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).

Traditional Korean islanders encounters with the British navy in the 1880s: The Port Hamilton Affair of 1885-1887

This article deals with the encounters between a traditional Korean rural and island population and western military forces when the British navy occupied Geomundo, an archipelago known to them as Port Hamilton, for 22 months between 1885 and 1887. The paper first outlines the sometimes painful process of East Asian countries being opened up to trade and outside influences in the 19th century, a process sometimes urged upon them by naval weapons in this era of gunboat diplomacy. This provides the setting for the Port Hamilton Affair itself when in preparation for possible war with Russia, a British naval squadron steamed into Port Hamilton and took it without reference to the local people or their national government. After brief reference to the political consequences of this action, the focus is then on what the records from the occupation and earlier investigations by the British, who had long coveted the islands’ strategic harbour, reveal about the life of the islanders. The article considers both their traditional life, from a time rather before western travel accounts were written about the Korean mainland, and how the islanders fared under the British.