72
3 Buzzing Lips: Sound Generation in Brass Instruments
the pitch and dynamic level of the note played (Fig. 3.9). For high-pitch notes the
relatively small height and width of the lip aperture were usually observed to vary
in proportion, resulting in values of the exponent q 2 for all dynamic levels. This
quadratic behaviour of the area-height function was also found for low-pitch notes
played quietly: an example is Fig. 3.9a.
Figure 3.9b, c illustrate an important aspect of the behaviour of the lip aperture
for low notes played loudly. It is not possible to fit an area-height function with a
single exponent in such cases. The plots for a pedal B 1 played mf and ff have a
characteristic dogleg shape: it is possible to fit these plots with two different slopes,
the first with q 2 for small height values and the second with q 1 for high height
values. Area functions with this type of dogleg slope have been used in simulations
(Vergez and Rodet 2001a).
The measurements shown in Fig. 3.10 help to clarify the reason for the dogleg
appearance of the area-height curve in low-pitch playing. Figure 3.10a shows the
variation of height, width and area of the lip aperture during one cycle of the note
B 1 played mf on a trombone. The curves are similar to those shown in Fig. 3.7,
although the measurements were made on two different trombonists. The dashed
vertical lines divide the period of the cycle into three time intervals. During the first
interval (red markers), the width increases; during the second (green markers), it
remains approximately constant; and during the third (blue markers), it decreases.
To simplify the discussion, these intervals are described as ‘opening’, ‘mid cycle’
and ‘closing’.
The corresponding intervals are identified by the same marker colours in
Fig. 3.10b, which is the corresponding area-height plot. The opening interval is fitted
by Eq. 3.1 with an exponent q = 2.2; the mid-cycle interval requires q = 1, while
the closing interval q = 2.7 gives the best fit. The linear behaviour in the midcycle interval is explained by the constancy of the width of the lip aperture, which
is probably due to the constraining effect of the mouthpiece rim.
3.1.5 Two-Dimensional Motion of the Brass Player’s Lips
The front view of the lips, shown in Fig. 3.4, gives valuable information about
the modulation of the air flow from the player’s mouth into the mouthpiece. It is
however important to recognise that the lips can also have a significant component
of motion along the direction of the air flow.
Figure 3.11 shows a transparent mouthpiece designed to view motion of the
vibrating lips in the yz plane. A Kelly bass trombone mouthpiece was modified
by planing one side of the cup and attaching a flat optical window which gave good
visibility over around half the cup diameter. A PCB microphone was also connected
by a short tube to the backbore of the mouthpiece to monitor the downstream
pressure signal.
The first image in the sequence in Fig. 3.12, reading from left to right, shows
the phase of the vibration in which the lips momentarily close completely. The
3 Buzzing Lips: Sound Generation in Brass Instruments
the pitch and dynamic level of the note played (Fig. 3.9). For high-pitch notes the
relatively small height and width of the lip aperture were usually observed to vary
in proportion, resulting in values of the exponent q 2 for all dynamic levels. This
quadratic behaviour of the area-height function was also found for low-pitch notes
played quietly: an example is Fig. 3.9a.
Figure 3.9b, c illustrate an important aspect of the behaviour of the lip aperture
for low notes played loudly. It is not possible to fit an area-height function with a
single exponent in such cases. The plots for a pedal B 1 played mf and ff have a
characteristic dogleg shape: it is possible to fit these plots with two different slopes,
the first with q 2 for small height values and the second with q 1 for high height
values. Area functions with this type of dogleg slope have been used in simulations
(Vergez and Rodet 2001a).
The measurements shown in Fig. 3.10 help to clarify the reason for the dogleg
appearance of the area-height curve in low-pitch playing. Figure 3.10a shows the
variation of height, width and area of the lip aperture during one cycle of the note
B 1 played mf on a trombone. The curves are similar to those shown in Fig. 3.7,
although the measurements were made on two different trombonists. The dashed
vertical lines divide the period of the cycle into three time intervals. During the first
interval (red markers), the width increases; during the second (green markers), it
remains approximately constant; and during the third (blue markers), it decreases.
To simplify the discussion, these intervals are described as ‘opening’, ‘mid cycle’
and ‘closing’.
The corresponding intervals are identified by the same marker colours in
Fig. 3.10b, which is the corresponding area-height plot. The opening interval is fitted
by Eq. 3.1 with an exponent q = 2.2; the mid-cycle interval requires q = 1, while
the closing interval q = 2.7 gives the best fit. The linear behaviour in the midcycle interval is explained by the constancy of the width of the lip aperture, which
is probably due to the constraining effect of the mouthpiece rim.
3.1.5 Two-Dimensional Motion of the Brass Player’s Lips
The front view of the lips, shown in Fig. 3.4, gives valuable information about
the modulation of the air flow from the player’s mouth into the mouthpiece. It is
however important to recognise that the lips can also have a significant component
of motion along the direction of the air flow.
Figure 3.11 shows a transparent mouthpiece designed to view motion of the
vibrating lips in the yz plane. A Kelly bass trombone mouthpiece was modified
by planing one side of the cup and attaching a flat optical window which gave good
visibility over around half the cup diameter. A PCB microphone was also connected
by a short tube to the backbore of the mouthpiece to monitor the downstream
pressure signal.
The first image in the sequence in Fig. 3.12, reading from left to right, shows
the phase of the vibration in which the lips momentarily close completely. The