The present invention relates to a rod-shaped tool holder (1) having a length (I) for the attachment of at least one machining cutting bit (2). The tool holder (1) is configured for being clamped at a first end (4) and has a second free end (3) and optionally a secondary support between the clamping point (4) and the at least one cutting bit (2). In operation, the tool holder oscillates in higher order bending oscillations about at least one node (6) located on a curvilinear axis (x) extending from the first end. The at least one cutting bit (2) is positioned substantially at the node (6) in a distance from the free end (3), towards the first end (4).