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Physical Modeling of the Plucking Process on a String

Physical Modeling of the Plucking Process on a String. By Bertrand Scherrer. Intro. Indirect acquisition of Instrumental Gesture. Intro. Indirect acquisition of Instrumental Gesture => Model of the interaction between the finger and the string. Intro.

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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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