Effect of amplitude envelope on the pitch of sine-wave tones

Psychophysical experiments show that the pitch of a short sine wave tone depends upon the amplitude envelope of the tone. Subjects find that the pitch of an exponentially decaying tone (1dB/ms) is higher than the pitch of a (20-ms) rectangularly gated tone of equal frequency. The percentage difference in frequency required to produce equal pitches with the two envelopes depends upon frequency fo: 2.6% at fo = 412 Hz, 1.4% at fo = 825 Hz, 1% at fo = 1650 Hz, and 0.7% at fo = 3300 Hz. The pitch change is insensitive to the relative intensities of the two tones. The spectra of tones with the two different envelopes suggest no obvious explanation for the pitch change. However, the weighted time-varying spectra for tones with two different envelopes evolve differently with time. Alternatively the pitch change can be derived from a modified version of the auditory phase theory of Huggins.