Applications of Fourier Series in Classical Guitar Technique
James R. Hughes · College Mathematics Journal · 2000
In elementary differential equations courses, the model of a (transversely) vibrating string is frequently used to motivate the one-dimensional wave equation and Fourier series. For musically-inclined students, the motivation can be strengthened by applying this model to techniques used by classical guitarists to vaiy tone quality. This note describes two such applications. The first application (harmonics) is well-known, eliciting nods of familiarity from guitar-playing students. The second application (sol tasto and sol ponticello) is less well-known outside the specific context of trained classical guitarists, but it is equally interesting, suggesting a surprisingly simple mathematical explanation for the technique where it is not immediately obvious that such an explanation exists. The physical model of a string in the xy-plane, with ends fixed at the points (0,0) and (tt,6), displaced to the shape of a curve y=f(x) at time ?=0 and then released to move in the j;-direction only (see Figure l), gives rise to the boundaiyvalue problem