Volume 5, 2021
|Number of page(s)||16|
|Published online||09 August 2021|
Multistability of saxophone oscillation regimes and its influence on sound production
Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR7031, 13453 Marseille, France
2 Laboratoire de Mécanique des Structures et des Systèmes Couplés, Conservatoire National des Arts et Métiers, 75003 Paris, France
* Corresponding author: email@example.com
Accepted: 30 June 2021
The lowest fingerings of the saxophone can lead to several different regimes, depending on the musician’s control and the characteristics of the instrument. This is explored in this paper through a physical model of saxophone. The harmonic balance method shows that for many combinations of musician control parameters, several regimes are stable. Time-domain synthesis is used to show how different regimes can be selected through initial conditions and the initial evolution (rising time) of the blowing pressure, which is explained by studying the attraction basin of each stable regime. These considerations are then applied to study how the produced regimes are affected by properties of the resonator. The inharmonicity between the first two resonances is varied in order to find the value leading to the best suppression of unwanted overblowing. Overlooking multistability in this description can lead to biased conclusions. Results for all the lowest fingerings show that a slightly positive inharmonicity, close to that measured on a saxophone, leads to first register oscillations for the greatest range of control parameters. A perfect harmonicity (integer ratio between the first two resonances) decreases first register production, which adds nuance to one of Benade’s guidelines for understanding sound production. Thus, this study provides some a posteriori insight into empirical design choices relative to the saxophone.
Key words: Saxophone / Sound synthesis / Harmonic balance method / Numerical continuation / Attraction basins
© T. Colinot et al., Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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