The sound of a sinusoid: Spectral models

Abstract

It is commonly believed that the spectrum of a sound can be used to explain not only the pitch and loudness of that sound but also its timbre, or sound quality. This paper presents an experimental refutation of this spectral timbre claim. Listeners were presented with pairs of ‘‘damped’’ and ‘‘ramped’’ sinusoids and asked to choose the one whose sound quality was most like a sinusoid. The damped sinusoids were constructed by repeating a short segment (25 ms) of a sinusoid with an exponential decay; the ramped sinusoids were constructed by reversing the damped sinusoids in time. The spectra of damped and ramped sinusoids are very simple, consisting of one main peak whose width broadens as the half-life of the decay function decreases. Fourier energy spectra of damped and ramped sounds with the same half-life are identical. Auditory spectra from a more realistic auditory model with a gammatone auditory filterbank show that the width of the spectral peak of the damped sinusoid is narrower than that of the ramped sinusoid for half-lives in the range 2–16 ms and more like the auditory spectrum of an unmodulated sinusoid. Nevertheless, for half-lives in this range, listeners consistently choose the ramped sinusoid as having the stronger sinusoidal quality.