The orbital angular momentum (OAM) spectrum of light, produced by superposition of vortex beams, is important for applications in optical metrology and classical and quantum communication. Nonetheless, manipulation of the OAM spectrum remains challenging. The authors propose a technique for control of the OAM spectrum using structured pinhole plates, which can generate both wide and narrow OAM spectra. In particular, a rather simple pinhole plate can produce an interesting series of discrete, equally spaced OAM modes: an OAM comb, akin to a frequency comb. This approach could be extended beyond photonics to work with rf, acoustic, electron, or neutron composite vortices.