From Physical Modeling to Piano Making (FPM2)

Project number:	FWF P 29386
Project leader:	Prof. Dr. Antoine Chaigne
Research facility:	Institute of Music Acoustics (IWK) University of Music and Performing Arts Vienna
Date of approval:	18.05.2016
Project start:	01.10.2016
Project end:	30.09.2017
Results & Media:	https://sites.google.com/view/achaigne-homepage/accueil

Abstract

For about two decades, physical models were used for simulating musical instruments. The method consists in solving the equations describing the motion of the constitutive parts of the instruments using appropriate numerical methods. The solutions of these equations are sound files, which can be heard through loudspeakers. The quality of the obtained synthezised sounds is dependent on the accuracy of the model. The main advantage of simulations based on physical models, compared to other tools based on sampling and/or signal processing procedures, lies in the direct links between the sounds produced and the geometrical/material properties of the modeled instrument. As a consequence, it becomes now conceivable to predict the sound quality of an instrument before its construction. In the case of the piano, the most recent simulations yield realistic tones, though suffering from some limitations, especialy for the lowest notes in the bass range. In addition, the simulated piano tones generally show a more monotonic decay that the one observed on real tones. For historic pianofortes, it is also necessary to refine the physical description of the three main registers (bass, medium, treble), each of which presenting its own character. Based on these observations, three main issues will be examined in the present project, related to the modeling of soundboard, string motion and acoustic field of the piano, respectively. The function of the soundboard in the characterization of the pianoforte registers is due to the fact that only a restricted part of it, with specific modal frequencies, is vibrating in each register: the aim of the project is thus to study these modal distributions using high-resolution spectral methods. For the string motion, we will take advantage of the most recent published results related to the non-planar motion of the piano strings in order to explain and reproduce the complex decay of piano tones convincingly. Finally, experiments on the acoustic field of a piano will be performed in the anechoic chamber of the Institute of Acoustics (IWK) at the University and Performing Arts in Vienna (MDW). Focus will be placed on the function of the lid and on the effects of the floor, especially in the bass range. In addition, an original method, based on multiple correlations, will be developed for determining which elements of the piano are the most efficient sound radiators, in each frequency range. From the results of these studies, it is expected to derive significant improvements in the piano model, so that it can be used as a guideline in piano making. The prime originality of the project is to combine advanced experimental studies with numerical simulations based on a comprehensive piano model, where strings, soundboard and acoustic field are coupled.

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