2.2 An Approach to Modelling Brass Instruments
51
Fig. 2.16 The first six natural notes of the B trumpet (sounding pitches)
G4 once the coupling to the instrument is made, because this note is intermediate
between the third and fourth natural notes of the trumpet (F4 and B 4). The feedback
from the instrument exerts a strong guidance on the lips towards a vibration at either
F4 or B 4. If the lips are buzzed at either of these pitches while the mouthpiece is
inserted, the sound is stabilised and reinforced by the coupling to the instrument.
The feedback arrow in Fig. 2.15 indicates the return of an acoustic signal from
the instrument resonator to modify the pressure difference across the lips. The way
in which this pressure difference controls the rate of air flow into the mouthpiece
is discussed in detail in Chap. 3. The strong preference of the lips to vibrate at
one of the natural note frequencies is due to the fact that the air flow is not
simply proportional to the pressure difference. This lack of simple proportionality
is expressed mathematically by describing the equation relating pressure and flow
(Eq. 3.27) as nonlinear, and the lips are shown in Fig. 2.15 as a nonlinear sound
generator.
The crucial importance of this nonlinearity can be understood by considering
a second experiment in which a trumpeter again buzzes the sounding pitch G4
into a mouthpiece. This time the mouthpiece is not inserted into a trumpet but
instead is held near a microphone connected to an amplifier and loudspeaker. If
this apparatus is of sufficiently high quality it will behave like a linear amplification
system, reproducing the sound more loudly but exerting no control over the player’s
lips. A continuous glissando will be just as easy with the amplification as without it.
The existence of preferred natural notes is proof that in normal performance a brass
instrument does not behave like a linear amplifier.
When the feedback from the instrument provides firm guidance towards a welldefined pitch, the note is sometimes described by the musician as ‘well centred’.
The strength and pitch accuracy of the feedback depend on the instrument and on
the playing range. In the higher registers of most brass instruments, the strength
of feedback diminishes substantially; in the highest pitch range, accessible only
to virtuoso performers, there is no significant feedback, and it is possible to play
continuous glissandi. In the lower registers of modern brass instruments, notes are
typically well centred, and a poorly centred note may indicate a lack of feedback
due to a leak in the instrument.
Powerful feedback from the instrument can force the player’s lips towards
vibration at a particular pitch. This strong ‘slotting’ (Sect. 1.2.2) is clearly only a
good thing if the enforced pitch is that desired by the musician. A player may wish
to ‘bend’ a note slightly for expressive reasons or to achieve perfect intonation in
an ensemble; it is important that the feedback is not so strong that the player finds
it impossible to make the necessary changes in lip vibration frequency. The ideal
51
Fig. 2.16 The first six natural notes of the B trumpet (sounding pitches)
G4 once the coupling to the instrument is made, because this note is intermediate
between the third and fourth natural notes of the trumpet (F4 and B 4). The feedback
from the instrument exerts a strong guidance on the lips towards a vibration at either
F4 or B 4. If the lips are buzzed at either of these pitches while the mouthpiece is
inserted, the sound is stabilised and reinforced by the coupling to the instrument.
The feedback arrow in Fig. 2.15 indicates the return of an acoustic signal from
the instrument resonator to modify the pressure difference across the lips. The way
in which this pressure difference controls the rate of air flow into the mouthpiece
is discussed in detail in Chap. 3. The strong preference of the lips to vibrate at
one of the natural note frequencies is due to the fact that the air flow is not
simply proportional to the pressure difference. This lack of simple proportionality
is expressed mathematically by describing the equation relating pressure and flow
(Eq. 3.27) as nonlinear, and the lips are shown in Fig. 2.15 as a nonlinear sound
generator.
The crucial importance of this nonlinearity can be understood by considering
a second experiment in which a trumpeter again buzzes the sounding pitch G4
into a mouthpiece. This time the mouthpiece is not inserted into a trumpet but
instead is held near a microphone connected to an amplifier and loudspeaker. If
this apparatus is of sufficiently high quality it will behave like a linear amplification
system, reproducing the sound more loudly but exerting no control over the player’s
lips. A continuous glissando will be just as easy with the amplification as without it.
The existence of preferred natural notes is proof that in normal performance a brass
instrument does not behave like a linear amplifier.
When the feedback from the instrument provides firm guidance towards a welldefined pitch, the note is sometimes described by the musician as ‘well centred’.
The strength and pitch accuracy of the feedback depend on the instrument and on
the playing range. In the higher registers of most brass instruments, the strength
of feedback diminishes substantially; in the highest pitch range, accessible only
to virtuoso performers, there is no significant feedback, and it is possible to play
continuous glissandi. In the lower registers of modern brass instruments, notes are
typically well centred, and a poorly centred note may indicate a lack of feedback
due to a leak in the instrument.
Powerful feedback from the instrument can force the player’s lips towards
vibration at a particular pitch. This strong ‘slotting’ (Sect. 1.2.2) is clearly only a
good thing if the enforced pitch is that desired by the musician. A player may wish
to ‘bend’ a note slightly for expressive reasons or to achieve perfect intonation in
an ensemble; it is important that the feedback is not so strong that the player finds
it impossible to make the necessary changes in lip vibration frequency. The ideal