The acoustical nature of the head joint of a transverse flute is examined in mathematical detail. The effective length of the flute is altered in the amount by an embouchure correction Δlc= (c/2πf) arctan{(e/2π) (f/r)/(2fr2 − f2)}, wherefis the playing frequency,eis the speed of sound in the contained air,rthe (17‐mm) cork‐to‐embouchure distance, andf1a parameter (near 1450 cps which is essentially the frequency of a Helmholtz resonator made by plugging the bore with a second cork a distancerbelow the embouchure. This correction is roughly constant at 42 mm over the normal playing range. Effects of cork position, lip position, and embouchure‐hole size are discussed in detail, as is the effect of cavity resonances in the player's own mouth. Tuning errors caused by the edgetone‐regeneration mechanism are shown to be correctible by a head joint taper perturbation. Three designs are analyzed, which produces a flattening at low frequencies, zero effect near 600 cps, and a maximum sharpening near 1000 cps. Above, this the correction returns smoothly to zero at the upper playing limit near 2000 cps. In the high register, the correction is produced jointly by the taper and the vent holes. The whole analysis is summarized by means of a detailed comparison of the Boehm design of flute with the older cylindrical‐head, taper‐bore model and with the purely cylindrical flute.