The simplified linear model of speech production predicts that when the rate of articulation is changed, the resulting waveform takes on the appearance of the original, except for a change in the time scale. The goal of this paper is to develop a time-scale modification system that preserves this shape-invariance property during voicing. This is done using a version of the sinusoidal analysis-synthesis system that models and independently modifies the phase contributions of the vocal tract and vocal cord excitation. An important property of the system is its capability of performing time-varying rates of change. Extensions of the method are applied to fixed and time-varying pitch modification of speech. The sine-wave analysis-synthesis system also allows for shape-invariant joint time-scale and pitch modification, and allows for the adjustment of the time scale and pitch according to speech characteristics such as the degree of voicing.