In a woodwind instrument, in particular a saxophon, the work to be performed by the fingers to open and close the tone holes is appropriately and ergonomically distributed among fingers 1 to 4 of both hands and the left thumb by means of an appropriate design of the tone hole cover system. When playing a chromatic scale from C sharp3 to b flatO, the fingers are decreasingly stressed in the following order: L1-L2-L3-L4-LT-R1-R2-R3-R4-RT. Figure 1 shows the finger stress characteristic curve of the disclosed saxophon ( ) against that of a conventional saxophon (----). On the abscissa are arranged the fingers, from the reed to the bell, the ordinate indicates their relative stress. In comparison to a conventional saxophon, the row of first order tone holes is increased from 7 to 8, in relation to the C major scale, four holes for fingers L1 to L4 and four holes for fingers R1 to R4. Concerning the notation c1, the finger sequence L1-L2-L3-L4-R1-R2-R3-R4 generates the scale h?1-b1-a1-g1-f1-e1-d1-c1¿. In the disclosed tone hole cover system, the h1,2 tone hole is a first order tone hole, dispensing with alternative auxiliary fingerings for the b1,2 tone. The bell buttons are operated by the thumb and inner surface of the left hand. The applicability of the basic idea of the invention to other woodwind instruments is demonstrated on the basis of the example of the transverse flute.