Musical Applications of Banded Waveguides

(Essl et al. 2003), we intro-duced the theory of banded waveguides, showingthe advantages of this synthesis technique that al-lows efficient simulation of highly inharmonic vi-brating structures. In this article, we provide anoverview of different musical instruments thathave been modeled efficiently using banded wave-guides. Additional detail can be found in Cook(2002); Essl and Cook (1999); Essl and Cook (2000);Essl (2002); Kapur et al. (2002); Serafin et al. (2002);and Serafin, Wilkerson, and Smith (2002). Links tosoftware implementations of these models avail-able online can be found in the conclusion of thisarticle.First, we discuss a banded-waveguide model ofbar percussion instruments followed by a model ofa musical saw. Next, we show how to use bandedwaveguides to model bowed glasses and bowls, andwe conclude by presenting models of a Tabla and abowed cymbal.

[1]  Dinesh K. Pai,et al.  The Sounds of Physical Shapes , 1998, Presence.

[2]  A. Chaigne,et al.  Numerical simulations of xylophones. I. Time-domain modeling of the vibrating bars , 1997 .

[3]  Stefania Serafin,et al.  Theory of Banded Waveguides , 2004, Computer Music Journal.

[4]  Perry R. Cook,et al.  Banded Waveguides: Towards Physical Modeling of Bowed Bar Percussion Instruments , 1999, ICMC.

[5]  M. Karjalainen,et al.  Discrete-time modelling of musical instruments , 2005 .

[6]  John Wawrzynek,et al.  VLSI models for sound synthesis , 1989 .

[7]  Stefania Serafin,et al.  Analysis and synthesis of unusual friction-driven musical instruments , 2002, International Conference on Mathematics and Computing.

[8]  Stefania Serafin,et al.  MODELING BOWL RESONATORS USING CIRCULAR WAVEGUIDE NETWORKS , 2002 .

[9]  Laboratorio Nacional de Música Electroacústica Proceedings of the 2001 International Computer Music Conference, ICMC 2001, Havana, Cuba, September 17-22, 2001 , 2001, ICMC.

[10]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[11]  Ajay Kapur,et al.  The Electronic Tabla Controller , 2002, NIME.

[12]  Stefania Serafin,et al.  The Mutha Rubboard controller , 2002 .

[13]  Atau Tanaka,et al.  Multimodal Interaction in Music Using the Electromyogram and Relative Position Sensing , 2002, NIME.

[14]  Cook,et al.  Measurements and efficient simulations of bowed bars , 2000, The Journal of the Acoustical Society of America.

[15]  John M. Eargle Acoustics of Percussion Instruments , 1995 .

[16]  Stefania Serafin,et al.  REAL-TIME SPATIAL PROCESSING AND TRANSFORMATIONS OF A SINGING BOWL , 2002 .

[17]  Perry R. Cook,et al.  Real Sound Synthesis for Interactive Applications , 2002 .

[18]  James L. Moore,et al.  Acoustics of bar percussion instruments , 1971 .

[19]  Perry R. Cook,et al.  Physical wave propagation modeling for real-time synthesis of natural sounds , 2002 .

[20]  Vesa Välimäki,et al.  Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques , 2000, IEEE Trans. Speech Audio Process..

[21]  Thomas D. Rossing,et al.  Acoustics of Percussion Instruments--Part I. , 1976 .

[22]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[23]  Stefania Serafin,et al.  The Mutha Rubboard Contoller: Interactive Heritage , 2002, NIME.

[24]  T. Rossing Acoustics of the glass harmonica , 1991 .

[25]  Xavier Serra,et al.  A Computer Model for Bar Percussion Instruments , 1986, ICMC.

[26]  A. Chaigne,et al.  Comparison between modal analysis and finite‐element modeling of a marimba bar , 1999 .

[27]  Unto K. Laine,et al.  Splitting the Unit Delay - Tools for fractional delay filter design , 1996 .

[28]  Miller Puckette,et al.  Pure Data , 1997, ICMC.

[29]  J. Scott,et al.  Vibration of an elastic strip with varying curvature , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[30]  Perry R. Cook,et al.  The Synthesis ToolKit (STK) , 1999, ICMC.

[31]  Perry R. Cook,et al.  Banded Waveguides on Circular Topologies and of Beating Modes: Tibetan Singing Bowls and Glass Harmonicas , 2002, ICMC.

[32]  James F. O'Brien,et al.  Synthesizing Sounds from Physically Based Motion , 2001, SIGGRAPH Video Review on Animation Theater Program.

[33]  Perry R. Cook,et al.  Physically Informed Sonic Modeling (PhISM): Synthesis of percussive sounds , 1997 .

[34]  Thomas D. Rossing,et al.  Science of Percussion Instruments , 2001 .

[35]  F. Orduña-Bustamante Nonuniform beams with harmonically related overtones for use in percussion instruments , 1991 .

[36]  David Zicarelli,et al.  An Extensible Real-time Signal Processing Environment for Max , 1998, ICMC.

[37]  Neville H Fletcher Nonlinear dynamics and chaos in musical instruments , 1993 .

[38]  Julius O. Smith,et al.  Physical Modeling with the 2-D Digital Waveguide Mesh , 1993, ICMC.

[39]  Ingolf Bork,et al.  Practical tuning of xylophone bars and resonators , 1995 .

[40]  S. Schwerman,et al.  The Physics of Musical Instruments , 1991 .

[41]  Felipe Orduña-Bustamante Erratum: ‘‘Nonuniform beams with harmonically related overtones for use in percussion instruments’’ [J. Acoust. Soc. Am. 90, 2935–2941 (1991)] , 1992 .

[42]  D. Matignon,et al.  Numerical simulations of xylophones. II. Time-domain modeling of the resonator and of the radiated sound pressure , 1998 .

[43]  Max V. Mathews,et al.  Current directions in computer music research , 1989 .

[44]  岸 憲史,et al.  The Physics of Musical Instruments (2nd ed.), Neville H. Fletcher and Thomas D. Rossing共著, Springer-Verlag, New York, 1998, 756頁 , 2000 .

[45]  J. Bretos,et al.  Finite element analysis and experimental measurements of natural eigenmodes and random responses of wooden bars used in musical instruments , 1999 .