Yesterday, I helped others to write a music analysis. My younger brother and sister insisted that I write this article about the three-point profit and loss method, and I have been wandering for fear of writing it badly. After all, to write such a theory, the written logic and one's own knowledge system must be clear enough to ensure that what is expounded can be accepted by everyone and not too literal. In short, it is very tangled, and now writing is also very tangled.

The method of three-point gain and loss was first seen in Guan Yuan Di. The calculation method uses "loss" and "gain" to reduce or increase the length of unit string as a reference for pitch frequency. According to legend, Guanzi was written by Guan Zhong and his disciples, and it is the earliest monograph on land classification in China. In fact, it is to teach people how to plant land or what landforms are suitable for planting, and the types of springs.

At the beginning of "Land Man", it says: "The husband is in charge of the world, and his application is seven feet." Nowadays, people in China are roughly as follows: Guan Zhong rules the world, and it is stipulated that one act represents seven feet deep. I won't quote the following words. Interested friends can search online.

Let's choose a passage about music and pick it out: "Anyone who listens to it is as scary as a pig." Whoever listens to feathers is like singing a horse in the wild. Anyone who listens to the palace is like a cow singing in the middle. Anyone who listens to business is like a lost sheep. If you listen to the horn, it will be as clear as a pheasant climbing a tree. All five tones are played first, the first three, the fourth and the ninth, so it is the first of Huang Zhong and Xiao Su, and it becomes a palace. One third is good, and eight percent is a sign. It's not that three points are not cheap and enough, so it's business. There are three points, each in its place, so it is feathered. There are three points, to ride, to be sufficient, so there is an angle. "

The first five sentences use five metaphors to describe the sound made by deep soil and underground springs. The key calculation method is the latter paragraph. To get the pentatonic scale, the chord length of a unit should be divided into three parts and then divided into four parts. That is to say, the four-part multiplication is 998 1, which produces the tonic "gong", which is the first step. To put it bluntly, Xiao Su refers to string, which is actually what we call string; Step 2, take the chord length of this palace, that is, 8 1, as the unit chord length, and each chord length is 27. On this basis, the chord length is increased by 27 units, and the sound sign with the chord length of 108 is obtained. Common sense tells us that the longer the chord length of a vibrating object, the lower the vibration frequency and thus the lower the pitch. So the "sign" generated in the second step is four degrees lower than the original "palace"; In the third step, we don't take 8 1 as the unit chord length, but choose the "symbol" 108 obtained in the second step as the unit chord length. The second step is a "gain", so now it is a "loss". As a result, 108 is divided into three parts, each of which is 36 unit chord lengths. The fourth step, the chord length is 72, which is divided into three parts, each part is 24 units, and then one part is "beneficial" to get the "feather" sound with a chord length of 96 units; Fifth, the chord length of 96 is divided into three parts, each part has 32 units, followed by a "loss" part, and the "angle" sound with a unit chord length of 64 is obtained. At this point, the general idea of this passage in the article of local staff has been clearly shown.

① Gong 8 1② Qian 108③ Quotient 724 Feathers 96⑤ Angle 64, which is a traditional national pentatonic sound pattern in China. Judging from the cultural relics unearthed from our Jia Hu bone flute, don't most bone flutes that can emit five to seven sounds well confirm the perfection of practical guiding theory? As a matter of fact, Jiao Zhengyu of Wuyin Gong once belonged to Jin Mu Fire and Water in the Yin-Yang and Five Elements, which has five directions: east, west, north, south, five internal organs, heart, spleen, lung, kidney, five tastes bitter, five tastes burnt and smelly, five colors blue, red, yellow, white, black, five senses, nose, eyes, mouth, ears and five emotions.

When we continue to use the three-point gain-loss method to gain and lose, the sixth step should be able to get a pure four-degree "palace change" below the angular tone, and the chord length will also become 64×? = 85 and1/3; The seventh step is to get a pure five-degree "variation symbol" above the "variation palace", and the string length has also become 56 8/9. The chord length is no longer an integer from the beginning. In fact, we can see the superb wisdom of our ancestors. Many musicologists in our later generations set the initial Gong Yin (Ling Huang) as 9 inches, while the three-point profit-loss method starts with 8 1. As you can see, the first five laws are all integers, the numbers are beautiful, the calculation is not complicated, and it is very aesthetic. Seven sounds are generated and arranged according to the chord length (pitch order): sign-feather-change palace-palace-quotient-angle-change sign. These seven tones are the seven-tone elegant music scale in our music theory, and the deviation is the palace tune and the sign change, which is also the "ancient scale" in our music theory. Because this scale can be obtained in only seven steps, it is the earliest seven-tone scale, so it is called "ancient scale".

Since there is a scale, then follow it. "Book of Rites": "Twelve tubes with five tones, six laws, and each other turns into a palace". Of course, the twelve laws should actually be involved here, but I want to introduce an interesting phenomenon to you first, and then introduce the twelve laws.

Just now, we found an ancient scale, and its tonic began with the gong sound of 8 1 Let's try to change it. Now, if we change the gong sound in the original ancient scale to the sign sound, then a new scale will appear: Gong (the pitch position is in the sign position of the ancient scale)-Shang-Jiao-Qing Jiao-Qian-Yu-Bian Gong. This scale is called Le Qing scale in our music theory. In the last step, we can change the "Shang" sound of the original ancient scale into a new gong sound, so that the name of the original ancient scale is changed to: Clear Angle-Sign-Feather-Clear Feather (Leap)-Palace-Quotient-Angle. This scale is called Yan Music Scale in our music theory. See the following example:

This is actually an example of turning each other into a palace. By changing the pitch position of the mode tonic (Gong Diao), three different modes are obtained, one is a pure four-tone melody with seven tones below the ancient scale and the other is a seven-tone melody with seven tones above the ancient scale. Of course, other changes can be made to get different timbres, so I won't go into details here. I just give an example to show that it is feasible and very convenient to turn the phase into a palace tune.

On the basis of this ancient scale, we can continue to "damage the income" and finally get the twelve methods.

How to deduce from the three-point profit and loss method to the twelve laws? What is the relationship between the twelve laws? What are the characteristics of the twelve laws? I won't write a series of questions, there are too many knowledge points ~

I don't know if it's to everyone's liking. After all, musicology is an interdisciplinary subject, with the interaction of physics, mathematics, music acoustics and other different disciplines. It is really beyond a few words and articles to explain clearly. I hope you like it.