Paper Archive

Efficient stable integration methods for nonlinear systems are of great importance for physical modeling sound synthesis. Specifically, a number of musical systems of interest, including vibrating strings, bars or plates may be written as port-Hamiltonian systems with quadratic kinetic energy and non-quadratic potential energy. Efficient schemes have been developed for such systems through the introduction of a scalar auxiliary variable. As a result, the stable real-time simulations of nonlinear musical systems of up to a few thousands of degrees of freedom is possible, even for nearly lossless systems. However, convergence rates can be slow and seem to be system-dependent. Specifically, at audio rates, they may suffer from numerical drift of the auxiliary variable, resulting in dramatic unwanted effects on audio output, such as pitch drifts after several impacts on the same resonator. In this paper, a novel method for mitigating this unwanted drift while preserving power balance is presented, based on a control approach. A set of modified equations is proposed to control the drift artefact by rerouting energy through the scalar auxiliary variable and potential energy state. Numerical experiments are run in order to check convergence on simulations in the case of a cubic nonlinear string. A real-time implementation is provided as a Max/MSP external. 60-note polyphony is achieved on a laptop, and some simple high level control parameters are provided, making the proposed implementation suitable for use in artistic contexts. All code is available in a public repository, along with compiled Max/MSP externals1.

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Modal methods for simulating vibrations of strings, membranes, and plates are widely used in acoustics and physically informed audio synthesis. However, traditional implementations, particularly for non-linear models like the von Kármán plate, are computationally demanding and lack differentiability, limiting inverse modelling and real-time applications. We introduce a fast, differentiable, GPU-accelerated modal framework built with the JAX library, providing efficient simulations and enabling gradientbased inverse modelling. Benchmarks show that our approach significantly outperforms CPU and GPU-based implementations, particularly for simulations with many modes. Inverse modelling experiments demonstrate that our approach can recover physical parameters, including tension, stiffness, and geometry, from both synthetic and experimental data. Although fitting physical parameters is more sensitive to initialisation compared to methods that fit abstract spectral parameters, it provides greater interpretability and more compact parameterisation. The code is released as open source to support future research and applications in differentiable physical modelling and sound synthesis.

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Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string, where geometric nonlinear effects lead to perceptually important effects including pitch glides and a dependence of brightness on striking amplitude. A modal decomposition leads to a coupled nonlinear system of ordinary differential equations. Recent work in applied machine learning approaches (in particular neural ordinary differential equations) has been used to model lumped dynamic systems such as electronic circuits automatically from data. In this work, we examine how modal decomposition can be combined with neural ordinary differential equations for modelling distributed musical systems. The proposed model leverages the analytical solution for linear vibration of system’s modes and employs a neural network to account for nonlinear dynamic behaviour. Physical parameters of a system remain easily accessible after the training without the need for a parameter encoder in the network architecture. As an initial proof of concept, we generate synthetic data for a nonlinear transverse string and show that the model can be trained to reproduce the nonlinear dynamics of the system. Sound examples are presented.

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This study investigates the use of an unsupervised, physicsinformed deep learning framework to model a one-degree-offreedom mass-spring system subjected to a nonlinear friction bow force and governed by a set of ordinary differential equations. Specifically, it examines the application of Physics-Informed Neural Networks (PINNs) and Physics-Informed Deep Operator Networks (PI-DeepONets). Our findings demonstrate that PINNs successfully address the problem across different bow force scenarios, while PI-DeepONets perform well under low bow forces but encounter difficulties at higher forces. Additionally, we analyze the Hessian eigenvalue density and visualize the loss landscape. Overall, the presence of large Hessian eigenvalues and sharp minima indicates highly ill-conditioned optimization. These results underscore the promise of physics-informed deep learning for nonlinear modelling in musical acoustics, while also revealing the limitations of relying solely on physics-based approaches to capture complex nonlinearities. We demonstrate that PI-DeepONets, with their ability to generalize across varying parameters, are well-suited for sound synthesis. Furthermore, we demonstrate that the limitations of PI-DeepONets under higher forces can be mitigated by integrating observation data within a hybrid supervised-unsupervised framework. This suggests that a hybrid supervised-unsupervised DeepONets framework could be a promising direction for future practical applications.

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The acoustic piano and its sound production mechanisms have been extensively studied in the field of acoustics. Similarly, digital piano synthesis has been the focus of numerous signal processing research studies. However, the role of the piano action in shaping the dynamics and nuances of piano sound has received less attention, particularly in the context of digital pianos. Digital pianos are well-established commercial instruments that typically use weighted keys with two or three sensors to measure the average key velocity—this being the only input to a sampling synthesis engine. In this study, we investigate whether this simplified measurement method adequately captures the full dynamic behavior of the original piano action. After a brief review of the state of the art, we describe an experimental setup designed to measure physical properties of the keys and hammers of a piano. This setup enables high-precision readings of acceleration, velocity, and position for both the key and hammer across various dynamic levels. Through extensive data analysis, we examine their relationships and identify the optimal key position for velocity measurement. We also analyze a digital piano key to determine where the average key velocity is measured and compare it with our proposed optimal timing. We find that the instantaneous key velocity just before let-off correlates most strongly with hammer impact velocity, indicating a target for improved sensing; however, due to the limitations of discrete velocity sensing this optimization alone may not suffice to replicate the nuanced expressiveness of acoustic piano touch. This study represents the first step in a broader research effort aimed at linking piano touch, dynamics, and sound production.

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This paper introduces Wave Pulse Phase Modulation (WPPM), a novel synthesis technique based on phase shaping. It combines two classic digital synthesis techniques: Phase Modulation (PM) and Phase Distortion (PD), aiming to overcome their respective limitations while enabling the creation of new, interesting timbres. It works by segmenting a phase signal into two regions, each independently driving the phase of a modulator waveform. This results in two distinct pulses per period that together form the signal used as the phase input to a carrier waveform, similar to PM, hence the name Wave Pulse Phase Modulation. This method provides a minimal set of parameters that enable the creation of complex, evolving waveforms, and rich dynamic textures. By modulating these parameters, WPPM can produce a wide range of interesting spectra, including those with formant-like resonant peaks. The paper examines PM and PD in detail, exploring the modifications needed to integrate them with WPPM, before presenting the full WPPM algorithm alongside its parameters and creative possibilities. Finally, it discusses scope for further research and developments into new similar phase shaping algorithms.

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This paper introduces a digital reconstruction of the morphophone, a complex magnetophonic device developed in the 1950s within the laboratories of the GRM (Groupe de Recherches Musicales) in Paris. The analysis, design, and implementation methodologies underlying the Digital Morphophone Environment are discussed. Based on a detailed review of historical sources and limited documentation – including a small body of literature and, most notably, archival images – the core operational principles of the morphophone have been modeled within the MAX visual programming environment. The main goals of this work are, on the one hand, to study and make accessible a now obsolete and unavailable tool, and on the other, to provide the opportunity for new explorations in computer music and research.

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Recently, differentiable multiple-input multiple-output Feedback Delay Networks (FDNs) have been proposed for modeling target multichannel room impulse responses by optimizing their parameters according to perceptually-driven time-domain descriptors. However, in spatial audio applications, frequency-domain characteristics and inter-channel differences are crucial for accurately replicating a given soundfield. In this article, targeting the modeling of the response of higher-order microphone arrays, we improve on the methodology by optimizing the FDN parameters using a novel spatially-informed loss function, demonstrating its superior performance over previous approaches and paving the way toward the use of differentiable FDNs in spatial audio applications such as soundfield reconstruction and rendering.

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The creation of personal sound zones is an effective solution for delivering personalized auditory experiences in shared spaces. Their applications span various domains, including in-car entertainment, home and office environments, and healthcare functions. This paper presents a novel approach for the creation of personal sound zones using a modified algorithm for multi-lobe control in loudspeaker line array. The proposed method integrates a pressurematching beamforming algorithm with an innovative technique for reducing side lobes, enhancing the precision and isolation of sound zones. The system was evaluated through simulations and experimental tests conducted in a semi-anechoic environment and a large listening room. Results demonstrate the effectiveness of the method in creating two separate sound zones.

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The common-slope model is used to model late reverberation of complex room geometries such as multiple coupled rooms. The model fits band-limited room impulse responses using a set of common decay rates, with amplitudes varying based on listener positions. This paper investigates amplitude estimation methods within the common-slope model framework. We compare several traditional least squares estimation methods and propose using LINEX regression, a Maximum Likelihood approach using logsquared RIR statistics. Through statistical analysis and simulation tests, we demonstrate that LINEX regression improves accuracy and reduces bias when compared to traditional methods.

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