The Cu(111) surface state has been mapped for vicinal surfaces with variable step densities by angle-resolved photoemission. Using tunable synchrotron radiation to vary the k dependence perpendicular to the surface, as well as the (k) dependence, we find a switch between two qualitatively different regimes at a miscut of 7 degrees (17 A terrace width). For larger miscut angles the step modulation of the wave function dominates, and for smaller miscut angles the terrace modulation dominates. These observations resolve an apparent inconsistency between prior photoemission and STM results.