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This paper proposes an interpolating extension to hidden Markov models (HMMs), which allows more accurate modeling of natural sounds sources. The model is able to produce observations from distributions which are interpolated between discrete HMM states. The model uses Gaussian mixture state emission densities, and the interpolation is implemented by introducing interpolating states in which the mixture weights, means, and variances are interpolated from the discrete HMM state densities. We propose an algorithm extended from the Baum-Welch algorithm for estimating the parameters of the interpolating model. The model was evaluated in automatic instrument classification task, where it produced systematically better recognition accuracy than a baseline HMM recognition algorithm.