Device for fastening a simple reed to the mouthpiece of a wind instrument with a simple reed, the fastening of the simple reed to the mouthpiece occurring due to the fact that the upper portion of surface of the simple reed is pressed against the lower portion of surface of the mouthpiece, comprising: ▪ fastening means, which exert on the lower portion of surface of the simple reed a fastening force that presses the upper portion of surface of the simple reed against the lower portion of surface of the mouthpiece and comprise at least one cord (13;3), which is arranged in such a way that it (13;3) extends at least along the lower portion of surface of the simple reed and along the side portions of surface of the mouthpiece and ▪ adjusting means, which adjust the intensity of said fastening force, and which consist of means for generating in the at least one cord (13;3) a tractive force of adjustable intensity and comprise in their turn: a resting element (14;4), which rests with a contact surface on the upper portion of surface of the mouthpiece; an active element (15;5) which is provided with a plurality of seats (15a,15b;5a,5b), in which some sections of the at least one cord extend and/or in which (15a,5b;5b) the ends of the at least one cord (13;3) are anchored, shifting means (16,15c;6,5c,7), which interact both with the resting element (14;4) and with the active element (15;5) and act on the active element (15;5) to shift it in both senses along a radial direction of the mouthpiece, the progressive shifting of the active element (15;5) along said radial direction and moving away from the mouthpiece causing an identical progressive shifting by pulling of said sections respectively of said ends of the at least one cord (13;3) and generating by effect of this in the at least one cord (13;3) a tractive force, whose intensity grows progressively in proportion to the increase in the shifting characterised in that the resting element (14;4) is placed, along said radial direction, between the active element (15;5) and the mouthpiece, in that, when the active element (15;5) performs along said radial direction said shifting moving away from the mouthpiece, it (15;5) moves away from the resting element (14;4) and in that said seats (15a,15b;5a,5b) are placed on some protruding portions of the active element (15;5), which protrude in an overhanging way from the main body of the active element (15;5) and extend in such a way beyond the perimeter of the upper portion of surface of the mouthpiece on which the resting element (14;4) rests that the projections of said seats (15a,15b;5a,5b) on the mouthpiece lie completely outside the upper portion of surface of the mouthpiece on which the resting element (14;4) rests. ▪ fastening means, which exert on the lower portion of surface of the simple reed a fastening force that presses the upper portion of surface of the simple reed against the lower portion of surface of the mouthpiece and comprise at least one cord (13;3), which is arranged in such a way that it (13;3) extends at least along the lower portion of surface of the simple reed and along the side portions of surface of the mouthpiece and ▪ adjusting means, which adjust the intensity of said fastening force, and which consist of means for generating in the at least one cord (13;3) a tractive force of adjustable intensity and comprise in their turn: a resting element (14;4), which rests with a contact surface on the upper portion of surface of the mouthpiece; an active element (15;5) which is provided with a plurality of seats (15a,15b;5a,5b), in which some sections of the at least one cord extend and/or in which (15a,5b;5b) the ends of the at least one cord (13;3) are anchored, shifting means (16,15c;6,5c,7), which interact both with the resting element (14;4) and with the active element (15;5) and act on the active element (15;5) to shift it in both senses along a radial direction of the mouthpiece, the progressive shifting of the active element (15;5) along said radial direction and moving away from the mouthpiece causing an identical progressive shifting by pulling of said sections respectively of said ends of the at least one cord (13;3) and generating by effect of this in the at least one cord (13;3) a tractive force, whose intensity grows progressively in proportion to the increase in the shifting characterised a resting element (14;4), which rests with a contact surface on the upper portion of surface of the mouthpiece; an active element (15;5) which is provided with a plurality of seats (15a,15b;5a,5b), in which some sections of the at least one cord extend and/or in which (15a,5b;5b) the ends of the at least one cord (13;3) are anchored, shifting means (16,15c;6,5c,7), which interact both with the resting element (14;4) and with the active element (15;5) and act on the active element (15;5) to shift it in both senses along a radial direction of the mouthpiece, the progressive shifting of the active element (15;5) along said radial direction and moving away from the mouthpiece causing an identical progressive shifting by pulling of said sections respectively of said ends of the at least one cord (13;3) and generating by effect of this in the at least one cord (13;3) a tractive force, whose intensity grows progressively in proportion to the increase in the shifting characterised