Recent Developments in Musical Sound Synthesis Based on a Physical Model

Julius O. Smith III (jos@ccrma.stanford.edu)
Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University
Stanford, California 94305

Detailed Contents (and Navigation)

• Outline
• Acoustic Modeling Elements
• Finite Difference Approximation (FDA)
  • Frequency Domain Analysis
  • Properties of Backwards Difference Frequency Mapping
  
  
• The Bilinear Transform
• Bilinear Transform of the Ideal Mass
  • Accuracy
  • Digital Filter Design Approach
  • Limitations of Digital Filter Design
  
  
• Digital Waveguide Modeling
  • Moving Termination: Ideal String
  • Waveguide ``Equivalent Circuits'' for the Uniformly Moving Rigid String Termination
  • String Snapshots for Moving Termination
  
  
• External String Excitation at a Point
• Bowed Strings
• Single-Reed Instruments
• 2D Waveguide Mesh
• Wave Digital Filters
  • Physical Construction of Traveling-Wave Element Interfaces
  • Wave Digital Mass Derivation
  • Elementary Wave Flow Diagrams
  
  
• Example: ``Piano hammer in flight''
  • Mass Velocity
  
  
• Spring and Free Mass
  • Wave Digital Spring-Mass System
  • Equivalent Diagram
  
  
• Wave Digital Mass-Spring Oscillator
  • Expanded Wave Digital Mass-Spring Oscillator
  • Kelly-Lochbaum Vocal Tract Model
  
  
• Digital Waveguide versus Wave Digital
• Selected Research Summaries
• String Collisions
  • Previous Solution
  • Refined Solution (WASPAA-03)
  • Coupled FDS for Distributed Collision Support
  
  
• Feathered Valve Closures
  • Aliasing During Upward Glissando
  • Solution
  • Effect of ``Feathering Term'' on Volume Flow
  • Volume Flow vs. Time in Syrinx Oscillation
  • Reduced Aliasing during Upward Glissando
  
  
• Voice Modeling
  • Linear Prediction (LP) Vocal Tract Model
  • Klatt Derivative Glottal Wave
  • Sequential Unconstrained Minimization
  • Liljencrantz-Fant Derivative Glottal Wave Model
  • Parametrized Phonation Types
  
  
• Conical Digital Waveguide Bore Models
  • Cylinder with Conical Cap
  • Sturm-Liouville Scattering
  • Traveling Mode through a Potential Barrier
  • Trapped Mode in a Potential Well
  
  
• Normalized Wave Digital Piano Hammer
  • Wave Digital Mass-Spring Oscillator
  • Normalized Wave Digital Mass-Spring Oscillator
  
  
• The Virtual Violin Project
• The Future of Musical Instruments?
  • Some Observations
  
  
• Speculations
• Related Fronts
• About this document ...