谁是9∶4的发现者——以中国管律律种学之倍半相生公式研究为例

Who Is the Finder of 9∶4 Formula——A Case Study of Beibanxiangsheng Formula of Chinese Bell Temperament

在中国律学史的管律律种学研究中,对于如何给出两支同径律管间相对稳定的"倍半相生"管长比数据,人们曾进行了长期而艰辛的实践与探索。本文即对20世纪下半叶以来对于两支同径律管间倍半相生的"9∶4"管长比经验值公式的争讼,以及"究竟谁是同径律管相对稳定的倍半相生9∶4经验值公式的发现者?"进行了综合梳理。在采撷中国历代相关文献和音乐考古学成果的基础上详加释证、补证与参证之外,笔者通过必要的制管验声,进行了深入的研究,进而阐明自己的观点,并提出总结性的意见。

For a long time, people have tried hard in order to provide a relatively stable data of beibanx-/angsheng （a law of producing temperaments） pipe-length ratio between two pitch pipes with the same diameter. This paper reviews previous disputes on the issue since the late half of 20th century and makes further explorations through experimental trials based on careful explanations, corrections of and references from literature and archaeological achievements.