Time Domain Emulation of the Clavinet (original) (raw)
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Time-domain simulation of a guitar
Journal of The Acoustical Society of America, 2002
Our purpose in this study is to present a time-domain numerical modeling of the guitar. The method consists in the modeling of the vibratory and acoustical phenomena from the initial pluck to the 3-D radiation. An idealized plucking force is acting on a 1-D damped string model. The string is coupled to the soundboard via the bridge. The soundboard is
The Portuguese guitar is a pear-shaped instrument with twelve metal strings, descendant from the renaissance European cittern. This instrument is widely used in Portuguese traditional music, mainly in Fado, and more recently also started to play a considerable role among urban Portuguese musicians. Unlike most common guitars, this guitar has a bent soundboard (arched top) with a bridge somewhat similar, although smaller in height, to the bridge of a violin. In spite of the large amount of research aiming the understanding of guitar dynamics, few results are currently available on the Portuguese guitar. Coupling between the different vibrating subsystems of a musical instrument is a very important feature, the reason why instruments of similar families have such different and characteristic sounds. Our recent work on this topic was somewhat restricted by several simplifications, including the assumption of planar string motions and an extremely simplified soundboard. In the present paper those restrictions are relaxed in the following manner : (a) A model for coupling the in-plane and out-of-plane string motions through the bridge kinematics is produced ; (b) A more realistic representation of the instrument dynamics is obtained through finite-element modelling of the soundboard typical of Portuguese guitars. We thus produce a set of time-domain simulations, based on coupling the unconstrained modes of the various subsystems (12 strings and the soundboard). These computations enable, in particular, to assert the dynamical significance of the string region beyond the bridge (the so-called "dead side" of the strings). Also, these simulations enable a close tracking of the energy flow between the instrument subsystems , in connection with sympathetic vibrations, beating phenomena and the sound identity of this instrument.
The first attempt to generate musical sounds by solving the equations of vibrating strings by means of finite difference methods (FDM) was made by Hiller and Ruiz [J. Audio Eng. Soc. 19, 462472 (1971)]. It is shown here how this numerical approach and the underlying physical model can be improved in order to simulate the motion of the piano string with a high degree of realism. Starting from the fundamental equations of a damped, stiff string interacting with a nonlinear hammer, a numerical finite difference scheme is derived, from which the time histories decay time angular frequency which define the instrument with a higher or lesser degree of perfection, is often referred to as a physical model. Due to the complex design of the traditional instruments, which in most cases also include a nonlinear excitation mechanism, no analytical solutions can, however, be expected from such a set of equations. Consequently, it is necessary to use numerical methods when testing the validity of a physical model of a musical instrument.
Real-time emulation of the Clavinet
A physical model has been developed for real-time sound synthesis of the Clavinet, an electromechanical keyboard instrument from the 20th century. The Clavinet has a peculiar excitation mechanism, relying on a tangent striking the string. The modeling paradigm chosen is waveguide synthesis and this paper suggests several novel techniques, such as a polynomial excitation pulse model and a beating generator, both of which have parameters depending on key velocity. Realistic emulation of the release part of Clavinet tones is based on a decrease in the decay rate of the tone and lengthening of a delay line, which corresponds to the physical string. A real-time implementation on Pure Data demonstrates the efficiency of proposed model.
Discrete-time modelling of musical instruments
Reports on progress in …, 2006
This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass-spring, modal, wave digital, finite difference, digital waveguide and source-filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.
SIMULATION AND VISUALIZATION OF STRING VIBRATION USING FINITE DIFFERENCE APPROXIMATION
Vibrating string is an important phenomenon in physics. It has practical applications in stringed musical instruments. In this study we present an application that simulates string motion using numerical methods. The user can adjust several physical parameters of vibration, and after the resulting motion is calculated for a specified period of time, he/she can view the resulting simulation in different ways. The application provides both a pedagogical tool to explain string motion, and a virtual experiment bench where effects of different parameters can be observed. This simulation software will lead to design and implementation of more optimized digital stringed musical instruments which can capture string motion more accurately.
Energy Conserving Schemes for the Simulation of Musical Instrument Contact Dynamics
Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are nonanalytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton’s equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton’s method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.
The scope of this paper is the time domain simulation of the sound field radiated by a string. Different time domain methods have been successfully implemented for string simulations. These methods not only perform realtime string sound synthesis, but also pressure and particle velocity generated around strings can be obtained. It is very useful to analyze the sound field interaction with external physical structures, as the body of a guitar, for example. This paper proposes a combination of two different time-domain methods for a complete description of the generated sound field. These methods are the Functional Transformation Method (FTM) and the Finite-Difference Time Domain (FDTD) method. They have different advantages, and when used in a mixed model scheme, give a wider broadband and more efficient solution of the sound field. Moreover, real-time modification of parameters without stability shortcomings is also feasible.
The scope of the paper is the simulation of the sound field radiated by a string in the time domain. Different time domain methods have been successfully implemented for string simulations. These methods not only perform real-time string sound synthesis, but also pressure and particle velocity generated near strings can be obtained. This is very useful to analyze sound field interaction with external physical structures, as well as body guitar, for example. In this paper, the use of a combination of timedomain methods to provide a complete and wider stable -in frequency range-description of sound field generated than classical finite differences approach is proposed. Functional Transformation Method (FTM) and Finite-Difference Time Domain (FDTD) Method supply different advantages, which used in a mixing scheme, give a wider broadband and efficient solution of sound field. Moreover, real-time modification of parameters without stability shortcomings is also feasible.
Numerical Modeling of Collisions in Musical Instruments
Collisions play an important role in many aspects of the physics of musical instruments. The striking action of a hammer or mallet in keyboard and percussion instruments is perhaps the most important example, but others include reed-beating effects in wind instruments, the string/neck interaction in fretted instruments such as the guitar as well as in the sitar and the wire/membrane interaction in the snare drum. From a simulation perspective, whether the eventual goal is the validation of musical instrument models or sound synthesis, such highly nonlinear problems pose various difficulties, not the least of which is the risk of numerical instability. In this article, a novel finite difference time domain simulation framework for such collision problems is developed, where numerical stability follows from strict numerical energy conservation or dissipation, and where a power law formulation for collisions is employed, as a potential function within a passive formulation. The power law serves both as a model of deformable collision, and as a mathematical penalty under perfectly rigid, non-deformable collision. Various numerical examples, illustrating the unifying features of such methods across a wide variety of systems in musical acoustics are presented, including numerical stability and energy conservation/dissipation, bounds on spurious penetration in the case of rigid collisions, as well as various aspects of musical instrument physics.