A machine, such as a coordinate measuring machine, uses a material measure with a periodic division in order to determine spatial positions of a working or measuring head. The periodic division of the material measure is further subdivided by interpolation values. For the purpose of correcting interpolation errors, the head is moved to a plurality of positions and a plurality of position data is determined. The plurality of position data represents a position curve of the head. A periodic component in the position curve is determined, which periodic component corresponds approximately to the periodic division of the material measure. Correction values are determined and the interpolation values are corrected using the correction values such that the periodic component is substantially reduced or largely eliminated.