Local Cochlear Correlations of Perceived Pitch

Pitch is one of the most salient attributes of the human perception of sound, but is still not well understood. This difficulty originates in the entwined nature of the phenomenon, in which a physical stimulus as well as a psychophysiological signal receiver are involved. In an electronic realization of a biophysically detailed nonlinear model of the cochlea, we find local cochlear correlates of the perceived pitch that explain all essential pitch-shifting phenomena from physical grounds.

Figure 1

Cochlea response $V(t)$ to an inharmonic AM tone $f(t,A=0.1,f_{\mathrm{car}}=1.65\mathrm{kHz},f_{\mathrm{mod}}=0.2\mathrm{kHz})$, waveforms $f(t)$, $V(t)$ (time origins artificially aligned) and their Fourier transforms. Stimulation (top line, three frequencies) and two frequency channels labeled by their characteristic frequencies $f_c$, revealing at $f_c=0.88\mathrm{kHz}$ a strong CT-generated signal that classically should be absent.

Figure 2

Left panels: $f_p(x)$ for $f(t,A=0.1,f_{\mathrm{mod}}=0.2\mathrm{kHz},f_{\mathrm{car}})$ measured at the cochlea sections (a) $f_c=1.76\mathrm{kHz}$, (b) $f_c=1.245\mathrm{kHz}$ and (c) $f_c=0.88\mathrm{kHz}$. From left to right: increasing harmonic numbers $k$. Dashed lines: de Boer’s rule for fixed $k$. The horizontal line through $f_p=0.2\mathrm{kHz}$: purely harmonic sounds providing no second effect ($\delta f=0$). Right panels: Total signal power (tsp) of AM vs single tones (identical input power $-20{\mathrm{dB}}_{1V}$, $f_{\mathrm{single}}=f_{\mathrm{car}}$). Labels: three regimes ($s$. text), shading: CT-generated signal surplus.

Figure 3

(a) $f_{\mathrm{mod}}$ is varied at fixed $f_{\mathrm{car}}=2.0\mathrm{kHz}$, $A=0.1$. Dots: Local pitch measurements at five sections. Dashed lines: Experimental data from two subjects [6]. Regime 1: For section $f_c=2.093(\sim f_{\mathrm{car}})\mathrm{kHz}$, a zero slope as predicted by de Boers rule emerges. Regime 2: Down the cochlea $f_c<f_{\mathrm{car}}$, the slope increases ($s$. text), (b) Loudness dependence of $f_p(x)$ for an AM tone ($f_{\mathrm{car}}=1.7\mathrm{kHz}$, $f_{\mathrm{mod}}=0.2\mathrm{kHz}$). Regime 1: $f_c=1.76\mathrm{kHz}$ (close to $f_{\mathrm{car}}$), reveals zero dependence. Regime 2: For $f_c<f_{\mathrm{car}}$, increasing deviation with increasing distance to $f_{\mathrm{car}}$.