Predictive Approach in Piano Acoustics

The ambition of the PAPA project is to establish links between physical piano design parameters and tone quality. The considered parameters are related to the geometrical data and material properties of the constitutive parts of the instrument. The project focuses on the vibratory and acoustical phenomena from the blow of the hammer against the strings to the radiated sound. The key mechanism and the interaction with the player, as well as the effects of the room, are left aside in this study. The results are expected to pave the way for a Predictive Approach in Piano Acoustics, where the tone quality of the instruments can be controlled on the basis of a physical model, thus reducing the part of empiricism. During the time of the project, the objective is to study a small number of selected instruments, with clearly representative and distinct tone qualities. Each instrument will be described by a set of parameters related to hammer, strings, bridges and soundboard properties. To achieve this, an original method is proposed, composed of three steps: dedicated experiments will be first conducted on significantly different modern and historical instruments in order to extract the values of the parameters. In a second step, these measured data will serve as input parameters for the simulation of piano tones. The simulations are based on a global model of a grand piano which is currently under development at ENSTA. This software will be used throughout the project, and continuing developments of the model will be made. By means of these simulations, we wish to evaluate the influence of the piano parameters on tone quality, and to predict the musical effects of structural modifications. Finally, comparisons in the form of listening tests will be made between measured and simulated tones in order to check the relevance of the model, and to determine the thresholds of variations of some parameters for which the listeners are sensitive. This project belongs to the field of musical acoustics which is a multidisciplinary domain ranging from the physics to sound perception. The intention to conduct this research in partnership with colleagues from the Institute of Music Acoustics (IWK) is motivated by a strong complementarity between our respective competencies: I will bring my expertise in physical modeling and numerical analysis of instruments, whereas my colleagues at IWK will contribute to the project through their experimental platforms dedicated to musical instruments and through their knowledge in the perception of musical sounds. In addition, IWK has collaborations with museums who agree to participate to the project by letting us conduct experiments on historical instruments. Finally, the environment in a Music University (MDW) is particularly appropriate for rewarding interaction with musicians.

The purpose of this PAPA project was to establish links between physical piano design parameters and tone quality. The considered parameters are related to the geometrical data and material properties of the constitutive parts of the instrument. The project was devoted to the vibratory and acoustical phenomena in the instrument from the blow of the hammer against the strings to the radiated sound. The results pave the way for a Predictive Approach in Piano Acoustics, where the tone quality of the instruments can be controlled on the basis of a physical model, thus reducing the part of empiricism.During the time of the project, half a dozen of selected instruments, with clearly representative and distinct tone qualities, were investigated. Each instrument has been described by a set of parameters related to hammer, strings, bridges and soundboard properties. To achieve this, dedicated experiments were conducted on significantly different modern and historical instruments in order to extract the values of the parameters. In a second step, these measured data were used as input parameters for the simulation of piano vibrations and tones. The simulations were based on a global model of a grand piano, recently developed at ENSTA and INRIA in France. A 3D model of each piano was built, which couples together the hammers the strings the soundboard and the surrounding acoustic field. For each soundboard, the geometrical design of ribs and bridges, as well as the material properties, can be easily modified, which could hardly be done on real instruments. In this respect, the present work can be viewed as a complementary approach to the one followed by piano makers.A theoretical study, based on energy analysis, has shown to what extent fundamental modifications of hammer mass, string tension and soundboard thickness affect both the time and spectral envelope of piano tones. These results were confirmed by experiments on historic pianos. Since the hammers cannot be always easily accessible, especially on historic instruments, a new method has been developed in order to reconstruct the hammer force from measurements of string velocity. These two studies can be considered as significant advances in the field of piano acoustics.In order to prepare future studies, sound radiation measurements were performed on a piano placed in the anechoic chamber of the MDW. The purpose of this campaign was to identify and compare quantitatively the main sources of radiation of the instrument. Not surprisingly, the soundboard appears as the prime source of sound. However, in the bass range, it turns out that the left side of the rim also vibrates and radiates significantly. This result should be used as a guideline for improving the piano model.Finally, some listening tests were conducted, in collaboration with colleagues from the University of Eindhoven. It was shown than the listeners can easily recognize difference in tone quality in the bass range, while they have more difficulties in the treble. In addition, a similarity matrix shows the perceived resemblances (resp. differences) between the tones recorded on the investigated pianos.