50
2 The Scientist’s Perspective on Brass Instrument Behaviour
acoustic pressure in the mouth is negligible, and in the model, it is set equal to
zero. This is equivalent to ignoring the effect of acoustic resonances in the vocal
tract, an approximation which becomes questionable for high-pitched notes and
is certainly inadequate when discussing the didgeridoo.
2. The static overpressure (above atmospheric) in the mouthpiece is very small
compared to the static overpressure in the mouth, and it is usual to make the
approximation that the static overpressure in the mouthpiece is zero.
3. A first approximation which is frequently made by physicists is that no sound is
radiated from the instrument. To a musician this must appear to be a shockingly
crude simplification, since it neglects the musical sound production which is the
instrument’s sole purpose! Nevertheless this approximation provides a good basis
for modelling the playable notes on a brass instrument.
4. In Sect. 2.1.6 it was pointed out that the sound pressure levels in the air column
of a brass instrument can be high enough to generate wall vibrations which can
be felt by the player. In normal performing conditions, the influence of these wall
vibrations on the sound heard by the listener in a concert hall is very slight, and
in simplified treatments, the approximation is made that the walls are completely
rigid.
2.2.2 Coupled Systems and Feedback Loops
In the block diagram of the brass instrument model shown in Fig. 2.15, the progress
of the sound signal from its generation at the player’s lips through the instrument and
into the external environment is shown symbolically by a series of arrows pointing
from left to right on the lines linking the subsystems. We noted in Sect. 2.2.1 that
Fig. 2.15 included a second line linking the musician and instrument subsystems,
with an arrow pointing from right to left. This indicates symbolically that the two
subsystems are coupled in a feedback loop: the first subsystem in such a loop
behaves differently depending on whether or not the second subsystem is present.
Any brass player will be familiar with the musical experience described by the rather
technical language of the previous sentence: the ability to buzz the lips at a given
pitch depends strongly on whether or not the lips are attached to the instrument.
A continuous glissando can be performed when the lips are vibrating against the
rim of an isolated mouthpiece, but when the mouthpiece is connected to the rest
of the instrument, only certain lip vibration frequencies can be easily sustained.
The pitches corresponding to these frequencies, which seem to be preferred by the
instrument, are called its natural notes (Sect. 1.2.2).
Figure 2.16 shows the first six natural notes of a B trumpet with no valves
operated. The figure shows the sounding pitches; in a performer’s score, the notes
are usually transposed a tone higher. It is an instructive exercise for a trumpet
player to sound the pitch G4 by buzzing the lips on a mouthpiece detached from
the instrument and to attempt to continue playing this note while inserting the
mouthpiece into the trumpet. It is very difficult to sustain the lip vibration at the pitch
2 The Scientist’s Perspective on Brass Instrument Behaviour
acoustic pressure in the mouth is negligible, and in the model, it is set equal to
zero. This is equivalent to ignoring the effect of acoustic resonances in the vocal
tract, an approximation which becomes questionable for high-pitched notes and
is certainly inadequate when discussing the didgeridoo.
2. The static overpressure (above atmospheric) in the mouthpiece is very small
compared to the static overpressure in the mouth, and it is usual to make the
approximation that the static overpressure in the mouthpiece is zero.
3. A first approximation which is frequently made by physicists is that no sound is
radiated from the instrument. To a musician this must appear to be a shockingly
crude simplification, since it neglects the musical sound production which is the
instrument’s sole purpose! Nevertheless this approximation provides a good basis
for modelling the playable notes on a brass instrument.
4. In Sect. 2.1.6 it was pointed out that the sound pressure levels in the air column
of a brass instrument can be high enough to generate wall vibrations which can
be felt by the player. In normal performing conditions, the influence of these wall
vibrations on the sound heard by the listener in a concert hall is very slight, and
in simplified treatments, the approximation is made that the walls are completely
rigid.
2.2.2 Coupled Systems and Feedback Loops
In the block diagram of the brass instrument model shown in Fig. 2.15, the progress
of the sound signal from its generation at the player’s lips through the instrument and
into the external environment is shown symbolically by a series of arrows pointing
from left to right on the lines linking the subsystems. We noted in Sect. 2.2.1 that
Fig. 2.15 included a second line linking the musician and instrument subsystems,
with an arrow pointing from right to left. This indicates symbolically that the two
subsystems are coupled in a feedback loop: the first subsystem in such a loop
behaves differently depending on whether or not the second subsystem is present.
Any brass player will be familiar with the musical experience described by the rather
technical language of the previous sentence: the ability to buzz the lips at a given
pitch depends strongly on whether or not the lips are attached to the instrument.
A continuous glissando can be performed when the lips are vibrating against the
rim of an isolated mouthpiece, but when the mouthpiece is connected to the rest
of the instrument, only certain lip vibration frequencies can be easily sustained.
The pitches corresponding to these frequencies, which seem to be preferred by the
instrument, are called its natural notes (Sect. 1.2.2).
Figure 2.16 shows the first six natural notes of a B trumpet with no valves
operated. The figure shows the sounding pitches; in a performer’s score, the notes
are usually transposed a tone higher. It is an instructive exercise for a trumpet
player to sound the pitch G4 by buzzing the lips on a mouthpiece detached from
the instrument and to attempt to continue playing this note while inserting the
mouthpiece into the trumpet. It is very difficult to sustain the lip vibration at the pitch