Challenges and requirements in the modelling of musical instruments Antoine Chaigne ENSTA UME, Franc

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Challenges and requirements in the modelling of
musical instrumentsAntoine ChaigneENSTA UME,
Francechaigne_at_ensta.fr
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Use and interest of models in musical acoustics

• Comprehension of the physics
• Numerical experimentation
• Design of new instruments
• Sound synthesis
• Psychoacoustical tests
• Recording and reproduction of sound

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Summary of presentation

• Mechanics of musical instruments
• Human perception of sound
• Time-domain modelling
• Examples of recently obtained results
• Conclusion

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Mechanics of musical instruments. Main features
1. Stringed instruments

• I) Material
• Anisotropic and heterogeneous material (wood).
  Sensitivity to moisture and temperature.
  Relevance of losses in the material
• II) Geometry
• Light structures. Complex geometry. Coupling with
  cavity. Bracing, soundpost
• III) Nonlinear excitation
• Finger or plectrum (plucked strings)
• Hammer (struck strings)
• Bow-string interaction (bowed strings)
  self-sustained oscillations

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Mechanics of musical instruments. 2. Percussive
instruments

• Keyboards (xylophone, vibraphone,)
• Tuning of the bars (undercut)
• Coupling with tubular resonator
• Gongs and cymbals
• Nonlinear effects due to large displacement
• Timpani
• Membrane-cavity coupling

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Mechanics of musical instruments. Main features
3. Wind instruments

• Brass (trumpet, horn,)
• Nonlinear wave propagation  brassy sounds .
• Lips-tube interaction
• Flutes and pipes
• Self-sustained oscillations driven by air flow
• Edge-flow interaction (figure)
• Reed instruments (clarinet, oboe,)
• Reed-tube interaction
• Nonlinear motion of the reed

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Requirements in view of human perception

• Audible range (steady sounds)
• 20 Hz to 20 kHz
• Loudness
• Just noticeable difference 1 dB
• (amplitude ratio of nearly 12 )
• Pitch
• Frequency difference limen nearly 1
• Timbre
• Relevance of spectral envelope
• Relevance of temporal envelope

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Arguments for time-domain modelling

• Perceptual relevance of transients
• Ex Allow recognition of the excitation
• Perceptual relevance of decay times
• Ex Allow recognition of materials (free
  vibrations)
• Presence of nonlinearities in the equations
• Possibility of step-by-step resolution

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Summary of instrument modelling

• Field equations
• Wave propagation in bounded media strings, air
  column, bars, membranes, plates, shells,
• Vibroacoustic coupling in stringed and percussive
  instruments
• Initial conditions
• Interaction between exciter (finger, hammer, bow,
  reed, lips, air jet,) and propagation medium
• Boundary conditions
• Fixed or moving end for strings
• Open or closed end for tubes

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A central question required accuracy of a model
?
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Other applications of new materials.
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Summary and conclusions

• Future directions of research in musical
  acoustics (non-limitative list)
• Nonlinearities in solids and fluids
• Material properties
• Experimentation visualization (vocal folds,
  PIV,.)
• Numerical methods and simulations
• Psychoacoustical experiments