曾侯乙编钟“大羽钟”复原探究——兼论音高与钟体尺寸的“标准化”原理及其应用

郭西洋, 谷杰

中央音乐学院学报 ›› 2025 ›› Issue (2) : 13-40.

中央音乐学院学报 ›› 2025 ›› Issue (2) : 13-40.
中国自主知识体系建构:“音乐考古研究新进展”

曾侯乙编钟“大羽钟”复原探究——兼论音高与钟体尺寸的“标准化”原理及其应用

  • 郭西洋, 谷杰
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A Study on the Restoration of the“Dayu Bell”of Zeng Houyi Chime Bells:Discussion on the “Standardized” Principle and Application of Pitch and Dimension

  • GUO Xiyang,GU Jie
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摘要

曾侯乙编钟出土40多年来,学术界涌现出一大批研究成果,然而其中鲜见有关“大羽钟”的专题研究,也缺少对编钟“标准化”的深入探讨。论文依据相关文献与考古实物,回溯先秦铸钟的标准化迹象,集中对曾侯乙编钟音高与钟体尺寸的标准化问题展开研究,得到以下认识:其一,对于单件钟而言,钟体各部位尺寸成一定的比例关系,且铣长(主量)对音高与钟体其他部位尺寸(他量)具有决定性影响;其二,对于一组编钟而言,各钟相同部位的尺寸成线性关系;其三,对于编钟壁厚而言,虽不存在比例关系和线性关系,但却具有正态分布的统计学规律——壁厚有向平均值靠近,并在平均值附近波动的趋势。在此基础上,论文结合数理统计学的分析方法,推求“大羽钟”的相关数据,以期为复原“大羽钟”提供一个新的理论参考方案。

Abstract

Over the four decades since the excavation of the Zeng Houyi Chime Bells,substantial scholarly achievements have emerged,yet it is deficient in specialized studies on the"Dayu Bell"and in-depth exploration of the“standardization”of chime bells.Based on relevant documents and archaeological artifacts,this paper retraces the phenomena of standardization of chime bell cast in the Pre-Qin period and focuses on the research of the standardization between pitch and bell dimension of the Zeng Houyi Chime Bells.The following findings are obtained:Firstly,for individual bell,each dimension of the bell has a certain proportional relationship,and Xian length(the key parameter)serves as the decisive factor affecting both pitch and other dimensions(other parameters).Secondly,for a group of chime bells,the dimensions of the same parts exhibit a linear relationship.Thirdly,for the thickness of chime bells,there is a statistical regularity of normal distribution in which the thickness is close to the average value and fluctuates around it despite no proportional or linear relationship.On these bases,the paper combines the analytical methods of mathematical statistics to deduce the relevant parameters of the“Dayu Bell”,with the expectation of providing a new theoretical reference scheme for the restoration of the“Dayu Bell”.

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郭西洋, 谷杰. 曾侯乙编钟“大羽钟”复原探究——兼论音高与钟体尺寸的“标准化”原理及其应用[J]. 中央音乐学院学报. 2025(2): 13-40
GUO Xiyang, GU Jie. A Study on the Restoration of the“Dayu Bell”of Zeng Houyi Chime Bells:Discussion on the “Standardized” Principle and Application of Pitch and Dimension[J]. Journal of Central Conservatory of Music. 2025(2): 13-40

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