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Contrabass Clarinet Physical Model. MMI504 Audio Synthesis and Analysis Final Project Nicholas J. Bryan and Trenton C. Watkins. *. Objectives. Understand the fundamentals behind basic clarinet physical models Implement a physical model in Matlab

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contrabass clarinet physical model

Contrabass Clarinet Physical Model

MMI504 Audio Synthesis and Analysis Final Project

Nicholas J. Bryan and Trenton C. Watkins


  • Understand the fundamentals behind basic clarinet physical models
  • Implement a physical model in Matlab
  • Create user friendly graphical user interface using GUIDE


  • Digital Waveguide Modeling
    • Simulates physics of acoustic instruments
      • Delay blocks (or length)
      • Transmission/Reflection filters (acoustic losses)

Delay Block

Transmission/Reflection Filter

Diagram taken from [2].

digital waveguide cont
Digital Waveguide Cont.
  • Waveguides can be implemented in cascade form to more accurately model given instrument


clarinet models
Clarinet Models
  • The basic clarinet can be broken into its corresponding waveguide blocks

Mouth Pressure





Nonlinear Element

Delay Line

Low-Pass Filter


clarinet block diagram
Clarinet Block Diagram

Nonlinear Element (Reed)

Delay Block (Bore)

Cross-over Filter Network (Bell)

Diagram taken from [3].

reed nonlinear element
Reed: Nonlinear Element)
  • Creates the oscillation of the instrument
    • Mouth pressure as input signal
    • Uses lookup table as a method of approximating the vibration of the reed
    • If pressure is too high, reed value clips
    • Matlab function: reedtable.m
      • Increased slope parameter to simulate increased reed stiffness
    • Scales pressure as a function of reed

Fig. Reed table look-up

reed ii
Reed II
  • Uses pressure wave as excitation
    • Difficult to control output volume from input pressure wave
    • Solution:
      • DC offset filter
      • Normalization
  • Amplitude envelope used for maximum control

Fig. Amplitude Envelope

pre post dc normalization
Pre/Post DC + Normalization



Fig. Original Audio Signal

Fig. Corrected Audio Signal

Note: Final audio signal uses separate volume control for amplitude


bore delay block
Bore: Delay Block
  • Simulates the length of the instrument

Delay Down

Delay Up



Delay Down

Delay Up

Overall Delay

Implementation: Combines two delay lines into a single delay


bell cross over filter
Bell: Cross-Over Filter
  • Low frequencies get reflected
    • As the delay line reflects the pressure wave back to the reed losses occur
    • For a clarinet, the cross over is appr. 1500 Hz
    • The filter cutoff required a lower cutoff for contrabass simulations
  • High frequencies are transmitted

Fig. 8th orderFIR moving average filter

Fig. 16th orderFIR moving average filter


Audio Out


matlab implementation
Matlab Implementation
  • Initial design using functions and script files
  • Integration into a user-friendly graphical interface
    • Music Application
      • Tempo, Note duration, Pitch, Volume
    • AB comparison with recorded contrabass


pitch duration considerations
Pitch/Duration Considerations
  • Use 12 value lookup table
  • Multiply by 2 to the power of octave
    • Pitch = Lookup*2^Octave
  • Convert BPM into # of samples
    • Samples = fs*note_value*60/BPM
    • ie. Samples =44100(sample/sec)*60(sec/min)/100(beats/min)*1(quarter note)
  • Reflection filter needs careful consideration
  • Low frequency synthesis diverges from the typical clarinet model at low frequencies
  • GUIDE provides an easy development environment for Matlab graphics
  • Cook, Perry R. Scavone, Gary P. “The Synthesis ToolKit in C++ (STK)”,
  • Smith, Julius O. “Woodwinds”,
  • Smith, Julius O. “Efficient Simulations of the Reed-Bore and Bow-String Mechanisms”, Proceedings of the 1986 International Computer Music Conference, 1986, pp. 275-280.
  • McIntyre, M. E., Schumacher, R. T. and Woodhouse, J., "On the Oscillations of Musical Instruments," Journal of the Acoustical Society of America, 74(5), 1983, pp. 1325-1345.
  • Boulanger, Richard. “The Csound Book”, MIT Press 2000