Iterated maps for clarinet-like systems
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Authors
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Publication date
2010
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01A - Journal article
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Parent work
Nonlinear Dynamics
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Volume
62
Issue / Number
Pages / Duration
253-271
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Springer
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Abstract
The dynamical equations of clarinet-like
systems are known to be reducible to a non-linear
iterated map within reasonable approximations. This
leads to time oscillations that are represented by
square signals, analogous to the Raman regime for
string instruments. In this article, we study in more detail
the properties of the corresponding non-linear iterations,
with emphasis on the geometrical constructions
that can be used to classify the various solutions (for
instance with or without reed beating) as well as on
the periodicity windows that occur within the chaotic
region. In particular, we find a regime where period
tripling occurs and examine the conditions for intermittency.
We also show that, while the direct observation
of the iteration function does not reveal much on
the oscillation regime of the instrument, the graph of
the high order iterates directly gives visible information
on the oscillation regime (characterization of the
number of period doubligs, chaotic behaviour, etc.).
Keywords
Musical acoustics
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ISBN
ISSN
1573-269X
0924-090X
0924-090X
Language
English
Created during FHNW affiliation
Yes
Strategic action fields FHNW
Publication status
Published
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Peer review of the complete publication
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Citation
Taillard, P.-A., Kergomard, J., & Laloë, F. (2010). Iterated maps for clarinet-like systems. Nonlinear Dynamics, 62, 253–271. https://doi.org/10.1007/s11071-010-9715-5