Line gratings were used to investigate the tactual discrimination thresholds for line frequency. In Experiment 1, participants were asked to discriminate between two gratings, each with a different line frequency. We used four standard frequencies in the eightfold range from 0.5 to 4 lines/cm. Thresholds were found to be constant at about 10.6%. In this experiment, we also measured hand speed and contact force. Hand speed was roughly in the range between 0.12 and 0.44 m/sec; contact force ranged from 0.62 to 2.76 N. In Experiment 2, we determined discrimination thresholds for line frequency transitions within a single grating. We used two frequencies and three transition lengths. The transition length had no effect on the threshold. In a third experiment, line frequency was modulated periodically. Varying the standard frequency and the size of the modulation period was found to have no effect on the discrimination thresholds. We conclude three things. First, Weber fractions for line frequency discrimination decrease as a function of line frequency within the experimental range. Second, discrimination thresholds are not altered by the length of the transition between two adjacent gratings with different line frequencies. And finally, the size of a modulation period in periodically modulated gratings is of no influence on the modulation detection threshold.