Techniques are described for reducing complexity in stringed instrument simulation for purposes of digital synthesis. These include commuting losses and dispersion to consolidate them into a single lter, replacing body resonators by look-up tables, simplied bow-string interaction, and single-lter, multiply-free coupled strings implementation. Contents 1 Digital Waveguide Theory 2 2 The Terminated String 4 3 Simplied Body Filters 5 4 Simplied Bowed Strings 8 5 Coupled Strings 10 6 Summary 14 7 Appendix 14 1 Page 2 1 Digital Waveguide Theory This section summarizes the digital waveguide model for vibrating strings. Further details can be found in [Smith 1992]. Position y (t,x) 0 x . . . . . . 0 K String Tension e = Mass/Length Figure 1: The ideal vibrating string. The wave equation for the ideal (lossless, linear, exible) vibrating string, depicted in Fig. 1, is given by Ky 00 = y where K = string tension y = y(t; x) = linear mass density _ y...

Recent research in physical modeling of musical instruments for purposes of sound synthesis is reviewed. Recent references, results, and outstanding problems are highlighted for models of strings, winds, brasses, percussion, and acoustic spaces. Emphasis is placed on digital waveguide models and the musical acoustics research on which they are based.

The feedback delay network (FDN) has been proposed for digital reverberation. Also proposed with similar advantages is the digital waveguide network (DWN). This paper notes that the commonly used FDN with an N × N orthogonal feedback matrix is isomorphic to a normalized digital waveguide network consisting of one scattering junction and a vector transformer joining N reflectively terminated branches. Generalizations of FDNs and DWNs are discussed. The general case of a losslessness FDN feedback matrix is shown to be any matrix having unit-modulus eigenvalues and linearly independent eigenvectors. A special class of FDNs using circulant matrices is proposed. These structures can be efficiently implemented and allow control of the time and frequency behavior. Applications of circulant feedback delay networks in

This paper begins with some of the topics and questions about music improvisation using computers, the author has posed himself during more than a decade experience as a performer, composer, software designer and educator. After a quick review of several of his previous interactive music systems, some of those issues are then confronted in FMOL, a program initially designed as a tool for on-line collaborative composition that has been used by hundreds of on-line composers, and which is also being employed by the author in free-form audiovisual improvisation concerts . 1

Starting from the waveguide model for plucked strings, a new digital signal processing model for the slapping technique on electric bassguitars is derived. The model includes amplitude limitations for the string at the frets and/or the fingerboard. These highly nonlinear elements are realized by conditional reflections which depend on the local string displacement. A model of the string dynamics for the two slapbass techniques --- knocking the string with the thumb knuckle and plucking very strong with the index or middle finger --- has been implemented both as MATLAB and C simulations and synthesizes sounds close to the natural instrument. 1. MODELING PLUCKED STRINGS One of the simplest musical instruments amenable to physical modeling is the plucked string. The string is modeled as a linear waveguide: two waves are traveling along the string, one in either direction. As a digital representation, simple delay lines can be used. Rigid terminations yield inverted reflections of the wa...

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.

This thesis proposes banded waveguide synthesis as an approach to real-time sound synthesis based on the underlying physics. So far three main approaches have been widely used: digital waveguide synthesis, modal synthesis and finite element methods. Digital waveguide synthesis is efficient and realistic and captures the complete dynamics of the underlying physics but is restricted to instruments that are well-described by the one-dimensional string equation. Modal synthesis is efficient and realistic yet abandons complete dynamical description and hence cannot used for certain types of performance interactions like bowing. Finite element methods are realistic and capture the behavior of the constituent physical equations but on current commodity hardware does not perform in real-time. Banded waveguides offer efficient simulations for cases for which modal synthesis is appropriate but traditional digital waveguide synthesis is not applicable. The key realization is that the dynamic behavior of traveling waves, which is being used in waveg-uide synthesis, can be applied to individual modes and that the efficient computational

Three types of ecological events (crushing, walking and running) have been considered. Their acoustic properties have been modeled following the physics-based approach. Starting from an existing physically-based impact model, we superimposed to it the dynamic and temporal stochastic characteristics governing crushing events. The resulting model was triggered by control rules realizing typical walking and running time patterns. This bottom-up design strategy was made possible because the sound synthesis and sound control models could be directly connected each other via a common switchboard of driving and control parameters. The existence of a common interface specification for all the models follows from the application of physics-based modeling, and translates in major advantages when those models are implemented as independent, self-contained blocks and procedures connected together in real-time inside a sw architecture like pd. 1.

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In multimedia art and communication, sound models are needed which are versatile, responsive to users’ expectations, and have high audio quality. Moreover, model flexibility for human–machine interaction is a major issue. Models based on the physics of actual or virtual objects can meet all of these requirements, thus allowing the user to rely on high-level descriptions of the sounding entities. As long as the sound description is based on the physics of sounding objects and not only on the characteristics of human hearing, an integration with physics-based graphic models becomes possible.