<P> 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 century BCE in the Chinese Bronze Age), covers five full 7 - note octaves in the key of C Major, including 12 note semi-tones in the middle of the range . </P> <P> An approximation for equal temperament was described by He Chengtian, a mathematician of Southern and Northern Dynasties around 400 AD . He came out with the earliest recorded approximate numerical sequence in relation to equal temperament in history: 900 849 802 758 715 677 638 601 570 536 509.5 479 450 . </P> <P> Historically, there was a seven - equal temperament or hepta - equal temperament practice in Chinese tradition . </P> <P> 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 律 暦 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 樂律 全書) 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 √ 2 ≈ 1.059463, and for pipe length by √ 2, such that after twelve divisions (an octave) the length was divided by a factor of 2: </P>

In western music the octave is divided into twelve equa