31 research outputs found
Analytical Determination of the Attack Transient in a Clarinet With Time-Varying Blowing Pressure
This article uses a basic model of a reed instrument , known as the lossless
Raman model, to determine analytically the envelope of the sound produced by
the clarinet when the mouth pressure is increased gradually to start a note
from silence. Using results from dynamic bifur-cation theory, a prediction of
the amplitude of the sound as a function of time is given based on a few
parameters quantifying the time evolution of mouth pressure. As in previous
uses of this model, the predictions are expected to be qualitatively consistent
with simulations using the Raman model, and observations of real instruments.
Model simulations for slowly variable parameters require very high precisions
of computation. Similarly, any real system, even if close to the model would be
affected by noise. In order to describe the influence of noise, a modified
model is developed that includes a stochastic variation of the parameters. Both
ideal and stochastic models are shown to attain a minimal amplitude at the
static oscillation threshold. Beyond this point, the amplitude of the
oscillations increases exponentially, although some time is required before the
oscillations can be observed at the '' dynamic oscillation threshold ''. The
effect of a sudden interruption of the growth of the mouth pressure is also
studied, showing that it usually triggers a faster growth of the oscillations
Response of an artificially blown clarinet to different blowing pressure profiles
Using an artificial mouth with an accurate pressure control, the onset of the
pressure oscillations inside the mouthpiece of a simplified clarinet is studied
experimentally. Two time profiles are used for the blowing pressure: in a first
set of experiments the pressure is increased at constant rates, then decreased
at the same rate. In a second set of experiments the pressure rises at a
constant rate and is then kept constant for an arbitrary period of time. In
both cases the experiments are repeated for different increase rates. Numerical
simulations using a simplified clarinet model blown with a constantly
increasing mouth pressure are compared to the oscillating pressure obtained
inside the mouthpiece. Both show that the beginning of the oscillations appears
at a higher pressure values than the theoretical static threshold pressure, a
manifestation of bifurcation delay. Experiments performed using an interrupted
increase in mouth pressure show that the beginning of the oscillation occurs
close to the stop in the increase of the pressure. Experimental results also
highlight that the speed of the onset transient of the sound is roughly the
same, independently of the duration of the increase phase of the blowing
pressure.Comment: 14 page
Oscillation threshold of a clarinet model: a numerical continuation approach
This paper focuses on the oscillation threshold of single reed instruments.
Several characteristics such as blowing pressure at threshold, regime
selection, and playing frequency are known to change radically when taking into
account the reed dynamics and the flow induced by the reed motion. Previous
works have shown interesting tendencies, using analytical expressions with
simplified models. In the present study, a more elaborated physical model is
considered. The influence of several parameters, depending on the reed
properties, the design of the instrument or the control operated by the player,
are studied. Previous results on the influence of the reed resonance frequency
are confirmed. New results concerning the simultaneous influence of two model
parameters on oscillation threshold, regime selection and playing frequency are
presented and discussed. The authors use a numerical continuation approach.
Numerical continuation consists in following a given solution of a set of
equations when a parameter varies. Considering the instrument as a dynamical
system, the oscillation threshold problem is formulated as a path following of
Hopf bifurcations, generalizing the usual approach of the characteristic
equation, as used in previous works. The proposed numerical approach proves to
be useful for the study of musical instruments. It is complementary to
analytical analysis and direct time-domain or frequency-domain simulations
since it allows to derive information that is hardly reachable through
simulation, without the approximations needed for analytical approach
Interaction of reed and acoustic resonator in clarinetlike systems
Sound emergence in clarinetlike instruments is investigated in terms of
instability of the static regime. Various models of reed-bore coupling are
considered, from the pioneering work of Wilson and Beavers ["Operating modes of
the clarinet", J. Acoust. Soc. Am. 56, 653--658 (1974)] to more recent modeling
including viscothermal bore losses and vena contracta at the reed inlet. The
pressure threshold above which these models may oscillate as well as the
frequency of oscillation at threshold are calculated. In addition to Wilson and
Beavers' previous conclusions concerning the role of the reed damping in the
selection of the register the instrument will play on, the influence of the
reed motion induced flow is also emphasized, particularly its effect on playing
frequencies, contributing to reduce discrepancies between Wilson and Beavers'
experimental results and theory, despite discrepancies still remain concerning
the pressure threshold. Finally, analytical approximations of the oscillating
solution based on Fourier series expansion are obtained in the vicinity of the
threshold of oscillation. This allows to emphasize the conditions which
determine the nature of the bifurcation (direct or inverse) through which the
note may emerge, with therefore important consequences on the musical playing
performances
Idealized digital models for conical reed instruments, with focus on the internal pressure waveform
International audienceTwo models for the generation of self-oscillations of reed conical woodwinds are presented. They use the fewest parameters (of either the resonator or the ex-citer), whose influence can be quickly explored. The formulation extends iterated maps obtained for loss-less cylindrical pipes without reed dynamics. It uses spherical wave variables in idealized resonators, with one parameter more than for cylinders: the missing length of the cone. The mouthpiece volume equals that of the missing part of the cone, and is implemented as either a cylindrical pipe (first model) or a lumped element (second model). Only the first model adds a length parameter for the mouthpiece and leads to the solving of an implicit equation. For the second model, any shape of nonlinear characteristic can be directly considered. The complex characteristics impedance for spherical waves requires sampling times smaller than a round trip in the resonator. The convergence of the two models is shown when the length of the cylindrical mouthpiece tends to zero. The waveform is in semi-quantitative agreement with experiment. It is concluded that the oscillations of the positive episode of the mouthpiece pressure are related to the length of the missing part, not to the reed dynamics
Idealized digital models for conical reed instruments, with focus on the internal pressure waveform
Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure
Simulations numériques dans les domaines temporels et fréquentiels. Etude comparative, application aux instruments à vent à anche simple
Time-domain simulations of single reed wind instruments can be powerfull tools if the differential equation governing the motion of the reed is solved with the help of a good numerical scheme. We present a set of different available numerical methods and pay attention to stability criteria and frequency response for each of them. We propose a modified second order implicit method and apply it to some resonators