The literary giants of the late Ming Dynasty began by copying books

Chapter 84 The Law of Twelve Equalities

Wang Wenlong smiled and said: "I calculated the Twelve Equal Temperaments for Prince Zheng. Mr. Boliang asked me what kind of music there is in Europe. In fact, our Ming Dynasty's Twelve Equal Temperaments are the real treasure."

As Wang Wenlong spoke, he explained the principle of the law of twelve equals. The key to this is to find out the twelfth root of two. The calculation was very difficult under the mathematical conditions at this time. In order to calculate the result, Zhu Zaiyu created an effective The extremely large abacus of 81 gears took several years of calculations to arrive at the final figure.

The principle of the law of twelve equals is not complicated. After Wang Wenlong explained it, several people understood the process after thinking for a while, and then they all praised the ingenuity of this law system.

Zhu Zaiyu was a great master of ritual music in this era. He revised the Twelve Equal Temperatures not out of hobby, but to solve problems during royal Yayue sacrifices.

The concept of twelve temperaments has long been proposed in Chinese classical music, but it has always been based on the mutual generation rate of fifths. After calculation, there is no way to form a perfect octave interval.

At this time, people associated the Twelve Laws with the twelve months. Since all phenomena cycle through the twelve months of the year, the Twelve Laws should also begin again and again.

Officially, in order to achieve this theoretical perfection, Zhu Zaiyu carried out the calculation of the twelve equal laws. This is a nationwide project. Although the twelve equal laws have not been published, they have been used in royal sacrifices. , Wang Wenlong would be crazy to compete with Zhu Zaiyu for this achievement.

Anyone who is familiar with music has heard of Zhu Zaiyu's name.

Wang Jide asked in confusion: "How come we don't know about this, but Jianyang is overseas and has better information?"

Wang Wenlong said vaguely: "I also learned about this matter by chance in the outer vassal. Prince Zheng calculated this result for at least more than ten years, and it was probably kept secret. At that time, I heard that the source of this matter was a maritime merchant, and he claimed to have gone there Crossing Henan, I don’t want to say more about the specific situation.”

After Wang Wenlong explained it, everyone doubted his presence. At this time, Zhu Zaiyu was known as the Sage of Law, and he was famous in the Ming Dynasty.

Many people know that there have been scandals in King Zheng's lineage where ten of his sons seized the throne. In order to inherit the throne, the descendants falsely accused each other of treason, which caused a lot of trouble for the whole family. Zhu Zaiyu has also seen this since he was a child. Therefore, he did not want to attack the king.

Everyone thought that the sea merchant Wang Wenlong saw must be a retainer who escaped during the chaos in King Zheng's lineage during the Jiajing period. At that time, it was normal for such things to happen to him and to travel to the West.

Wang Wenlong smiled at Wang Jide and said: "I have also communicated with some European missionaries in the West. Their music is different from the music of the Ming Dynasty and has a lot of mathematical emphasis. For example, there is a kind of counterpoint in their music..."

Wang Jide also studied the law a lot. Although the terminology of the law between China and foreign countries is different, Wang Wenlong explained it and Wang Jide quickly understood the principle of counterpoint.

Wang Jide is very interested in this composition method that is similar to the mathematical reasoning process: "The music of these Europeans is quite interesting."

Wang Wenlong said with a smile: "Europeans have been pursuing strict counterpoint, but they have always been unable to achieve the level of harmony when changing the tone. At that time, I have been thinking about the effect of their method if they use the twelve equal laws... …”

When Wang Wenlong said this, he saw Wang Jide's eyes getting bigger and bigger. Wang Wenlong smiled inwardly, knowing that Wang Jide understood what he meant.

The law of twelve equals was not shelved and never used after being studied by Zhu Zaiyu, as many people have said.

Books such as "Zi Gong Riyue Shu", which records the sacrificial music of the palace and ancestral temples in the Ming Dynasty, are full of the name of "Zheng Shizi", and highly praise Zhu Zaiyu's achievements. In fact, many elegant music occasions in China in later generations used twelve Well-tempered instrument.

However, the influence of the Twelve Equal Temperaments in traditional music is limited to this. For the court music of these years, due to the pursuit of neutrality and balance without complex tones, the advantages of the Twelve Equal Temperaments are basically not revealed.The reason why European music uses equal temperament is that they began to study harmony. The so-called harmony is the combination of several different melodies to achieve a beautiful effect.

This requires that notes and notes maintain a harmonious interval relationship. As European music becomes more and more complex and changeable in melody, without twelve equal temperaments, what is played after several key changes will be inaudible.

Therefore, Europeans had to study the law of twelve equals and apply it greatly.

The charm of the Twelve Equal Temperaments can only be revealed after you are familiar with harmony and composing music. After opening this door, European music officially stepped out of the Middle Ages and entered the era of classicism with numerous masters.

Wang Wenlong asked himself that he did not have the ability to compose music, but Wang Jide who was present was an expert at it.

Wang Jide was prompted by Wang Wenlong and he became interested. He nodded repeatedly: "It's interesting. I will try to compose a piece like this using the harmonic method when I go back."

Wang Wenlong took the initiative and suggested: "I thought that if I want to show the benefits of equal temperament, I need to use each temperament of the twelve temperaments as the main tone, and each main tone adopts two modes, and make a total of 24 songs."

Wang Jide's eyes became brighter and brighter as he thought about it, and he said excitedly: "This is a good idea."

Wang Wenlong smiled, this was the creative idea behind the "Well-Tempered Clavier" by Bach, the "Father of Classical Music" in his previous life, which was known as the "Old Testament of Classical Music". As soon as this book was published, European music has left the world behind. other areas.

Wang Wenlong drew the pattern of the staff on the paper and briefly introduced it to Wang Jide. This thing came from the twelve equal temperament. Wang Jide could quickly understand it at his level, and he admired the notation method of the staff.

Then Wang Wenlong drew two staffs played simultaneously on the paper and quickly marked out the melody.

Wang Jide found it quite difficult at first glance, but soon became familiar with it and sang softly according to the notes.

He had an absolute sense of pitch and it was not difficult to sing the music. As he sang, Wang Jide showed a look of surprise on his face again.

"These two melodies are inverted, how can they still be in such perfect alignment?"

He confirmed again and again, and sure enough, he saw the two melodies written by Wang Wenlong that were played at the same time. One melody was played in the forward direction, and the other melody was flipped left and right and played in reverse starting from the last note of the first melody.

Moreover, the two melodies actually counterpoint each other, forming a harmonious relationship.

"The above melody is what Europeans call a 'canon'. The writing method is such that a piece of music in one tone chases a piece of music in another tone from beginning to end. The two pieces of music are entangled with each other, giving people a sense of infatuation. I occasionally had a small work, and at that time I wrote two canons that were turned over and harmoniously counterpointed on a sea ship, one running forward and one running backwards, which probably showed the essence of European counterpoint."

What Wang Wenlong wrote was actually Bach's masterpiece Canon the Crab, which is also the work that best reflects his integration of mathematics into composition.

(End of this chapter)