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We present a computational model of musical instrument sounds that focuses on capturing the dynamic behaviour of the spectral envelope. A set of spectro-temporal envelopes belonging to different notes of each instrument are extracted by means of sinusoidal modeling and subsequent frequency interpolation, before being subjected to Principal Component Analysis. The prototypical evolution of the envelopes in the obtained reduced-dimensional space is modeled as a nonstationary Gaussian Process. This results in a compact representation in the form of a set of prototype curves in feature space, or equivalently of prototype spectro-temporal envelopes in the time-frequency domain. Finally, the obtained models are successfully evaluated in the context of two music content analysis tasks: classification of instrument samples and detection of instruments in monaural polyphonic mixtures.