Konsonanzempfinden und Periodizitätsanalyse im auditorischen System

Abstract

Since ancient times, regular pulses of the air beating against the ear have been regarded as the cause of pitch. Until the time of Leonhard Euler, theorists plotted point sequences to represent these regular pulses of the air. Two parallel point sequences symbolized an interval. The number of coinciding points of both point sequences determined the degree of consonance or dissonance. This so called “coincidence theory of consonance” lost its importance with the rise of modern science. Georg Simon Ohm introduced Jean Baptiste Joseph Fourier’s theorem to acoustics which allowed precise spectral analysis and calculation of any vibration. A tone was no longer described by a sequence of points symbolizing pulses of the air but by sine or cosine functions and their sums. Spectral analysis led to considerations in the frequency-domain. Combining it with the phenomenon of roughness, Hermann von Helmholtz developed a consonance theory based on the disturbance of harmony by roughness. Today, his idea forms the basis of the concept of sensory consonance. In contrast to computations in the frequency domain, however, sound is neuronally processed in the time domain. A single tone, for example, is neuronally represented by a periodic pulse train. Musical intervals produce firing patterns in the auditory nerve with regularities depending on the vibration ratio of the fundamental pitches. A mathematical model can be described that makes it possible to define a value to calculate the degree of these regularities for each vibration ratio. It turns out that this value, called Generalized coincidence function (Allgemeine Koinzidenzfunktion) is quite similar to the degree of tonal fusion as described by Carl Stumpf. This finding makes it probable that tonal fusion is a consequence of certain properties of the neuronal periodicity detection mechanism. Together with the roughness of intervals, this neuronal mechanism may be regarded as the basis of consonance and dissonance.