Regularity of Spike Trains and Harmony Perception in a Model of the Auditory System

Spike train regularity of the noisy neural auditory system model under the influence of two sinusoidal signals with different frequencies is investigated. For the increasing ratio $m/n$ of the input signal frequencies ($m$, $n$ are natural numbers) the linear growth of the regularity is found at the fixed difference ($m-n$). It is shown that the spike train regularity in the model is high for harmonious chords of input tones and low for dissonant ones.

Figure 1

The investigated model. $N_1$, $N_2$ are the sensors, $N_3$ is the interneuron. ${\xi }_1(t)$, ${\xi }_2(t)$, and ${\xi }_3(t)$ are the statistically independent white Gaussian noises.

Figure 2

Regularity of the interneuron’s spike train depending on the frequency ratio of input sinusoidal signals $m/n={\Omega }_1/{\Omega }_2$. Near each point there is the exact ratio $m/n$. The bold solid lines approximate the locus of the $R(m/n)$ points for constant differences ($m-n$). The dashed line is the example of locus change for $m-n=1$ (see text for clarification). The constant frequency of the second sensor’s sinusoidal signal is ${\Omega }_2=0.4\mathrm{rad}/\sec$. The first sensor’s frequency varies: ${\Omega }_1=\frac{m}{n}{\Omega }_2$. The noise intensity is the same for all three noise sources: $D=1.6\times {10}^{-3}$. Inset: informational entropy of the interneuron’s spike train versus the frequency ratio of input sinusoidal signals $m/n$.