From Physical Modeling to Piano Making

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.

This project (From Physical Modeling to Piano Making: FPM2) is a one-year extension of a former FWF 2-years Lise-Meitner program (M 1653: Predictive Approach in Piano Acoustics (PAPA)) which was conducted by the same project leader. Both projects took place in the Department of Music Acoustics (IWK) of the University of Music and Performing Arts Vienna (MDW). The main goal of the former PAPA project was to develop efficient numerical models of pianos, with emphasis on Viennese pianos made during the nineteenth century. In continuity with this previous project, the new FPM2 project was twofold: improve the quality of the piano simulations, and conduct experiments in order to include new extensions in future versions of the piano models. The ultimate objective behind these tasks is to obtain models and simulations of sufficient quality so that they can be of use for piano makers.In collaboration with INRIA Bordeaux (France), an important effort was first put to improve the numerical model of the pianos. New features such as the possibility of modeling refined variations of soundboard thickness, and calculation of the piano farfield, were used in the model. Through a collaboration with ENSTA ParisTech (France), additional advances were made in the modeling of the coupling between strings and bridge, which yields more realistic temporal evolution of the piano tones. This work is still in progress. Systematic series of simulations were carried out for testing the influence of string parameters, string-soundboard coupling, soundboard geometry and material, and of the piano environment (reflectors, walls, lid, cavities,...) on the resulting sound. The listening test on the similarity of piano tones, which was carried out during the PAPA project, was analyzed, and significant correlations were found between piano properties and the subjective evaluation of sound by listeners. A campaign of measurements was conducted in order to investigate the influence of the stringing scheme on the tone quality of the piano. It was found that the parallel stringing used by makers during the 19th century induces clear differentiation of tone quality between the three main registers of the piano: bass, medium, and treble. Finally, a significant part of the work was devoted to the communication and sharing of the results through national and international conferences, symposia and peer-review papers. One major event was the organisation of the "Piano Day" during the MDW Festival in October 2016, which brought together musicians, makers, tuners, acousticians and piano amateurs around the history of the instrument.