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Estimation of Saxophone Control Parameters by Convex Optimization.

Cheng-I Wang1, Tamara Smyth1, Zachary C Lipton2

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Summary

This study presents a new method for identifying saxophone fingerings and reed parameters simultaneously. This approach improves accuracy in musical instrument analysis and sound synthesis.

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Area of Science:

  • Acoustics
  • Musical Instrument Analysis
  • Signal Processing

Background:

  • Estimating saxophone fingering is complex due to overblowing and embouchure variations.
  • Spectral envelope alone is insufficient for accurate fingering identification.
  • Existing methods lack the precision to account for source-filter interactions.

Purpose of the Study:

  • To develop a joint estimation method for saxophone fingering and reed parameters.
  • To create a saxophone model integrating filter responses and a reed model.
  • To enhance the accuracy of fingering identification in musical instruments.

Main Methods:

  • Utilized convex optimization to jointly estimate reed (source) and fingering (filter) parameters.
  • Employed a bank of measured frequency responses for all possible fingerings.
  • Developed a saxophone model coupling frequency responses with a quasi-static reed model.

Main Results:

  • Successfully estimated applied fingering and reed parameters for recorded notes.
  • Achieved higher accuracy in fingering identification compared to previous methods.
  • Demonstrated the effectiveness of the joint estimation approach in a complex acoustic system.

Conclusions:

  • The proposed joint estimation method accurately identifies saxophone fingerings and reed parameters.
  • Convex optimization provides a robust solution for the nonlinear, non-differentiable minimization problem.
  • This approach offers significant advancements in musical instrument modeling and analysis.