Parameter fitting for piano sound synthesis by physical modeling

Authors: Bensa J., Gipouloux O., Kronland-Martinet R.
Publication Date: July 2005
Journal: Journal of the Acoustical Society of America (JASA) (vol. 118(1), pp. 495-504, 2005)

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Abstract

A difficult issue in the synthesis of piano tones by physical models is to choose the values of the parameters governing the hammer–string model. In fact, these parameters are hard to estimate from static measurements, causing the synthesis sounds to be unrealistic. An original approach that estimates the parameters of a piano model, from the measurement of the string vibration, by minimizing a perceptual criterion is proposed. The minimization process that was used is a combination of a gradient method and a simulated annealing algorithm, in order to avoid convergence problems in case of multiple local minima. The criterion, based on the tristimulus concept, takes into account the spectral energy density in three bands, each allowing particular parameters to be estimated. The optimization process has been run on signals measured on an experimental setup. The parameters thus estimated provided a better sound quality than the one obtained using a global energetic criterion. Both the sound’s attack and its brightness were better preserved. This quality gain was obtained for parameter values very close to the initial ones, showing that only slight deviations are necessary to make synthetic sounds closer to the real ones.

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Sound examples illustrating the paper

Reference signals measured on an experimental setup using a laser vibrometer. The sounds corresponds to different hammer velocities.

1- Sound corresponding to the vibration obtained with a hammer velocity of 0.618 m/s (pianissimo)

2- Sound corresponding to the vibration obtained with a hammer velocity of 0.844 m/s

3- Sound corresponding to the vibration obtained with a hammer velocity of 1.299 m/s (mezzo-forte)

Synthetic sounds generated using the initial parameters obtained from basic measurements and from the litterature.

4- Synthetic sound corresponding to the vibration obtained with a hammer velocity of 0.618 m/s (to be compared with 1)

5- Synthetic sound corresponding to the vibration obtained with a hammer velocity of 0.844 m/s (to be compared with 2)

6- Synthetic sound corresponding to the vibration obtained with a hammer velocity of 1.299 m/s (to be compared with 3)

Synthetic sounds obtained using optimized parameters estimated with the tristimulus based criterion.

7- Optimized synthetic sound corresponding to the vibration obtained with a hammer velocity of 0.618 m/s (to be compared with 1 and 4)

8- Optimized synthetic sound corresponding to the vibration obtained with a hammer velocity of 0.844 m/s (to be compared with 2 and 5)

9- Optimized synthetic sound corresponding to the vibration obtained with a hammer velocity of 1.299 m/s (to be compared with 3 and 6)