On the modeling of self‐oscillation in brass instruments

Abstract

It is recognized that the lips of brass players vibrate two‐dimensionally, i.e., in parallel and perpendicularly to the direction of the air flow as the excitatory source. This two dimensionality gives two different models of lip motion in brass instruments: (1) the parallel model as a “reed striking outwards,” which is the reverse to the model of a woodwind reed as a “reed striking inwards” [N.H. Fletcher, Acustica 43, 63–72 (1979)], and (2) the perpendicular model as a “one‐mass vocal cord striking laterally” [J. Saneyoshi, H. Teramura, and S. Yoshikawa, Acustica 62, 194–210 (1987)]. The phase difference between the lip displacement and the acoustic pressure acting on the lips, or the frequency difference between the antiresonance of the horn itself and the sound excited, can determine which model is actually dominant. This paper describes some attempts to find these quantities on a cylindrical pipe blown by lips without a mouthpiece. The discussion of the experimental results and the modeling of the lip vibration is presented after briefly explaining the differences between the regeneration theories based on the above models.