We report the dependence of the intrinsic spin wave spectra on the three-dimensional shape in single FePtnanomagnetic elements. In contrast to the well-known center and edge modes in flat, circular nanodisks, curved nanomagnets with identical nominal thickness and footprint exhibit a rich multi-mode spectrum with qualitatively different dependence on applied field, such as a low-frequency "pinned" mode. Dynamic micromagnetic modeling shows that the experimentally observed modes originate from different sections of the nanomagnet with vastly different demagnetization field. Thus, controlled shaping of a nanomagnet in all three dimensions creates the possibility of magnetization dynamics by design.2