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.

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.

An efficient harmony search with new pitch adjustment for dynamic economic dispatch

A simple yet efficient harmony search (HS) method with a new pitch adjustment rule (NPAHS) is proposed for dynamic economic dispatch (DED) of electrical power systems, a large-scale non-linear real time optimization problem imposed by a number of complex constraints. The new pitch adjustment rule is based on the perturbation information and the mean value of the harmony memory, which is simple to implement and helps to enhance solution quality and convergence speed. A new constraint handling technique is also developed to effectively handle various constraints in the DED problem, and the violation of ramp rate limits between the first and last scheduling intervals that is often ignored by existing approaches for DED problems is effectively eliminated. To validate the effectiveness, the NPAHS is first tested on 10 popular benchmark functions with 100 dimensions, in comparison with four HS variants and five state-of-the-art evolutionary algorithms. Then, NPAHS is used to solve three 24-h DED systems with 5, 15 and 54 units, which consider the valve point effects, transmission loss, emission and prohibited operating zones. Simulation results on all these systems show the scalability and superiority of the proposed NPAHS on various large scale problems.

Museum City - Improvisation and the narratives of space

This paper provides four viewpoints on the narratives of space, allowing us to think about possible relations between sites and sounds, reflecting on how places might tell stories, or how practitioners embed themselves in a place in order to shape cultural, social and/or political narratives through the use of sound. I propose four viewpoints that investigate the relationship between sites and sounds, where narratives are shaped and made through the exploration of specific sonic activities. These are:
- sonic activism
- sonic preservation
- sonic participatory action
- sonic narrative of space

I examine each of these ideas in turn before focusing in more detail on the final viewpoint, which provides the context for discussing and analysing a recent site-specific music improvisation project, entitled ‘Museum City’, a work that aligns closely with my proposal for a ‘sonic narrative of space’.
The work ‘Museum City’ by Pedro Rebelo, Franziska Schroeder, Ricardo Jacinto and André Cepeda specifically enables me to reflect on how derelict and/or transitional spaces might be re-examined through the use of sound, particularly through means of live music improvisation. The spaces examined as part ‘Museum City’ constitute either deserted sites or sites about to undergo changes in their architectural layout, their use and sonic make-up. The practice in ‘Museum City’ was born out of a performative engagement with[in] those sites, but specifically out of an intimate listening relationship by three improvisers situated within those spaces.
The theoretical grounding for this paper is situated within a wider context of practising and cognising musical spatiality, as proposed by Georgina Born (2013), particularly her proposition for three distinct lineages that provide an understanding of space in/and music. Born’s third lineage, which links more closely with practices of sound art and challenges a Euclidean orientation of pitch and timbre space, makes way for a heightened consideration of listening and ‘the place’ of sound. This lineage is particularly crucial for my discussion, since it positions music in relation to social experiences and the everyday, which the work ‘Museum City’ endeavoured to embrace.