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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