A Hybrid Resynthesis Model for Hammer-String Interaction of Piano Tones
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A Hybrid Resynthesis Model for Hammer-String Interaction of Piano Tones Julien Bensa Laboratoire de M´ecanique et d’Acoustique, Centre National de la Recherche Scientifique (LMA-CNRS), 13402 Marseille Cedex 20, France Email: [email protected]
Kristoffer Jensen Datalogisk Institut, Københavns Universitet, Universitetsparken 1, 2100 København, Denmark Email: [email protected]
Richard Kronland-Martinet Laboratoire de M´ecanique et d’Acoustique, Centre National de la Recherche Scientifique (LMA-CNRS), 13402 Marseille Cedex 20, France Email: [email protected] Received 7 July 2003; Revised 9 December 2003 This paper presents a source/resonator model of hammer-string interaction that produces realistic piano sound. The source is generated using a subtractive signal model. Digital waveguides are used to simulate the propagation of waves in the resonator. This hybrid model allows resynthesis of the vibration measured on an experimental setup. In particular, the nonlinear behavior of the hammer-string interaction is taken into account in the source model and is well reproduced. The behavior of the model parameters (the resonant part and the excitation part) is studied with respect to the velocities and the notes played. This model exhibits physically and perceptually related parameters, allowing easy control of the sound produced. This research is an essential step in the design of a complete piano model. Keywords and phrases: piano, hammer-string interaction, source-resonator model, analysis/synthesis.
1.
INTRODUCTION
This paper is a contribution to the design of a complete piano-synthesis model. (Sound examples obtained using the method described in this paper can be found at www.lma.cnrs-mrs.fr/∼kronland/JASP/sounds.html.) It is the result of several attempts [1, 2], eventually leading to a stable and robust methodology. We address here the modeling for synthesis of a key aspect of piano tones: the hammerstring interaction. This model will ultimately need to be linked to a soundboard model to accurately simulate piano sounds. The design of a synthesis model is strongly linked to the specificity of the sounds to be produced and to the expected use of the model. This work was done in the framework of the analysis-synthesis of musical sounds; we seek both reconstructing a given piano sound and using the synthesis model in a musical context. The perfect reconstruction of given sounds is a strong constraint: the synthesis model must be designed so that the parameters can be extracted
from the analysis of natural sounds. In addition, the playing of the synthesis model requires a good relationship between the physics of the instrument, the synthesis parameters, and the generated sounds. This relationship is crucial to having a good interaction between the “digital instrument” and the player, and it will constitute the most important aspects our piano model has to deal with. Music based on the so-called “sound objects”—like electro-acoustic music or “musique concr`ete”—lies on synthesis models allowing subtle and natur
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