A random-interval pulse train or wide-band noise when delayed (τ) and added back to itself (cos+) produces a stimulus with a cosinusoidally varying (or rippled) power spectrum. The spacing between the peaks in the spectrum is equal to the reciprocal of the delay (1/τ). If the stimulus is delayed and added back at 180° phase reversal (cos−), then a cosinusoidally varying power spectrum is generated whose spectral peaks are separated by 1/τ, but whose peaks are displaced by 1/2τ relative to the power spectrum of the cos+ stimulus generated with the same delay, τ. These stimuli yield a pitch, such that the pitch of the cos+ stimulus is equal to approximately 1/τ and the pitches of the cos− stimuli are equal to approximately 0.9/τ and 1.1/τ. These pitch matching results were studied using a variety of matching stimuli and conditions. Following the identification of the pitches, a method of limits and a same–different procedure were used to study the pitch discriminability of both the cos+ and cos− stimuli. Delays (τ) ranging from 1 to 10 ms were studied covering a pitch range of 90–1100 Hz. The pitch discriminations associated with the cos+ and cos− stimuli were essentially the same for both the random-interval pulse train and the wide-band stimuli. These pitch-discrimination results are compared to those associated with a periodic pulse train. The research is also discussed in terms of discriminations of delayed sounds in reverberant environments. These results are consistent with assumptions concerning the autocorrelation of the rippled stimuli within the dominant frequency region for pitch perception.