Physical modelling synthesis is the synthesis of sound by using a set of equations and algorithms to simulate a physical source of sound. Sound is then generated using parameters that describe the physical materials used in the instrument and the user's interaction with it, for example, by plucking a string, or covering toneholes, and so on. A synthesizer (or synthesiser) is an electronic musical instrument designed to produce electronically generated sound, using techniques such as additive, subtractive, FM, physical modelling synthesis, phase distortion, or Scanned synthesis. ... This article is about compression waves. ... An equation is a mathematical statement, in symbols, that two things are the same. ... In mathematics, computing, linguistics, and related disciplines, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. ...

For example, to model the sound of a drum, there would be a formula for how striking the drumhead injects energy into a two dimensional membrane. Thereafter the properties of the membrane (mass density, stiffness, etc.), its coupling with the resonance of the cylindrical body of the drum, and the conditions at its boundaries (a rigid termination to the drum's body) would describe its movement over time and thus its generation of sound. Classic-Spanish Marching Drum A drum is a musical instrument in the percussion family, technically classified as a membranophone. ...

Similar stages to be modelled can be found in instruments such as a violin, though the energy excitation in this case is provided by the slip-stick behavior of the bow against the string, the width of the bow, the resonance and damping behavior of the strings, the transfer of string vibrations through the bridge, and finally, the resonance of the soundboard in response to those vibrations. The violin is a bowed string instrument with four strings tuned in perfect fifths. ...

Although physical modelling was not a new concept in acoustics and synthesis, having been implemented using finite difference approximations of the wave equation by Hiller and Ruiz in 1971, it was not until the development of the Karplus-Strong algorithm, the subsequent refinement and generalization of the algorithm into the extremely efficient digital waveguide synthesis by Julius O. Smith III and others, and the increase in DSP power in the late 1980s that commercial implementations became feasible. Acoustics is a branch of physics and is the study of sound (mechanical waves in gases, liquids, and solids). ... 1971 (MCMLXXI) was a common year starting on Friday (the link is to a full 1971 calendar). ... Karplus-Strong string synthesis is a method of physical modelling synthesis that loops a short waveform through a filtered delay line to simulate the sound of a hammered or plucked string or some types of percussion. ... A digital signal processor (DSP) is a specialized microprocessor designed specifically for digital signal processing, generally in real-time. ... The 1980s refers to the years of 1980 to 1989. ...

Yamaha signed a contract with Stanford University in 1989 to jointly develop digital waveguide synthesis, and as such most patents related to the technology are owned by Stanford or Yamaha. The Yamaha Corporation (ヤマハ株式会社; TYO: 7951 ) is a Japanese company with a large number of product areas. ... The Leland Stanford Junior University, commonly known as Stanford University (or simply Stanford), is a private university located approximately 37 miles (60 kilometers) southeast of San Francisco and approximately 20 miles northwest of San José in an unincorporated area of Santa Clara County. ... 1989 (MCMLXXXIX) was a common year starting on Sunday of the Gregorian calendar. ...

The first commercially available physical modelling synthesizer made using waveguide synthesis was the Yamaha VL1 in 1994. 1994 (MCMXCIV) was a common year starting on Saturday of the Gregorian calendar, and was designated as the International Year of the Family and the International Year of the Sport and the Olympic Ideal by United Nations. ...

While the efficiency of digital waveguide synthesis made physical modelling feasible on common DSP hardware and native processors, the convincing emulation of physical instruments often requires the introduction of non-linear elements, scattering junctions, etc. In these cases, digital waveguides are often combined with FDTD, finite element or wave digital filter methods, increasing the computational demands of the model. Finite-Difference Time-Domain (FDTD) is a popular electromagnetic modeling technique. ...

Examples of physical modelling synthesis:

• Karplus-Strong string synthesis
• Digital waveguide synthesis
• Formant synthesis

Karplus-Strong string synthesis is a method of physical modelling synthesis that loops a short waveform through a filtered delay line to simulate the sound of a hammered or plucked string or some types of percussion. ... Digital waveguide synthesis is the synthesis of audio using a digital waveguide. ... A formant is a preferred resonating frequency of any acoustical system. ...

References

• Hiller, L.; Ruiz, P. (1971). "Synthesizing Musical Sounds by Solving the Wave Equation for Vibrating Objects". Journal of the Audio Engineering Society. 

• Karplus, K.; Strong, A. (1983). "Digital synthesis of plucked string and drum timbres". Computer Music Journal. 

• Julius O. Smith III (December 2005). "Physical Audio Signal Processing". Draft.

External links

• Julius. O Smith III's A Basic Introduction to Digital Waveguide Synthesis
• Music synthesis approaches sound quality of real instruments — Stanford University's 1994 news release
• Audities Foundation Yamaha VL-1
• SoundSynthesis project
• Virtual Violin using finite elements by Christian Geiger und Michael Schreiner (including sound samples)
• ACROE Physical modelling Sound Library
• Physical Modeling on the Nord Modular G2