The sound of a sinusoid: Time‐interval models

When an amplitude modulator that is asymmetric in time is applied to a sinusoid, the direction of the asymmetry affects the timbre of the sound. If the modulator is a decaying exponential with a 4‐ms half‐life and a repetition period of 25 ms, the resulting ‘‘damped’’ sinusoid does not have the sound quality of a sinusoid. But if the modulator is reversed in time to produce a ‘‘ramped’’ sinusoid, the sound of a sinusoid returns [R.D. Patterson, J. Acoust. Soc. Am. (1994)]. This paper extends the domain of the phenomenon with an experiment in which the modulator period varies with the carrier frequency to fix the number of carrier periods per envelope period. This fixes the shape of the wave within a cycle of the sound across carrier frequencies, and it fixes the shape of the main peak in the spectrum of the sound. When presented with pairs of damped and ramped sounds having the same half‐life, listeners choose the ramped sound as having the stronger sinusoidal component provided the sinusoids are discriminable. Discrimination is limited to conditions where the half‐life is 1 ms or more. At longer half‐lives, performance is near ceiling for carrier frequencies up to 1600 Hz; above this, performance falls off as carrier frequency increases. The sound quality differences in damped and ramped sinusoids are explained in terms of a time‐interval model of hearing that simulates our auditory images of sounds. The number of carrier periods in the auditory image is greater for the ramped sinusoid in most conditions where the ramped perception is judged to have a stronger sinusoidal quality. Many of these carrier‐period intervals are in channels well away from the carrier channel indicating that the sound of a sinusoid is more closely associated with time intervals at the carrier period than with energy in the carrier channel.