Skip to Main content Skip to Navigation
New interface
Journal articles

Emergence of quasiperiodic regimes in a neutral delay model of flute-like instruments: Influence of the detuning between resonance frequencies

Abstract :

Musical instruments display a wealth of dynamics, from equilibria (where no sound is produced) to a wide diversity of periodic and non-periodic sound regimes. We focus here on two types of flute-like instruments, namely a recorder and a pre-hispanic Chilean flute. A recent experimental study showed that they both produce quasiperiodic sound regimes which are avoided or played on purpose depending on the instrument. We investigate the generic model of sound production in flute-like musical instruments, a system of neutral delay-differential equations. Using time-domain simulations, we show that it produces stable quasiperiodic oscillations in good agreement with experimental observations. A numerical bifurcation analysis is performed, where both the delay time (related to a control parameter) and the detuning between the resonance frequencies of the instrument – a key parameter for instrument makers – are considered as bifurcation parameters. This demonstrates that the large detuning that is characteristic of prehispanic Chilean flutes plays a crucial role in the emergence of stable quasiperiodic oscillations.

Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03766798
Contributor : Soizic Terrien Connect in order to contact the contributor
Submitted on : Thursday, September 1, 2022 - 2:23:38 PM
Last modification on : Monday, November 7, 2022 - 1:43:26 PM
Long-term archiving on: : Friday, December 2, 2022 - 6:30:28 PM

File

QPflutemodel_hal.pdf
Files produced by the author(s)

Identifiers

Citation

Soizic Terrien, Christophe Vergez, Benoît Fabre, Patricio de la Cuadra. Emergence of quasiperiodic regimes in a neutral delay model of flute-like instruments: Influence of the detuning between resonance frequencies. Journal of Computational Dynamics, 2022, 9 (3), pp.465. ⟨10.3934/jcd.2022011⟩. ⟨hal-03766798⟩

Share

Metrics

Record views

20

Files downloads

3