从文化史角度看十二平均律的发现

The Significance of the Discovery of the Musical Equal Temperament In the Cultural History

作为一个文化事件,本文试图将朱载土育发现十二平均律的数式这一伟大成就重新置放在东西方文化史的宏阔视场中加以阐述。首先,分别从音乐与数学、音乐与历学两个角度阐释东西方在相关问题上所表现出来的思维异同,继而,阐释朱载土育发现十二平均律数式与古代中国将历学与律学两个学科交织在一起的学术实践的历史关联与继承性,进而,揭示朱载土育律学思维的独特性与突破性。此外,还重新审视被西方人奉为十二平均律数式"首创者"的西蒙.斯蒂芬所使用的数式的失误,从而推翻西方人将其视为"十二平均律数式首创者"的武断结论。正是因为朱载土育的这一律学成果中的某些关键数据信息,被明末来华传教士无意中传到西方,从而促成西方人对斯蒂芬错误数式的修正,也由此说明现在通用于世界乐坛的十二平均律数式的原创权,终归朱载土育所有。

The present article attempts to place Zhu Zaiyu＇s singular discovery of the musical equal temperament in the wider context of the intellectual history of the Eastern and Western hemispheres as a cultural event. First, the article will discuss the sired＇ arities and differences in regard to mathematical, musical, and calendrical perspectives between the East and the West, followed by a summary review of the theory and practice in the ancient China in continual （ and failed） attempts to negotiate the differences between the sciences of calendar and tuning （ i. e. acoustics）, and, finally, the study will conclude with an appraisal of the unparalleled and penetrating wisdom of Zhu Zaiyu in both the cal- endrical and mathematical sciences in arriving at the mathematics for the equal temperament. Additionally,the present study will offer a critical reassessment of the works of the Dutch mathematicial-engineer, Simon Stevin, and to point out the Mathematical errors and other shortcomings in Stevin＇ s （unpublished） study, thereby to refute the earlier claims （omstly by the Western scholars ） of Stevin＇ s priority of discovery of the （methematical formulae ） of the musical equal temperament. The article will conclude with offering of documentary evidence to the fact that it was this historic discovery of Zhu Zaiyu＇ s mathematical formula for the ＇ correct＇ musical equal temperament via the twelfth root of two （12/2） that had attracted the attention of and prompted the Jesuit missionary in late Ming Dynasty to transmin the information to the West,thereby rightfully bestow on Zhu Zaiyu the distinction of the discoverer the mathematics of the equal temperament.