This is the homepage of the paper

Balázs Bank and László Sujbert, "A Piano Model Including Longitudinal String Vibrations," Proceedings of the 7th International Conference on Digital Audio Effects (DAFx-04), pp. 89-94, Naples, Italy, Oct. 2004.

Abstract

In this paper a mixed-paradigm piano model is presented. The major development is the ability of modeling longitudinal string vibrations. Longitudinal string motion is the reason for the metallic sound of low piano notes, therefore its modeling greatly improves the perceptual quality of synthesized piano sound. In this novel approach the transversal displacement of the string is computed by a finite-difference string model and the longitudinal motion is calculated by a set of second-order resonators, which are nonlinearly excited by the transversal vibration. The soundboard is modeled by a multi-rate filter based on measurements of real pianos. The piano model is able to produce high-quality piano sounds in real-time with about 5-10 note polyphony on an average personal computer.

Sound examples

Original

Here a recorded C2 piano note is presented:

C2 Original

First unaltered, then the transversal components resynthesized by additive synthesis (the longitudinal components and the attack transients are filtered out), and last, the residual containing longitudinal components and attack transients. As the objective is not to perfectly resynthesize a given sound, this example is presented to show the preceptual importance of these components.

Modeling using independent strings

Here is an example generated by digital waveguide modeling:

C2 SMAC03

One digital waveguide is used for the transversal partials, one for the phantom partials and a resonator bank is applied for simulationg the longitudinal modes. This sound example was presented as a demo for our paper at SMAC03. In this case the free motion of the longitudinal modes is simulated only, and the forced motion is neglected. This results in a tone where the transversal and longitudinal components sound separated.

The composite model

The examples generated by our novel approach based on finite-difference modeling for the transversal vibration and nonlinearly excited resonators for the longitudinal motion:

C2 without longitudinal modeling
C2 with longitudinal modeling
G1 without longitudinal modeling
G1 with longitudinal modeling

G1 dynamics (piano to forte) without longitudinal modeling
G1 dynamics (piano to forte) with longitudinal modeling

The sound examples without the longitudinal modeling are presented for easier comparison. These were calculated by using the same parameters for the transversal string model and for the soundboard, but the longitudinal force at the bridge was set to zero. The examples show that now the longitudinal components remain an inherent part of the tone, while it is still possible to perceive their pitch, similalry in the case of real piano tones.

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