Institute of Inclusive Science and Solutions

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.

Digital waveguides and finite difference time domain schemes have been used in physical modeling of spatially distributed systems. Both of them are known to provide exact modeling of ideal one-dimensional (1D) band-limited wave propagation, and both of them can be composed to approximate two-dimensional (2D) and three-dimensional (3D) mesh structures. Their equal capabilities in physical modeling have been shown for special cases and have been assumed to cover generalized cases as well. The ability to form mixed models by joining substructures of both classes through converter elements has been proposed recently. In this paper, we formulate a general digital signal processing (DSP)-oriented framework where the functional equivalence of these two approaches is systematically elaborated and the conditions of building mixed models are studied. An example of mixed modeling of a 2D waveguide is presented.

Sound synthesis based on physical modeling of stringed instruments has been an active research field for the last decade. The most efficient synthesis models have been obtained using the theory of digital waveguides . Commuted waveguide synthesis ) is based on the linearity and time-invariance of the synthesis model and is an important method for developing a generic string instrument model. Recently, such a model has been presented including consolidated pluck and body wavetables, a pluck-shaping filter, a pluck-position comb filter, string models with loop filters and continuously variable delays, and sympathetic couplings between the strings .

The five-string Finnish kantele is a traditional folk music instrument that has unique structural features, resulting in a sound of bright and reverberant timbre. This article presents an analysis of the sound generation principles in the kantele, based on measurements and analytical formulation. The most characteristic features of the unique timbre are caused by the bridgeless string termination around a tuning pin at one end and the knotted termination around a supporting bar at the other end. These result in prominent second-order nonlinearity and strong beating of harmonics, respectively. A computational model of the instrument is also formulated and the algorithm is made efficient for real-time synthesis to simulate these features of the instrument timbre.

We present two physics-based analysis, synthesis, and control systems for synthesizing hand clapping sounds. They both rely on the separation of the sound synthesis and event generation, and both are capable of producing individual hand-claps, or mimicking the asynchronous/synchronized applause of a group of clappers. The synthesis models consist of resonator filters, whose coefficients are derived from experimental measurements. The difference between these systems is mainly in the statistical event generation. While the first system allows an efficient parametric synthesis of large audiences, as well as flocking and synchronization by simple rules, the second one provides parametric extensions for synthesis of various clapping styles and enhanced control strategies. The synthesis and the control models of both systems are implemented as software running in real time at the audio sample rate, and they are available for download at http://ccrma-www.stanford.edu/software/stk and http://www.acoustics.hut.fi/go/clapd.

A sound synthesis algorithm for the harpsichord has been developed by applying the principles of digital waveguide modeling. A modification to the loss filter of the string model is introduced that allows more flexible control of decay rates of partials than is possible with a one-pole digital filter, which is a usual choice for the loss filter. A version of the commuted waveguide synthesis approach is used, where each tone is generated with a parallel combination of the string model and a second-order resonator that are excited with a common excitation signal. The second-order resonator, previously proposed for this purpose, approximately simulates the beating effect appearing in many harpsichord tones. The characteristic key-release thump terminating harpsichord tones is reproduced by triggering a sample that has been extracted from a recording. A digital filter model for the soundboard has been designed based on recorded bridge impulse responses of the harpsichord. The output of the string models is injected in the soundboard filter that imitates the reverberant nature of the soundbox and, particularly, the ringing of the short parts of the strings behind the bridge.

We apply a recently developed nonlinear string synthesis algorithm to modeling and synthesis of the kantele, which is a plucked string instrument used in traditional Finnish music for the past few thousand years. The new model combines formerly proposed linear plucked-string models with recent nonlinear extensions. As a result, a dual-polarization nonlinear model is obtained where the difference in the effective string length in two polarizations is accounted for, together with effects caused by the yielding termination of kantele strings and tension modulation. Calibration of model parameters is discussed. The model is also applicable to physical modeling of other plucked string instruments. Sound examples are available at www.acoustics.hut.fi/~vpv/publications/icmc99.htm.

The one-dimensional digital waveguides, combined with the commuted synthesis method, allow modeling and high-quality synthesis of plucked string instrument tones in a very efficient manner. However, the increasing computational power of the modern processors makes it feasible to experiment with more complex algorithms also for real-time sound synthesis purposes. By certain simplifications, time-domain methods based on finite differences (FDTD) are efficient enough to run in real time on modern processors and yet they are more flexible than the computationally less expensive commuted synthesis. The resulting structures, which are called 1-D FDTD waveguides, have previously been shown to be equal to or to approximate many properties of digital waveguides, including lossless and lossy propagation, input and output ports, terminations, and scattering junctions. The numerical stability of the 1-D FDTD waveguides, as well as their initialization and formation of the traveling waves are well understood. However, a careful comparison between 1-D FDTD waveguides and conventional digital waveguides in terms of their limitations, computational efficiency, accuracy, and interaction has not been carried out. The aim of this paper is to fill this gap by highlighting important properties of both methods side by side in string instrument modeling and synthesis. We then try to combine the best properties of both methods and discuss the interaction of the two model structures. Synthetic tones and short musical phrases obtained by both synthesis models will be demonstrated during the presentation.

The one-dimensional digital waveguide structures based on finite difference time domain (FDTD) formulations provide a flexible approach for real-time sound synthesis of simple one-dimensional (1-D) structures, such as a vibrating string. This paper summarizes the basic 1-D FDTD waveguide theory, carries out the stability analysis of the model, and presents a sufficient condition for the stability. The simulation of frequency-independent losses has also been covered. The formation of the traveling waves and initialization of the 1-D FDTD waveguides are investigated. The methods shown in the paper may be used to interconnect the 1-D FDTD waveguides to other model-based sound synthesis structures, such as digital waveguides that are based on the traveling wave solution of the wave equation.

Recently, a nonlinear discrete-time model that simulates a vibrating string exhibiting tension modulation has been presented. This paper elaborates the previous model by taking into account two phenomena: 1) coupling of the tension modulation force to the instrument body and 2) feedback of the tension modulation force to the vibrating string. The two phenomena are investigated by analysis of plucked string instrument tones. Sound synthesis examples are available at www.acoustics.hut.fi/˜ttolonen/icmc99/ including tones by the proposed model, and by a linear model and a previous nonlinear model. The examples show that tension modulation coupling phenomena are important for the quality of synthesized tones and that the tones by the presented model are more natural than with the previous models.

Physics-based simulation and sound synthesis of the tanbur, a traditional Turkish long-necked lute is tackled by two computational models based on digital waveguides. A linear generic dual-polarization simulation including sympathetic coupling is calibrated according to recorded sound examples. The other approach utilizes a specific model that incorporates a nonlinear tension modulation mechanism that is pronounced in the tanbur. The nonlinear implementation can accurately reproduce features such as variation of the fundamental frequency, nonlinear coupling of the harmonic partials, and tension modulation driving force coupling to the body. The synthesis results of both models are justified by audio demonstrations available at

We describe techniques for sound synthesis of the ud and the Renaissance lute using the physical modeling approach. In the present model, novel methods have been used for the design of the loop filters, as well as for the implementation of the glissando effect. With its realistic synthetic sounds, our system can provide new tools and a test-bed platform for researchers, educators and composers of both the Western world and of the Eastern traditions.

In this paper, a technique for inferring the configuration of a clapper's hands from a hand clapping sound is described. The method was developed based on analysis of synthetic and recorded hand clap sounds, labeled with the corresponding hand configurations. A naïve Bayes classifier was constructed to automatically classify the data using two different feature sets. The results indicate that the approach is applicable for inferring the hand configuration.

The analysis of historical or ethnical musical instruments can provide means to verify and broaden our knowledge on musical acoustics. The Turkish tanbur, a member of evidently the oldest group of lute instruments, is a good example. Some important features of the instrument include its body resonator (a wooden hemispherical shell covered with a shallow plate) without a sound hole, its violin-like bridge, and its paired strings with an unusual tuning scheme. In this study we introduce the tanbur and discuss the results of an acoustical analysis of the instrument. The analysis data consists of various sound recordings and measurements realized in an anechoic chamber. Using time-frequency analysis techniques, we capture some of the acoustically important features of the tanbur, such as linear and nonlinear string vibration behavior. We interpret the analysis results combining and comparing with the research results available on string instruments of the western world.

The focus of this work is in modeling the unique sound and the playing practices of the acoustic guitar. The results can be applied to other plucked string instruments too. A new extended notation package is used to produce expressive control information. This tool allows the user to add to the input score instrumental expressions and tempo functions. The system includes also a rule formalism that permits further fine tuning of the computer-generated performance. A real-time synthesis engine has been developed based on earlier results in digital waveguide modeling. We also describe an analysis of vibrato in acoustic guitar tones, which provides control information for realistic synthesis.

Physical modeling and model-based sound synthesis have recently been among the most active topics of computer music and audio research. In the modeling approach one typically tries to simulate and duplicate the most prominent sound generation properties of the acoustic musical instrument under study. If desired, the models developed may then be modified in order to create sounds that are not common or even possible from physically realizable instruments. In addition to physically related principles it is possible to combine physical models with other synthesis and signal processing methods to realize hybrid modeling techniques. This article gives an overview of some recent results in modelbased sound synthesis and related signal processing techniques. The focus is on modeling and synthesizing plucked string sounds, although the techniques may find much more widespread application. First, as a background, an advanced linear model of the acoustic guitar is discussed along with model control principles. Then the methodology to include inherent nonlinearities and time-varying features is introduced. Examples of nonlinearities are studied in the context of two string instruments, the kantele and the tanbur, which exhibit interesting nonlinear effects.