Equal Temperament in China
The origin of the Chinese pentatonic scale is traditionally ascribed to the mythical Ling Lun. Allegedly his writings discussed the equal division of the scale in the 27th century BC. However, evidence of the origins of writing in this period (the early Longshan) in China is limited to rudimentary inscriptions on oracle bones and pottery.
A complete set of bronze chime bells, among many musical instruments found in the tomb of the Marquis Yi of Zeng (early Warring States, c 5th c BCE in the Chinese Bronze Age), covers 5 full 7 note octaves in the key of C Major, including 12 note semi-tones in the middle of the range.
Jing Fang (78–37 BC) observed that using the Pythagorean comma of 53 just fifths approximates to 31 octaves. This later led to the discovery of 53 equal temperament.
An approximation for equal temperament was described by He Chengtian, a mathematician of Southern and Northern Dynasties around 400 AD.
Historically, there was a seven-equal temperament or hepta-equal temperament practice in Chinese tradition.
Zhu Zaiyu (朱載堉), a prince of the Ming court, spent thirty years on research based on the equal temperament idea originally postulated by his father. He described his new pitch theory in his Fusion of Music and Calendar 乐律融通 published in 1580. This was followed by the publication of a detailed account of the new theory of the equal temperament with a precise numerical specification for 12-TET in his 5.000-page work Complete Compendium of Music and Pitch (Yuelü quan shu 乐律全书) in 1584. An extended account is also given by Joseph Needham. Zhu obtained his result mathematically by dividing the length of string and pipe successively by
=1.059463094359295264561825, and for pipe diameter by
(still in tune after 84/12 = 7 octaves)
According to Gene Cho, Zhu Zaiyu was the first person to solve the equal temperament problem mathematically. Murray Bardour said, "The first known appearance in print of the correct figures for equal temperament was in China, where Prince Tsaiyii's brilliant solution remains an enigma." The 19th-century German physicist Hermann von Helmholtz wrote in On the Sensations of Tone that a Chinese prince (see below) introduced a scale of seven notes, and that the division of the octave into twelve semitones was discovered in China.
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