云杉木材共振板的振动特性与钢琴声学品质评价的研究
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摘要
钢琴音板的质量在很大程度上决定了钢琴声学品质，在生产中，钢琴音板的选材主要依赖于技师的主观评判，这种方式不但效率低，而且科学依据不足，误差大，无法满足在大批量生产的条件下，以最适当的材料制作最多、最高品质钢琴音板的要求。
为能建立钢琴音板的客观选材方法和实现对钢琴共振板振动特性的客观评价，以4种适合制作乐器音板的云杉属木材(俄罗斯远东红皮云杉、东北长白鱼鳞云杉、西藏林芝云杉及美国西加云杉)为研究对象，进行了从共振板素材、共振板，到音板，直至钢琴产品的声学特性的追踪研究。
采用综合坐标法、综合评分法对共振板素材的综合振动性能进行区分，根据区分结果，每树种均选出区分度大的两组共振板素材(分别为第1组与第2组素材，对应为第1块与第2块共振板，对应为第1号与第2号钢琴)，用以制备钢琴共振板；基于钢琴共振板的振动理论，分析了共振板的振动特性；将共振板制成钢琴后，采用主观评价、客观评价、生理心理指标评价方法对钢琴的声学品质进行评价；在综合分析共振板振动特性、钢琴声学品质之间的关系的基础上，建立钢琴共振板振动特性的客观评价方法以及钢琴共振板用木材的客观选取方法。
本文的主要研究内容和结果如下：
(1)在实际尺寸木材振动特性检测的探索性研究基础上，对实际尺寸的钢琴共振板用木材振动特性进行检测，并采用综合分析的方法，实现对俄罗斯远东红皮云杉、东北长白鱼鳞云杉、西藏林芝云杉及美国西加云杉树种的试验样本进行振动特性的综合评价与区分，对每个树种均挑选出两组综合振动特性区分明显的共振板素材。
(2)将素材拼板胶合，形成共振板。分析了钢琴共振板基本振动理论，得出钢琴共振板自由振动的频率方程。根据自由振动的频率方程计算得出钢琴共振板x方向与y方向的弹性模量(MOE_x，MOE_y)，并用纵波传播速度方程计算得出钢琴共振板x方向与y方向的纵波传播速度(V_(Lx)，V_(Ly))，通过比较发现：同树种的两块共振板，无论是x方向，还是y方向，第2块共振板的弹性模量值、纵波传播速度基本要比第1块的大；所有的共振板，y方向的弹性模量(MOE_y)、纵波传播速度(V_(Ly))均要大于x方向(MOE_x，V_(Lx))。对共振板裁边后剩余的边角试件(45°斜纹理试件)进行力学性能分析，得出与共振板整板弹性模量值的分析结果较为一致的结论。
(3)在共振板上粘贴肋木，形成音板。通过肋木对钢琴共振板声传播速度影响的分析，结果表明肋木可显著提高共振板横纹理方向的振动传播响应速率。比较音板不同方向之间及同树种内两块音板的对应方向的振动响应时间发现，顺纹理方向的振动响应时间与横纹理方向之间相差不大，这主要是肋木起到了很好的增加横纹理方向振动传播速度的作用。
(4)利用上述4个树种各2组音板制作了8台钢琴。采用主观评价、客观评价方法对8台钢琴的声学品质进行评价，主观评价人员为从事钢琴演奏与教学工作多年的专家，客观评价的指标主要包括钢琴的音强、音长、动态范围及音色等。评价的结果表明：同树种的两台钢琴，第2号的钢琴声学品质客观评价指标值、音质主观评价项目得分基本都优于第1号。可认为，同树种的第2号钢琴声学品质优于第1号钢琴。
(5)以没有音乐专业背景的大学生群体为研究对象，以心率、血压、皮肤温度及呼吸几项指标为变量，分析了不同钢琴对受验者生理的影响。结果表明：与正常静息状态比较，听赏钢琴曲后，引起受验者的生理信号相应改变，表现为交感神经活动张力降低，迷走神经活动水平上升，自主神经活动状态发生改变，但尚未失去均衡性，综合表现为自主神经系统活动性降低，受验者精神处于松驰状态；比较受验者听赏同树种内两台钢琴演奏的曲子对受验者的生理影响可以表明，受验者听赏第2号钢琴时，交感神经活动张力比听赏第1号钢琴有所降低，而迷走神经活动水平上升，受验者精神处于更为放松的状态。
(6)从共振板弹性模量(MOE_x，MOE_y)、纵波传播速度(V_(Lx)，V_(Ly))、共振板边部斜纹理试件弹性模量(MOE_(45x)，MOE_(45y)及音板的振动响应时间(顺纹理振动响应时间T_L，横纹理振动响应时间T_R)4个方面分析了共振板的振动特性与钢琴声学品质的主观评价得分(总项平均得分、总体音质得分及计权得分)、客观评价指标(强奏音强值、弱奏音强值、音长、音色)之间的关系。共振板y方向弹性模量(MOE_y)、纵波传播速度(V_(Ly))、共振板边部斜纹理试件弹性模量(MOE_(45y))与主观评价得分、客观评价指标之间的相关关系大于x方向，其原因可能与音板上的琴弦排列与音板的y方向接近平行，或与y方向的夹角小于x方向的结构特点有关；主、客观评价指标与音板横纹理方向振动响应时间之间的相关性高于顺纹理方向的振动响应时间。因此，通过提高共振板弹性模量、纵波传播速度，尤其是y方向，可提高钢琴的声学品质；若能降低音板的横纹理方向的振动响应时间，以减小与顺纹理方向的声振动传播速度的差异，使整个音板在最短的时间内均匀振动起来，也可提高钢琴的声学品质。
(7)通过综合分析得出钢琴共振板的振动性能客观评价方法：测量钢琴共振板，或者直接测量钢琴共振板边部斜纹理试件的弹性模量值，主要是y方向弹性模量值；测量钢琴共振板的纵波传播速度，或者测量音板的振动响应时间，主要是y方向的纵波传播速度，或者横纹理方向的振动响应时间。
(8)通过综合分析得出钢琴音板用木材的客观选取方法：采用综合坐标法、综合评分法的综合分析方法对钢琴音板用木材的综合振动性能进行计算，参与计算的振动性能指标需要包括纵向的振动性能指标与横向或斜纹理方向的振动性能指标。
The piano acoustical quality is decided by the soundboard to a great extent. In the producing, the technician evaluates and chooses the wood for piano soundboard subjectively for the moment. It is inefficient, large error, and insufficiency of the scientific foundation. It does not satisfy the requirement to produce the excellent piano soundboard in the condition of volume-produce.
In order to establish the objective selection method of wood selection for piano soundboard and objective evaluation method of vibration property of piano resonance board, track-study of vibration properties from the wood used for resonance board 1) of Picea glehnii, Picea jezoensis, Picea likiangensis var. linzhiensis, and Picea sitchensis, resonance board 2), to soundboard 3), until the acoustical quality of piano were studied.
The comprehensive vibration properties of the samples of every species were analyzed and differentiated respectively by the comprehensive coordinate method and comprehensive marking method. According to the results of differentiation, two groups of samples used for producing the resonance boards in every species were selected respectively, and the distinction between the both groups was obvious (the No.1 and No.2 groups of samples respectively, correspond to the No.1 and No.2 piece of resonance board, correspond to the No.1 and No.2 piano). The vibration properties of resonance board were analyzed base on the vibration theory of thin plate. After the pianos were producing, the acoustical qualities of pianos were evaluated by the subjective method, objective method, and psycho-physiological index method. On the basis of the comprehensive analysis of the correlation between vibration properties of the resonance board and the acoustical quality of pianos, the objective evaluation method of the resonance board of piano and the objective selection method of wood used for soundboard were established.
The main research contents and results were summarized as follows:
(1) On the basis of studying exploringly on the vibration properties measurement of full - size wood samples, the vibration properties of full-size wood used for resonance board of piano were measured. The comprehensive vibration properties of samples of Picea glehnii, Picea jezoensis, Picea likiangensis var. linzhiensis, and Picea sitchensis were analyzed and differentiated by comprehensive analysis methods. And finally, two groups of samples were selected for producing the resonance board of piano, and that the distinction of vibration properties between the No.1 groups and the No.2 groups was obvious in every species.
(2) The samples of wood used for resonance board were glued to resonance board. The foundation theory of vibration of piano resonance board was analyzed, and the frequency equation of free vibration was acquired. The MOE, velocity of longitudinal wave of resonance board on the x (MOE_x, VL_(Lx)) and y (MOE_y, V_(Ly)) direction were computed by the frequency equation and longitudinal wave transmittal equation. The results were: the MOE_x, MOE_y, VL_x, V_(Ly) of the No.2 piece of resonance board (correspond to the No.2 group of wood samples) are larger than the No.1 (correspond to the No.1 group of wood samples) in every species; for all resonance boards, the MOE_y, V_(Ly) are larger than MOE_x, V_(Lx). The mechanical, properties of the 45°grain samples in the edge of the resonance board were analyzed, and the results were same to the resonance board.
(3) The soundboard is the resonance board that the ribs were glued on it. The influence of ribs on the sound transmit velocity of piano resonance board was analyzed. The result shows that the ribs can enhance the sound transmit velocity on the radius direction of resonance board. The response time of vibration on the radius direction is near to that on the longitudinal direction. That is because the ribs enhance the sound transmittal velocity on radius direction of resonance board.
(4) The acoustical quality of the pianos was evaluated by the subjective and objective method. The experts of subjective evaluation were engaged in piano performance and education many years. The indexes of objective evaluation were loudness, sound length, dynamic range, and tone. The results of evaluation were: the acoustical quality of the No.2 piano was more excellent than the No.1 piano in the same species.
(5) The influence of the piano music on psycho-physiological reaction (the main indexes are Heart Rate Variability, Blood Pressure Variability, Skin Temperature, and Respiration Frequency) of the subjects who are undergraduate without the background of musical training were analyzed. Compared with the resting state, the subjects' physiological reaction was changed when they enjoyed the piano music. The subjects' sympathetic nerves activity decreased, and the parasympathetic nerves activity increased, but the equilibrium was not broke. The synthetical presentation was that the activity of autonomic nervous system was weakening, and the subjects were more comfortable than they were resting. Then the differentiation of the influence of two pianos music of the same species on the subjects' physiological reaction was analyzed. The results show: when the subjects were enjoying the music of the No.2 piano the sympathetic nerves activity of the subjects decreased, the parasympathetic nerves activity increased, and they were more comfortable than that the No.1 piano of the same species.
(6) The correlation between the vibration properties of resonance board (MOE_x, MOE_y, V_(Lx), V_(Ly)), MOE of the 45°grain sample in the edge of the resonance board (MOE_(45x), MOE_(45y)), response time of vibration of soundboard (T_L—time of longitudinal direction, T_R—time of radius direction) and the score of subjective evaluation, indexes of objective evaluation of piano acoustical quality were analyzed. The correlation between subjective evaluation score, objective evaluation indexes and the vibration properties in the y-direction of resonance board were more significant than that in the x-direction. That may be related to the strings array frame. Because the strings axis in high and intermediate frequency region is near parallel to y-direction and the angle between strings axis and y-direction in low frequency region is smaller than that between strings axis and x-direction of the soundboard. The correlation between subjective evaluation score, objective evaluation indexes and the response time of vibration of soundboard in the radius direction were more significant than that in the longitudinal direction of wood. So, the acoustical quality of piano is improved with the MOE (MOE_x, MOE_y), velocity of longitudinal wave of resonance board (V_(Lx), V_(Ly)) increased, especially in the y-direction. If the discrepancy between T_L and T_R is abated with T_R reduced, the piano acoustical quality is improved.
(7) The objective evaluation method of wood used for piano resonance board is: the MOE of the resonance board or the 45°grain sample in the edge of the resonance board is measured, especially the y-direction(MOE_y, MOE_(45y)); And the velocity of longitudinal wave transmittal, or response time of vibration of soundboard is measured, especially the y-direction velocity (V_(Ly)) or the response time of vibration in the radius direction of the soundboard (T_R).
(8) The objective selection method of wood used for piano soundboard is: the comprehensive vibration properties of wood used for piano soundboard are computed by comprehensive coordinate method and comprehensive marking method, and the indexes include wood longitudinal and radius (or 45°direction of grain) vibration properties.
为能建立钢琴音板的客观选材方法和实现对钢琴共振板振动特性的客观评价，以4种适合制作乐器音板的云杉属木材(俄罗斯远东红皮云杉、东北长白鱼鳞云杉、西藏林芝云杉及美国西加云杉)为研究对象，进行了从共振板素材、共振板，到音板，直至钢琴产品的声学特性的追踪研究。
采用综合坐标法、综合评分法对共振板素材的综合振动性能进行区分，根据区分结果，每树种均选出区分度大的两组共振板素材(分别为第1组与第2组素材，对应为第1块与第2块共振板，对应为第1号与第2号钢琴)，用以制备钢琴共振板；基于钢琴共振板的振动理论，分析了共振板的振动特性；将共振板制成钢琴后，采用主观评价、客观评价、生理心理指标评价方法对钢琴的声学品质进行评价；在综合分析共振板振动特性、钢琴声学品质之间的关系的基础上，建立钢琴共振板振动特性的客观评价方法以及钢琴共振板用木材的客观选取方法。
本文的主要研究内容和结果如下：
(1)在实际尺寸木材振动特性检测的探索性研究基础上，对实际尺寸的钢琴共振板用木材振动特性进行检测，并采用综合分析的方法，实现对俄罗斯远东红皮云杉、东北长白鱼鳞云杉、西藏林芝云杉及美国西加云杉树种的试验样本进行振动特性的综合评价与区分，对每个树种均挑选出两组综合振动特性区分明显的共振板素材。
(2)将素材拼板胶合，形成共振板。分析了钢琴共振板基本振动理论，得出钢琴共振板自由振动的频率方程。根据自由振动的频率方程计算得出钢琴共振板x方向与y方向的弹性模量(MOE_x，MOE_y)，并用纵波传播速度方程计算得出钢琴共振板x方向与y方向的纵波传播速度(V_(Lx)，V_(Ly))，通过比较发现：同树种的两块共振板，无论是x方向，还是y方向，第2块共振板的弹性模量值、纵波传播速度基本要比第1块的大；所有的共振板，y方向的弹性模量(MOE_y)、纵波传播速度(V_(Ly))均要大于x方向(MOE_x，V_(Lx))。对共振板裁边后剩余的边角试件(45°斜纹理试件)进行力学性能分析，得出与共振板整板弹性模量值的分析结果较为一致的结论。
(3)在共振板上粘贴肋木，形成音板。通过肋木对钢琴共振板声传播速度影响的分析，结果表明肋木可显著提高共振板横纹理方向的振动传播响应速率。比较音板不同方向之间及同树种内两块音板的对应方向的振动响应时间发现，顺纹理方向的振动响应时间与横纹理方向之间相差不大，这主要是肋木起到了很好的增加横纹理方向振动传播速度的作用。
(4)利用上述4个树种各2组音板制作了8台钢琴。采用主观评价、客观评价方法对8台钢琴的声学品质进行评价，主观评价人员为从事钢琴演奏与教学工作多年的专家，客观评价的指标主要包括钢琴的音强、音长、动态范围及音色等。评价的结果表明：同树种的两台钢琴，第2号的钢琴声学品质客观评价指标值、音质主观评价项目得分基本都优于第1号。可认为，同树种的第2号钢琴声学品质优于第1号钢琴。
(5)以没有音乐专业背景的大学生群体为研究对象，以心率、血压、皮肤温度及呼吸几项指标为变量，分析了不同钢琴对受验者生理的影响。结果表明：与正常静息状态比较，听赏钢琴曲后，引起受验者的生理信号相应改变，表现为交感神经活动张力降低，迷走神经活动水平上升，自主神经活动状态发生改变，但尚未失去均衡性，综合表现为自主神经系统活动性降低，受验者精神处于松驰状态；比较受验者听赏同树种内两台钢琴演奏的曲子对受验者的生理影响可以表明，受验者听赏第2号钢琴时，交感神经活动张力比听赏第1号钢琴有所降低，而迷走神经活动水平上升，受验者精神处于更为放松的状态。
(6)从共振板弹性模量(MOE_x，MOE_y)、纵波传播速度(V_(Lx)，V_(Ly))、共振板边部斜纹理试件弹性模量(MOE_(45x)，MOE_(45y)及音板的振动响应时间(顺纹理振动响应时间T_L，横纹理振动响应时间T_R)4个方面分析了共振板的振动特性与钢琴声学品质的主观评价得分(总项平均得分、总体音质得分及计权得分)、客观评价指标(强奏音强值、弱奏音强值、音长、音色)之间的关系。共振板y方向弹性模量(MOE_y)、纵波传播速度(V_(Ly))、共振板边部斜纹理试件弹性模量(MOE_(45y))与主观评价得分、客观评价指标之间的相关关系大于x方向，其原因可能与音板上的琴弦排列与音板的y方向接近平行，或与y方向的夹角小于x方向的结构特点有关；主、客观评价指标与音板横纹理方向振动响应时间之间的相关性高于顺纹理方向的振动响应时间。因此，通过提高共振板弹性模量、纵波传播速度，尤其是y方向，可提高钢琴的声学品质；若能降低音板的横纹理方向的振动响应时间，以减小与顺纹理方向的声振动传播速度的差异，使整个音板在最短的时间内均匀振动起来，也可提高钢琴的声学品质。
(7)通过综合分析得出钢琴共振板的振动性能客观评价方法：测量钢琴共振板，或者直接测量钢琴共振板边部斜纹理试件的弹性模量值，主要是y方向弹性模量值；测量钢琴共振板的纵波传播速度，或者测量音板的振动响应时间，主要是y方向的纵波传播速度，或者横纹理方向的振动响应时间。
(8)通过综合分析得出钢琴音板用木材的客观选取方法：采用综合坐标法、综合评分法的综合分析方法对钢琴音板用木材的综合振动性能进行计算，参与计算的振动性能指标需要包括纵向的振动性能指标与横向或斜纹理方向的振动性能指标。
The piano acoustical quality is decided by the soundboard to a great extent. In the producing, the technician evaluates and chooses the wood for piano soundboard subjectively for the moment. It is inefficient, large error, and insufficiency of the scientific foundation. It does not satisfy the requirement to produce the excellent piano soundboard in the condition of volume-produce.
In order to establish the objective selection method of wood selection for piano soundboard and objective evaluation method of vibration property of piano resonance board, track-study of vibration properties from the wood used for resonance board 1) of Picea glehnii, Picea jezoensis, Picea likiangensis var. linzhiensis, and Picea sitchensis, resonance board 2), to soundboard 3), until the acoustical quality of piano were studied.
The comprehensive vibration properties of the samples of every species were analyzed and differentiated respectively by the comprehensive coordinate method and comprehensive marking method. According to the results of differentiation, two groups of samples used for producing the resonance boards in every species were selected respectively, and the distinction between the both groups was obvious (the No.1 and No.2 groups of samples respectively, correspond to the No.1 and No.2 piece of resonance board, correspond to the No.1 and No.2 piano). The vibration properties of resonance board were analyzed base on the vibration theory of thin plate. After the pianos were producing, the acoustical qualities of pianos were evaluated by the subjective method, objective method, and psycho-physiological index method. On the basis of the comprehensive analysis of the correlation between vibration properties of the resonance board and the acoustical quality of pianos, the objective evaluation method of the resonance board of piano and the objective selection method of wood used for soundboard were established.
The main research contents and results were summarized as follows:
(1) On the basis of studying exploringly on the vibration properties measurement of full - size wood samples, the vibration properties of full-size wood used for resonance board of piano were measured. The comprehensive vibration properties of samples of Picea glehnii, Picea jezoensis, Picea likiangensis var. linzhiensis, and Picea sitchensis were analyzed and differentiated by comprehensive analysis methods. And finally, two groups of samples were selected for producing the resonance board of piano, and that the distinction of vibration properties between the No.1 groups and the No.2 groups was obvious in every species.
(2) The samples of wood used for resonance board were glued to resonance board. The foundation theory of vibration of piano resonance board was analyzed, and the frequency equation of free vibration was acquired. The MOE, velocity of longitudinal wave of resonance board on the x (MOE_x, VL_(Lx)) and y (MOE_y, V_(Ly)) direction were computed by the frequency equation and longitudinal wave transmittal equation. The results were: the MOE_x, MOE_y, VL_x, V_(Ly) of the No.2 piece of resonance board (correspond to the No.2 group of wood samples) are larger than the No.1 (correspond to the No.1 group of wood samples) in every species; for all resonance boards, the MOE_y, V_(Ly) are larger than MOE_x, V_(Lx). The mechanical, properties of the 45°grain samples in the edge of the resonance board were analyzed, and the results were same to the resonance board.
(3) The soundboard is the resonance board that the ribs were glued on it. The influence of ribs on the sound transmit velocity of piano resonance board was analyzed. The result shows that the ribs can enhance the sound transmit velocity on the radius direction of resonance board. The response time of vibration on the radius direction is near to that on the longitudinal direction. That is because the ribs enhance the sound transmittal velocity on radius direction of resonance board.
(4) The acoustical quality of the pianos was evaluated by the subjective and objective method. The experts of subjective evaluation were engaged in piano performance and education many years. The indexes of objective evaluation were loudness, sound length, dynamic range, and tone. The results of evaluation were: the acoustical quality of the No.2 piano was more excellent than the No.1 piano in the same species.
(5) The influence of the piano music on psycho-physiological reaction (the main indexes are Heart Rate Variability, Blood Pressure Variability, Skin Temperature, and Respiration Frequency) of the subjects who are undergraduate without the background of musical training were analyzed. Compared with the resting state, the subjects' physiological reaction was changed when they enjoyed the piano music. The subjects' sympathetic nerves activity decreased, and the parasympathetic nerves activity increased, but the equilibrium was not broke. The synthetical presentation was that the activity of autonomic nervous system was weakening, and the subjects were more comfortable than they were resting. Then the differentiation of the influence of two pianos music of the same species on the subjects' physiological reaction was analyzed. The results show: when the subjects were enjoying the music of the No.2 piano the sympathetic nerves activity of the subjects decreased, the parasympathetic nerves activity increased, and they were more comfortable than that the No.1 piano of the same species.
(6) The correlation between the vibration properties of resonance board (MOE_x, MOE_y, V_(Lx), V_(Ly)), MOE of the 45°grain sample in the edge of the resonance board (MOE_(45x), MOE_(45y)), response time of vibration of soundboard (T_L—time of longitudinal direction, T_R—time of radius direction) and the score of subjective evaluation, indexes of objective evaluation of piano acoustical quality were analyzed. The correlation between subjective evaluation score, objective evaluation indexes and the vibration properties in the y-direction of resonance board were more significant than that in the x-direction. That may be related to the strings array frame. Because the strings axis in high and intermediate frequency region is near parallel to y-direction and the angle between strings axis and y-direction in low frequency region is smaller than that between strings axis and x-direction of the soundboard. The correlation between subjective evaluation score, objective evaluation indexes and the response time of vibration of soundboard in the radius direction were more significant than that in the longitudinal direction of wood. So, the acoustical quality of piano is improved with the MOE (MOE_x, MOE_y), velocity of longitudinal wave of resonance board (V_(Lx), V_(Ly)) increased, especially in the y-direction. If the discrepancy between T_L and T_R is abated with T_R reduced, the piano acoustical quality is improved.
(7) The objective evaluation method of wood used for piano resonance board is: the MOE of the resonance board or the 45°grain sample in the edge of the resonance board is measured, especially the y-direction(MOE_y, MOE_(45y)); And the velocity of longitudinal wave transmittal, or response time of vibration of soundboard is measured, especially the y-direction velocity (V_(Ly)) or the response time of vibration in the radius direction of the soundboard (T_R).
(8) The objective selection method of wood used for piano soundboard is: the comprehensive vibration properties of wood used for piano soundboard are computed by comprehensive coordinate method and comprehensive marking method, and the indexes include wood longitudinal and radius (or 45°direction of grain) vibration properties.
引文
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