Figure 3.

Domain of existence of pitch. A, Within-channel structure produced by a periodic sound can be decoded if the sound’s period is smaller than the maximal neural delay δ_max. When δ_max = 4 ms, it occurs for sounds of fundamental frequency greater than 250 Hz. B, A pure tone or resolved harmonic produces cross-channel structure with arbitrarily small delays between channels, corresponding to the phase difference between the two filters at the sound’s frequency: here a 100 Hz tone produces two identical waveforms delayed by δ = 2 ms, while the sound’s period is 10 ms. C, A transposed tone with a high-frequency carrier (>4 kHz) modulated by a low-frequency envelope (<320 Hz) elicits a very weak pitch (Oxenham et al., 2004a) (top: f0 = 120 Hz). Such sounds produce only within-channel structure because they only have high-frequency content (middle). The structural theory of pitch predicts an absence of pitch when the envelope’s periodicity is larger than δ_max, which is consistent with psychophysics if δ_max< 3 ms. D, A pure tone with the same fundamental frequency (f0 = 120 Hz) produces cross-channel structure with short delays. The structural theory of pitch predicts the existence of pitch in this case, consistently with psychophysical results (Oxenham et al., 2004a). E, Complex tones with f0 between 400 Hz and 2 kHz and all harmonics above 5 kHz elicit a pitch (Oxenham et al., 2011) (top, spectrum of a complex tone; middle, temporal waveform). Such tones produce only within-channel structure in high frequency (bottom), and the structural theory of pitch predicts the existence of pitch if the sound’s period is smaller than δ_max, which is consistent with psychophysics if δ_max > 2.5 ms.