On the Frequency Limits of Binaural Beats

Abstract

The report describes measurements of the frequency limits of binaural beats and outlines a theory of binaural beats, based on synchronous discharges in the two auditory nerves. Two sinusoids of frequencies f1 (fixed) and f2 (variable) were led separately to the two ears; and the difference Δf= |f1—f2 | that marked the disappearance of the fluctuating loudness or roughness that is characteristic of binaural beats was determined. δf was maximal (approximately 35 c.p.s.) for frequencies in the neighborhood of 400 c.p.s. Binaural beats were heard above 1000 c.p.s., but careful attention was required and Δf was small. The shape of the curve relating Δf to f1 provides an explanation for the fact that determinations of the upper frequency limit of binaural beats have not been in agreement; the upper frequency limit depends markedly on Δf. The theory, given to account for the fact that Δf is smaller both at low and at high frequencies than it is near 400 c.p.s., combines elements of the Hill-Rashevsky theory of the excitation of neurons with elements of Wever's volley theory. At low frequencies neurons can discharge in some degree of synchrony with the stimulus wave form, yet fail to coincide within the time interval necessary for synaptic summation. At high frequencies the neurons must take turns discharging, and relatively few can participate in any given volley. At intermediate frequencies, however, each neuron participates in many volleys and the neurons participating in each volley fire almost simultaneously. The result is that at intermediate frequencies synchrony is relatively precise in each afferent pathway and, when the two afferent streams join in a common neural center, beats appear. © 1950, Acoustical Society of America. All rights reserved.