Sound Synthesis for Contact-Driven Musical Instruments via Discretisation of Hamilton's Equations

Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).

Energy conserving schemes for the simulation of musical instrument contact dynamics

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton׳s equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton׳s method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

Perception and Automatic Recognition of Laughter from Whole-Body Motion: Continuous and Categorical Perspectives

Despite its importance in social interactions, laughter remains little studied in affective computing. Intelligent virtual agents are often blind to users’ laughter and unable to produce convincing laughter themselves. Respiratory, auditory, and facial laughter signals have been investigated but laughter-related body movements have received less attention. The aim of this study is threefold. First, to probe human laughter perception by analyzing patterns of categorisations of natural laughter animated on a minimal avatar. Results reveal that a low dimensional space can describe perception of laughter “types”. Second, to investigate observers’ perception of laughter (hilarious, social, awkward, fake, and non-laughter) based on animated avatars generated from natural and acted motion-capture data. Significant differences in torso and limb movements are found between animations perceived as laughter and those perceived as non-laughter. Hilarious laughter also differs from social laughter. Different body movement features were indicative of laughter in sitting and standing avatar postures. Third, to investigate automatic recognition of laughter to the same level of certainty as observers’ perceptions. Results show recognition rates of the Random Forest model approach human rating levels. Classification comparisons and feature importance analyses indicate an improvement in recognition of social laughter when localized features and nonlinear models are used.

Inhabiting Sound: Tactile-sonic links in musical meaning

Connections can be suggested between music’s occupation of physical space, its relative ‘presence’ (using Edward Hall’s notion of proxemics), and the various senses of movement which pervade it. Movement might be seen to operate with respect to music at a variety of levels of metaphorisation – as increasingly complex chains of analogy which point back to our early physical experience of the world. But of course music is, fundamentally, action. Humans put energy into systems - external or internal to themselves - which transduce that energy into the movement of air. At the acoustic level music is, emphatically and unmetaphorically, movement. Perhaps such simple physical perceptions form one route through which we might understand and explore shared senses of meaning and their capacity for ‘transduction’ between multiple individuals. Our (developmentally) early sensory models of the world, built from encounters with its physical resistances and affordances, might be a route to understanding our more clearly encultured and abstracted ('higher' level) understandings of music.