Current location - Music Encyclopedia - QQ Music - What are the maths in music?
What are the maths in music?
everyone loves music, regardless of ancient or modern times. In ancient China, Confucius regarded music as one of the "six arts" and stipulated that all his students must master it. Many mathematicians also like music very much, and the great mathematician Euler even published a paper on studying music with mathematics. It's just that this paper is too musical for mathematicians and too mathematical for musicians. So that it is not easy for everyone to understand.

in p>1978, a set of ***65 chimes was unearthed from the tomb of Zeng Houyi in Leigudun, Suizhou, Hubei Province, which was called "Ceng Houyi Bell". This ancient musical instrument, which has been buried underground for more than 2,4 years, has a total weight of more than 5 tons and a range of five 8 degrees. Its scale structure is the same as that of modern C major, and twelve semitones are complete. This set of chimes can be used to play all kinds of music, ancient and modern, Chinese and foreign, and is called "the eighth wonder of the world" by foreigners.

In the past, the West always thought that China's seven-tone scale was formed later than Greece's, and China's seven-tone scale was "imported", because the ancient music in China mainly used five-tone scale ("Gong, Shang, Jiao, Zheng and Yu", that is, there were only five tones of "1, 2, 3, 5 and 6" but no partials of "4 and 7". )

In fact, the proper names of twelve tones are recorded in Zhou Yu: Huang Zhong, Da Lu, Tai Cluster, Jia Zhong, Gu Xi, Zhong Lu, Yan Bin, Lin Zhong, Yi Ze, Nan Lu, Wu She, Ying Zhong, Semi-Huang Zhong ... And these tones can be obtained by the "three-point profit and loss method". This shows that the seven-tone scale was invented very early in China.

Ceng Houyi Zhong proved in kind that the development level of Chinese ancient music theory was extremely high, and also proved that Chinese ancient music law and western music law developed independently of each other.

since it developed independently, why not be as different as the independently developed languages, but so close that Chinese musical instruments 2,4 years ago can play modern western music without any difficulty? This is related to the mathematical characteristics of musical sounds.

sound is generated by vibration, and the vibration frequency (the number of vibrations per second) determines the sound level. The two tones with a difference of 8 degrees (such as "C1" and "C2" on the piano or "1' and" I "sung) are harmonious, which is unique in ancient and modern times.

in p>1834, physicists stipulated G1 = 44 times/second, which was later designated as the international standard sound. A keyboard instrument pioneered in the west (such as piano), a complete set of sounds includes seven white keys, five black keys * * * and 12 different tones, which are arranged in descending order as follows:

... C, #C, D, #D, E, F, #F, G, #G, A, #A, B, C. (and the wavelength is divided by q) If the audio frequency of "C" is n, the audio frequency of "C" is 2n, so

this gives the ratio table of the audio frequency of each tone to the audio frequency of "C":

This regulation is very easy to be tone-shifted, and any tone can be easily tone-shifted, which is the twelve-average law, which is Zhu in Ming Dynasty in China.

in ancient China, the string length was calculated according to the "three-point gain and loss method". From the above table, we can see that the five-point gain and loss of C is

2 wavelengths, and these two sounds are similar and harmonious. (second only to the eighth degree) use this "d" sound. One meter of the "D" audio is the "D" sound. 1.5 times the audio frequency of "D" is the sound of "A", and then we can get the audio frequency table of 12 tones:

(the corresponding wavelength ratio is C ∶ D ∶ E ∶ G ∶ A = 81 ∶ 72 ∶ 64 ∶ 54 ∶ 48)

This kind of melody is elegant to play, but its tone sandhi is poor.

Note that there is little difference between them, which is difficult for human ears to distinguish clearly. Therefore, it is not difficult to play western music with China's musical instruments.

It can be seen from this that Chinese culture is indeed profound and profound.