Reflecting on Tradition: Four Ulster Musical Lives

Communicating musical knowledge through gesture: Piano teachers’ gestural behaviours across different levels of student proficiency

Teachers’ communication of musical knowledge through physical gesture represents a valuable pedagogical field in need of investigation. This exploratory case study compares the gestural behaviour of three piano teachers while giving individual lessons to students who differed according to piano proficiency levels. The data was collected by video recordings of one-to-one piano lessons and gestures were categorized using two gesture classifications: the spontaneous co-verbal gesture classification (McNeill, 1992; 2005) and spontaneous co-musical gesture classification (Simones, Schroeder & Rodger, 2013). Poisson regression analysis and qualitative observation suggest a relationship between teachers’ didactic intentions and the types of gesture they produced while teaching, as shown by differences in gestural category frequency between teaching students of higher and lower levels of proficiency. Such reported agreement between teachers’ gestural approach in relation to student proficiency levels indicates a teachers’ gestural scaffolding approach whereby teachers adapted gestural communicative channels to suit students’ specific conceptual skill levels.

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.

(Dis‑)Harmony in movement: effects of musical dissonance on movement timing and form

While the origins of consonance and dissonance in terms of acoustics, psychoacoustics and physiology have been debated for centuries, their plausible effects on movement synchronization have largely been ignored. The present study aims to address this by investigating whether, and if so how, consonant/dissonant pitch intervals affect the spatiotemporal properties of regular reciprocal aiming movements. We compared movements synchronized either to consonant or to dissonant sounds, and showed that they were differently influenced by the degree of consonance of the sound presented. Interestingly, the difference was present after the sound stimulus was removed. In this case, the performance measured after consonant sound exposure was found to be more stable and accurate, with a higher percentage of information/movement coupling (tau-coupling) and a higher degree of movement circularity when compared to performance measured after the exposure to dissonant sounds. We infer that the neural resonance representing consonant tones leads to finer perception/action coupling which in turn may help explain the prevailing preference for these types of tones.

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.