86
3 Buzzing Lips: Sound Generation in Brass Instruments
Fig. 3.23 Helmholtz’s model
of an inward-striking reed.
Arrows indicate the direction
of air flow. From Helmholtz
(1877)
in an increase in the reed opening. This classification was also adopted by Bouasse
(1929) and many subsequent researchers.
Figure 3.23 is a sketch of the rubber model which Helmholtz used to investigate
the behaviour of an inward-striking reed. Air enters the model through the narrow
slit on the left-hand side; as the angled flaps swing towards each other, the area
of the entrance channel diminishes. This ‘inward-swinging door’ type of motion
is found in the single reeds of the clarinet and saxophone and in the double reeds
of the oboe and bassoon (Wilson and Beavers 1974; Fletcher 1993; Dalmont et al.
1995; Nederveen 1998a). Helmholtz noted that the rubber model reed could also be
sounded by blowing from the other end; the flaps then swing outward in the direction
of air flow, demonstrating the behaviour of an outward-striking reed. Helmholtz
unambiguously identified the brass player’s lips as ‘membranous tongues which
strike outwards’, and the outward-swinging lips shown in Fig. 3.21 clearly fall into
Helmholtz’s outward-striking category.
Outward-striking and inward-striking reeds can also be distinguished by the way
in which their behaviour depends on the pressure difference p across the reed.
When p is slowly increased, an outward-striking reed tends to open, while an
inward-striking reed tends to close. The specification of a slow pressure increase
is necessary, since when an oscillating pressure difference is applied across the
reed, the phase difference between pressure and reed opening depends on frequency.
When an outward-striking reed is subjected to a pressure difference well above its
natural resonance frequency, it closes as the pressure difference increases.
Equation 3.6 describes the dynamics of the 1DOF sliding door lip model. In
considering the effect of a very slow change in the mouthpiece pressure p(t), the
first two terms on the left-hand side of this equation can be neglected, yielding the
approximate equation:
ω
2
l (h(t) − h eq )
p(t)
μ
.
(3.13)
Inspection of this equation shows that the behaviour of the sliding door lip valve
has the character of an inward-striking reed: a decrease in the outlet pressure p(t),
3 Buzzing Lips: Sound Generation in Brass Instruments
Fig. 3.23 Helmholtz’s model
of an inward-striking reed.
Arrows indicate the direction
of air flow. From Helmholtz
(1877)
in an increase in the reed opening. This classification was also adopted by Bouasse
(1929) and many subsequent researchers.
Figure 3.23 is a sketch of the rubber model which Helmholtz used to investigate
the behaviour of an inward-striking reed. Air enters the model through the narrow
slit on the left-hand side; as the angled flaps swing towards each other, the area
of the entrance channel diminishes. This ‘inward-swinging door’ type of motion
is found in the single reeds of the clarinet and saxophone and in the double reeds
of the oboe and bassoon (Wilson and Beavers 1974; Fletcher 1993; Dalmont et al.
1995; Nederveen 1998a). Helmholtz noted that the rubber model reed could also be
sounded by blowing from the other end; the flaps then swing outward in the direction
of air flow, demonstrating the behaviour of an outward-striking reed. Helmholtz
unambiguously identified the brass player’s lips as ‘membranous tongues which
strike outwards’, and the outward-swinging lips shown in Fig. 3.21 clearly fall into
Helmholtz’s outward-striking category.
Outward-striking and inward-striking reeds can also be distinguished by the way
in which their behaviour depends on the pressure difference p across the reed.
When p is slowly increased, an outward-striking reed tends to open, while an
inward-striking reed tends to close. The specification of a slow pressure increase
is necessary, since when an oscillating pressure difference is applied across the
reed, the phase difference between pressure and reed opening depends on frequency.
When an outward-striking reed is subjected to a pressure difference well above its
natural resonance frequency, it closes as the pressure difference increases.
Equation 3.6 describes the dynamics of the 1DOF sliding door lip model. In
considering the effect of a very slow change in the mouthpiece pressure p(t), the
first two terms on the left-hand side of this equation can be neglected, yielding the
approximate equation:
ω
2
l (h(t) − h eq )
p(t)
μ
.
(3.13)
Inspection of this equation shows that the behaviour of the sliding door lip valve
has the character of an inward-striking reed: a decrease in the outlet pressure p(t),