From a physical point of view, the pitches of the mid-tones in the music system are different even if the vibration frequencies only differ by one hertz. However, such subtle differences are almost indistinguishable to human hearing. In order to make the music better adapt to people's hearing needs and adapt to the development of music, people gradually began to consciously formulate certain standards for the pitch of the music. Hence the law was born.

In the music system, temperament specifically refers to the pitch of the music, which is a regular and systematic standard pitch.

In ancient my country, "law", like "degree", "quantity" and "balance" (referring to the length, volume (volume) size and weight of objects respectively), must be formulated and promulgated in every dynasty. National standards show its importance.

So far, people have discovered and formulated various temperament systems such as the pure temperament, the law of three-point profit and loss, and the equal temperament (there are many kinds). However, the twelve equal temperaments are the most widely used in the world today. , and has the greatest impact.

The so-called equal temperament refers to a temperament system that divides the intervals of an octave (octave) evenly into several equal parts. Equal temperament is a temperament system that divides the octave interval into twelve equal parts (semitones). The first person in the world to theoretically calculate the twelve equal laws was Zhu Zaiyu (1536-about 1610), a legal scholar in the Ming Dynasty of my country. He had determined the twelve equal laws before 1581. However, his achievement could not be applied in music practice in time. In Europe, keyboard music in the 17th century began to require the use of twelve equal temperaments, which were not suitable for people's hearing at the time. Since the 18th century, due to the development of modulation and the expansion of tonality, Well-Tempered has been increasingly used by composers in the practice of their works (such as Bach's Well-Tempered Clavier). Since then, the law of twelve equals has gradually been widely adopted. The founder who has very little research in China should be Helmholtz who studied more physics, such as the formation of human hearing, hearing thresholds, etc., and temperament is based on long-term music practice. Formed during the development, there are many types of temperament, and the main well-known temperaments are "pure temperament", "intergenerational temperament of fifths" and "twelve equal temperament". Among them, the "law of twelve equals" is currently widely used by countries around the world. The formation of musical temperament is different for each nation. To this day, other regions such as India and Southeast Asia also retain other temperaments. From the perspective of auditory harmony, the twelve equal temperaments have great advantages. The pure temperament refers to The simpler the ratio of the sound wave vibrations of two tones, the more harmonious the two tones will sound, and vice versa. This is also an innate characteristic of the human ear. The most harmonious interval is of course a perfect first, followed by a perfect octave, but the second and seventh are quite disharmonious intervals. The vibration ratio must be a very strange ratio. Although pure temperament best meets the requirements of human ears for bel canto and can produce very beautiful harmonic sound effects, it is not very practical. Because such a ratio will cause a lot of trouble due to shifting the tonality. For example, the main note of C major is DO. The pitch of other notes should be determined based on DO as the starting point, but if it is transferred to G major, The pitch of all the notes will change slightly. Before the Baroque era, there were few modulations because the form of the music was simple. However, as the form of the music became more complex, pure temperament became a rather troublesome system. With the development of music, the shortcomings of pure temperament were revealed. In order to solve this problem, the twelve equal temperaments came into being. Twelve equal temperament divides an octave into 12 equal intervals, each interval is defined as a semitone, and two semitones constitute a whole tone. The biggest advantage of Twelve Equal Temperament: No matter how you transpose or modulate, you can get equal musical effects. But this is relative, because the twelve equal temperament divides an octave into 12 equal parts, so the vibration ratio between each semitone is an infinite decimal that cannot be divided, so no matter which chord is played, it will not It is possible to obtain a truly completely harmonious musical effect, but the magnitude of the influence of the twelve equal temperaments is quite small. In comparison, it is still a very good interval system. The reason why MIDI cannot replace the effect of real-person performance no matter how much progress is made is because when real-person performance is performed, the performer will use his or her own ears to judge the degree of harmony of the intervals. It is usually closer to pure temperament, but it cannot be done on a computer. The fundamental reason is the interval definition system. There are fundamental differences, but the differences are not too big.

Teacher Han Baoqiang from the Central Conservatory of Music has a book called "The Journey of Music - Introduction to Modern Music Acoustics". You can buy or borrow it and read it. You will gain something