Download Modal Spring Reverb Based on Discretisation of the Thin Helical Spring Model The distributed nature of coupling in helical springs presents specific challenges in obtaining efficient computational structures
for accurate spring reverb simulation. For direct simulation approaches, such as finite-difference methods, this is typically manifested in significant numerical dispersion within the hearing range.
Building on a recent study of a simpler spring model, this paper presents an alternative discretisation approach that employs
higher-order spatial approximations and applies centred stencils at
the boundaries to address the underlying linear-system eigenvalue
problem. Temporal discretisation is then applied to the resultant
uncoupled mode system, rendering an efficient and flexible modal
reverb structure. Through dispersion analysis it is shown that numerical dispersion errors can be kept extremely small across the
hearing range for a relatively low number of system nodes. Analysis of an impulse response simulated using model parameters calculated from a measured spring geometry confirms that the model
captures an enhanced set of spring characteristics.
Download Numerical Calculation of Modal Spring Reverb Parameters In the design of real-time spring reverberation algorithms, a modal
architecture offers several advantages, including computational efficiency and parametric control flexibility. Due to the complex,
highly dispersive behavior of helical springs, computing physically accurate parameters for such a model presents specific challenges. In this paper these are addressed by applying an implicit
higher-order-in-space finite difference scheme to a two-variable
model of helical spring dynamics. A novel numerical boundary
treatment is presented, which utilises multiple centered boundary
expressions of different stencil width. The resulting scheme is unconditionally stable, and as such allows adjusting the numerical
parameters independently of each other and of the physical parameters. The dispersion relation of the scheme is shown to be
accurate in the audio range only for very high orders of accuracy
in combination with a small temporal and spatial step. The frequency, amplitude, and decay rate of the system modes are extracted from a diagonalised form of this numerical model. After
removing all modes with frequencies outside the audio range and
applying a modal amplitude correction to compensate for omitting
the magnetic transducers, a light-weight modal reverb algorithm is
obtained. Comparison with a measured impulse response shows a
reasonably good match across a wide frequency range in terms of
echo density, decay characteristics, and diffusive nature.
Download An Explorative String-bridge-plate Model with Tunable Parameters The virtual exploration of the domain of mechano-acoustically produced sound and music is a long-held aspiration of physical modelling. A physics-based algorithm developed for this purpose combined with an interface can be referred to as a virtual-acoustic instrument; its design, formulation, implementation, and control are subject to a mix of technical and aesthetic criteria, including sonic complexity, versatility, modal accuracy, and computational efficiency. This paper reports on the development of one such system, based on simulating the vibrations of a string and a plate coupled via a (nonlinear) bridge element. Attention is given to formulating and implementing the numerical algorithm such that any of its parameters can be adjusted in real-time, thus facilitating musician-friendly exploration of the parameter space and offering novel possibilities regarding gestural control. Simulation results are presented exemplifying the sonic potential of the string-bridgeplate model (including bridge rattling and buzzing), and details regarding efficiency, real-time implementation and control interface development are discussed.
Download Modal Based Tanpura Simulation: Combining Tension Modulation and Distributed Bridge Interaction Techniques for the simulation of the tanpura have advanced significantly in recent years allowing numerically stable inclusion of bridge contact. In this paper tension modulation is added to a tanpura model containing a stiff lossy string, distributed bridge contact and the thread. The model is proven to be unconditionally stable and the numerical solver used has a unique solution as a result of choices made in the discretisation process. Effects due to the distribution of the bridge contact forces by comparison to a single point bridge and of introducing the tension modulation are studied in simulations. This model is intended for use in furthering the understanding of the physics of the tanpura and for informing the development of algorithms for sound synthesis of the tanpura and similar stringed instruments.
Download A Real-Time Synthesis Oriented Tanpura Model Physics-based synthesis of tanpura drones requires accurate simulation of stiff, lossy string vibrations while incorporating sustained contact with the bridge and a cotton thread. Several challenges arise from this when seeking efficient and stable algorithms for real-time sound synthesis. The approach proposed here to address these combines modal expansion of the string dynamics with strategic simplifications regarding the string-bridge and stringthread contact, resulting in an efficient and provably stable timestepping scheme with exact modal parameters. Attention is given also to the physical characterisation of the system, including string damping behaviour, body radiation characteristics, and determination of appropriate contact parameters. Simulation results are presented exemplifying the key features of the model.
Download Tunable Collisions: Hammer-String Simulation with Time-Variant Parameters In physical modelling synthesis, articulation and tuning are effected via time-variation in one or more parameters. Adopting hammered strings as a test case, this paper develops extended forms of such control, proposing a numerical formulation that affords online adjustment of each of its scaled-form parameters, including those featuring in the one-sided power law for modelling hammerstring collisions. Starting from a modally-expanded representation of the string, an explicit scheme is constructed based on quadratising the contact energy. Compared to the case of time-invariant contact parameters, updating the scheme’s state variables relies on the evaluation of two additional analytic partial derivatives of the auxiliary variable. A numerical energy balance is derived and the numerical contact force is shown to be strictly non-adhesive. Example results with time-variant tension and time-variant contact stiffness are detailed, and real-time viability is demonstrated.