The variables that influence listeners' perceptions of steady-state acoustic gratings (ripple spectra or profiles) are explored. Subjects identified gratings by the frequency of sinusoidal modulation of their envelopes independently of envelope phases. The gratings or ``profiles'' were synthesized with 193 log-spaced tones (200--3200 Hz). Sinusoidal modulations of 0.5, 1.0, 2.0, 4.0, and 8.0 cycles/oct and a peak-to-valley depth of 20 dB were used. Three listeners performed the identification task with feedback and completed 75 blocks of 125 trials each. The listeners scores changed from the first ten to the last ten blocks as follows: 91% to 98%, 62% to 91%, and 56% to 70%, respectively. The gratings appeared to vary along perceptual dimensions of (1) noisiness, (2) roughness, (3) tonality, (4) chord quality, and (5) base/treble quality. The first four dimensions allowed identification of the gratings by envelope frequency, while the base/treble quality seemed most related to the envelope phase. Additional experiments explore the effects of the widths of the spectral peaks, the peak-to-valley depth in decibels, and earphone-response equalization. Effects of individual differences and practice are discussed as are relations to the perception of vowels, of musical intervals and chords, and of optical gratings or ``stripe'' patterns.