[X. Rodet and C. Vergez]X. Rodet and C. Vergez [proc. ICMC96, Hong-Kong, August 1996]proc. ICMC96, Hong-Kong, August 1996 [] [X. Rodet and C. Vergez]X. Rodet and C. Vergez [proc. ICMC96, Hong-Kong, August 1996]proc. ICMC96, Hong-Kong, August 1996

Physical Models of Trumpet-like Instruments
Detailed Behavior and Model Improvements

X. RODET
rod@ircam.fr - C. VERGEZ
vergez@ircam.fr

IRCAM,1 place Igor-Stravinsky
75004 PARIS, FRANCE

Abstract:

A simple physical model of trumpet-like instruments is studied. Its functioning is analysed from the point of view of the theory of nonlinear dynamical systems. Using Hopf theorem, it is proved that the system has a unique stable periodic orbit in the vicinity of the principal fixed point. Then the model is improved with a better approximation of a natural instrument sound production. This is done while carefully preserving the possibility of understanding and controlling the behavior of the model.

 
• Introduction
• The Basic Model
• Theoretical study
  • Calculation of Fixed Points
  • The Hopf theorem
    • Presentation
    • Conditions Required
    • Graphical Approach
    • Periodic Solution
  • Application to our model
    • Conditions fulfillment
    • Theoretical Results
    • Numerical Simulation
    • Theory Versus Experimentation
• Improvements
  • A More Precise Model of the Bore
  • Refined Lip Dynamic
  • The Attack Transients
• Playing Interface
• Conclusion
• References
• About this document ...