What is the Law of Twelve Equals and what does the Law of Twelve Equals mean?

12. The law of equality, also known as ".The law of the twelfth degree", is a universal set of tones (octaves) divided into twelve semitonesIntervalsThe ratio of wavelengths between the two adjacent laws is exactly equal. The law of twelve equals was discovered by Zhu Zaiyu, the royal son of the Ming Dynasty of China.

The twelfth equal temperament is that the octave interval is divided into twelve equal parts in proportion to the wavelength, and each equal part is called a semitone (minor second). A major second is divided into two equal parts and is called a whole tone. Dividing an octave into 12 equal parts has some surprising coincidences.

This is because the wavelength ratio of the two tones of its pure fifth interval (i.e. 1 2 to the 7 to the 12th power) is about, which is very close to 2 3, approx.

Wavelength and chord length.

The ancients had a superficial understanding of the phenomenon of sound, and they did not know that sound was a mechanical wave, and it was impossible for the concept of modern standard sound to exist. However, because in the acoustic phenomenon, the chord length is linked to the physical wavelength, and the wavelength is linked to the tone, so the ancients actually used the physical relationship between the string length and the wavelength to design the rhythm, which fully reflects the wisdom of the ancients.

All waves (including mechanical waves, electromagnetic waves.

Gravitational waves, etc.) have three most essential properties: frequency, wavelength, and amplitude.

Phase. For mechanical waves (sound waves), at the same speed of sound.

Next, the wavelength of the mechanical wave determines the tone of the sound, and the amplitude of the mechanical wave determines the magnitude (intensity) of the sound, and the human ear is not sensitive to the phase, so the phase of the mechanical wave is generally not considered when studying **.

12. The law of equality, also known as ".The law of the twelfth degree", a set of tones (octaves) that are common in the world are divided into twelve semitonesIntervalsThe ratio of the number of vibrations between the two adjacent laws is exactly equal. The twelfth equal temperament refers to the fact that the octave interval (octave) is divided into twelve equal parts proportional to frequency, and each equal part is called a semitone minor second.

A major second degree is divided into two equal parts. Dividing an octave into 12 equal parts has some surprising coincidences. The frequency ratio of the two tones of its pure fifth interval (i.e., the 7th and 12th power of 2) is so close to that the human ear is basically inaudible to the difference between the fifths of the "fifths" and the "twelve equals".

The 12 equal temperament is widely used in symphony orchestras and keyboard instruments, and the piano today is based on the 12 equal temperament.

History. It is said that the law of twelve equals was established in the 16th century by Zhu Zaiyu, the son of the Ming Dynasty.

Found. Due to the wavelength and chord length.

There is a direct proportionality.

relationship, so the wavelength relation can be converted into the long and short relation of the string. So even in the 16th century, when Western physics was just starting and mechanical waves had not yet been discovered, Zhu Zaiyu, the royal son of the Ming Dynasty of China, used his superb mathematical calculation ability to discover this law of approximation, which is also a very great and amazing thing.

In the middle of the Ming Dynasty, Zhu Zaiyu, the prince of the imperial family, invented the method of opening the square with abacus to obtain the proportional number series on the legal system.

Specifically, the pitch is calculated by the length of the articulating body, assuming that the yellow bell is 1 foot, finding the lower octave chord length is 2 feet, and then 2 open 12 times to obtain the wavelength ratio, the common ratio is multiplied 12 times to obtain the pitch of each law in the twelve laws, and the yellow bell is just restored, which just corresponds to the proportional relationship of wavelength in physics. Zhu Zaiyu used this method to solve the eternal problem of the rotation of the 12-law free rotation palace for the first time.

Fifty-two years after Zhu Zaiyu published his theory of the twelve equal laws, Pere Marin Mersenne published a similar theory in his (1636) book The General Theory of Harmonics.

The rhythm that divides a pure octave into twelve equal parts is called the twelve equal temperament.

Each of these parts is a semitone, and the distance between each semitone is equal, and its greatest advantage is that it is easy to transpose.

The law of twelve equals was first proposed in ancient Greece, but it was not scientifically calculated at that time. The first in the world to formulate the law of twelve equals according to mathematics was Zhu Zai (1584), a great master of the Ming Dynasty in China.

In the twelve equal temperaments, the semitone is the smallest pitch distance in the twelve equal temperament organization. A distance between two tones equal to two semitones is called a whole tone. There are twelve semitones within the octave, which means that Lu Yin is six whole tones.

In the basic scale of the sequence, except for E to F and B to C are semitones, the distance between the other two adjacent notes is whole tone.

Since the semitones of the twelve equal temperaments are the same, there is a "equal tone"—each sound with the same pitch but different notation and meaning is called "equal tone".

The 12 equal temperament is mostly used in keyboard instruments such as piano, accordion, electronic organ, and organ, where two adjacent keys (including the black keys) form a semitone, and the two notes separated by a key form a whole tone.