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 Efficient simulation of the yaybahar using a modal approach This work presents a physical model of the yaybahar, a recently invented acoustic instrument. Here, output from a bowed string is passed through a long spring, before being amplified and propagated in air via a membrane. The highly dispersive character of the spring is responsible for the typical synthetic tonal quality of this instrument. Building on previous literature, this work presents a modal discretisation of the full system, with fine control over frequency-dependent decay times, modal amplitudes and frequencies, all essential for an accurate simulation of the dispersive characteristics of reverberation. The string-bow-bridge system is also solved in the modal domain, using recently developed noniterative numerical methods allowing for efficient simulation.
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 Measurement-Informed Nonlinear Modal Synthesis of 65 Classical Guitars When a classical guitar string is plucked, vibration energy flows through the bridge into the body and is radiated as sound. Synthesising this process for a large collection of instruments requires both an efficient nonlinear string model and a robust method for extracting instrument-specific parameters from measurements. This paper addresses both issues. Starting from the publicly available dataset of Mores, which provides impulse-response measurements on 65 classical guitars, modal parameters of the bridge compliance and of the bridge-to-air radiation path are extracted for each instrument. These feed a nonlinear string model in which transverse vibration is governed by a geometrically exact elastic potential coupled at an interior bridge point to the measured body data. The nonlinear potential is quadratised via the Scalar Auxiliary Variable (SAV) method, so that the equations of motion become linear in a scalar variable and a known gradient vector, even at the continuous level. After time discretisation, the coupled system is inverted through two sequential Sherman–Morrison rank-one updates (one for the bridge coupling, one for the SAV nonlinearity), yielding an O(N) algorithm per time step. Two regularisation techniques prevent long-term drift of the auxiliary variable. The complete pipeline is demonstrated by synthesising plucked notes across all frets and strings for each of the 65 guitars.
Download A Corpus-Driven Parametric Modal Reverberator A parametric modal reverberator is presented in which synthesis parameters are derived from a large, curated corpus of room impulse responses (IRs). The collected responses are subjected to modal decomposition, yielding per-mode frequencies, damping coefficients, and residue amplitudes, together with a short early-reflection finite impulse response (FIR) filter. From the decomposed data, a feature table is constructed per IR comprising standard acoustic indices, per-band damping and density statistics, amplitude distributions, and FIR descriptors—50 variables in total. Six acoustically meaningful user controls are selected; since these exhibit substantial pairwise correlations across the corpus, they are orthogonalised via principal component analysis (PCA) prior to regression.