Jose Kevin, Chatterjee Anindya, Gupta Anurag
Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India.
J Acoust Soc Am. 2018 May;143(5):3184. doi: 10.1121/1.5038111.
The vibration of a homogeneous circular membrane backed by two taut strings is shown to yield several harmonic overtones for a wide range of physical and geometric parameters. Such a membrane is present at each end of the barrel of an idakkā, an Indian snare drum well known for its rich musicality. The audio recordings of the musical drum are analyzed and a case is made for the strong sense of pitch associated with the drum. A computationally inexpensive model of the string-membrane interaction is proposed assuming the strings to be without inertia. The interaction essentially entails wrapping/unwrapping of the string around a curve on the deforming membrane unlike the colliding strings in Western snare drums. The range of parameters for which harmonicity is achieved is examined and is found to be conforming with what is used in actual drum playing and construction.
研究表明，由两根拉紧的弦支撑的均匀圆形膜的振动，在广泛的物理和几何参数范围内会产生多个谐波泛音。这种膜存在于伊达卡（一种以丰富音乐性而闻名的印度小军鼓）鼓身的两端。对这种音乐鼓的音频记录进行了分析，并说明了与该鼓相关的强烈音高感。提出了一种计算成本较低的弦 - 膜相互作用模型，假设弦没有惯性。与西方小军鼓中弦的碰撞不同，这种相互作用本质上是弦在变形膜上的曲线周围缠绕/解缠绕。研究了实现谐波的参数范围，发现其与实际鼓演奏和制作中使用的参数相符。
