Guan, Xiao-wu (Author)
Dong Shu-yan, Dai Nian-zu and Luo Lin presented with the view in their article that the temperament lengths recorded in lüshu of Shi Ji were essentially about pitch-pipes with pipe-mouth correction, not pitch-strings. This article supposes an interpretation different from that of Dong, Dai and Luo's: the twelve temperament lengths recorded in lüshu of Shi Ji were derived from turning twelve dimensionless temperament numbers (based on the temperament number 81 of Huang-Zhong) into the temperament lengths with dimensions as Cun, Fen, and the seven non-integral temperament lengths in the twelve temperament lengths were gained by choosing 3 as the denominator of their fraction parts, and omitting the fractions in the numerator parts. By means of this interpretation, it makes the method of San-Fen Sunyi ( one method of circle-of-fifths system), Xianxia Houshang (first time, then time), Ruibin Chongshang (temperament length of Ruibin also time to generate next temperament length) of developing the temperament lengths in lüshu of Shi Ji more clearly. It also discusses the representation method of numbers in Han dynasty and before by the temperament lengths recorded in lüshu of Shi Ji, which might be very important to the study on the history of mathematics in ancient China.
...MoreDescription Argues that this ancient Han Chinese text was referring to pitch-pipes not strings.
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