On the uncertainty principle for the pitch of brief tones

Abstract

Many experiments have shown that the ability of human listeners to discriminate the frequencies of brief tones can violate the wave uncertainty principle that applies to linear systems. Several observations can be made: (1) Experiments that associate the duration of the tone envelope, or the second central moment of the squared envelope, with temporal uncertainty are consistent with the application of the energy-time principle in non-relativistic quantum mechanics. (2) The role of echoic memory in confounding the definition of duration can be avoided by immediately following the target tone to be judged by a tone of different frequency. (3) Whereas the uncertainty principle relates well-defined conjugate variables, such as time and frequency, listeners in psychoacoustical experiments may benefit from comparisons in both the pitch dimension (coding frequency) and a timbral dimension associated with the spectral distribution of energy. The latter provides additional information that is outside the context for the uncertainty principle. Its influence can be reduced by experiments in which the listener compares target tones having different brief durations. When these considerations are applied, it is found that human listeners still beat the uncertainty principle, but not as impressively.