Virtual Musical Instruments

This chapter discusses aspects of synthesis models for specific musical instruments such as guitars, pianos, woodwinds, bowed strings, and brasses. Initially we look at model components for electric guitars, followed by some special considerations for acoustic guitars. Next we focus on basic models for string excitation, first by a mass (a simplified piano hammer), then by a damped spring (plectrum model). Piano modeling is then considered, using commuted synthesis for the acoustic resonators and a parametric signal-model for the force-pulse of the hammer. Finally, elementary synthesis of single-reed woodwinds, such as the clarinet, and bowed-string instruments, such as the violin, are summarized, and some pointers are given regarding other wind and percussion instruments.

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Subsections

• Electric Guitars
  • Length Three FIR Loop Filter
  • Brightness and Sustain Control
  • One-Zero Loop Filter
  • The Karplus-Strong Algorithm
  • The Extended Karplus-Strong Algorithm
  • Nonlinear Distortion
    • Tension Modulation
    • String Length Modulation
    • Hard Clipping
    • Soft Clipping
    • Enhancing Even Harmonics
    • Software for Cubic Nonlinear Distortion
  • Amplifier Feedback
  • Cabinet Filtering
  • Duty-Cycle Modulation
  • Vacuum Tube Modeling
  
  
• Acoustic Guitars
  • Bridge Modeling
    • Passive String Terminations
    • A Terminating Resonator
    • Bridge Reflectance
    • Bridge Transmittance
    • Digitizing Bridge Reflectance
    • A Two-Resonance Guitar Bridge
    • Measured Guitar-Bridge Admittance
    • Building a Synthetic Guitar Bridge Admittance
    • Passive Reflectance Synthesis--Method 1
    • Passive Reflectance Synthesis--Method 2
    • Matlab for Passive Reflectance Synthesis Method 1
    • Matlab for Passive Reflectance Synthesis Method 2
    • Matrix Bridge Impedance
  • Body Modeling
  
  
• String Excitation
  • Ideal String Struck by a Mass
    • Mass Termination Model
    • Mass Reflectance from Either String
    • Simplified Impedance Analysis
    • Mass Transmittance from String to String
    • Force Wave Mass-String Model
    • Summary of Mass-String Scattering Junction
    • Digital Waveguide Mass-String Model
    • Displacement-Wave Simulation
  • Piano Hammer Modeling
    • Nonlinear Spring Model
    • Including Hysteresis
    • Piano Hammer Mass
  • Pluck Modeling
    • Digital Waveguide Plucked-String Model
    • Incorporating Control Motion
    • Successive Pluck Collision Detection
    • Plectrum Damping
    • Digitization of the Damped-Spring Plectrum
    • Feathering
  
  
• Piano Synthesis
  • Stiff Piano Strings
    • Piano String Wave Equation
    • Damping-Filter Design
    • Dispersion Filter-Design
  • Nonlinear Piano Strings
    • Nonlinear Piano-String Synthesis
    • Regimes of Piano-String Vibration
    • Efficient Waveguide Synthesis of Nonlinear Piano Strings
    • Checking the Approximations
  • High-Accuracy Piano-String Modeling
    • A Stiff Mass-Spring String Model
    • Nonlinear Piano-String Equations of Motion in State-Space Form
    • Finite Difference Implementation
  • Commuted Piano Synthesis
    • Force-Pulse Synthesis
    • Multiple Force-Pulse Synthesis
    • Commuted Piano Synthesis Architecture
    • Progressive Filtering
    • Excitation Factoring
    • Excitation Synthesis
    • Coupled Piano Strings
    • Commuted Synthesis of String Reverberation
    • High Piano Key Numbers
    • Force-Pulse Filter Design
  • Literature on Piano Acoustics and Synthesis
  
  
• Woodwinds
  • Single-Reed Instruments
    • Digital Waveguide Single-Reed Implementation
  • A View of Single-Reed Oscillation
  • Single-Reed Theory
    • Scattering-Theoretic Formulation
    • Computational Methods
    • Clarinet Synthesis Implementation Details
  • Tonehole Modeling
    • The Clarinet Tonehole as a Two-Port Junction
    • Tonehole Filter Design
    • The Tonehole as a Two-Port Loaded Junction
  
  
• Bowed Strings
  • Digital Waveguide Bowed-String
  • The Bow-String Scattering Junction
  • Bowed String Synthesis Extensions
  • Linear Commuted Bowed Strings
    • Bowing as Periodic Plucking
    • More General Quasi-Periodic Synthesis
    • Stochastic Excitation for Quasi-Periodic Synthesis
  
  
• Brasses
  • Modeling the Lips and Mouthpiece
  • Bell Models
    • Literature Relevant to Brasses
  
  
• Other Instruments
  • Singing Voice
  • Flutes, Recorders, and Pipe Organs
  • Percussion Instruments

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Next: Electric Guitars

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About the Author: 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.