Imperfect pitch: Gabor's uncertainty principle and the pitch of extremely brief sounds

Abstract

How brief must a sound be before its pitch is no longer perceived? The uncertainty tradeoff between temporal and spectral resolution (Gabor's principle) limits the minimum duration required for accurate pitch identification or discrimination. Prior studies have reported that pitch can be extracted from sinusoidal pulses as brief as half a cycle. This finding has been used in a number of classic papers to develop models of pitch encoding. We have found that phase randomization, which eliminates timbre confounds, degrades this ability to chance, raising serious concerns over the foundation on which classic pitch models have been built. The current study investigated whether subthreshold pitch cues may still exist in partial-cycle pulses revealed through statistical integration in a time series containing multiple pulses. To this end, we measured frequency-discrimination thresholds in a two-interval forced-choice task for trains of partial-cycle random-phase tone pulses. We found that residual pitch cues exist in these pulses but discriminating them requires an order of magnitude (ten times) larger frequency difference than that reported previously, necessitating a re-evaluation of pitch models built on earlier findings. We also found that as pulse duration is decreased to less than two cycles its pitch becomes biased toward higher frequencies, consistent with predictions of an auto-correlation model of pitch extraction.

Keywords: Computational modeling; Discrimination; Pitch.