It has been shown repeatedly that Weber's law does not hold for intensity discrimination of pulsed tones. The masking function for such waveforms (10 logδ/ vs 10 log I, for constant performance) typically is linear with a slope of 0.9 over a range in I of at least 60 dB. The present experiment indicates that the slope of the masking function increases from 0.9 to 1.0 as regions above the signal frequency are masked by filtered noise. A sufficient condition for a slope of 1.0 is a high-pass noise which masks regions at and above the second harmonic of the signal. This suggests that the “near miss” to Weber's law reflects the observer's use of information at aural harmonics. A model based upon this notion gives a good quantitative account of the data. The amount of distortion assumed in the model is in reasonable agreement with other data.