Onset conditions for a duct with varying length, or with side holes. For the case without side holes, the onset frequency f_onset and the corresponding feedback gain Γ_onset are plotted as functions of the length L, with solid blue lines. For the case with side holes (red markers), the length of the duct is fixed to L_d = 31.1 cm, the holes (5 mm in diameter) are left open one by one starting from the open termination, and the corresponding onset frequency and feedback gain are plotted for each fingering. The positions of the holes are set such that the 8 notes of a musical scale can be played, from a G2 up to a G3.