Modelling the dynamics of the piano action: is apparent success real?

International audienceThe kinematics and the dynamics of the piano action mechanism have been much studied in the last 50 years and fairly sophisticated models have been proposed in the last decade. Surprisingly, simple as well as sophisticated models seem to yield very valuable simulations when compared to measurements. We propose here a very simple model, with only 1-degree of freedom, and compare its outcome with force and motion measurements obtained by playing a real piano mechanism. The model, purposely chosen as obviously too simple to be predictive of the dynamics of the grand piano action, appears either as very good or as very bad, depending on which physical quantities are used as the input and output. We discuss the sensitivity of the simulation results to the initial conditions and to noise and the sensitivity of the experimental/simulation comparisons to the chosen dynamical model. It is shown that force-driven simulations with position comparisons, as they are proposed in the literature, do not validate the dynamical models of the piano action. It is suggested that these models be validated with position-driven simulations and force comparisons

Non-smooth simulation of a 6-DOF dynamical model of the grand piano action

International audienceTwo models of the grand piano key mechanism are presented: single-degree-of-freedom and 6 rigid rotating bodies coupled by 13 contact zones with nonlinear springs. Coulomb friction is considered in pivots and at several contact zones, introducing discontinuities in the velocities. Therefore, some problems are raised by the usual regular-dynamics formulation. The results given by the single-degree-of-freedom show that these problems must be addressed. A non-smooth dynamics approach is proposed using the XDE (eXtended Dynamic Engine) software developed at CEA LIST. Simulation results are compared to experiments for several playing nuances. Sensitivity analysis and model simplification will be discussed

Acoustic features of piano sounds

To date efforts of music transcription indicate the need for modelling the data signal in a more comprehensive manner in order to improve the transcription process of music performances. This research work is concerned with the investigation of two features associated with the reproduced sound of a piano; the inharmonicity factor of the piano strings and the double decay rate of the resulting sound. Firstly, a simple model of the inharmonicity is proposed and the factors that affect the modelled signal are identified, such as the magnitude of the inharmonicity, the number of harmonics, the time parameter, the phase characteristics and the harmonic amplitudes. A formation of a socalled “one-sided” effect appears in simulated signals, although this effect is obscured in real recordings potentially due to the non-uniformly varying amplitudes of the harmonic terms. This effect is also discussed through the use of the cepstrum by analysing real piano note recordings and synthesized signals. The cepstrum is further used to describe the effect of the coupled behaviour of two strings through digital waveguides. Secondly, the double decay rate effect is modelled through coupled oscillators and digital waveguides. A physical model of multiple strings is also presented as an extension to the simple model of coupled oscillators and various measurements on a real grand piano are carried out in order to investigate the coupling mechanism between the strings, the soundboard and the bridge. Finally, a model, with reduced dimensionality, is proposed to represent the signal model for single and multiple notes formulated around a Bayesian framework. The potential of such a model is illustrated with the transcription of simple examples of real monophonic and polyphonic piano recordings by implementing the Metropolis-Hastings algorithm and Gibbs sampler for multivariate parameter estimation

Musical Haptics

Haptic Musical Instruments; Haptic Psychophysics; Interface Design and Evaluation; User Experience; Musical Performanc

A complex dynamical systems approach to the development of feeding problems in early childhood

Though it is commonly agreed upon that the development of feeding problems in early childhood is a complex process, much of the research on these problems has a component-oriented focus, and very little attention is paid to the mechanisms that lead to these kinds of problems in individual children. The aim of this theoretical paper is to interpret the development of feeding problems in early childhood from a complex dynamical systems viewpoint. In addition to its focus on self-organization and nonlinearity, this approach defines several central properties of development: soft-assembly, embodiment, iterativity, the emergence of higher-order properties, and intra-individual variability. In this paper, I argue that each of these properties is highly relevant for understanding feeding problems and discuss the implications of this for both clinical practice and research purposes