Springer, 2013. — 475 p.Self-organization, and nonlinearities play crucial roles in Musical Acoustics and Music Psychology, and are formulated in modern Physical Modelling techniques and Signal Processing tools. Many musical instruments have nonlinear driving mechanisms which are crucial for producing an oscillation at all, a tight harmonic overtone spectrum, sudden phase changes, or the ability to play different tones on the instrument. Although linear theories of strings, bars, or membranes are often used to approach Musical Acoustics in general, when investigating the fundamental mechanisms nearly everywhere synchronization is the basic mode of operation. Additionally, nonlinearities are often additional components of the instrument sounds which produce their musically interesting parts. Also in Music Psychology self-organizing neural nets are capable of explaining basic musical perception and also very complex and high-level categorization. With performance tasks, synergetic models are often the only ones able to explain sudden phase-transitions in music performances. They also help to explain the interaction of psychoacoustic dimensions which appear with nearly all sensory information. Global self-organizing theories of brain behaviour in interacting models of perception, expectation, and action reasonably explain adaptation and learning. Nonlinear models of musical instruments, as well as complex Signal Processing tools using phase-plots and fractal dimension analysis are often capable to explain fast and robust the dynamical behaviour of musical instruments, as well as music perception. These tools are often able to connect low-level time-series to high-level perception or phenotypical behaviour by only one step. They are also suitable for dynamical subsystem analysis which clearly relates to tonal fusion of auditory perception of frequencies into a virtual pitch which is hard-wired in the human auditory system. Modern efficient coding models of auditory perception reproduce old ideas of tonality as economic hearing proposed by Hugo Riemann and Hermann Lotze about a century ago. The present volume tries to give an overview of models, measurements, calculations, and examples in this field and tries to connect Musical Acoustics and Music Psychology. Indeed, many mathematical formulations able to explain Musical Acoustics are also able to predict human auditory perception. As self-organization and synchronization appear naturally, the idea of the brain having adapted to the working principles of musical instruments is attractive. In terms of perception it also challenges the so-called binding problem of perception, the many-stage fusion of integrating sensory data into a Gestalt or Schemata. The proposed alternative is a one-stage detection by an adaptive dynamical system. Also it does not necessarily need a clear differentiation of the brain into e.g. an auditory and an motion region. In accordance with auditory-motor theories which find music perception starting in the supplementary motor area it need not necessarily associate different brain regions with different tasks. Musical instruments nearly all work with impulses travelling along strings, air columns, or bars and plates. In this volume an Impulse Pattern formulation is proposed which holds as a global mathematical framework for all musical instruments as iterative systems using scattered impulses. This theory is not only able to derive sudden phase-changes in musical instruments, it also can explain why some instruments like e.g. the guitar are much more stable in tone production than e.g. the saxophone. It also results in a formulation of the initial transient of musical instruments, a part most crucial for instrument identification as well as music articulation. Here a comparison between instruments in terms of basic patterns of initial transients is shown which relates e.g. violin ’scratching’ and trumpet ’spitting’ as being caused by the same iterative process.Introduction I Signal Processing Frequency Representations Embedding Representations II Physical Modelling Applications to Musical Instruments Finite-Difference Simulation Finite-Element Simulation III Musical Acoustics Musical Instruments Impulse Pattern Formulation Examples of Impulse Pattern Formulation IV Music Psychology Psychoacoustics Timbre Rhythm Pitch, Melody, Tonality CD Tracks
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