小提琴运弓和发音的声学基本原理——从《试论小提琴弓对弦压力的物理特性》等文谈起

The Basic Principles in the Bowing and Articulation of Violin

国内近期出现了用物理模型来研究小提琴运弓问题的尝试。本文第一部分首先指出握弓类似于一个以拇指(F3)为支点的跷跷板,主要以食指(F1)和小指(F2)的施力配合,产生握弓力矩M;随后用“P(弓压)-x(弓位)-M直线法”证明演奏下弓是M随的增加而逐渐增大并转换方向的过程,此过程取决于P、弓的重力和重心;并首创“P-x-F(握弓施力)平面法”,在x,F1,F2空间中证明省力的运弓路径应在该平面中处于较低的位置。第二部分通过分析“赫尔姆霍茨运动”和“Schelleng图表”指出P及其变化范围和音量、弓速、弓与琴码的接近程度成正比,并与琴弦和弓自身的性质有关。

Holding the bow is like a teeterboard supported by thumb as the pivot and the cooperated forcing of forefinger andlittle finger produces a moment M. The “P(pressure)-x(position)-M Line Method” shows when playing a down bow,M increases with x and gradually changes its direction and this process is determined by P, the gravity and barycenter ofbow. The “P-x-F(force of fingers) Plane Method” shows that the most force-saving bowing path should locate in thelower part of this plane. The analyses of “Helmholtz Motion” and “Schelleng Diagram” indicate P and its range is in directratio with volume, velocity of bow, the approaching degree of the bow to the bridge and has some relationship with thequality of string and bow.