Piano

There has been much research into the musical acoustics of the piano, including models of piano strings [559,22,78,79,144,41] and the piano hammer [505,64,181,60,501,165]. Additionally, there has been considerable work to date on the problem of piano synthesis by digital waveguide methods [475,528,531,56,41]. In this chapter (adapted from [475]), we will consider commuted waveguide synthesis of the piano. This method is capable of high quality piano synthesis at extremely low cost relative to other model-based approaches.

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Subsections

• Introduction
• The Piano String
  • Wave Equation
  • Stiff-String Dispersion Filter Design
  
  
• Commuted Piano Synthesis
  • Excitation Factoring
  • String Interface
  • Coupled Piano Strings
  • Commuted Synthesis of String Reverberation
  • High Key Numbers
  • Force-Pulse Filter Design
  
  
• Further Reading in Piano Synthesis
• Piano Modeling Problems

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.