On the bore shape of conical instruments
Keywords:Algorithms, Geometry, Resonance, Appropriate models, Fundamental resonance, Harmonicity, Musical scale, Optimization algorithms, Standard practices
AbstractA study that examines the impact of the bore shape on the harmonicity of the resonances for each note of simplified saxophone-like instruments is presented. The idea involves calculating the positions of the toneholes on a given bore shape for the fundamental resonance to correspond with the notes of the musical scale and then to calculate the deviation of the second resonance from perfect harmonicity. Many bore shapes were simulated. Four of them were selected for this paper. All geometries are made of a cylindrical mouthpiece of 15.8 mm diameter and 50 mm length followed by the air-columns. Approximating the mouthpiece as a cylinder may not be the most appropriate model but this is standard practice in the literature and no better geometry appears obvious. The application of an optimization algorithm that allows simultaneous variation of tonehole positions and bore shape could potentially lead to an improved design and a better understanding of the relation between the geometry of the bore and the quality of the instruments.
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