Tuning of turbine bucket torsional and stripe mode natural frequencies can be effected without altering any turbine bucket physical features, such as weight and/or shape, and without affecting flexure frequencies. The tuning of certain turbine bucket natural frequencies serves to avoid detrimental blade resonance, thus improving the reliability of a gas turbine. The method includes investment casting the turbine bucket with a single crystal alloy, and tuning the natural frequency of the turbine bucket without modifying physical features of the turbine bucket by placing a crystal seed along a desired direction according to a relative orientation of an engine axial direction.