Abstract: A cylindrical head joint has an internal cross-section that tapers down from a cylindrical shape at the tenon to a non-cylindrical shape at the embouchure end by means of a wedge internally bonded to the cylinder. The relative tuning of the three octaves of the flute can be achieved by varying the position of the wedge either rotationally or longitudinally inside the cylinder. The laborious method of tapering the head by forced shrinking of a cylindrical tube is thus avoided and a superior tone quality is achieved because the air jet that enters the embouchure hole hits a non-cylindrical wall which has a favorable effect on transient sounds and harmonics.