A tightening structure of a musical instrument stand includes stationary or immovable member and a movable member. The movable member includes a cylindrical shaft extending outward in an axial direction. One side of the immovable member has a recess. A bottom of the recess forms a semi-circular arc with a radius of curvature corresponding to that of the shaft. When the shaft is inserted into the recess it abuts against the bottom of the recess. The immovable member has a screw hole communicating with the recess. The screw hole is perpendicular to the axial direction of the cylindrical shaft. A fastening bolt is screwed into the screw hole. One end of the first fastening bolt is inserted into the recess and has a flared end portion to press against the shaft, and another end is connected with a handle. By rotating the handle, the flared end portion is drawn against the shaft, thereby rendering the movable member stationary.