Contrabass Clarinet Physical Model

1. Contrabass Clarinet Physical Model MMI504 Audio Synthesis and Analysis Final Project Nicholas J. Bryan and Trenton C. Watkins *

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

3. Fundamentals: • 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].

4. Digital Waveguide Cont. • Waveguides can be implemented in cascade form to more accurately model given instrument *

5. Clarinet Models • The basic clarinet can be broken into its corresponding waveguide blocks Mouth Pressure Reed Bore Bell Output Nonlinear Element Delay Line Low-Pass Filter *

6. Clarinet Block Diagram Nonlinear Element (Reed) Delay Block (Bore) Cross-over Filter Network (Bell) Diagram taken from [3].

7. 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

8. 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

9. Pre/Post DC + Normalization DC Normalization Fig. Original Audio Signal Fig. Corrected Audio Signal Note: Final audio signal uses separate volume control for amplitude *

10. 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 *

11. 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 HP Audio Out LP

12. 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 *

13. GUFI: Graphical User-Friendly Interface *

14. 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)

15. Conclusions • 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

16. References • Cook, Perry R. Scavone, Gary P. “The Synthesis ToolKit in C++ (STK)”, http://ccrma.stanford.edu/software/stk/ • Smith, Julius O. “Woodwinds”, http://ccrma.stanford.edu/~jos/pasp/Woodwinds.html • 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