A Dynamical Systems Approach to Spectral Music: Modeling the Role of Roughness and Inharmonicity in Perception of Musical Tension

Michal Hadrava,Jaroslav Hlinka

doi:10.3389/fams.2020.00018

Abstract

Tension-resolution patterns seem to play a dominant role in shaping our emotional experience of music. In traditional Western these patterns are mainly expressed through harmony and melody. However, many contemporary musical compositions employ sound materials lacking any perceivable pitch structure, rendering the two compositional devices useless. Still, composers like Tristan Murail or Gerard Grisey manage to implement the patterns by manipulating attributes like roughness and inharmonicity. However, in order to understand the music of theirs and the other proponents of the so-called spectral music, one has to eschew traditional categories like pitch, harmony, and tonality in favor of a lower-level, more general representation of sound -- which, unfortunately, music-psychological research has been reluctant to do. In the present study, motivated by recent advances in music-theoretical and neuroscientific research into a the highly related phenomenon of dissonance, we propose a neurodynamical model of musical tension based on a representation of sound which reproduces existing empirical results on correlates of tension. By virtue of being neurodynamical, the proposed model is generative in the sense that it can simulate responses to arbitrary sounds.

Highlights

Music gives rise to some of the strongest emotional experiences in our lives
We show how the system of Equations (16) and (17) reacts to stimulation with complex tones varying in relative periodicity and inharmonicity
We propose the absence of a stable unambiguous pitch detection modeled as the absence of a pronounced amplitude peak in an array of oscillators to be a correlate of timbre-induced musical tension

Summary

Introduction

Music gives rise to some of the strongest emotional experiences in our lives. Even though the first surviving theoretical treatments of the power of music to move the soul were written in the fifth century B.C. [1], the origin of this power still largely remains a mystery. Over the course of the twentieth century, many composers enriched their palette with sounds possessing neither definite pitch (precluding melody) nor perceivable voice structure (precluding harmony), venturing out into territories about which traditional theory has nothing to say but hic sunt leones [5]. Still, while tantalizing their audience with a sound palette ranging from pure tones to the most atrocious noises, they seek control over how their music is experienced by the listener as much as their more conservative colleagues do [6]

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Conclusion