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Physical Modeling of the Plucking Process on a String

This paper by Bertrand Scherrer discusses the physical modeling of the plucking process in string instruments, focusing on the interaction between the player's finger and the string. It utilizes a finite difference approach to simulate the dynamics of the excitation, damping, and release phases during plucking. Key concepts include the decoupling of excitation waves, the impact of finger positioning on string vibration, and methods for simulating various playing techniques like “flageolet” tones. The implementation discusses parameters and results, aiming to enhance the understanding and realism of string instrument sounds.

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Physical Modeling of the Plucking Process on a String

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  1. Physical Modeling of the Plucking Process on a String By Bertrand Scherrer MUMT-614-Winter 2006

  2. MUMT-614-Winter 2006 Intro • Indirect acquisition of Instrumental Gesture

  3. MUMT-614-Winter 2006 Intro • Indirect acquisition of Instrumental Gesture => Model of the interaction between the finger and the string.

  4. MUMT-614-Winter 2006 Intro • Finite Difference Approach [Cuzzucoli97,99]

  5. MUMT-614-Winter 2006 Intro • Finite Difference Approach [Cuzzucoli97,99] • Finger = Md mass, Kd stiffness, Rd damping • Newton's Law • Decoupling of Excitation / “Regular” Wave • Centered Finite Difference

  6. MUMT-614-Winter 2006 Intro • Fig11 [Cuzzucoli99]

  7. MUMT-614-Winter 2006 Intro • Finite Difference Approach [Cuzzucoli97,99] • Some data missing. • Written in Italian => hard for me to read. • Sound examples “clippy”

  8. MUMT-614-Winter 2006 Intro • Finite Difference Approach [Cuzzucoli97,99] • Plucking Process = • Damping • Excitation • Release

  9. MUMT-614-Winter 2006 Structure • I- WDF Approach • II- Implementation and Results • III- Conclusion

  10. MUMT-614-Winter 2006 I-WDF Approach a- Pakarinen05 Summary b- Why a Damper ? c- Reflectance of a Damper d- Connecting the Finger to the String

  11. MUMT-614-Winter 2006 I-WDF Approach a- Pakarinen05 Summary Model of “Flageolet” tones using WDF damper to simulate the damping finger.

  12. MUMT-614-Winter 2006 I-WDF Approach b- Why a Damper ? Mass neglected <= no significant motion of finger due to the string. Stiffness neglected <= Compression small.

  13. MUMT-614-Winter 2006 I-WDF Approach c- Reflectance of a Damper ? R : damping coefficient R0: Impedance of the infinitesimal WG

  14. MUMT-614-Winter 2006 I-WDF Approach c- Reflectance of a Damper ? Choosing R0=R :

  15. MUMT-614-Winter 2006 I-WDF Approach d- Connection of the Finger to the String ? 3 port series adaptor

  16. MUMT-614-Winter 2006 I-WDF Approach d- Connection of the Finger to the String ? Junction Velocity :

  17. MUMT-614-Winter 2006 I-WDF Approach d- Connection of the Finger to the String ?

  18. MUMT-614-Winter 2006 II-Implementation and Results a- The string + Simulation Parameters b- Control Parameters c- Scattering Junction d- Results & Problems ...

  19. MUMT-614-Winter 2006 II-Implementation and Results a- The string + Simulation Parameters .fs =44 kHz .Tension obtained using : .L = 65cm .μ = 0.0059 kg/m

  20. MUMT-614-Winter 2006 II-Implementation and Results b- Control Parameters Re : Relative Excitation Position Rf : Relative Damping Position Zf/Zo : Normalized Damping Coeff.

  21. MUMT-614-Winter 2006 II-Implementation and Results c- Scattering Junction

  22. MUMT-614-Winter 2006 II-Implementation and Results c- Scattering Junction Z1=Z2=Zo : Impedance of the string Z3=Zf : Impedance of the finger

  23. MUMT-614-Winter 2006 II-Implementation and Results c- Scattering Junction

  24. MUMT-614-Winter 2006 II-Implementation and Results c- Scattering Junction: Initialization see DamperSchema1-bis see DamperSchema1-ter => Simulate “Perfect Pluck”

  25. MUMT-614-Winter 2006 II-Implementation and Results d- Results Re = 0.1 , Rf =0.5 and Zf/Zo = 0.001, 0.003, 0.005

  26. MUMT-614-Winter 2006

  27. MUMT-614-Winter 2006 II-Implementation and Results d- Results Re = 0.1 , Zf/Zo = 0.003 and Rf = 0.125 , 0.25 , 0.33, 0.5

  28. MUMT-614-Winter 2006

  29. MUMT-614-Winter 2006 II-Implementation and Results d- Results Feedforward Comb Filtering => Problem !

  30. MUMT-614-Winter 2006 II-Implementation and Results d- Results Linear variation of Zf/Zo with fixwd Re and Rf

  31. MUMT-614-Winter 2006

  32. MUMT-614-Winter 2006

  33. MUMT-614-Winter 2006 III-Conclusion - Damping Phase: Solve Comb filtering effect problem ! - Excitation Phase: Not ideal but similar to “stick” phase in bowed strings + Angle of Excitation

  34. MUMT-614-Winter 2006 III-Conclusion - Release Phase: Incorporate the fingerboard/fret collisions.

  35. MUMT-614-Winter 2006 References • Cuzzucoli G., Lombardo V.,"Physical Model of the Plucking Process in the Classical Guitar," in Proc. of the ICMC, pp. 172-179, San Francisco : International Computer Association, pp 172-179, 1997.

  36. MUMT-614-Winter 2006 References • Cuzzucoli G., Lombardo V.,"A Physical Model of the Classical Guitar, Including the Player's Touch," in Computer Music Journal, 23:2, pp52-69, MIT Press, 1999.

  37. MUMT-614-Winter 2006 References • Pakarinen J., "Physical Model of Flageolet Tones in String Instruments," in EUSIPCO , Antalya, Turkey, September 4-8, 2005, http://www.acoustics.hut.fi/~jykke/publications.html

  38. MUMT-614-Winter 2006 References • Smith, J. O. Physical Audio Signal Processing, “Wave Digital Filters” section, <http://ccrma.stanford.edu/~jos/pasp/Wave_Digital_Filters_I.html> • Smith, J. O. Physical Audio Signal Processing, “Moving Rigid Termination” section, http://ccrma.stanford.edu/~jos/pasp/Moving_Rigid_Termination.html

  39. MUMT-614-Winter 2006 References • Smith, J. O. Physical Audio Signal Processing, “Bowed Strings” section,http://ccrma.stanford.edu/~jos/pasp/Bowed_Strings.html

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