Virtual Stringed Instruments

Nelson Lee and Julius O. Smith III,
RealSimple Project¹

Abstract:

This reader contains an overview of physical-modeling methods for stringed instruments. It should be entirely self-contained, including external links to labs and more detailed content on relevant subjects. By thoroughly understanding this reader, you should be well equipped to tackle the ensuing advanced labs in the RealSimple tree.

Detailed Contents (and Navigation)

• Introduction
• Elements of Stringed Instruments
  • Vibrating String
    • D'Alembert's Wave Equation
    • The Delay Line
    • Digital Waveguide Models
    • Natural Decay of the String
    • Modeling Two Planes of Vibration
    • Varying the Digital Waveguide
  • Plucking the String
    • Theoretical Plucks
    • Complexities of Real Plucks
  • Body Resonance
    • Driving-Point Admittance
    • Filtering with the Driving-Point Admittance
    • Bi-directional Interaction
    • String-Body Scattering Junction
  • Pressure Radiation
    • Integrating over Radiating Surface Areas
    • Point-to-Point Modeling
  
  
• Measurements
  • String Vibration
  • Bridge Force
    • Excitation Force
  • Body Vibration
  • Pressure Radiation
  
  
• Parameter Estimation
  • Excitation
  • String
    • Single Plane of Vibration
    • Loop Filter Estimation
    • Two Orthogonal Planes of Vibration
  • Body Resonator
    • Low-Order Filter Implementations
  • Radiated Sound Pressure
    • Low-Order Filter Implementations
    • Interpolating Between Measurements
  
  
• Review of Methods and Final Words
• Bibliography
• About this document ...