The inventive clamping member is a rigid clamp having a generally "U"-shaped configuration the base of which is defined by two arms each terminating in an upwardly directed clamping finger adapted to engage the rim of a bottom of a violin or the like at opposed sides of the body of the instrument. A pivot, usually in the form of a threaded stem projects from the base of the "U" in a direction opposite to that of the projection of the clamping fingers. It normally secures free pivotal mounting of the clamping members at the ends of a shoulder rest bridge. The stem defines an axis of pivot of the clamping member which is offset to one of the clamping fingers, whereby the two arms are of uneven length. The shorter arm is relatively proximal to the tail of the instrument, while the longer arm is relatively distal from the tail. The advantage of the clamping members is in that they each enable the clamping of a shoulder rest to an instrument at opposed sides of a transverse axis of the body of the instrument, at which the body is widest, while allowing the location of the bridge of the shoulder rest to be closer to the chin rest of the instrument to improve convenience