A Dynamical Systems Approach to Spectral Music: Modeling the Role of Roughness and Inharmonicity in Perception of Musical Tension
Frontiers in Applied Mathematics and Statistics
Tension-resolution patterns seem to play a dominant role in shaping our emotional experience of music. In traditional Western music, 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 Gérard Grisey manage to implement the patterns by manipulating spectral attributes like roughness and
... 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 spectral representation of sound which reproduces existing empirical results on spectral correlates of tension. By virtue of being neurodynamical, the proposed model is generative in the sense that it can simulate responses to arbitrary sounds.