Une approche scientifique de la tension et de l’attraction harmonique

At the present day, music theory is enriched by the extensive use of scientific methods for the analysis of harmonic phenomena. This implies purely mathematical approaches, and approaches related to the psychology of perception and psychoacoustics. In the context of these approaches, researchers successfully analyse sounds and chords, as well as the relationship between them. But despite all the successes of applying scientific methods in the analysis of harmonic pheno- mena, there is one aspect that is most difficult to analyse. This aspect concerns the dynamics of the relationship between the elements of harmony, for which we still use functional analysis, which does not explain the effects of perception. Thus, it often turns out that it is easier to talk about the functional difference between authentic and plagal cadences than about the diffe- rence in their psychoacoustic effect. A similar problem manifests itself at a higher level, when it is easier to determine tonality from the point of view of functional analysis than of perception and acoustic effects.
Although back in 1989 Richard Parncutt proposed a method for determining tonality in a series of chords taking into account a number of parameters in the context of a psychoacoustic approach, such a phenomenon as harmonic attraction remains difficult to explain scientifically. And it seems that the scientific analysis of this phenomenon, together with the phenomenon of tension, will finally make us free from the need to appeal to a functional approach in harmonic analysis.
In the proposed report, the attention is paid to a special approach for studying the dyna- mics of relations between harmonic elements. This approach is based on a new understanding of tension and harmonic attraction as projections of the effect of synchronisation of oscillations on psychoacoustic processes. The discussion concerns a physico-mathematical model, which, presumably, could allow estimating the strength of harmonic attraction. The model is based on the hypothesis of the predominant role of subharmonic effects in the perception of harmony, since they are amplified under the same conditions as synchronisation.