9.2 Brass Instruments in the Digital World
411
playing frequencies of notes whose spectra satisfy an additional ‘realistic sound’
criterion were averaged to give an estimate of the playing frequency for that note.
A derivative-free optimisation algorithm was then used to find the modification to
the trumpet leadpipe bore which minimised the discrepancies between the equal
temperament target pitches and the pitches of the simulated played notes.
The results of the optimisation based on physical modelling were encouraging,
and the optimised instrument had significantly improved intonation. There is considerable scope for extensions of this approach to other aspects of brass instrument
behaviour such as timbre and playability, since frequency spectra and threshold
pressures can be extracted from the simulations. Further developments of the model,
including more sophisticated treatment of the lip valve and the inclusion of windway
resonances, will probably be necessary as the virtual trumpeter makes the long
journey from beginner to expert.
9.2.2 Modification of Instruments Using Active Control
A performance on a brass instrument involves two partners: the player and the
instrument. The simple model illustrated in Fig. 2.15 showed that these two partners
are intimately linked in a feedback loop, each partner exerting an important
influence on the other. In Sect. 9.2.1 an approach to optimising the design of a
trumpet was described in which the player was replaced by a ‘virtual musician’ – a
sound generator controlled by computer software which reproduced the behaviour
of human lips in the interaction with the real instrument. In this section we describe
some preliminary studies of the inverse process, in which the real musician is
presented with an instrument whose acoustical behaviour is computer controlled.
The process of real-time modification of the resonances of an acoustical system
through a feedback loop is described as active control (Nelson and Elliott 1991).
The basic idea behind active control is simple, although its practical implementation
is often far from straightforward. Consider, for example, an elementary wind
instrument whose resonator is a cylinder closed at the far end. A resonant mode
of the air column arises from the reflection of a forward-travelling wave at the
closed end. If a loudspeaker at the end generates a signal which exactly cancels
the backward-travelling reflected wave, the resonance will disappear; if, on the
other hand, the loudspeaker signal reinforces the reflection, the strength of the
resonant mode will be enhanced. Additional resonances can be introduced by
suitably programming the software controlling the loudspeaker.
This approach was implemented in the creation of an active-controlled endblown flute by Jean Guérard as part of his PhD studies at the Université Paris
6 (Guérard 1998; Guérard and Boutillon 1998). In Guérard’s experimental setup,
illustrated in Fig. 9.10, five miniature microphones mounted in the walls of the
cylindrical tube were used to measure separately the forward- and backward-going
waves (see Sect. 4.2.3). A suitable signal fed to the control loudspeaker cancelled the
reflected wave; in this state the acoustical behaviour of the cylinder resembled that
411
playing frequencies of notes whose spectra satisfy an additional ‘realistic sound’
criterion were averaged to give an estimate of the playing frequency for that note.
A derivative-free optimisation algorithm was then used to find the modification to
the trumpet leadpipe bore which minimised the discrepancies between the equal
temperament target pitches and the pitches of the simulated played notes.
The results of the optimisation based on physical modelling were encouraging,
and the optimised instrument had significantly improved intonation. There is considerable scope for extensions of this approach to other aspects of brass instrument
behaviour such as timbre and playability, since frequency spectra and threshold
pressures can be extracted from the simulations. Further developments of the model,
including more sophisticated treatment of the lip valve and the inclusion of windway
resonances, will probably be necessary as the virtual trumpeter makes the long
journey from beginner to expert.
9.2.2 Modification of Instruments Using Active Control
A performance on a brass instrument involves two partners: the player and the
instrument. The simple model illustrated in Fig. 2.15 showed that these two partners
are intimately linked in a feedback loop, each partner exerting an important
influence on the other. In Sect. 9.2.1 an approach to optimising the design of a
trumpet was described in which the player was replaced by a ‘virtual musician’ – a
sound generator controlled by computer software which reproduced the behaviour
of human lips in the interaction with the real instrument. In this section we describe
some preliminary studies of the inverse process, in which the real musician is
presented with an instrument whose acoustical behaviour is computer controlled.
The process of real-time modification of the resonances of an acoustical system
through a feedback loop is described as active control (Nelson and Elliott 1991).
The basic idea behind active control is simple, although its practical implementation
is often far from straightforward. Consider, for example, an elementary wind
instrument whose resonator is a cylinder closed at the far end. A resonant mode
of the air column arises from the reflection of a forward-travelling wave at the
closed end. If a loudspeaker at the end generates a signal which exactly cancels
the backward-travelling reflected wave, the resonance will disappear; if, on the
other hand, the loudspeaker signal reinforces the reflection, the strength of the
resonant mode will be enhanced. Additional resonances can be introduced by
suitably programming the software controlling the loudspeaker.
This approach was implemented in the creation of an active-controlled endblown flute by Jean Guérard as part of his PhD studies at the Université Paris
6 (Guérard 1998; Guérard and Boutillon 1998). In Guérard’s experimental setup,
illustrated in Fig. 9.10, five miniature microphones mounted in the walls of the
cylindrical tube were used to measure separately the forward- and backward-going
waves (see Sect. 4.2.3). A suitable signal fed to the control loudspeaker cancelled the
reflected wave; in this state the acoustical behaviour of the cylinder resembled that