Modelling the spectral evolution of transients in wind instruments

![CDATA[Notes produced by self-sustained musical wind instruments are characterised by relatively long stretches of sound where the waveform has limited variation. However, for notes begun by tonguing, the initial transient or attack is characterised by a rapid, nearly exponential rise in the amplitude of the pressure oscillations. In recent articles, we have studied and modelled tonguing in the clarinet, played by human or machine players. Here, the initial displacement of the reed creates a pressure pulse with a mechanism rather like that of the 'water hammer' in hydraulics, giving pressure and flow proportional to aperture-until the first reflection returns from the bore. Superposition of the reed effect and the reflection makes the spectral content of the early transient strongly dependent on details of the reed motion and the extent of overlap with the returning reflection. The feedback gain of the reed then produces an exponential rise in amplitude until saturation is approached. The shape and characteristic times of the sound envelope are modelled as a function of the details of how the opening valve is changed during the initiation of the sound. During the attack, the oscillations change not only in amplitude but also in shape, and the gain and rise times for different harmonics and other partials may vary. This paper investigates how the time course of the initial displacement of the reed produces different initial wave shapes, and how the spectral content is shaped by reed motion and its overlap with returning pulses from the resonator.]]