Mechanism of harmonic structure change with jet angle in flute playing

This study performed direct aeroacoustic simulations for two flute headjoints to clarify the mechanism by which the harmonic structure changes with jet angle (angle between jet and the mouth opening in flute playing). As jet angle is increased (jet is directed perpendicular to mouth opening), the second harmonic is intensified more than the third harmonic. This harmonic structure change occurs because the jet deflects towards the inside of the pipe with increasing jet angle, which increases the actual jet offset (relative height of jet to edge). This jet deflection was found to be caused by the pressure gradient between the inside and outside of the pipe. As jet angle was increased, the jet was directed horizontally to the inner edge wall, resulting in a decrease in the pressure inside the pipe, whereas the angle between the jet and outer edge wall increased to increase the pressure outside. When the inclination of the inner edge wall was changed to be more perpendicular to the jet, the pressure around the wall increased, and the jet was deflected further outward. The angle between the jet and the edge wall affects the jet deflection and harmonic structure.