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Communication Dans Un Congrès Année : 2020

Objective Metrics to Identify the Tonehole Lattice Cutoff Frequency of Conical Woodwind Instruments

Résumé

The tonehole lattice cutoff frequency is a characteristic of many woodwinds that is generally assumed to be linked to the ``musical personality'' of a given instrument. For frequencies below the cutoff, the input impedance peaks have large amplitudes and regular spacing in frequency, while the peaks above the cutoff are attenuated and often irregularly spaced. An approximate cutoff of an instrument is often identified as a perturbation in the magnitude or phase of the input impedance that separates these two frequency bands. A precise definition of the cutoff exists only for infinite, loss- less lattices, and has been worked out for the cylindrical resonators. Conical resonators are more challenging because there is no possibility of a strict geometric regularity. Here, three objective metrics to identify the cutoff are proposed and compared. The first defines a cutoff frequency band that is defined by thresholds on the modulus of the reflection coefficient. The second metric divides the lattice into &_Pi; shaped cells, each of which consists of two toneholes and the section of main bore between them. For a real instrument, the resonance of the cells varies across the length of the resonator, and the variation is interpreted as a degree of acoustic irregularity. The third metric divides the geometry of the lattice into asymmetric unit cells all of which have the same eigenfrequency. The range of eigenfrequencies for which this is possible is interpreted as the range of frequencies for which the lattice can be considered acoustically regular. These three metrics are applied to the measured input impedance and geometries of the saxophone and bassoon, which have significantly different global cutoff frequencies and acoustic regularity across the range of the resonators.
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hal-03234064 , version 1 (26-05-2021)

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Erik Petersen, Vincent Turcotte, Tom Colinot. Objective Metrics to Identify the Tonehole Lattice Cutoff Frequency of Conical Woodwind Instruments. Forum Acusticum, Dec 2020, Lyon, France. pp.3177-3180, ⟨10.48465/fa.2020.0996⟩. ⟨hal-03234064⟩
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