The saxophone’s tone production works through turbulence. When blowing into the mouthpiece, the air flow forms a vortex inside the mouthpiece. At the place of the vortex a strong pressure gradient appears. This is a temporal impulse which travels down the tube, is reflected and comes back to the mouthpiece.
During its travel through the tube the impulse is heavily distorted by the horn, fingerholes or complex tube geometry. Still the impulse returning to the reed is only triggering a new impulse, it makes the reed move again and therefore a new inflow of air is changing the vortex in the mouthpiece. This produces a new impulse which looks perfectly like the previous one. Only if the impulses are the same each time, a harmonic overtone spectrum is the result. So this self-organizing process is necessary for a regular tone production.
In a Finite-Element Physical Model of the reed and mouthpiece the vortex and the pressure gradient can be seen. When the impulse return it triggers the reed to reform the vortex.
The geometry of the model
The vortex formed
The pressure gradient forming
Players use different reeds for different musical styles, jazz, traditional, soft or hard. Different reed shapes have been used in the Physical Model. Depending on the geometry of the reed it moves more or less in its eigenmode after it has been triggered by the returning impulse. This creates a formant region in the spectrum which is stronger or weaker. Stronger formants are associated with a ‘speaking tone’, weaker are less bright. The formant region is around 3 kHz, corresponding to measurements.
The different reed forms
The different spectra around 3 kHz.
Bader, R.: Individual reed characteristics due to changed damping using coupled flow-structure and time-dependent geometry changing Finite-Element calculation. In: Forum Acusticum joined with American Acoustical Society Paris 08, 3405-3410, 2008.