A Modal-Based Real-Time Piano Synthesizer

Abstract

This paper presents a real-time piano synthesizer where both the transverse and longitudinal motion of the string is modeled by modal synthesis, resulting in a coherent and highly parallel model structure. The paper applies recent developments in piano modeling and focuses on the issues related to practical implementation (e.g., numerical stability, aliasing, and efficiency). A strong emphasis is given to modeling nonlinear string vibrations, and a new variation of earlier synthesis techniques is proposed which is particularly well suited for modal synthesis. For soundboard modeling, the possibilities of using fast Fourier transform-based fast convolution and parallel second-order filters are discussed. Additionally, the paper describes the details of the software implementation and discusses the computational complexity of each model block. The piano model runs on current computer hardware with full polyphony in real time

Parallel digital signal processing for efficient piano synthesis

“…Popular choices are finite differences or digital waveguides [5,6]. During our preliminary investigation phase, we opted instead for a variation of Modal Synthesis [7], which we found sensibly better in terms of calibration flexibility and modelling accuracy.…”

“…force, displacement) and the modal variables is regulated by a set of input and output weights W in,k , W out,k . Even if the algorithm at its core is intrinsically parallelizable, we had to simplify the hammer-string interaction from the algorithm previously proposed in [7], partly for overcoming some calibration issues and also for better exploiting the capabilities of modern hardware. As it can be seen from the diagram in Fig.…”

“…1, the hammer model has a feedforward connection to the string model, allowing efficient block-based computation. We designed a parametric synthesis algorithm which is able to qualitatively reproduce the signals of the former feedback version employed in [7], but whose parameters are decoupled from the string parameters.…”

“…They are used to model secondary features of piano strings which are not captured by the one-dimensional string PDE. Longitudinal string vibration is approximated with a feed-forward, parallel set of resonators whose parameters are set in order to match as closely as possible the output of the modulationbased algorithm proposed in [7]. Secondary resonators are slightly detuned groups of resonators which are needed for simulating the complex beating envelopes found in piano partials.…”

A digital waveguide-based approach for Clavinet modeling and synthesis

“…Some strictly adhere to an underlying physical model and require minimal assumptions, such as finite-difference time-domain methods (FDTD) [10,12]. Modal synthesis techniques, *Correspondence: l.gabrielli@univpm.it 1 Department of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche 12, Ancona 60131, Italy Full list of author information is available at the end of the article which enable accurate reproduction of inharmonicity and beating characteristics of each partial, have recently become popular in the modeling of stringed instruments [11,[13][14][15]. However, the computational model proposed in this paper is based on digital waveguide (DWG) techniques, which prove to be computationally more efficient than other methods while adequate for reproducing tones of slightly inharmonic stringed instruments [8,16,17] including keyboard instruments [18].…”