The human auditory system is designed to capture and encode sounds from our surroundings and conspecifics. However, the precise mechanisms by which it adaptively extracts the most important spectro-temporal information from sounds are still not fully understood. Previous auditory models have explained sound encoding at the cochlear level using static filter banks, but this vision is incompatible with the nonlinear and adaptive properties of the auditory system. Here we propose an approach that considers the cochlear processes as envelope interpolations inspired by cochlear physiology. It unifies linear and nonlinear adaptive behaviors into a single comprehensive framework that provides a data-driven understanding of auditory coding. It allows simulating a broad range of psychophysical phenomena from virtual pitches and combination tones to consonance and dissonance of harmonic sounds. It further predicts the properties of the cochlear filters such as frequency selectivity. Here we propose a possible link between the parameters of the model and the density of hair cells on the basilar membrane. Cascaded Envelope Interpolation may lead to improvements in sound processing for hearing aids by providing a non-linear, data-driven, way to preprocessing of acoustic signals consistent with peripheral processes.