河图洛书:朱载堉十二平均律的理论原点——兼论依傍经典观念何以能实现其律学之创新

He tu and Luo shu:The Theoretical Origin of Zhu Zaiyu's Twelve-note Equal Temperament

明代乐律学家朱载堉,在总结前人的乐律理论基础上,纠偏救弊,加以发展,通过精密计算与科学实验,创造出"新法密律",是世界音乐史上最早用等比级数平均划分音律、精确计算出系列相关数值、系统阐明十二平均律理论的杰出成果。朱载堉将易学中"图书学"所阐发的"河图"洛书"图式及其意蕴,作为其律学思想及律数计算的理论原点。虽然他在观念上依傍古老的经典学说,但在思路和方法上采取了循理求数、以数明理的思路,又以深厚精湛的数学计算功力作为有力的工具性配合,并注重实践性的检验,从而实现了律学的创新。

On the basis of summarizing,rectifying deviations,and remedying defects of his predecessors＇ temperament-related theories,the famous Ming dynasty（1368-1644） expert at temperament Zhu Zaiyu（1536-1611） developed and created a new system of temperament through precise calculation and scientific experiments,which was an achievement equally dividing temperament by geometric progression for the first time in the world history of musicology,precisely figuring out series of related numerical values,and systematically explicating the twelve-note equal temperament.Zhu Zaiyu made use of the He tu（Yellow River Map） and the Luo shu（Luo River Chart） as the theoretical origin of his temperament research and calculation.Although his theory conceptually relied on the ancient classic,he followed the route of seeking numbers by principles,and expounding principles by numbers.In addition,taking exquisite mathematical calculating ability as a tool,and laying emphasis on practical verification,he realized an innovation of temperament theories.