We examine the encoding of acoustic spectra by parameters derived from singularities found in their multiscale auditory representations. The multiscale representation is a wavelet transform of an auditory version of the spectrum, formulated based on findings of perceptual experiments and physiological research in the auditory cortex. The multiscale representation of a spectral pattern usually contains well-defined singularities in its phase function that reflect prominent features of the underlying spectrum such as its relative peak locations and amplitudes. Properties (locations and strength) of these singularities are examined and employed to reconstruct the original spectrum by using an iterative projection algorithm. Although the singularities form a nonconvex set, simulations demonstrate that a well-chosen initial pattern usually converges on a good approximation of the input spectrum. Perceptually intelligible speech can be resynthesized from the reconstructed auditory spectrograms, and hence these singularities can potentially serve as efficient features in speech compression. Besides, the singularities are very noise-robust which makes them useful features in various applications such as vowel recognition and speaker identification