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ON THE PHYSICO-ACOUSTICAL BASES OF SONANCE AND TENSION

Y. Stanishevskiy

Abstract

Up to the present moment the musical science explains the fundamental phenomena of harmony, such as sonance and tension, either by the abstract numerical logic in the frequency relations of sounds, or by the individual specifics of perception. And though the regularities of perception of sonance are well-known, their objective reasons exist only at the level of hypotheses, and the phenomenon of tension is still regarded only as a result of the perceptual effects. However, the above-mentioned phenomena are the reflection of real acoustic processes and physical phenomena. It is known that the perception of sonance depends on frequency relations. The most famous objective explanations of this touch upon the role of coincidence of waves (e. g. in L. EulerВ’s "Tentamen novae theoriae musucae", 1739) or overtones (e. g. in H. HelmholtzВ’s "Die Lehre von den Tonempfindungen", 1863). But the latter contradicts to the fact of saving the quality of sonances regardless of inexactness of tuning and non-coincidence of harmonics. The former, however, donВ’t have the strong base because in real acoustical conditions there is no complete coincidences of waves and their phases. So, the idea of dependency of the perception of sonance on the length of combined period is not correct too because this last may be absent and going to infinity. As for tension, it is obvious that its reason consists not only in tendency to simplify the relations and in logic of succession of fundamental tones, as it is generally considered. Nevertheless, I. Orlov's research "On musical and acoustical illusions" (1929) showed that objectively the perception of tension depends on tuning of frequency relations, but this dependency is not simple and has some regularities. Besides this, the modern physics of nonlinear processes has revealed the universal laws in dynamic systems including both acoustical systems and homo sapiens as a biological organism. So, the remarkable works by I. Blekhman ("Synchronization in the nature and technologies", 1981) and by A. Pikovsky, M. Rozenblyum, J. Kurts ("Synchronization. The fundamental nonlinear phenomenon", 2003) allow discovering exact correlations between regularities of physical processes (resonance and synchronization) and regularities of perception of sonance and tension. These all may help to create the physical and mathematical models of the processes corresponding to conditions of perception of sonance and tension. The resolution of the problem is connected with finding the correlations between physical, acoustical and perception phenomena. And as a result, it is possible to create a new theory of harmony is based on the objective reasons of their regularities, which are the consequences of real psycho-acoustical events.

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