Department of Information Engineering, University of Padova, Via G Gradenigo 6/A, IT-35131 Padova, Italy.
J Acoust Soc Am. 2012 Jan;131(1):897-906. doi: 10.1121/1.3651097.
String and membrane vibrations cannot be considered as linear above a certain amplitude due to the variation in string or membrane tension. A relevant special case is when the tension is spatially constant and varies in time only in dependence of the overall string length or membrane surface. The most apparent perceptual effect of this tension modulation phenomenon is the exponential decay of pitch in time. Pitch glides due to tension modulation are an important timbral characteristic of several musical instruments, including the electric guitar and tom-tom drum, and many ethnic instruments. This paper presents a unified formulation to the tension modulation problem for one-dimensional (1-D) (string) and two-dimensional (2-D) (membrane) cases. In addition, it shows that the short-time average of the tension variation, which is responsible for pitch glides, is approximately proportional to the system energy. This proportionality allows the efficient physics-based sound synthesis of pitch glides. The proposed models require only slightly more computational resources than linear models as opposed to earlier tension-modulated models of higher complexity.
由于弦或膜的张力发生变化，弦和膜的振动不能在一定幅度以上被视为线性振动。一个相关的特例是，当张力在空间上保持恒定，而仅随弦长或膜面的整体变化而随时间变化时。这种张力调制现象最明显的感知效果是音高随时间的指数衰减。由于张力调制而产生的音高滑音是几种乐器（包括电吉他和汤姆鼓以及许多民族乐器）的重要音色特征。本文提出了一种用于一维（1-D）（弦）和二维（2-D）（膜）情况的张力调制问题的统一公式。此外，它表明负责音高滑音的张力变化的短时平均值近似与系统能量成正比。这种比例关系允许基于物理的音高滑音的高效合成。与更高复杂性的早期张力调制模型相比，所提出的模型仅需要略多的计算资源，而不是线性模型。
