Download A Coupled Resonant Filter Bank for the Sound Synthesis of Nonlinear Sources This paper is concerned with the design of efficient and controllable filters for sound synthesis purposes, in the context of the generation of sounds radiated by nonlinear sources. These filters are coupled and generate tonal components in an interdependent way, and are intended to emulate realistic perceptually salient effects in musical instruments in an efficient manner. Control of energy transfer between the filters is realized by defining a matrix containing the coupling terms. The generation of prototypical sounds corresponding to nonlinear sources with the filter bank is presented. In particular, examples are proposed to generate sounds corresponding to impacts on thin structures and to the perturbation of the vibration of objects when it collides with an other object. The different sound examples presented in the paper and available for listening on the accompanying site tend to show that a simple control of the input parameters allows to generate sounds whose evocation is coherent, and that the addition of random processes allows to significantly improve the realism of the generated sounds.
Download Digitizing the Schumann PLL Analog Harmonizer The Schumann Electronics PLL is a guitar effect that uses hardwarebased processing of one-bit digital signals, with op-amp saturation and CMOS control systems used to generate multiple square waves derived from the frequency of the input signal. The effect may be simulated in the digital domain by cascading stages of statespace virtual analog modeling and algorithmic approximations of CMOS integrated circuits. Phase-locked loops, decade counters, and Schmitt trigger inverters are modeled using logic algorithms, allowing for the comparable digital implementation of the Schumann PLL. Simulation results are presented.
Download Learning Nonlinear Dynamics in Physical Modelling Synthesis Using Neural Ordinary Differential Equations 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.
Download Zero-Phase Sound via Giant FFT Given the speedy computation of the FFT in current computer
hardware, there are new possibilities for examining transformations for very long sounds. A zero-phase version of any audio
signal can be obtained by zeroing the phase angle of its complex
spectrum and taking the inverse FFT. This paper recommends additional processing steps, including zero-padding, transient suppression at the signal’s start and end, and gain compensation, to
enhance the resulting sound quality. As a result, a sound with the
same spectral characteristics as the original one, but with different temporal events, is obtained. Repeating rhythm patterns are
retained, however. Zero-phase sounds are palindromic in the sense
that they are symmetric in time. A comparison of the zero-phase
conversion to the autocorrelation function helps to understand its
properties, such as why the rhythm of the original sound is emphasized. It is also argued that the zero-phase signal has the same
autocorrelation function as the original sound. One exciting variation of the method is to apply the method separately to the real
and imaginary parts of the spectrum to produce a stereo effect. A
frame-based technique enables the use of the zero-phase conversion in real-time audio processing. The zero-phase conversion is
another member of the giant FFT toolset, allowing the modification of sampled sounds, such as drum loops or entire songs.
Download Efficient Simulation of the Bowed String in Modal Form The motion of a bowed string is a typical nonlinear phenomenon resulting from a friction force via interaction with the bow. The system can be described using suitable differential equations. Implicit numerical discretisation methods are known to yield energy consistent algorithms, essential to ensure stability of the timestepping schemes. However, reliance on iterative nonlinear root finders carries significant implementation issues. This paper explores a method recently developed which allows nonlinear systems of ordinary differential equations to be solved non-iteratively. Case studies of a mass-spring system and an ideal string coupled with a bow are investigated. Finally, a stiff string with loss is also considered. Combining semi-discretisation and a modal approach results in an algorithm yielding faster than real-time simulation of typical musical strings.
Download Real-time Gong Synthesis Physical modeling sound synthesis is notoriously computationally intensive. But recent advances in algorithm efficiency, accompanied by increases in available computing power have brought real-time performance within range for a variety of complex physical models. In this paper, the case of nonlinear plate vibration, used as a simple model for the synthesis of sounds from gongs is considered. Such a model, derived from that of Föppl and von Kármán, includes a strong geometric nonlinearity, leading to a variety of perceptually-salient effects, including pitch glides and crashes. Also discussed here are input excitation and scanned multichannel output. A numerical scheme is presented that mirrors the energetic and dissipative properties of a continuous model, allowing for control over numerical stability. Furthermore, the nonlinearity in the scheme can be solved explicitly, allowing for an efficient solution in real time. The solution relies on a quadratised expression for numerical energy, and is in line with recent work on invariant energy quadratisation and scalar auxiliary variable approaches to simulation. Implementation details, including appropriate perceptuallyrelevant choices for parameter settings are discussed. Numerical examples are presented, alongside timing results illustrating realtime performance on a typical CPU.
Download Real-Time Guitar Synthesis The synthesis of guitar tones was one of the first uses of physical modeling synthesis, and many approaches (notably digital waveguides) have been employed. The dynamics of the string under playing conditions is complex, and includes nonlinearities, both inherent to the string itself, and due to various collisions with the fretboard, frets and a stopping finger. All lead to important perceptual effects, including pitch glides, rattling against frets, and the ability to play on the harmonics. Numerical simulation of these simultaneous strong nonlinearities is challenging, but recent advances in algorithm design due to invariant energy quadratisation and scalar auxiliary variable methods allow for very efficient and provably numerically stable simulation. A new design is presented here that does not employ costly iterative methods such as the Newton-Raphson method, and for which required linear system solutions are small. As such, this method is suitable for real-time implementation. Simulation and timing results are presented.
Download Power-Balanced Drift Regulation for Scalar Auxiliary Variable Methods: Application to Real-Time Simulation of Nonlinear String Vibrations 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.