Musical tension in harmonic intervals: behavioral and neural correlates

Musical tension is what drives our emotional experience in music listening. However, the specific role of the musical elements involved in tension-resolution perception remains largely unclear. This dissertation aims to advance the understanding of tension perception dynamics related to sensory consonance-dissonance. The first experiment aimed to design and validate a new crossmodal proprioceptive device for tension rating that overcomes some of the limitations of known tools. As a result, a psychophysical equation for the matching of physical force and psychological force was presented. The same tool was subsequently used in the second and third experiments to collect ratings of perceived tension and movement in harmonic musical intervals and standard noises. Besides, a visual analog scale (VAS) was used to allow a comparison of these two methods. The results confirmed the close relationship between sensory dissonance and perceived tension. Moreover, stimuli in the higher pitch register were perceived as more tense, confirming the primary role of pitch as a mediator of tension. The comparison between ratings obtained with the proprioceptive device and the VAS highlighted the tendency to give higher tension ratings using the VAS compared to the proprioceptive device. In the last experiment, brain electrical activity was recorded during the presentation of short tension-resolution patterns created using the most tense (perfect unison, fourth, and fifth) and the least tense harmonic intervals (augmented fourth, minor second, and inverted major seventh) to understand how consonance-dissonance can convey meaningful information on perceived tension-resolution. Results showed overall larger effects during the ‘resolution’ condition compare to the ‘tension induction’ condition, indicating that the resolution of harmonic instability towards a state of stability may be more salient than its opposite. A late positive component (LPC) was elicited, possibly reflecting deeper processing of tension-related meaning within a minimal harmonic context.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.