千年聚讼的《史记·律书》律数考

Textual Research on Book of Temperament of Historical Records

从唐代司马贞起直至今日,不同时期的学者对《史记.律书》中一组十二律寸分之数的性质认定及数据校勘方面各有解释。而本文发现,北宋沈括早已以定性为管积的"实积之数"说,给这一组律数究竟应该阐释为何数的问题,基本画上了句号。沈括之后的历代探索,大多追寻小司马"九分之寸法"说的思路,将其视作本质为数字律数的管长分数以十约成的管长寸分之数,即间接的管长之数,然其说明显不如沈括之说更符合数理;有的则提出了先秦"管长之数"说,将这组律数视作经过管口校正的、真正的管长之数。但本文在《史记.律书》这一"案发现场"发现的种种线索与证据表明,其说与司马迁所说没有联系,它只是一个具有打开思路作用的"大胆假设"。

Scholars in different times have defined and calibrated the length of the twelve temperaments recorded in Book of Temperament of Historical Records in distinctive ways since the Tang Dynasty.However,this paper argues that Shen Kuo in the Northern Song Dynasty has properly solved the question by proposing the shiji-number (arithmetic product) concept.Most scholars after Shen Kuo followed Sima Zhen s idea of "novenary",which is obviously not so logic as Shen s explanation;some other people put forward the pre...