302
6 Shocks and Surprises: Refining the Elementary Model
the pressure. The diaphragm, very active during inspiration, appears to be relaxed
during tone production; this mechanically guarantees an optimal coupling between
the abdominal and rib-cage compartments and an optimal transmission of the
abdominal pressure generated by abdominal muscles to the lungs. Interestingly,
an almost linear relationship was observed between the net pressure developed
by expiratory muscles and the playing frequency, as if a linear mapping of the
respiratory muscular activity on playing frequency was adopted by the performer
(when no constraints on the sound dynamic were applied).
The respiratory pressure measurements also allowed an estimate of the glottal
resistance, which is associated with the opening area of the glottis. An increase of
glottal resistance for high notes suggests that control of the glottis could possibly be
correlated with the acoustical control of the player’s windway.
6.4 Improving the Lip Model
The mechanical behaviour of the brass player’s lips, which was described in detail
in Chap. 3, plays a crucial role in the generation of sound by the instrument. It is
therefore important that a model of brass playing includes an adequate treatment
of lip dynamics. In the elementary model developed in Chap. 5, the vibrating lips
are represented by a single mass-spring system with only one degree of freedom.
This simple 1DOF model has been widely used in simulations, and realistic sounds
have been generated using physical modelling synthesis based on a 1DOF outwardstriking lip valve. It was noted however in Sect. 3.4 that in describing the quite
similar physiological systems involved in singing and snoring, it has been found
necessary to employ models with two masses and two or more degrees of freedom
(Ishizaka and Flanagan 1972; Lous et al. 1999; Auregan and Depollier 1995). In this
section we review the limitations of the 1DOF model and outline some approaches
which extend the model to describe more accurately the observed behaviour of brass
playing lips.
6.4.1 Evidence from Mechanical Response Measurements
The mechanical response of the lips at an angular frequency ω was defined in
Sect. 3.3 as
H mr (ω) =
h(ω)
p(ω)
,
(3.16)
where h(ω) is the lip opening height resulting from forcing by a sinusoidal pressure
difference across the lip opening. An ideal 1DOF oscillator has only one
mode of vibration, and its mechanical response curve has a single peak at the modal
6 Shocks and Surprises: Refining the Elementary Model
the pressure. The diaphragm, very active during inspiration, appears to be relaxed
during tone production; this mechanically guarantees an optimal coupling between
the abdominal and rib-cage compartments and an optimal transmission of the
abdominal pressure generated by abdominal muscles to the lungs. Interestingly,
an almost linear relationship was observed between the net pressure developed
by expiratory muscles and the playing frequency, as if a linear mapping of the
respiratory muscular activity on playing frequency was adopted by the performer
(when no constraints on the sound dynamic were applied).
The respiratory pressure measurements also allowed an estimate of the glottal
resistance, which is associated with the opening area of the glottis. An increase of
glottal resistance for high notes suggests that control of the glottis could possibly be
correlated with the acoustical control of the player’s windway.
6.4 Improving the Lip Model
The mechanical behaviour of the brass player’s lips, which was described in detail
in Chap. 3, plays a crucial role in the generation of sound by the instrument. It is
therefore important that a model of brass playing includes an adequate treatment
of lip dynamics. In the elementary model developed in Chap. 5, the vibrating lips
are represented by a single mass-spring system with only one degree of freedom.
This simple 1DOF model has been widely used in simulations, and realistic sounds
have been generated using physical modelling synthesis based on a 1DOF outwardstriking lip valve. It was noted however in Sect. 3.4 that in describing the quite
similar physiological systems involved in singing and snoring, it has been found
necessary to employ models with two masses and two or more degrees of freedom
(Ishizaka and Flanagan 1972; Lous et al. 1999; Auregan and Depollier 1995). In this
section we review the limitations of the 1DOF model and outline some approaches
which extend the model to describe more accurately the observed behaviour of brass
playing lips.
6.4.1 Evidence from Mechanical Response Measurements
The mechanical response of the lips at an angular frequency ω was defined in
Sect. 3.3 as
H mr (ω) =
h(ω)
p(ω)
,
(3.16)
where h(ω) is the lip opening height resulting from forcing by a sinusoidal pressure
difference across the lip opening. An ideal 1DOF oscillator has only one
mode of vibration, and its mechanical response curve has a single peak at the modal