Twelve equal temperament: A temperament that divides a pure octave into twelve equal parts is called twelve equal temperament. Each part is a semitone, and the distance between each semitone is equal. Its biggest advantage is that it is easy to modulate. The law of twelve equals was proposed as early as ancient Greece, but it was not scientifically calculated.

The first person in the world to formulate the twelve equal temperaments based on mathematics was Zhu Zaiyu (1584), a great musician of the Ming Dynasty in my country. In equal temperament, a semitone is the smallest pitch distance in the equal temperament structure. The distance between two tones is equal to two semitones and is called a whole tone. There are twelve semitones in the octave, which is six whole tones. In the basic tone classes of the tone sequence, except for E to F and B to C, which are semitones, the distance between the other two adjacent tones is a whole tone.

Extended information:

The frequency ratio of the pure fourth and major third of the "Twelve Equal Temperament" is relatively close to 4/3 and 5/4 respectively. In other words, the main chord notes of "Twelve Equal Temperament" are consistent with the notes in the natural overtone sequence, with only minimal differences. This makes it ideal for trumpet and other key-playing instruments to be used in bands. Provides necessary conditions, because these musical instruments rely on natural overtone levels (natural overtone sequences, whose frequencies are integer multiples of the fundamental frequency, in an arithmetic sequence) to form musical scales.

A semitone is the smallest pitch distance in the twelve equal temperament structure, and a whole tone is composed of two semitones. Divide between 1-Ⅰ into 12 parts. Specifically, 1-2 whole tones, 2-3 whole tones, 3-4 semitones, 4-5 whole tones, 5-6 whole tones, 6-7 whole tones, and 7-i semitones.

The twelve equal temperament is widely used in symphony orchestras and keyboard instruments. The piano is tuned according to the twelve equal temperament, because only the "twelve equal temperament" can be easily transposed. Melody is made up of scales, and scales are made up of notes. There are absolute pitch and relative pitch. Sound is emitted by vibration (vocal cords, strings, etc.), and the frequency of vibration (the number of vibrations per second) determines the absolute height of the sound. Different sounds have different vibration frequencies. People select sounds of a certain frequency to form the pitch required by the music system.

In short, the twelve equal temperament is to divide half a string into twelve equal parts according to the geometric sequence. The length of a string is set to 1, which can be expressed as (1/2)^(0/12). The position of the first fret is (1/2)^(1/12), and the position of the second fret is ( 1/2)^(2/12), and so on, the position of the nth item is (1/2)^(n/12). Because such a set of notes is in an equal proportion, the melody will be the same no matter where you start playing it.

The semitone of the equal temperament is larger than the semitone of the fifth temperament and smaller than the pure temperament. Therefore, using twelve equally tempered chords is not pure and the melody is not oriented enough. Therefore, in the performance of the music, especially when the band plays a multi-part ensemble, multiple temperaments are actually used. According to the actual situation, during the performance Among them, the preference for one type of discipline is not static.

According to the characteristic of equal temperament, all semitones are equal, so "equal tones" are also produced.

Baidu Baidu--Twelve Laws of Equals