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5 Blow That Horn: An Elementary Model of Brass Playing
Fig. 5.11 Simulation of the set of natural notes of a trombone using a linear lip frequency
sweep, the mouth pressure being maintained constant. Horizontal axis: time. Upper graph: acoustic
pressure at bell exit plane. Lower graph: playing frequency (blue), and control parameter F lip (red)
(Color figure online)
and 5.18). Each plateau corresponds to a natural note, from the lowest one (the
pedal note) to the highest one supported by an acoustic resonance of the brass bore.
In performance, a human player will normally use mouth pressures well above the
oscillation threshold values: Fig. 5.11 shows the result of an FDTD simulation using
a realistic mouth pressure. The simulation is carried out using a lip frequency sweep,
the mouth pressure and other control parameters being maintained constant. The
plateaus in the playing frequency are clearly visible.
Although brass players are all able to get the lowest natural notes, they do not
have the same ability to get the highest ones. A relatively unskilled player may have
difficulty ascending beyond the eighth natural note, while the embouchure control
developed by years of practice allows professional performers to play glissandos
beyond the highest air column resonance (Fig. 2.20). This can be partially illustrated
using simulations in which the lip resonance quality factor and other embouchure
parameters are varied.
5 Blow That Horn: An Elementary Model of Brass Playing
Fig. 5.11 Simulation of the set of natural notes of a trombone using a linear lip frequency
sweep, the mouth pressure being maintained constant. Horizontal axis: time. Upper graph: acoustic
pressure at bell exit plane. Lower graph: playing frequency (blue), and control parameter F lip (red)
(Color figure online)
and 5.18). Each plateau corresponds to a natural note, from the lowest one (the
pedal note) to the highest one supported by an acoustic resonance of the brass bore.
In performance, a human player will normally use mouth pressures well above the
oscillation threshold values: Fig. 5.11 shows the result of an FDTD simulation using
a realistic mouth pressure. The simulation is carried out using a lip frequency sweep,
the mouth pressure and other control parameters being maintained constant. The
plateaus in the playing frequency are clearly visible.
Although brass players are all able to get the lowest natural notes, they do not
have the same ability to get the highest ones. A relatively unskilled player may have
difficulty ascending beyond the eighth natural note, while the embouchure control
developed by years of practice allows professional performers to play glissandos
beyond the highest air column resonance (Fig. 2.20). This can be partially illustrated
using simulations in which the lip resonance quality factor and other embouchure
parameters are varied.