In this paper, we demonstrate a general technique for building superconducting cavities without loss from joints and seams, achieving coherences determined only by intrinsic material properties. The technique, dubbed the flute method is made by drilling overlapping holes into a monolithic block of superconductors. We use the location and depth of the holes to adjust the cavity mode frequencies and interactions with a superconducting circuit. We demonstrated a multimode cavity with 9 operable modes with photon lifetimes ~ 2 ms. With only a single control line, we demonstrated a variety of techniques for universal cavity control, applicable over the entire multimode cavity spectrum.