Amplitude fluctuations of natural sounds carry multiple types of information represented at different time scales, such as syllables and voice pitch in speech. However, it is not well understood how such amplitude fluctuations at different time scales are processed in the brain. In the present study we investigated the effect of the stimulus rate on the cortical evoked responses using magnetoencephalography (MEG). We used a two-tone complex sound, whose envelope fluctuated at the difference frequency and induced an acoustic beat sensation. When the beat rate was continuously swept between 3Hz and 60Hz, auditory evoked response showed distinct transient waves at slow rates, while at fast rates continuous sinusoidal oscillations similar to the auditory steady-state response (ASSR) were observed. We further derived temporal modulation transfer functions (TMTF) from amplitudes of the transient responses and from the ASSR. The results identified two critical rates of 12.5Hz and 25Hz, at which consecutive transient responses overlapped with each other. These stimulus rates roughly corresponded to the rates at which the perceptual quality of the sound envelope is known to change. Low rates (> 10Hz) are perceived as loudness fluctuation, medium rates as acoustical flutter, and rates above 25Hz as roughness. We conclude that these results reflect cortical processes that integrate successive acoustic events at different time scales for extracting complex features of natural sound.