也论《史记·律书》中的律数

An Interpretation on the Temperament Lengths Recorded in Lüshu(律书) of Shi Ji(史记)

结合汉及以前的数值记数法,对《史记.律书》中记载的数据提出了不同于前人的另一种解读方法,认为它可能是将无单位量纲的(以81为黄钟律数生律所得的)十二律律数转化为以寸、分表示的有单位量纲的律长而得到的.对其中的7个非整数律长取到寸、分及分的约数,约数的分数部分统一以3为分母,舍去分子上的非整数部分.这样所得各律律长数据与原文数值吻合得较好,相互之间的联系痕迹也很明显.《史记.律书》"律数"节记载的律长数值与同节所记的五音律数是一致的,皆为三分损益法生律.

Dong Shu-yan,Dai Nian-zu and Luo Lin presented with the view in their article that the temperament lengths recorded in Liishu 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 Liishu of Shi Ji were derived from turning twelve dimensionless temperament numbers （based on the temperament number 81 of Huang-Zhong 黄钟） into the temperament lengths with dimensions as Cun（寸）, Fen（分）, 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 SanFen Sunyi （三分损益, one method of circle-of-fifths system）, Xianxia Houshang （先下后上, first time, then time）,Ruibin Chongshang （蕤宾重上,temperament length of Ruibin also time to generate next temperament length） of developing the temperament lengths in Liishu of Shi Ji more clearly. It also discusses the representation method of numbers in Han dynasty and before by the temperament lengths recorded in Liishu of Shi Ji, which might be very important to the study on the history of mathematics in ancient China.