Sensitivity to relative phase was measured for central and peripheral vision using stimuli comprising 256 harmonics, smoothly filtered in amplitude. With these stimuli, peripheral phase sensitivity was much higher than that previously reported with two-harmonic stimuli. Sensitivity did not depend on the average phase of the stimuli, nor on their second-order statistics, irrespective of the spatial frequency of the stimulus or the position in the visual field. After scaling for size, peripheral sensitivity was as high as central sensitivity. The scaling factor required to equate phase sensitivity was the same as that required to equate contrast sensitivity and grating acuity. These results suggest that phase sensitivity decreases with eccentricity at a similar rate as contrast sensitivity and grating acuity, much more slowly than the positional acuities. This is consistent with the suggestion that phase discrimination is mediated by discriminating the amplitude of the response of quasi-linear filters, and does not require mechanisms that evaluate position. It is suggested that previous measurements on peripheral phase sensitivity may reflect positional uncertainty in the periphery, rather than a deficit in phase sensitivity per se.