Group theory approach to combination tones

Abstract

Traditional approaches to combination tones based on Helmholtz theory encounter essential interpreting difficulties, which the most known example is the anomalous behaviour of the combination tone 2f1-f2. Without doubt the phenomenon of combination tones is connected with nonlinear phenomena in the human ear. Therefore, it is generally assumed that the explanation of this phenomenon is possible on the level of the ear. This paper proposes different approach, which assumes the existence of an additional mechanism beyond the ear. The aim of this mechanism is to diminish sensitivity of the auditory process to nonlinear distortions by appropriate decoding of sound information. The general rule of construction and the mathematical model of such a mechanism is proposed, which allows for the explanation of many problems associated with combination tones. As a consequence an unexpected result is obtained with regard to a combination tone 2f1-f2 that it can originate already from the nonlinear distortion of the second order. This mathematical model is formulated in terms of finite groups.