西晋孟康异径管律考证──中国古代最早的异径管律管口校正方案

Research on Meng Kang's Pitch-Pipes of Different Diameters

一般认为，《汉书·律历志》孟康注是中国古代最早出现的异径管律设想，但均以为这一设想还不完善，未给出全部数据。经作者研究考证发现，虽然孟康只给出三只律管的数据，但参照三分损益法，他已给出一个异径管律整体方案─—管径的缩小也按三分损益的规则进行，对此，孟康在后续注文中有明确表述。更令人惊奇的是，按现代物理的声学原理，对孟康的异径管律进行理论测算发现，孟康提出的这套异径管律，在理论上已经很好地解决了全套律管的系统管口校正问题，可以使管律发音和弦律一致。或许是因为实际制作的困难，孟康没有对全部律管作更多讨论，但运用管径随三分损益比率依次缩小的方法进行管口校正，却是中国古代声学史上的一大成就，应该予以更积极的肯定。

Meng Kang's commentary for the Section on Pitch-Pipes in Han Shu (History of the Han Dynasty) is commonly thought to be the earliest suggestion of ancient China about three pitch-pipes with different diameters. Though Meng did not give out all data for other pipes, he did lay down a rule for making all the other pipes with their diameters also decreasing according to the rule of San- Fen- Sun- Yi (Addition or Substraction of a Third). Using the contemPOrary theory of acoustics in physics, this paper proves that the design made by Meng Kang can successfully solve the problem of 'end effect'in theory, which means that the frequency of each of the pipes is consistent with the same note of string while every two pipes with an octave interval have exactly two times frequency. Perhaps there still existed some diffiulties for practical manufacturing, for Meng Kang did not discuss further on other pipes. Meng Kang's design of decreasing diameter according to the above rule to make end correction is indeed a great achievement in the history of ancient Chinese acoustics, and should receive more positive affirmation.