296
6 Shocks and Surprises: Refining the Elementary Model
where L is the sounding length of the instrument air column and L ec the equivalent
cone length. As explained in Part III, the utility of the brassiness potential parameter
in characterising brass instruments is established, and the graphical presentation of
results in a 2D space defined by bore size and brassiness potential is very fruitful
to compare brass instruments, and for historical evolution, taxonomy and quality
evaluation of brass instruments.
6.3 The Player’s Windway
The act of producing a sound from a brass instrument is complex, requiring
control of respiratory muscles and adjustment of the lip embouchure to get the
lips to vibrate. The coupling between the buzzing lips (giving the valve effect by
periodic modulation of the volume flow) and the downstream acoustic resonator
(the instrument itself) is the main factor determining the playable notes. There is,
however, another resonator in the story: the player’s windway, between the lungs
and the lips. The assumption that there are no significant acoustic resonances in the
player’s windway leads to the prediction that the acoustic pressure in the mouth is
zero. The experimental measurements described in Sects. 2.1.2 and 2.1.3 show that
in a realistic playing situation, the acoustic mouth pressure amplitude can be more
than 10% of the acoustic pressure amplitude in the mouthpiece. In this section we
explain how the elementary model can be extended to include the coupling of the
lips to both upstream and downstream resonances and review the role played by
modifications of windway resonances and respiratory activity in brass playing.
6.3.1 Coupling of Upstream and Downstream Resonances
The windway of a brass instrument player can be seen as an auxiliary resonator,
upstream of the lips, in series with the downstream resonator formed by the tubing
of the instrument (Elliott and Bowsher 1982; Benade 1983). The influence of this
additional resonance can be included in the elementary model by adding a second
feedback loop, as shown in Fig. 6.16.
Following Elliott and Bowsher (1982) and Hoekje (1986) in assuming the
continuity of acoustic flow u from upstream to downstream leads to the following
impedance relationship:
u(ω) =
p d (ω)
Z d (ω)
= −
p u (ω)
Z u (ω)
,
(6.38)
where p d and p u are the acoustic pressures in the mouthpiece (downstream) and
in the mouth (upstream), respectively, and Z d and Z u the input impedances of the
instrument and the windway, respectively.
6 Shocks and Surprises: Refining the Elementary Model
where L is the sounding length of the instrument air column and L ec the equivalent
cone length. As explained in Part III, the utility of the brassiness potential parameter
in characterising brass instruments is established, and the graphical presentation of
results in a 2D space defined by bore size and brassiness potential is very fruitful
to compare brass instruments, and for historical evolution, taxonomy and quality
evaluation of brass instruments.
6.3 The Player’s Windway
The act of producing a sound from a brass instrument is complex, requiring
control of respiratory muscles and adjustment of the lip embouchure to get the
lips to vibrate. The coupling between the buzzing lips (giving the valve effect by
periodic modulation of the volume flow) and the downstream acoustic resonator
(the instrument itself) is the main factor determining the playable notes. There is,
however, another resonator in the story: the player’s windway, between the lungs
and the lips. The assumption that there are no significant acoustic resonances in the
player’s windway leads to the prediction that the acoustic pressure in the mouth is
zero. The experimental measurements described in Sects. 2.1.2 and 2.1.3 show that
in a realistic playing situation, the acoustic mouth pressure amplitude can be more
than 10% of the acoustic pressure amplitude in the mouthpiece. In this section we
explain how the elementary model can be extended to include the coupling of the
lips to both upstream and downstream resonances and review the role played by
modifications of windway resonances and respiratory activity in brass playing.
6.3.1 Coupling of Upstream and Downstream Resonances
The windway of a brass instrument player can be seen as an auxiliary resonator,
upstream of the lips, in series with the downstream resonator formed by the tubing
of the instrument (Elliott and Bowsher 1982; Benade 1983). The influence of this
additional resonance can be included in the elementary model by adding a second
feedback loop, as shown in Fig. 6.16.
Following Elliott and Bowsher (1982) and Hoekje (1986) in assuming the
continuity of acoustic flow u from upstream to downstream leads to the following
impedance relationship:
u(ω) =
p d (ω)
Z d (ω)
= −
p u (ω)
Z u (ω)
,
(6.38)
where p d and p u are the acoustic pressures in the mouthpiece (downstream) and
in the mouth (upstream), respectively, and Z d and Z u the input impedances of the
instrument and the windway, respectively.