Gong, Shang, Jiao, Zheng, Yu", but "Gong, Zheng, Shang, Yu, Jiao".

In the record of "Guanzi", Guan Zhong actually only gave birth to five sounds: Gong, Shang, Jiao, Zheng, and Yu.

"Lü's Spring and Autumn Period" continued to give birth to each other eleven times on the basis of Guan Zhong's five tones, so that the symbiosis of the twelve laws was completed - Huang Zhong, Lin Zhong, Tai Tuan, Nan Lu, Gu Xian, Ying Zhong, Rui Bin, Da Lu, Yi Ze, Jia Zhong, Wu Ji, Zhong Lu.

These twelve laws are further distinguished, and there are six yang laws and six yin laws, the six yang laws are called "laws" and the six yin laws are called "lu".

This is the origin of the saying "Lu Lu Tunes Yang" in "Thousand Character Text".

Intervals are important because the ratio of the lengths of two homogeneous strings is equal to the inverse proportion of the frequency of the sound they emit. If you know the exact ratio between these lengths, you can work out the best standard of rhythm.

Unfortunately, there is a problem with the three-point profit and loss method - when the "Qinghuang Bell" after the 12th law is born, the "Qinghuang Bell" cannot return to the original starting law, which leads to the fact that the 12 laws cannot be repeated, and the perfect cycle and transposition cannot be realized.

Because the 12th is related to the lunar season, the people who studied this issue in ancient China were generally mathematicians, astronomers, and people who had a deep study of the calendar, and then they studied this musical problem.

Waves of geniuses have studied for thousands of years, and there have been many masters in the middle, until the Ming Dynasty, the ninth grandson of the musician Wang Ye Ming Taizu in the Wanli period, the sixth generation of the son of Zheng Fan, Zhu Zaiyu, who is known as the "law saint", studied the "new law secret rate", and perfectly and accurately calculated the interval of the uniform scale, which can be taken as the twelfth root of two - that is, the twelve equal temperaments that guide modern music.

By the end of the sixteenth century, the missionary Matteo Ricci had brought the Law of the Twelve Equals back to the West from China, and it was not until the seventeenth century that it began to spread widely on the European continent.

Since then, Chinese civilization has entered a period of decline, which has made the theoretical level of Chinese classical music and Western music more and more wide.

In the West, the golden rule of the 12 equal temperaments was obtained, and new harmonic theories, natural keys, and various related keys were developed, and new performance and composition techniques were developed, as well as more complex harmonic techniques, counterpoint techniques, and of course, most importantly, staves—and finally modern music theory.

The 12 equal temperament is easy to remember: two monotones with a frequency ratio of 1 to 2, that is, the interval between two strings with a length ratio of 2 to 1, is defined as a "pure octave", and this pure octave is divided into twelve segments according to the twelve equal law - and thirteen monotones can be constructed, a perfect cycle.

As an engineering dog who has a deep understanding of ancient cold knowledge, Su You often uses this example to educate the students of the guitar club in the university dormitory, of course, all of them are white eyes - are you here to be funny? Come on, come on guitar for you, come on a song to listen to?

Anyway, by now, all that's left is the interesting math problem, and the method that Su You knows is to turn irrational numbers into continuous fractions, and then calculate the approximate value of the twelfth power root of two by truncating the value.

Accurate to six decimal places.

This method was seriously doubted by Su You, a Chinese mathematician and astronomer Zu Chongzhi. For he raised the ratio between the return year and the synodic month of the previous calendarists from seven leaps in nineteen years to one hundred and forty-four leaps in three hundred and ninety-one years—two ratios that coincide with the different truncated values of the consecutive fractions.

Similarly, pushing the π value from 22 to 7 to 355 to 113 is the same as the different cut-off values of the fraction.

However, Zu Dada's mathematical works have been invited out of the imperial court Ming arithmetic examination textbooks since the Tang Dynasty - too advanced and profound, and no one can understand them.

Then, bitterly lost. This is the pathos of mathematics expressed in square words.

This is a digression, Su You wrote the calculated value of the twelve equal laws into the letter, and asked Ke Longli to make thirteen copper rods of different exact lengths according to the recorded length.

The copper rod has just arrived, so we won't discuss the map today, Old Man Zhao, hurry up and stretch your face over!

For the Song people, there is no dispute that is a gamble - now called Guan Pu - cannot be resolved, and if there is, then two ...... Well, it still depends on whether one side loses all of them.

This is a big gamble, Old Man Zhao gambled on his white turtle, and Su You gambled - a pair of glasses, plus a set of "Southwest Atlas" sorted out by Longchang Period.

It's quite shameless, but you have to speak with conscience, for the bigwigs in the DPRK and China, the value of the white turtle really can't be compared with the "Southwest Atlas".

Everyone felt that they had won and that it was a good deal—until Old Man Zhao took turns striking thirteen copper rods with small copper sticks.

Thirteen copper rods, the vertices are exactly the same, and the bottoms are connected to make a beautiful curve.

A pleasant voice sounded, but Old Man Zhao's face became more and more pale.

Knocked again, knocked again, knocked again......

Old man Zhao finally gave up struggling, and the copper rod in his hand trembled as much as the beard on his face: "You...... How do you do it......"

Su You was proud: "This is an interesting mathematical problem, and mathematics is my forte. If you give me the white turtle, I will give you glasses, give you the "Southwest Atlas", and then tell you this principle, how about it? ”

Old man Zhao didn't hesitate at all: "Deal!" ”

That's a huge achievement! It's not a musical achievement, it's a political achievement!

The Song Dynasty tried many times to restore and reconstruct ancient ritual music, and the biggest problem was the Dinghuang Bell and Zhulu.

This is really not an exaggeration, the Song Dynasty gathered the best politicians, historians, musicians, scientists, mathematicians, astronomers to solve this problem, Taichang Temple about the dispute over the law, are about to overthrow the imperial court!

Zhao Pan continued to tremble with a small copper stick in his hand, he didn't know whether to call the kid in front of him a stupid donkey or a genius. He is said to be as stupid as a donkey because this kid has no idea what is going on. said that he was a genius because the problem of free transfer that had plagued people for thousands of years was solved by this kid in front of him!