1978, a set of ***65 bells, called "Ceng Houyi Bell", was unearthed from the tomb of Zeng Houyi in Leigudun, Suizhou, Hubei Province. This ancient musical instrument, which has been buried underground for more than 2400 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, with twelve semitones complete. This set of chimes can be used to play all kinds of music in ancient and modern times, at home and abroad, 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 that of Greece, while 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, only "1, 2, 3, 5 and 6" had five tones, while "4 and 7". )
In fact, in Zhou Yu, the proper names of twelve tones are recorded: Huang Zhong, Luda, Taicong, Jiazhong, Gu Xi, Zhonglu, Yan Bin, Lin Zhong, Yize, Nanlu, Wushe, Ying Zhong, and Semi-Huang Zhong ... These tones can be found by the "three-point gain and loss method", which is better than Pythagoras in Greece. This shows that China invented the seven-tone scale very early.
Zhong used facts to prove that the development level of China's ancient music theory was extremely high, and also proved that China's ancient music law and western music law developed independently of each other.
Since it was developed independently, why is it not as different as the independently developed languages, but so close that Chinese musical instruments 2,400 years ago can play modern western music without any difficulty? This is related to the mathematical characteristics of music.
Sound is produced by vibration, and the frequency of vibration (the number of vibrations per second) determines the size of sound. Two notes with a difference of 8 degrees (such as "C 1" and "C2" on the piano or "1' and" I ") are harmonious, no exception at any time.
1834, physicists stipulated that G 1=440 = 440 times per second, which was later designated as the international standard sound. Keyboard instruments pioneered in the West (such as the piano), the whole set of sounds includes seven white keys, and the five black keys *** 12 have different tones, which are arranged in descending order as follows:
……C、C、D、D、E、F、F、G、G、A、A、B、C、C、d……
In this sequence, the audio of any tone is equal to the audio of its previous tone multiplied by a constant Q. (And the wavelength is divided by Q.) If the audio of "C" is n, the audio of "C" is 2n, so
This gives a table of the ratio of the audio of each tone to the audio of "C":
This rule can be easily transferred, and any sound such as "1" can be easily transferred. This is the law of twelve averages, which was first put forward by Zhu Zaiyu in Ming Dynasty in China. Bach in Western Europe was first used in practice, and keyboard music was based on the law of twelve averages.
China's ancient calculation of chord length was based on the "three-point gain and loss method". From the above table, we can know the five gains and losses of C.
Two wavelengths, so the two sounds are similar and harmonious. (second only to octave) use this "d" sound. One meter of the "D" audio is the "D" sound. 1.5 times of the audio of "d" is "A" sound, and the audio multiple table of 12 sound is calculated in turn:
(The corresponding wavelength ratio is c ∶ d ∶ e ∶ g ∶ a = 81∶ 72 ∶ 64 ∶ 54 ∶ 48).
This melody sounds elegant, but its tone sandhi is poor. In China, pipa, sheng, flute and Xiao are mostly made by the "three-point profit and loss method".
Note that there is little difference between the two, and it is difficult for the human ear to distinguish them clearly. So it is not difficult to play western music with China's instruments.
It can be seen that China culture is indeed profound.