The seven-stringed zither qin had been finalized in the Han Dynasty,and its 13 huis(inlaid markers for pitch fingering positions)were decorated on the surface of the qin in the Han and Wei Dynasties.Although qin-hui originated in the Han and Wei dynasties,the mathematical origin of the equal division on one string can be traced back to bian-nao(set of cymbals)compiled in Shang Dynasty and yong-zhong(bronze bell)in Western Zhou Dynasty."Tuning on one single string"(yi-xian-jun-zhong)may be a real fact set by musicians in Shang and Zhou Dynasties,or it may not be a real thing,but just a virtual mathematics hidden in thinking.The five-string tuning bell from the tomb of Marquis Yi of Zeng State and the five-string tuning on the bell and drum of the period between the two Zhou Dynasties indicate that this period is not only the upper limit of the application time of the five-string tuning,but also the lower limit of the application time of the one-string tuning.Since the shape and structure of the qin had not been unified before the Qin Dynasty,there was a time gap in the mathematical application of the above two types of musical instruments.From the equal node of one string to the four tones of the bells and cymbals in Shang and Zhou Dynasties,from the equal node of five string to the seven tones of the bell-chimes in Eastern Zhou Dynasty and even the keys and modes changes(xuan-gong),the brilliance of bell/chime music always depended on the support of the nodes on the string and on the mathematical cognition of the court musicians.This shows the early application and historical contribution of mathematics before the use of the qin inlaid markers.
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