The method comprises the steps of: filtering the audio signal by means of a lowpass filter (101) with a cutoff frequency substantially equal to said cutoff frequency (F0) of the sound playback device; determining a fundamental frequency for reconstituting from the lowpass filtered audio signal; and generating a harmonic signal (Sharm) associated with said fundamental frequency to be reconstituted. It also comprises the steps of: detecting a time envelope (env(t)) of the lowpass filtered audio signal; adapting the dynamic range of said time envelope (env(t)) as a function of the frequency band under consideration; and reinjecting said harmonic signal in phase into said audio signal by addition after multiplying said harmonic signal (Sharm) with the adapted time envelope (envadapt(t)). The adaptation is performed by compression/expansion of the time envelope with feedback loop control that is adjusted automatically on the value of the envelope as a function of the mean energy of the input signal to a value that maximizes said energy within a defined limit.