Vesa Välimäki et al 2006 Rep. Prog. Phys. 69 1 doi:10.1088/0034-4885/69/1/R01
Vesa Välimäki, Jyri Pakarinen, Cumhur Erkut and Matti Karjalainen
Show affiliationsThis 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.
43.75.Yy Instrumentation and techniques for measurements
43.75.Gh Plucked stringed instruments
43.75.De Bowed stringed instruments
Issue 1 (January 2006)
Received 31 March 2005, in final form 1 September 2005
Published 17 October 2005
Vesa Välimäki et al 2006 Rep. Prog. Phys. 69 1
J M Butterworth and M Wing 2005 Rep. Prog. Phys. 68 2773
Heinrich B Stuhrmann 2004 Rep. Prog. Phys. 67 1073
G D'Agostini 2003 Rep. Prog. Phys. 66 1383
Ch Jooss et al 2002 Rep. Prog. Phys. 65 651
S Hofmann 1998 Rep. Prog. Phys. 61 639
M Protopapas et al 1997 Rep. Prog. Phys. 60 389
W Arter 1995 Rep. Prog. Phys. 58 1
L D Marks 1994 Rep. Prog. Phys. 57 603
R Gomer 1990 Rep. Prog. Phys. 53 917