Clamp comprising two conical components, one being a flexible, interior component in contact with the barrel and the other a rigid, exterior component in contact with the interior component. The former has a longitudinal cut over the entire length thereof, and the interior component is closed. The interior component has, in that part which enters into contact with the barrel, two central recesses. The flexibility thereof allows the exertion of pressure just sufficient to secure the barrel without breaking the latter. Furthermore, the interior component has a ring on the exterior thereof, and the end closest to the opening of the mouthpiece, with a view to preventing the exterior component from sliding out. This exterior component, which is rigid, acts on the interior component, and has the same conicity as the interior component. The exterior component has the function of preventing unwanted opening of the interior component, exerting a pressure on the interior component that is just sufficient. Given that both components of the clamp have a central recess within, it forms, as a whole, a mouthpiece resonating box, providing greater sound volume and different timbres, depending on the size, in terms of length and depth, of the recess and on the material from which it is produced. The flexibility of the interior component prevents breaking of the barrel even though the three interior rings thereof are placed in different planes.